Deconvolution of ASCA X-ray data II. Radial temperature and metallicity profiles for 106 ga

Thermochimica Acta 424(2004)131–142Thermal decomposition (pyrolysis)of urea in an open reaction vesselPeter M.Schaber a ,∗,James Colson b ,Steven Higgins b ,Daniel Thielen b ,Bill Anspach b ,Jonathan Brauer baDepartment of Chemistry and Biochemistry,Canisius College,2001Main Street,Buffalo,NY 14208,USAb OxyChem Technology Center,2801Long Road,Grand Island,NY 14072,USAReceived 30April 2003;accepted 4May 2004Available online 6July 2004AbstractA study was done of the thermal decomposition of urea under open reaction vessel conditions by thermogravimetric analysis (TGA),high performance liquid chromatography (HPLC),Fourier transform-infrared (FT-IR),and an ammonium ion-selective electrode (ISE).Both evolved gases and urea residue were analyzed,and profiles of substances present versus temperature are given.Major reaction intermediates are also identified.Plausible reaction schemes based on product distribution in relation to temperature are proposed.Our data indicate that at temperatures in excess of 190◦C,cyanuric acid (CY A),ammelide and ammeline are produced primarily from biuret.Biuret itself is a result of prior reaction of cyanic acid,HNCO,with intact urea.Cyanic acid is primarily a result of urea decomposition at temperatures in excess of 152◦C.CYA and ammelide first appear at approximately 175◦C,but the reaction rate is very slow.At temperatures in excess of 193◦C,alternate reactions involving the decomposition of biuret substantially increases reaction rates.Several parallel processes compete for the production of products.Production of CY A,ammeline and ammelide appears complete at 250◦C,after which sublimation and eventual decomposition of products occurs.©2004Elsevier B.V .All rights reserved.Keywords:Urea;Pyrolysis;Thermal decomposition;Open vessel1.IntroductionThe thermal decomposition (pyrolysis)of urea to pro-duce cyanuric acid (CY A:2,4,6-trihydroxy-1,3,5-triazine)was discovered by Wöhler approximately 175years ago [1].Details of the reaction mechanism have been studied for many years and recently a plausible temperature dependent reaction scheme,based primarily on product distribution,has been proposed [2].It is apparent that this reaction proceeds by a very complex and diverse pathway.For ex-ample,it is known that the primary decomposition products exhibit high reactivity and undergo a series of secondary reactions.Reaction conditions such as temperature,heating time,closed or open reaction vessel,atmosphere make-up and pressure,have all been shown to affect the outcome of this reaction process in terms of total product distribution and intermediates observed [2–15].Pyrolysis of urea is not∗Corresponding author.Tel.:+17168882351;fax:+17168883112.E-mail address:Schaber@ (P.M.Schaber).just a topic of academic concern.The industrial production of CYA from urea is a widely used process and one that has been practiced for several decades.Industrial interest in CY A is based on its widespread use as a precursor for the production of disinfectants,sanitizers,bleaches and herbicides [16].In addition,ammonia generated from urea decomposition is currently being considered by the diesel engine industry in an effort to develop a selective NO x cat-alytic reduction process (to nitrogen and water)for engine exhaust.There is present,continuing,and growing interest in the details of this reaction and its associated mechanism.Stradella and Argentero [12]recently published a study on the thermal decomposition of urea and related com-pounds with TGA (thermogravimetric analysis)and DSC (differential scanning calorimetry)measurements,together with EGA (evolved gas analysis).Chen and Isa [13],and Carp [15]published related studies using simultaneous TGA,DTA,and MS (mass spectroscopy).These studies focus on the decomposition of urea under purge gas (Ar,He or air)conditions.Tracking of residue species and account-ing for the production of by-products such as ammeline0040-6031/$–see front matter ©2004Elsevier B.V .All rights reserved.doi:10.1016/j.tca.2004.05.018132P .M.Schaber et al./Thermochimica Acta 424(2004)131–142and ammelide and accompanying synthetic details,were not included in these reports.In this study,an analysis of urea decomposition under open reaction vessel conditions utilizing TGA,high performance liquid chromatography (HPLC),Fourier transform-infra red (FT-IR),and an am-monium ion-selective electrode (ISE),is reported.Both evolved gases and urea residue were analyzed and profiles of substances present versus temperature are given.Major reaction intermediates are identified.Although others are considered,plausible reaction schemes based on product distribution in relation to temperature,favoring those with observable intermediates,are proposed.2.ExperimentalUrea was obtained from Aldrich Chemical Co.,Milwau-kee,WI (99%pure,ACS reagent grade),and used without further purification.Biuret was obtained from Fisher Scien-tific Co.,Pittsburgh,PA (99.9%pure,ACS reagent grade)and also used without further purification.CY A,ammelide,ammeline,and melamine were obtained from OxyChem’s industrial process and purified in-house.Urea residue in an open reaction vessel was obtained by heating 3.0g samples of urea in a 10mL Pyrex TM beaker on a sand bath until the desired temperature was reached.The sample was then quickly cooled to room temperature in a water bath and the residue collected.Chromatographic analyses of urea residues were con-ducted with HPLC methods previously described in the lit-erature [2].Samples were analyzed for the presence of urea,biuret,CY A,ammelide,ammeline and melamine.An HPLC Mass Table (Table 1)and an HPLC Mass Plot (Fig.1)were constructed from the data obtained.Thermogravimetric analysis (TGA)and measurements of mass losses (and the 1st derivative)versus temperature were determined using a Hi-Res TGA 2950Thermogravimetric Analyzer under N 2(g)purge.The “high resolution”op-tion was routinely used.Typically,30–50mg of sample was placed on a Pt pan and heated at 10◦C min −1.Urea “critical temperatures”,defined as those temperatures corresponding to plateau regions,points of rapidly changing mass,or where phase changes are known to occur (melting points,etc.),were identified from the TGA data plot (Fig.2).Table 1HPLC Mass Table (urea pyrolysis)open reaction vessel a Temperature (◦C)Mass (g)Urea (g)Biuret (g)CY A (g)Ammelide (g)Ammeline (g)Melamine (g)Total %recovery 133100.098.7 1.0––––99.719080.060.520.00.60.5––102.022533.0 6.0 4.615.6 6.10.9–100.525029.00.30.219.97.7 1.30.058101.427528.00.50.318.97.5 1.30.056102.332020.0––12.1 4.9 1.10.04490.73505.0––3.11.00.50.10094.0aThese data were calculated based on the results obtained from HPLC analysis assuming 100.0g of urea initially present.Table 2Urea pyrolysis residue analysis;ammonium ion (NH 4+)analysis with an ion-selective electrode a Temperature (◦C)Concentration of NH 4+ion (ppm)13370190380225260025026027515032512035090aResults in ppm are based upon the mass of the original sample.Table 3Urea pyrolysis off-gas;ammonium ion (NH 4+)analysis with an ion-selective electrode a Temperature range (◦C)Concentration of NH 4+ion (ppm)Room temperature to 133210133–21011900210–2258500225–2551210255–3505200350–400450aResults in ppm are based upon the mass of the original sample.Ammonium ion [NH 4+]analysis of both urea residue and pyrolysis off-gases were accomplished using an ammonium ISE (Orion,Beverly,MA).Typically for urea residues,a 1%aqueous solution was made and analyzed.Resultant con-centration versus temperature data are collected in Table 2.Urea pyrolysis off-gases were generated by placing a 3.0g sample of urea in a three-neck round bottom flask fitted with a thermometer,a thermal watch device,a N 2(g)purge,and an NH 3(g)scrubber (gas trap)consisting of 50.0mL of 12.0M HCl.As the urea sample was heated,the gases that evolved between the desired “critical temperature”points were allowed to pass through the scrubber and collected.Ammonium ion analysis was conducted on diluted scrubber solutions.Results are collected in Table 3.FT-IR spectra of the urea melt were collected using the Applied Systems Inc.(ASI)REACT-1000system (ASI SensIR Technologies,Danbury,CT),fitted with a sili-con (Si)probe.A spectrum was acquired every 2min asP .M.Schaber et al./Thermochimica Acta 424(2004)131–142133Fig.1.HPLC Mass Plot:urea pyrolysis reaction (assume 100.0g of urea initially).“critical temperature”points,between 133and 225◦C,were ramped to and held with the aid of an Omega thermocou-ple (Fig.3).Qualitative analysis was performed using the REACT-1000soft-ware package supplied by ASI.Analy-Fig.2.TGA:urea pyrolysis reaction.sis of urea pyrolysis off-gases were conducted by placing a 1.0g sample of urea into a glass vial and inserting into a tube furnace fitted with a N 2(g)purge and gas collec-tion adapter.The urea sample was heated to the desired134P .M.Schaber et al./Thermochimica Acta 424(2004)131–142Fig.3.FT-IR Si-probe spectra:urea pyrolysis reaction.“critical temperature”and held there for several minutes with the aid of a thermal watch device.Evolved gases were subsequently swept into an IR gas cell fitted with NaCl windows.FT-IR spectra of urea off-gases were obtained with a Nicolet 20SXB Spectrometer (Nicolet,Madison,WI).Condensed materials adhering to the surface of the gas collection adapter were collected and subjected to melting point determination with a 510Melting Point ap-paratus (Brinkmann Instruments,Inc.,Westbury,NY),and HPLC analysis using methods previously referenced in this section.3.Results and discussion 3.1.Process overviewThe TGA of urea measured with a heating rate of 10◦C min −1under N 2(g)purge between 50and 600◦C is given in Fig.2.Three major stages of mass loss are ob-served and calculated to be approximately 72,24,and 4%.The pyrolysis reaction of urea in an open reaction vessel can be divided into four major “reaction”regions.“Reaction”regions are dominated by different chemical processes asso-ciated with the mass loss stages observed in the TGA.What follows is a detailed description of the chemical process in each of the urea pyrolysis “reaction”regions.3.2.First “reaction”region (room temperature to 190◦C)Little significant mass loss (0.01%)is observed when heating urea in an open reaction vessel from room tem-perature to its melting point 133◦C.HPLC analysis of the residue at the melting point,gives 98.7%urea and 1.0%biuret (Table 1).The biuret present at this point primarily represents contamination in the original sample.Only a small relative amount of [NH 4+]ion is observed in both the residue and off-gas analysis (Tables 2and 3)and a very small [NCO −]absorption peak at 2156cm −1is noted in the FT-IR spectra (Si-probe)of the melt (Fig.3).These observations are consistent with a very small amount of urea decomposition and vaporization.Recently,Chen and Isa [13]have also observed only a small mass change prior to urea’s melting point,which is consistent with our data.Mass loss begins in earnest at approximately 140◦C as observed from the TGA (Fig.2).The loss observed between 140and 152◦C,is associated primarily with urea vaporiza-tion.(Condensed material adhering to the surface walls of the gas collection adapter (see Section 2),in this temper-ature range was identified as urea from melting point and HPLC determinations.)A more significant mass loss is ob-served between approximately 152and 160◦C and proceeds via two processes;continued urea vaporization and decom-position [9].P.M.Schaber et al./Thermochimica Acta424(2004)131–142135 Urea decomposition:H2N–CO–NH2(m)urea+heat→NH+4NCO−(m) ammonium cynate →NH3(g)ammonia+HNCO(g)cyanic acid(1)At152◦C decomposition begins[4],Eq.(1),accompanied by vigorous gas evolution from the melt.Above152◦C the decomposition rate of urea increases rapidly.At160◦C,the FT-IR Si-probe spectra of the melt,indicates an increase in intensity of the[NCO−]peak from that observed at140◦C (Fig.3).The FT-IR spectrum of gases evolved at160◦C in-dicates the strong presence of NH3(g)(peaks at3333,965 and930cm−1),but little discernible HNCO(g).Stradella and Argentero[12]have,however,observed HNCO(g)in the evolved gases at this temperature.Chen and Isa[13],and Carp[15]have also identified evidence of HNCO(g)pro-duction in their studies.That the ammonium cyanate salt, [NH4+NCO−],is formed as an intermediate in Eq.(1)has recently been confirmed by Carp[15].These data are all con-sistent with urea’s initial decomposition to[NH4+NCO−], which itself decomposes resulting in the evolution of NH3 (g)and HNCO(g).A product of urea decomposition,HNCO,begins to react with intact urea to produce biuret at approximately160◦C, Eq.(2).1This is supported by an increase in the intensity of a peak unique to biuret at1324cm−1,in the FT-IR Si-probe spectra(Fig.3).Biuret production:H2N–CO–NH2(m)urea +HNCO(g)cyanic acid→H2N–CO–NH–CO–NH2(m)biuret(2)Between160and190◦C urea continues to vaporize and decompose and HNCO,continues to react with intact urea to produce biuret.However,complications also begin to enter the system in this temperature range.A small amount of HNCO can now begin to react with biuret[10],Eq.(3),or itself,Eq.(4),to produce CYA,or with urea,Eq.(5),to produce ammelide.From the FT-IR Si-probe data,it appears that the production of both CY A and ammelide commence simultaneously at approximately175◦C.This is supported by an increase in the intensity of respective peaks unique to CYA at1058cm−1,and ammelide,at977cm−1,in the FT-IR Si-probe spectra(Fig.3).CYA production:H2N–CO–NH–CO–NH2(m)biuret+HNCO(g)cyanic acid →CY A(s)cyanuric acid+NH3(g)ammonia(3)via Eq.(4)is a reasonable candidate and one that has been known experimentally for many years.Herzberg and Reid1The actual reaction to form biuret likely involves the interaction of urea with[NCO−]in the melt[11].The form of the equation used here is for convenience,and will be used throughout this document.However, it should be realized that reactions in the melt involving HNCO are likely to proceed via[NCO−]interaction.[17]have observed that if HNCO(g)exceeds a critical vapor pressure,3HNCO(g)cyanic acid→CY A(s)cyanuric acid(4)spontaneous and rapid polymerization to CY A can oc-cur.This critical vapor pressure can be quite low,espe-cially in the presence of a metal surface.2Another po-tential route to CY A involves the cyclicization of triuret (H2N–CO–NH–CO–NH–CO–NH2)with the evolution of NH3[3].Chen and Isa[13]identify the existence of urea trimer under TGA conditions.However,since no triuret is observed in these studies,its existence under open reaction vessel conditions is questionable.Ammelide production:2HNCO(g)cyanic acid+H2N–CO–NH2(m)urea→ammelide(s)+2H2O(g)(5) The intermediate for Eq.(5)could be either biuret,via Eq.(2),or dicyanic acid(H2N2C2O2).Biuret is observed in the reaction sequence and if it also serves as an intermedi-ate to ammelide,Eq.(5)is then very similar in essence to that represented in Eq.(7).Dicyanic acid would be very un-stable at these temperatures and if behaving as the interme-diate,would not be expected to accumulate to a significant extent.However,since not a hint of dicyanic acid was de-tected in this study,its contribution to ammelide production is questionable under the reaction conditions imposed. The conceptually simplest route to ammelide involves the direct reaction of CY A with available NH3(ammination), Eq.(6).This is a seeming logical path but one that has been determined to occur only under conditions of high pressure [18]or temperatures above300◦C[19].In the industrial preparation of CY A using a kiln,less ammelide is in general, CY A(s)cyanuric acid+NH3(g)ammonia→ammelide(s)+H2O(g)(6)produced when NH3is removed from the system.Although this would seem consistent with Eq.(6),the situation is likely more reflective of the different environmental aspects of lab-oratory versus industrial preparation of CY A,where temper-ature gradients in the kiln may produce conditions favorable to the production of ammelide in this fashion.A more likely laboratory route is one that parallels the formation of CY A, that is,the direct reaction of biuret with HNCO,Eq.(7), but with the formation of ammelide[20,21].Other possible routes to ammelide have been suggested,however,theyH2N–CO–NH–CO–NH2(s)biuret+HNCO(g)cyanic acid→ammelide(s)+H2O(g)(7)2Under TGA conditions,or with the use of a purge gas,this route is expected to be somewhat curtailed.However,Eq.(4)may be significant in the industrial preparation of CY A where metal kilns are often used.136P.M.Schaber et al./Thermochimica Acta424(2004)131–142typically require the presence of a precursor such as ammi-nated bi-or triuret,guanidine[10],or cyanamide[19].These proposed precursor species are stable in this“reaction”re-gion and if present,evidence of their existence would be expected.Our HPLC data give no indication any exist in measurable amounts in the residue(see Table1;note ap-proximately100%recoveries at these temperatures),nor are any detected in the FT-IR data.Under the conditions imposed,the reaction scheme most likely to produce ammelide,Eq.(7),operates in parallel to the one most likely to produce CYA,Eq.(3).Both prod-ucts are produced at about the same overall rate,and begin to appear at approximately the same temperature(175◦C). This suggests the reactions producing them share common reactants,(i.e.biuret and HNCO)and possess similar acti-vation energies.In addition,since relatively small amounts of CYA and ammelide are observed in the residue(Table1), whatever route adapted,reaction rates are rather sluggish for their production in this temperature range.Up to190◦C,the net mass loss for the system is pre-dominately the result of urea decomposition.By this same temperature,urea mass has decreased by38.2%,biuret mass has increased by19.0%and has reached a maximum ac-cording to HPLC analysis(Table1).The FT-IR of evolved gases is dominated by NH3due primarily to the contin-ual and increased decomposition rate of urea.Peaks in the 2100–2300cm−1region indicate the presence of HNCO, or of volatile salts of HNCO3such as ammonium cyanate, [NH4+NCO−],or hydronium cyanate,[H3O+NCO−][22]. Continued build up of[NH4+NCO−]in the melt is indicated by both the FT-IR Si-probe data(Fig.3),and the[NH4+]ion analysis of the residue(Table2).However,although build-ing,the amount of[NH4+]ion in the residue(380ppm)is still not significantly large.These data indicate that much of the NH3formed escapes the system without further reaction and that HNCO has either reacted to produce biuret,CY A, or ammelide,or escaped the system in the vapor form.In addition,the vaporization of volatile HNCO salts,has just begun.3.3.Second“reaction”region(between190and250◦C) As temperature exceeds190◦C,alternate reaction se-quences begin to dominate the process.At approximately 193◦C,the increased evolution of gases from the urea melt reflects the beginning of biuret decomposition(biuret melts with decomposition at193◦C),Eq.(8).A corresponding mass maximum for biuret(Table1),and1st derivative peak in the urea TGA near this temperature are observed(Fig.2). However,the gas evolution rate increase is not only the result of biuret and continuing urea decomposition.3In our studies,unequivocal identification of the HNCO salts cannot be made at this temperature due to poor resolution in this region of the FT-IR spectrum.Biuret decomposition:H2N–CO–NH–CO–NH2(m)biuret→H2N–CO–NH2(m)urea+HNCO(g)cyanic acid(8)(The urea produced by biuret decomposition in Eq.(8),is unstable in this“reaction”region and will itself decompose further to HNCO(g)and NH3(g),Eq.(1)).It also results from gas producing,auto-condensation reactions associated with biuret decomposition,Eqs.(9)and(10),to produce CY A and ammelide.CY A production:2H2N–CO–NH–CO–NH2(m)biuret→CY A(s)cyanuric acid+HNCO(g)cyanic acid+2NH3(g)ammonia(9)Ammelide production:2H2N–CO–NH–CO–NH2(m)biuret→ammelide(s)+HNCO(g)cyanic acid+NH3(g)ammonia+H2O(g)(10) Although Eqs.(3),(4)and(9)all contribute to the produc-tion of CY A,Eq.(3)is expected to predominate at lower temperatures[9](first“reaction”region),Eqs.(4)and(9) become more competitive at higher temperatures(second “reaction”region)where biuret begins to decompose.It is also expected that Eq.(4)will begin to play an increased role in CY A production if,or when,critical vapor pressure is achieved[17].A similar situation exists with respect to the production of ammelide.Eq.(7)is expected to predomi-nate at lower temperatures(first“reaction”region),Eq.(10) above193◦C(second“reaction”region).However,only small amounts of CY A and ammelide are observed prior to the decomposition temperature of biuret.At this point the production rate for both CY A and ammelide increase rapidly.The close relationship between the onset of biuret decomposition and increased production rates suggests that both CY A and ammelide are produced largely from biuret and in parallel fashion within the second“reaction”region [8].In addition,Eqs.(9)and(10)involve stoichiometric larger amounts of gaseous products than reaction candidates previously considered.The large increase in gas evolution physically observed in the urea melt above193◦C and the large amount of[NH4+]detected(11,900ppm)in the py-rolysis off-gas analysis between133and210◦C(Table3) are consistent with both continued urea and biuret decom-position and the production of CY A and ammelide by ki-netically faster mechanisms.TGA and DTA data collected on biuret itself indicates ready transformation to CY A upon heating[8,23].Stradella and Argentero[12]estimate that about50%of biuret is converted to CY A.At temperatures exceeding the melting point of biuret,conversion to CY A most probably involves Eqs.(4)and(9).At lower tem-peratures an alternative reaction path,be it minor,is one reminiscent of the production of CY A from urea and in-volves the initial decomposition of biuret to urea and HNCO.P.M.Schaber et al./Thermochimica Acta424(2004)131–142137Fig.4.TGA:biuret pyrolysis reaction.(Although the melting point of biuret is193◦C,our TGA analysis indicates mass loss prior to this temperature(Fig.4). These data are consistent with other investigators including Nelson et al.[8,23]).Biuret decomposition is followed by reaction of intact biuret with HNCO to produce CY A as in the urea process.The beginning of ammeline production is also observed in the second“reaction”region as noted by its detection in the HPLC analysis of the residue at250◦C(Table1).Al-though CY A and ammelide are most likely produced via parallel processes,ammeline could be produced either by ammination of ammelide,Eq.(11),or as suggested by Ha-effele et al.[20],by the direct reaction between HNCO and remaining urea,Eq.(12),or some modification thereof.No other species is detected in our analysis that could serve as a precursor to ammeline.However,at all temperatures up to350◦C,the mass amounts of ammelide exceed ammeline in the residue(Table1).Although this is not proof of a lin-ear process,it has been used as supporting evidence[24]. As previously mentioned,however,ammination reactions are only likely to occur at elevated pressures[18]or tem-peratures[19].The intermediate for Eq.(12)is most likely biuret.Ammeline production:ammelide(s)+NH3(g)→ammeline(s)+H2O(g)(11)or2HNCO(g)cyanic acid+H2N–CO–NH2(m)urea→ammeline(s)+2H2O(g)(12) If this occurs,Eq.(12)can be written in the following com-bined form assuming the previous occurrence of Eq.(2). This is a very likely scenario:4H2N–CO–NH–CO–NH2(m)biuret+HNCO(g)cyanic acid→ammeline(s)+2H2O(g)(12a) The evolution of gases begins to visibly slow as a white precipitate forms at temperatures exceeding210◦C.Con-version of the melt into a“sticky”solid matrix is complete at225◦C,and CY A becomes the major component of the residue.Analysis of trapped off-gases for[NH4+]ion col-lected between210and225◦C,gives8500ppm(Table3). This is an indication that decomposition of urea and biuret4Eq.(12a)is very similar to Eqs.(3)and(7).The latter two reactions are relatively slow and most likely continue to be so even at elevated temperatures.Eq.(12a)is probably even slower than either Eq.(3) or Eq.(7)at all temperatures,and is likely the reason ammeline is not observed until this point.(Biuret+HNCO reaction rates:Eq.(3) producing CY A>Eq.(7)producing ammelide>Eq.(12a)producing ammeline.)138P.M.Schaber et al./Thermochimica Acta424(2004)131–142Table4HPLC Mass Table(biuret pyrolysis)aTemperature(◦C)Mass(g)Biuret(g)CY A(g)Ammelide(g)Ammeline(g)Melamine(g)Total(%)recovery 22565.028.634.5 2.860.26–101.826051.0 6.6340.8 3.830.36–101.227539.00.0835.5 3.470.35–101.0a These data were calculated based on the results obtained from HPLC and TGA analysis assuming100.0g of urea initially present.continue in this temperature range.The continued produc-tion of CY A and ammelide,Eqs.(9)and(10),are also ex-pected to contribute to the NH3(g)production as well.Analysis for[NH4+]ion gives a maximum in the residueat225◦C.This represents a substantial increase from thevalue observed at190◦C(Table2).Accumulation of[NH4+]is a direct consequence of system precipitation.As the ureamelt is transformed into a solid matrix,the rate at whichNH3(g)and HNCO(g)can diffuse from the system is di-minished.These species are either trapped in the solid ma-trix,or interact with each other,Eq.(13),and exist in theresidue in ionic form.The fact that ionic formation occurs issupported by the[NH4+]analysis of the residue from thesestudies,and by the MS data collected by Carp[15].Just asdecomposition species are“tied up”in ionic formAmmonium cyanate production:NH3(g)ammonia +HNCO(g)cyanic acid→NH4+NCO−(s)ammonium cyanate(13)in the matrix,5it is also likely that the remaining urea and biuret are likewise converted to ionic cyanurates via inter-action with CYA,Eqs.(14)and(15).Urea cyanurate production:H2N–CO–NH2(m)urea+CY A(s)→H2N–CO–NH3+CY A−(s)urea cyanurate(14)Biuret cyanurate production:H2N–CO–NH–CO–NH2(m)biuret+CYA(s)→H2N–CO–NH–CO–NH3+CY A−(s)biuret cyanurate(15)The narrow plateau region observed near225◦C in the urea TGA corresponds very well to a more demonstrable one exhibited by biuret at approximately the same temper-ature(Figs.2and4,respectively).In the biuret system, the residue is primarily composed of biuret and CY A,with lesser amounts of ammelide and ammeline(Table4).Since all the product species are thermally stable at225◦C,a plateau region is observed in both the urea and biuret TGA at this temperature.FT-IR data collected on the off-gases resulting from the urea residue at this temperature illustrates that gaseous emissions have greatly decreased.Only a small5Eq.(13)is in essence the reverse of the latter portion of Eq.(1).amount of NH3(g),HNCO(g)and HNCO salt speciesare emitted from the residue matrix.Emission thereforecontinues,but at a much reduced rate[12].Melamine is positively identified for thefirst time at250◦C6(Table1).This represents a departure from thetemperature and level at which this product isfirst observedunder TGA conditions(350◦C,and in substantially smalleramounts)[2].The direct ammination of ammeline,Eq.(16),is one possible route to melamine.Once again,althoughthis may be the simplest conceptual route,it is one likelyonly to be observed atMelamine production:ammeline(s)+NH3(g)→melamine(s)+H2O(g)(16) elevated pressures[18]or temperatures[19].However,openreaction vessel conditions as applied here may produce lo-calized temperature conditions favoring this process to alimited extent.Another possibility is cyanamide(H2NC≡N) trimerization[10],Eq.(17).Although cyanamide has notbeen isolated from urea decomposition under normal3H2NC≡N(g)cyanamide→melamine(s)(17)pressure[11],it could be produced via an alternate decom-position route associated with urea dehydration,Eq.(18), or by ammination of cyanic acid[10],possibly within the solid matrix,Eqs.(19)and(19a),and behave as a very reac-tive intermediate at these temperatures.The small amounts of melamine observed may be reflective of small Cyanamide production:H2N–CO–NH2(m)urea→H2O(g)+H2NC≡N(g)cyanamide(18)6This is somewhat of an anomaly since melamine is reported to melt with accompanying sublimation below250◦C.It is therefore necessary to assume that if melamine forms,it sublimes simultaneously as it is being produced.The sublimation of melamine may therefore also contribute to the mass loss observed between225and250◦C in the TGA(Fig.2). Accumulation of measurable amounts of melamine,result from production that is kinetically faster that sublimation.It should also be noted that melamine is observed at250,275,and350◦C,but not at320◦C(Table1). This would suggest different mechanisms for its production in different temperature ranges.At lower temperatures(below300◦C),Eq.(17),or some other unidentified reaction,results in production of melamine.At higher temperatures,Eq.(16)is expected to predominate.。

ORIGINAL PAPERLow-Temperature Complete Oxidation of Ethyl Acetate Over CeO 2-Supported Precious Metal CatalystsTomohiro Mitsui ÆToshiaki Matsui ÆRyuji Kikuchi ÆKoichi EguchiPublished online:3March 2009ÓSpringer Science+Business Media,LLC 2009Abstract Catalytic combustion of ethyl acetate was investigated over various CeO 2-supported precious metal catalysts prepared by impregnation method,and the effect of reduction treatment on the activity was examined.Among the catalysts tested,Ru/CeO 2achieved the highest activity for ethyl acetate combustion,and the activity was almost unchanged by the heat treatment in a hydrogen atmosphere.In the cases of Pt/CeO 2,Pd/CeO 2,and Rh/CeO 2,the catalytic activity was enhanced by the reduction treatment at 400°C,though the activity of the reduced catalysts was still inferior to that of Ru/CeO 2.It was con-firmed by temperature-programmed reduction that the reduction of the ruthenium species was initiated at the lowest temperature among the CeO 2-supported precious metals.The precious metal species reducible at lower temperatures should be responsible for the high activity in the complete oxidation of ethyl acetate.Keywords Volatile organic compounds ÁCatalytic combustion ÁCeO 2ÁEthyl acetate1IntroductionVolatile organic compounds (VOCs)have relatively high-vapor pressure,and thus readily vaporize under ambient conditions.These compounds are known as a major cause of photochemical smog,ground-level ozone,sick housesyndrome and chemical sensitivity [1–3].Among VOCs,ethyl acetate is widely used as a solvent for varnishes,coatings,plastics,and so on.Consequently,even through the concentration of ethyl acetate at application sites in dilute,the amount of ethyl acetate emitted into the atmo-sphere will eventually be huge in total.Therefore,it is desired to abate the emissions totally.Catalytic combustion is regarded as one of the effective methods for VOC removal,since complete combustion of dilute fuel proceeds stably at low temperatures,leading to low emission of NO x and unburned fuels [4].Alumina is the most popular support material for precious metals to disperse on it,and many researchers have reported that Al 2O 3-supported precious metal catalysts exhibit high activity for the combustion of VOCs [5–10].However,higher temperature is required for the catalytic oxidation of ethyl acetate over this catalyst system as compared with that of the other VOCs such as alcohol and aromatic compounds [11].Thus,it is required to develop combustion catalysts with high activity so as to reduce the operating temperature.As an alternative to alumina,cerium oxide is one of the attractive supports due to its high oxygen transport and storage capacities.Ceria-supported precious metal catalysts exhibit high activity for various reactions such as purifying of automotive exhaust,water–gas shift reaction,CO oxidation,and hydrocarbon combustion [12–16].Accordingly,it can be expected that this catalyst system is a promising candidate for ethyl acetate combustion.In this study,combustion characteristics of ethyl acetate over CeO 2-supported precious metal catalysts were inves-tigated,and the catalytic activity of the catalysts was compared with that of Al 2O 3-supported precious metal catalysts.In addition,the influence of oxidation–reduction treatment on the catalytic activity was also examined.T.Mitsui ÁT.Matsui ÁR.Kikuchi ÁK.Eguchi (&)Department of Energy and Hydrocarbon Chemistry,Graduate School of Engineering,Kyoto University,Nishikyo-ku,Kyoto 615-8510,Japane-mail:eguchi@scl.kyoto-u.ac.jpTop Catal (2009)52:464–469DOI 10.1007/s11244-009-9186-42Experimental2.1Catalyst PreparationCeria-supported precious metal catalysts were prepared by the impregnation method.For comparison,c-Al2O3(JRC-ALO-8,The Catalysis Society of Japan)was used as a sup-port for precious metal catalysts,and c-Al2O3-supported samples were prepared in the same way.A solution of Pt(NO2)2(NH3)2(Tanaka Kikinzoku Kogyo),Pd(NO2)2 (NH3)2(Tanaka Kikinzoku Kogyo),Ru(NO3)3(Tanaka Ki-kinzoku Kogyo),or Rh(NO3)3(Tanaka Kikinzoku Kogyo) was used as a precious metal source.Ceria(CeO2,Aldrich) was impregnated with the solution.The mixture was kept on a steam bath at80°C until the solvent was evaporated. Subsequently,the resulting powder was calcined at400°C for30min in air.Metal loading in the samples was1.0or 10wt%.The catalysts with high loading were prepared to clarify the changes in crystalline phase and electronic state of precious metals.Part of the calcined catalysts was heat-treated at400°C for15min in50%H2/N2prior to charac-terizations and catalytic reactions.2.2Catalytic Combustion of Ethyl AcetateAfixed-bedflow reactor made of quartz tubing of8mm inner diameter was used,and the prepared catalyst (600mg)was set in the reactor.Each catalyst was tabletted and pulverized into0.85–1.7mm before catalytic reaction tests.A gaseous mixture composed of0.1%ethyl acetate and99.9%air was fed with aflow rate of100cm3min-1 (space velocity:10,000L kg-1h-1).The catalyst bed length of Al2O3-supported metal catalysts was longer than that in CeO2-supported metal catalysts:GHSV(Al2O3 -supported catalysts)=4,000h-1;GHSV(CeO2-supported catalysts)=15,000h-1.The outlet gas compositions were analyzed by an on-line micro-gas chromatograph with a thermal conductivity detector(TCD)(VARIAN,CP-4900) and aflame ionization detector(FID)(Shimadzu,GC-8A). The temperature was raised from room temperature up to 250°C in a heating process.The measurements were car-ried out at afixed temperature.Ethyl acetate conversion to carbon dioxide was defined as follow:Ethyl acetate conversion to CO2ð%Þ¼F CO2out4ÂF EAinÂ100where F EA in is the influent molarflow rate of ethyl acetate,and F CO2outis the effluent molarflow rate of CO2.2.3Catalyst CharacterizationThe samples were characterized by X-ray diffraction(XRD), X-ray photoelectron spectroscopy(XPS),temperature-programmed reduction(TPR),and BET surface area.XRD patterns were recorded by Cu K a radiation on a RIGAKU Rint2500diffractometer for phase identification in the samples.XPS measurements were conducted on Shimadzu ESCA-850using a Mg K a source.In the case of the reduced catalysts,the samples were transferred directly into XPS chamber without exposure to air after the reduction treat-ment.The binding energy was referenced to the C1s peak (284.3eV).BET surface area was determined by N2 adsorption at the liquid nitrogen temperature using a Shi-madzu Gemini2375analyzer.TPR measurements were conducted using a Quantachrom CHEMBET3000system, and the amount of consumed hydrogen was measured by a thermal conductivity detector(TCD).A weighed amount (25mg)of the as-calcined catalysts was placed in a quartz tube reactor,and then a gaseous mixture of5%H2-95%Ar was fed to the reactor at30mL min-1.The temperature was raised up to800°C at a heating rate of10°C min-1.The size and dispersion of precious metal particles on CeO2support were determined from the chemisorption of carbon monoxide.The CO adsorption was carried out by an O2-CO2-H2-CO pulse method(Quantachrom CHEMBET 3000system)because the conventional method is ineffec-tive for the supports with large oxygen storage capacity due to the overestimation of adsorbed carbon monoxide[17]. First,the sample(25mg)was heat-treated at300°C in an oxygen atmosphere,and then cooled down to room tem-perature.The resultant sample was secondly reduced at 400°C in a hydrogen atmosphere and cooled down to room temperature.Subsequently,O2,CO2,and H2gases were fed to the sample in a sequential manner at room temperature for5min,and carbon monoxide(0.224mL) was pulsed repeatedly to the sample until the amount of CO at the outlet reached a constant value at room temperature. The dispersion and the diameter of precious metals were calculated by assuming the adsorption stoichiometry of CO/M s=1(M s:Surface atom of the precious metal).3Results and Discussion3.1Ethyl Acetate Combustion Over As-CalcinedCatalystsThe results for the catalytic activity tests over CeO2and as-calcined1.0wt%Pt/CeO2,Pd/CeO2,Ru/CeO2,and Rh/ CeO2are shown in plete oxidation of ethyl acetate over CeO2was not achieved even at high temper-atures,and many by-products such as hydrogen, hydrocarbon,and so on,were formed at above400°C.On the other hand,ethyl acetate was completely oxidized over CeO2-supported metal catalysts below250°C,and only carbon dioxide was detected as afinal product.Among thecatalysts,Ru/CeO2exhibited the highest activity at low temperatures;ignition temperature was ca.130°C and the conversion of90%was attained at180°C.The results for the catalytic activity tests over as-calcined1.0wt%Ru/ CeO2,Pt/c-Al2O3,Pd/c-Al2O3,and Ru/c-Al2O3are shown in Fig.2.The diameter of platinum particles on c-Al2O3 was2.0nm,and the BET surface area was higher than 140m2g-1.The activity of Ru/CeO2was higher than that of Al2O3-supported precious metal catalysts,in spite of the low surface area as summarized later in Table2.The effect of precious metals loaded on CeO2was also confirmed in the reaction products at low temperatures.The unreacted ethyl acetate and products selectivity at210°C over CeO2,Pt/CeO2,Pd/CeO2,Ru/CeO2,and Rh/CeO2are summarized in Table1.The main by-products were etha-nol and acetaldehyde at low temperatures,which started to form below100°C.In the cases of Pt/CeO2,Pd/CeO2,and Rh/CeO2,the selectivity to ethanol was lower than that to acetaldehyde,whereas over CeO2,the ethanol selectivity was higher.A small amount of methanol and acetic acid was also detected.Thus,it can be expected that precious metals loaded on CeO2promoted the ethanol oxidation as well as ethyl acetate oxidation.In ethyl acetate combustion over Al2O3-and TiO2-supported metal catalysts,it has been reported that acetaldehyde was formed by ethanol oxidation[18,19].In this study,therefore,a part of ethyl acetate oxidation over CeO2-supported metal catalysts should proceed via the formation of ethanol.3.2Characterization of As-Calcined CatalystsSurface characteristics of the as-calcined samples are summarized in Table2.The diameter and dispersion of precious metal particles on CeO2were confirmed to depend on the metal species,although BET surface area wasTable1Selectivity of unreacted ethyl acetate and products at210°C over CeO2,Pt/CeO2,Pd/CeO2,Ru/CeO2,and Rh/CeO2Catalyst Ethyl acetate(%)Acetaldehyde(%)Ethanol(%)Methanol(%)Aceticacid(%)Carbon dioxide(%)CeO245.7 1.27.20.40.240.8 Pt/CeO2 6.5 3.5 1.4––85.6 Pd/CeO230.38.2 1.2––60.2 Ru/CeO2000––100 Rh/CeO20 2.80.9––96.6comparable in each sample.The particle size of ruthenium on CeO2was the largest among all samples despite the high activity for ethyl acetate combustion.Temperature-programmed reduction profiles of pre-cious metal/CeO2catalysts are shown in Fig.3.All profiles consisted of three main peaks.The sharp peak below200°C corresponds to the reduction of precious metal oxide,and the other two peaks at high temperatures are ascribed to the reduction of the surface capping oxygen of CeO2[20].The reduction of ruthenium oxide on CeO2was initiated at the lowest temperature among the samples tested.Rh/CeO2exhibited a broad peak starting to rise at low temperature,and a maximum of this peak appeared at higher temperature as compared with that of Ru/CeO2.Thus,the precious metal species reducible at lower temperatures should be responsible for the high activity to the complete oxidation of ethyl ace-tate,as can be seen in Fig.1.These results indicate that ethyl acetate combustion proceeds through the reduction of the precious metal oxide.3.3Ethyl Acetate Combustion and Characterization ofthe Reduced CatalystsThe reduction treatment in a hydrogen atmosphere has significantly affected the activity.The results for the cat-alytic activity tests over reduced1.0wt%Pt/CeO2,Pd/ CeO2,Ru/CeO2,and Rh/CeO2are shown in Fig.4.As in the case of the as-calcined catalysts,Ru/CeO2exhibited the highest activity.Furthermore,the activity was almost unchanged before and after the reduction treatment.We have previously reported that the reduced ruthenium spe-cies readily reacted with the lattice oxygen of CeO2[21]. Thus,this can be the reason for the ineffectiveness of the reduction treatment.In contrast,the catalytic activity of other reduced catalysts was enhanced as compared with that over the as-calcined catalysts.In the case of Pt/CeO2,a remarkable effect of the reduction treatment was observed at lower conversion.For acetaldehyde combustion over Pt/ CeO2and Pd/CeO2,the activity was also improved by the reduction treatment[22].The electronic state of precious metal species on CeO2 was investigated by XPS measurement(Table3).All reduced samples were not exposed to air in this experi-ment,while the combustion was conducted in an oxidizing atmosphere.The binding energy of Pt4f7/2,Pd3d5/2,Ru 3d5/2,and Rh3d5/2was recorded.The energy of the as-calcined catalysts agreed well with those reported for precious metals in the oxidized state:PtO(Pt4f7/2= 73.8eV),PdO(Pd3d5/2=336.3eV),RuO2(Ru3d5/2= 280.7eV),and Rh2O3(Rh3d5/2=308.8eV)[23].On theTable2Physical properties of CeO2-supported1wt%metal catalystsCatalyst Surface area(m2g-1)Particle size ofprecious metal(nm)Dispersion(%)CeO265––Pt/CeO270 2.839 Pd/CeO272 2.741 Ru/CeO265 4.530 Rh/CeO269 2.839other hand,the reduced catalysts exhibited binding energy almost identical to that of Pt0(Pt4f7/2=71.2eV),Pd0(Pd 3d5/2=335.1eV),Ru0(Ru3d5/2=280.1eV),and Rh0 (Rh3d5/2=307.2eV)[23].Accordingly,by the reduction treatment,the precious metal species were reduced to the metallic state,resulting in the enhancement of the activity for ethyl acetate combustion.In the case of Ru/CeO2, however,different redox characteristics of ruthenium spe-cies were observed:reoxidation of metallic Ru is facilitated by the lattice oxygen of CeO2.As shown in Fig.3,this can be explained by the partial reduction of CeO2at400°C in a hydrogen atmosphere,leading to stabilization of ruthe-nium species in the metallic state.3.4Reoxidation Effect of the Reduced SamplesThe influence of reoxidation treatment for Pt/CeO2reduced at400°C was studied because the catalytic activity was significantly enhanced by the initial reduction treatment. The reduced Pt/CeO2was heat-treated at400°C for 30min in air prior to catalytic reaction(reoxidized-sam-ple).The results for the catalytic activity tests over 1.0wt%Pt/CeO2heat-treated in various conditions are shown in Fig.5.The high activity for the reduced-sample was deteriorated significantly by the subsequent reoxida-tion treatment.However,the activity was regenerated when the reoxidized-sample was subjected to the second-reduc-tion(reduced2)at400°C for15min in a hydrogen atmosphere.Then,the characterizations for the reoxidized and sub-sequently reduced samples were conducted.Figure6 shows the XRD patterns of10wt%Pt/CeO2heat-treated in various conditions.The diffraction patterns of as-calcined, reduced,and reoxidized samples were consistent with that of CeO2,and the intensity was increased as the oxidation–reduction treatment was repeated.In the case of the Pt/CeO2sample after the second-reduction(reduced2),a new phase of metallic platinum was observed.The XPS spectra of10wt%Pt/CeO2heat-treated in various condi-tions are shown in Fig.7.The two peaks at high and low binding energy correspond to Pt4f5/2and Pt4f7/2, respectively.As summarized in Table3,both peaks were negatively shifted by thefirst-reduction treatment.The transition between platinum oxide and platinum on CeO2 surface was induced by the repetitive oxidation–reduction treatment:the positively shifted peaks in the reoxidized-sample were moved to negative side again by the second-Table3Binding energy of the CeO2-supported10wt%metal catalystsCatalyst Binding energy(eV)As-calcined ReducedPt/CeO2a72.971.1 Pd/CeO2b337.1335.1 Ru/CeO2c280.7279.6 Rh/CeO2d308.5307.4Binding energy is value of a Pt4f7/2,b Pd3d5/2,c Ru3d5/2,and d Rh 3d5/2reduction treatment.Thus,the precious metals in the metallic state should be responsible for the high catalytic activity.We have previously reported that precious metal species on ZrO2were stabilized in the reduced state even under an oxidizing atmosphere at400°C,resulting in the maintenance of high activity for VOC combustion[21,22]. Accordingly,the stability of the reduced-sample can be lower than that of ZrO2-supported metal samples,since reduced precious metal species on CeO2surface were readily oxidized.4ConclusionsVarious CeO2-supported precious metal catalysts were investigated for low-temperature oxidation of ethyl acetate. Ethyl acetate was completely oxidized over the catalysts below250°C.Among them,Ru/CeO2exhibited the highest activity for the combustion despite the largest particle size of the precious metals examined.The reduc-tion of ruthenium oxide on CeO2was initiated at lower temperature than the other precious metals,resulting in the highest activity.It was noted that the catalytic activity of Ru/CeO2was almost unchanged by the reduction treat-ment.On the other hand,the catalytic activity of the other CeO2-supported precious metal catalysts was enhanced due to the formation of precious metals in the metallic state. The precious metals in the metallic state should be responsible for the high catalytic activity. 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Mon.Not.R.Astron.Soc.000,000–000(1997)The ASCA X-ray spectrum of the powerful radio galaxy3C109S.W.Allen1,A.C.Fabian1,E.Idesawa2,H.Inoue3,T.Kii3,C.Otani41.Institute of Astronomy,Madingley Road,Cambridge CB30HA,2.Department of Physics,University of Tokyo,Hongo,Bunkyo-ku,Tokyo,Japan3.Institute of Space and Astronautical Science,Yoshinodai,Sagamihara,Kanagawa229,Japan4.RIKEN,Institute of Physical and Chemical Research,Hirosawa,Wako,Saitama351-01,Japan10January1997ABSTRACTWe report the results from an ASCA X-ray observation of the powerful Broad LineRadio Galaxy,3C109.The ASCA spectra confirm our earlier ROSAT detection of in-trinsic X-ray absorption associated with the source.The absorbing material obscures acentral engine of quasar-like luminosity.The luminosity is variable,having dropped bya factor of two since the ROSAT observations4years before.The ASCA data also pro-vide evidence for a broad iron emission line from the source,with an intrinsic FWHMof∼120,000km s−1.Interpreting the line asfluorescent emission from the inner partsof an accretion disk,we can constrain the inclination of the disk to be>35degree,and the inner radius of the disk to be<70Schwarzschild radii.Our results supportunified schemes for active galaxies,and demonstrate a remarkable similarity betweenthe X-ray properties of this powerful radio source,and those of lower luminosity,Seyfert1galaxies.Key words:galaxies:active–galaxies:individual:3C109–X-rays:galaxies1INTRODUCTIONUnified models of radio sources propose that radio galaxies and radio-loud quasars are basically the same population of objects,viewed at different orientations(Orr&Browne 1982;Scheuer1987;Barthel1989).The nucleus is only di-rectly visible in quasars,the radio axis of which points within ∼45degree of the line of sight.In the case of radio galaxies the axis is closer to the plane of the Sky and the nucleus is obscured from view by material in the host galaxy,possibly in a toroidal distribution.The powerful Broad Line Radio Galaxy(BLRG)3C109 appears to be oriented at an intermediate angle.The nucleus is reddened,E(B−V)∼0.9,and polarized in the optical waveband(Rudy et al.1984;Goodrich&Cohen1992),sug-gesting that our line of sight passes through the edge of the obscuring material.The dereddened luminosity of the nucleus,V=−26.2(Goodrich&Cohen1992)identifies the source as an intrinsically luminous quasar.Obscuration is also seen at X-ray wavelengths(Allen&Fabian1992). 3C109was serendipitously observed with the Position Sen-sitive Proportional Counter(PSPC)on ROSAT in1991Au-gust.The PSPC spectrum exhibits soft X-ray absorption in excess of that expected from material within our own Galaxy,implying an intrinsic equivalent hydrogen column density at the redshift of the source(z=0.3056;Spinrad et al.1985)of∼5×1021atom cm−2.The intrinsic(unab-sorbed)X-ray luminosity of the source(0.1−2.4keV)de-termined from the PSPC data is∼5×1045erg s−1,making it one of the most X-ray luminous objects within z∼0.5; only the QSOs3C273and E1821+643have higher X-ray lu-minosities(and3C273may have a significant beamed com-ponent to its X-ray emission).We present here the results of an ASCA X-ray observa-tion of3C109.The ASCA data confirm the results of Allen &Fabian(1992)on excess absorption,and allow us to ex-plore further the X-ray properties of this remarkable source. We show that3C109has decreased in brightness by about a factor of two since the ROSAT observations,to aflux level comparable with that observed with the Imaging Propor-tional Counter(IPC)on the Einstein Observatory in1979 (Fabbiano et al1984).Also,of particular interest is the de-tection of a strong,broad iron line in the ASCA spectra. This result implies that most of the X-ray emission from 3C109is unbeamed.Modelling the line asfluorescent Fe K emission from an accretion disk,we are able to constrain both the inclination and inner radius of the disk.The X-ray properties of3C109are shown to be remarkably similar to those of many lower-power,Seyfert1galaxies.Throughout this paper we assume a value for the Hubble constant of H0=50km s−1Mpc−1and a cosmological deceleration pa-rameter q0=0.5.22THE ASCA OBSER V ATIONSThe ASCA X-ray astronomy satellite(Tanaka,Inoue& Holt1994)consists of four separate nested-foil telescopes, each with a dedicated X-ray detector.The detectors in-clude two Solid-state Imaging Spectrometers or SISs(Burke et al.1991,Gendreau1995)and two Gas scintillation Imaging Spectrometers or GISs(Kohmura et al.1993). The SIS instruments provide high quantum efficiency and good spectral resolution,∆E/E=0.02(E/5.9keV)−0.5.The GIS detectors provide a lower resolution,∆E/E= 0.08(E/5.9keV)−0.5,but cover a larger(∼50arcmin diam-eter)circularfield of view.3C109was observed with ASCA on1995Aug28-29. The SIS observations were made in the standard1-CCD mode(Day et al.1995)with the source positioned at the nominal pointing position for this mode.X-ray event lists were constructed using the standard screening criteria and data reduction techniques discussed by Day et al.(1995). The observations are summarized in Table1.Source spectra were extracted from circular regions of radius4arcmin(SIS0),3.5arcmin(SIS1)and6arcmin (GIS2,GIS3),respectively.For the SIS data,background spectra were extracted from regions of the chip relatively free of source counts.For the GIS data,background spectra were extracted from circular regions,the same size as the source regions,and at similar distance from the optical axes of the telescopes.Spectral analysis was carried out using the XSPEC spectralfitting package(Shafer et al.1991).For the SIS data,the1994Nov9version of the SIS response matrices were used.For the GIS data the1995Mar6response ma-trices were used.The spectra were binned to have a mini-mum of20counts per Pulse Height Analysis(PHA)channel, thereby allowingχ2statistics to be used.In general,best-fit parameter values and confidence limits quoted in the text are the results from simultaneousfits to all4ASCA data sets,with the normalization of the power-law continuum al-lowed to vary independently for each data set.3RESULTS3.1Confirmation of excess X-ray absorptionin3C109The principal result of the ROSAT PSPC observation of 3C109(Allen&Fabian1992)was the detection of X-ray absorption in excess of the Galactic value determined from 21cm HI observations.The ASCA data allow us to verify and expand upon this result.The ASCA data werefirst examined using a simple ab-sorbed power law model.This allows direct comparison with the results of Allen&Fabian(1992).The free parameters in thefits were the column density of the absorbing mate-rial,N H,the photon index of the power law emission,Γ, (both parameters were forced to take the same value in all4 ASCA data sets)and the normalizations,A1,of the power-law emission.(Due to the range of source extraction regions used,and known systematic differences in theflux calibra-tion of the different ASCA detectors,the value of A1was allowed to vary independently for each data set).The best fit parameter values and90per cent(∆χ2=2.71)confi-Figure1.(Upper panel)The SIS and GIS spectra of3C109with the bestfitting absorbed power-law model(Model A)overlaid. (Lower panel)The residuals to thefit in units ofχ.(For plotting purposes the data have been rebinned along the energy axis by a factor7.)Figure2.(Upper panel)The ratio of data to model,where the model is the best-fit Model A,but with the absorption reset to the Galactic value(assumed to be3×1021atom cm−2).Note the large negative residuals at energies below2keV which are due to the excess absorption,and the evidence for a broad,redshifted emission line feature at∼5keV.For plotting purposes,the SIS (open circles)and GIS(filled squares)data sets have been av-eraged together and binned by a factor of20along the energy axis.The ASCA X-ray spectrum of the powerful radio galaxy 3C1093Table 1.Observation summaryInstrument Observation Date Exposure (ks)ASCA SIS01995Aug 28/2936.0ASCA SIS1””35.0ASCA GIS2””35.0ASCA GIS3””35.0ROSAT PSPC 1991Aug 3022.1Einstein IPC1979Mar 71.86Notes:X-ray observations of 3C109.Exposure times are for the final X-ray event lists after standard screening criteria and corrections have beenapplied.Figure 3.Joint confidence contours on the photon index and total column density,determined with spectral Model A (Table 3).Contours mark the regions of 68,90and 99per cent confidence (∆χ2=2.30,4.61and 9.21respectively).dence limits obtained with this simple model are presented in Table 3(Model A).The SIS and GIS spectra with their best-fitting models (Model A)overlaid are plotted in Fig.1.For illustrative purposes,in Fig.2we show the best fit model with the column density reset to the Galactic value (assumed to be 3.0×1021atom cm −2).Note the large negative residuals at energies,E <2keV,which demonstrate the effects of the excess absorption,and the broad positive residual at E ∼5keV,which will be discussed in more detail in Section 3.3.The ASCA results clearly confirm the PSPC result on excess absorption in the X-ray spectrum of 3C109.Assuming that the absorber lies at zero redshift we determine a total column density along the line of sight of 5.30±0.42×1021Figure 4.Joint confidence contours (68,90and 99per cent con-fidence)on the column density and redshift of the excess absorber in 3C109(using spectral Model B).atom cm −2(90per cent confidence limits).This is in goodagreement with the PSPC result of 4.2+1.9−1.6×1021atom cm −2.The ASCA result on the photon index,Γ=1.78+0.05−0.06,is also in excellent agreement with the PSPC result of1.78+0.85−0.76,although is more firmly constrained.The joint confidence contours on Γand N H are plotted in Fig.3.We have examined the constraints the ASCA spectra can place on the redshift of the excess absorbing mate-rial.The Galactic column density along the line of sight to 3C109,determined from 21cm observations,is 1.46×1021atom cm −2(Jahoda et al.1985;Stark et al.1992),although Johnstone et al.(1992)suggest a slightly higher value of ∼2.0×1021atom cm −2,and Allen &Fabian (1996)in-fer a value of ∼3.0×1021atom cm −2from X-ray stud-ies of the nearby cluster of galaxies Abell 478.Modelling4the ASCA spectra with a two-component absorber,with a Galactic(zero-redshift)column density of3.0×1021atom cm−2,and a component with variable column density and redshift,we obtain the joint confidence contours on the red-shift and column density of the excess absorption plotted in Fig.4.The best-fit parameter values and90per cent confidence limits for the two-component absorption model (Model B)are also summarized in Table3.3.2Variation of the X-ray luminosityTheflux measurements for3C109are summarized in Table2.Results are presented for both SIS instruments in the1.0−2.0and2.0−10.0keV(observer frame)energy bands.(The GIS detectors provide less accurateflux esti-mates).Also listed in Table2are thefluxes observed with the ROSAT PSPC in August1991and the IPC on Einstein Observatory in March1979.We see that in the overlapping 1.0−2.0keV energy band,the brightness of3C109has de-creased by a factor∼2since1991.Theflux determination from the ASCA data is now consistent with that inferred from the IPC observation in1979.Also listed in Table2are the intrinsic(absorption-corrected)X-ray luminosities of the source inferred from the observations.(Here the energy bands correspond to the rest-frame of the source).The absorption-corrected2−10keV luminosity inferred from the ASCA spectra is2.1×1045 erg s−1.(We assume that during the Einstein IPC observa-tions the source had the same spectral shape as determined from the ASCA observations.)3C109has also been observed to vary at near-infrared wavelengths.Rudy et al.(1984)found variations of a factor ∼2in the J band over afive year span from1978to1983. Elvis et al.(1984)similarly reported variations in the J,H and K bands of∼50per cent(in the same sense)on a timescale of2–3years between1980and1983.3.3Discovery of a broad iron lineThe residuals to thefits with the simple power-law mod-els,presented in Figs.1and2,exhibit an excess of counts in a line-like feature at E∼5.0keV.X-ray observations of Seyfert galaxies(Nandra&Pounds1994and references therein)show that many such sources exhibit a strong emis-sion line at E∼6.40keV(in the rest frame of the object). This is normally attributed tofluorescent Fe K emission from cold material irradiated by the nucleus.Wefind that thefit to the ASCA data for3C109is sig-nificantly improved by the introduction of a Gaussian line at E∼5keV(∆χ2=9.2for3extrafit parameters;an F-test indicates this to be significant at the97per cent level.)The best-fit line energy is5.09+0.44−0.38keV(corresponding to6.61+0.57−0.50keV in the rest frame of the source.Note that if afixed rest-energy of6.4keV is assumed,the introduction of the Gaussian component becomes significant at the∼99per cent confidence level).The data also indicate that the line isbroad,with a1sigma width of0.65+0.81−0.36keV.The equivalentwidth of the line is300+600−200eV.The width and energy of theline suggest that it is due tofluorescence from a rapidly ro-tating accretion disk–as is thought to be the case in lower luminosity Seyfert galaxies(Tanaka et al.1995;Fabianet Figure5.Joint confidence contours(68,and90per cent confi-dence)on the normalization,A2,and inclination,θ,of the disk line using spectral Model D(following Fabian et al.1989).al.1995).The bestfitting parameters and confidence limits for the power-law plus Gaussian model(Model C)are sum-marized in Table3.Note that the emission feature is not well-modelled by the introduction of an absorption edge at higher energies[the introduction of an edge into the simple absorbed power-law model(Model A)does not significantly improve thefit].Note also that the measured lineflux is not significantly affected by the small systematic bump in the XRT response at E∼5.5keV(which produces a nar-row,positive residual with aflux of a few per cent of the continuumflux at that energy).3.4Modelling the line as a disklineAlthough the simple Gaussian model provides a reason-able description of the5.0keV emission feature,the ASCA data suggest that the line profile is probably more ing two Gaussian components to model the line profile,we obtain the bestfit for a broad component with a rest energy consistent with6.4keV,and a narrow com-ponent with an energy6.8±0.1keV(in the rest-frame of the source).These results are similar to those obtained for nearby,lower-luminosity Seyfert galaxies(e.g.Mushotzky et al1995;Tanaka et al1995;Iwasawa et al.1996)where the line emission is thought to originate from the inner regions of an accretion disk surrounding a central,massive black hole(Fabian et al.1989).We have therefore modelled the broad line in3C109us-ing the Fabian et al.(1989)model for line emission from a relativistic accretion disk.The rest-energy of the line(in the emitted frame)wasfixed at6.40keV,the energy appropri-ate for Fe Kfluorescence from cold material.(The effects of cosmological redshift were incorporated into the model.) The accretion disk was assumed to extend over radii from3The ASCA X-ray spectrum of the powerful radio galaxy3C1095 Table2.X-rayflux of3C109Instrument Date F X L X2-10keV1-2keV2-10keV1-2keV ASCA SIS01995Aug28/2948.5±1.69.50±0.2321.4±0.36.69+0.76−0.71 ASCA SIS1””46.3±2.19.76±0.3221.3±0.37.68+1.10−0.890.1-2.4keV1-2keV0.1-2.4keV1-2keVROSAT PSPC1991Aug3028.9±2.618.2±0.745+147−2512.1+6.3−3.50.5-3.0keV1-2keV0.5-3.0keV1-2keVEinstein IPC1979Mar720±68.3±2.516.5±5.06.2±1.9Notes:The X-rayflux and luminosity of3C109measured with ASCA,ROSAT and the Einstein Observatory.Fluxes are in units of10−13erg cm−2s−1and are defined in the rest frame of the observer.Luminosities are in1044erg s−1,are absorption corrected,and are quoted in the rest frame of the source.Errors are90per cent(∆χ2=2.71)confidence limits.to500Schwarzschild radii(hereafter R s)and cover a solid angle of2πsteradians.The emissivity was assumed to follow a standard disk radiation law.Only the disk inclination and line strength were free parameters in thefit.The bestfit parameters and90per cent confidence limits obtained with the diskline model are listed in Table3(Model D).The in-troduction of the diskline component significantly improves thefit to the ASCA data with respect to the power-law model(∆χ2=8.9for2extrafit parameters,which an F-test indicates to be significant at the99per cent confidence level).In Fig.5we show the joint confidence contours on the inclination of the disk,θ,versus the line strength,A2.The 90per cent(∆χ2=2.71)constraint on the inclination is θ>35degree.We have also examined the constraints that may be placed on the inner radius,r in,of the accretion disk with the diskline model.The data were re-fitted with r in included as a free parameter.The preferred value for r in is3R s,with a90per cent confidence upper limit of70R s. (Note that for an ionized disk,with a rest-energy for the line of6.7keV,the inclination is constrained toθ>18degree.) The effects of introducing a further,flatter power-law component into thefits,such as may be required to ac-count for reflected emission from the illuminated face of an accretion disk,or synchrotron self-Compton emission from within a jet,were also examined.The introduction of aflat-ter power-law component does not significantly improve the fits.However,the ASCA spectra permit(with no significant change inχ2)the inclusion of a continuum spectrum appro-priate for reflection from a cold disk,subtending a solid angle of2πsteradians to the primary X-ray source,oriented at any inclination consistent with the results from the disklinefits. 4DISCUSSIONThe ASCA results on excess X-ray absorption in3C109con-firm and refine the earlier ROSAT results(Allen&Fabian 1992).The ASCA data show(under the assumption that all of the absorbing material lies at zero redshift)that theX-ray spectrum of the source is absorbed by a total col-umn density of5.30+0.42−0.42×1021atom cm−2(Model A).This compares to a Galactic column density of∼3.0×1021atom cm−2(Allen&Fabian1996).If we instead assume that the excess absorption,over and above the Galactic value,is due to material at the redshift of3C109,we determine an in-trinsic column density of4.20+0.83−0.78×1021atom cm−2.Note that these results assume solar abundances in the absorbing material(Morrison&McCammon1983).The X-ray absorption measurements are in good agree-ment with optical results on the polarization and intrinsic reddening of the source.Goodrich&Cohen(1992)deter-mine an intrinsic continuum reddening of E(B−V)∼0.9, in addition to an assumed Galactic reddening of E(B−V)= ing the standard(Galactic)relationship between E(B−V)and X-ray column density,N H/E(B−V)= 5.8×1021atom cm−2mag−1(Bohlin,Savage&Drake1978), the total reddening observed,E(B−V)∼1.2,implies a total X-ray column density(Galactic plus intrinsic)of∼7.0×1021 atom cm−2.This result is similar to the X-ray column den-sity inferred from the ASCA spectra using model B and confirms the presence of significant intrinsic absorption at the source.Note that this result also suggests that the dust-to-gas ratio in3C109is similar to that in our own Galaxy.Further constraints on the distribution of the absorbing gas are obtained from the optical emission-line data pre-sented by Goodrich&Cohen(1992).In the narrow line re-gion(NLR),the observed Blamer decrement of Hα/Hβ= 5.8implies(for an assumed recombination ratio of3.2)an E(B−V)value∼ing the relationship of Bohlin, Savage&Drake(1978)this implies an X-ray column den-sity to the NLR of∼2.8×1021atom cm−2,in good agree-ment with the Galactic column density of∼3.0×1021atom cm−2determined by Allen&Fabian(1996)and adopted in the X-ray analysis presented here.The Balmer decrement in the broad line region(BLR)is very steep(Hα/Hβ=13.2). Although this value cannot be reliably used to infer the ex-tinction to the BLR,the intrinsic line ratio is unlikely to6Table3.Results of the spectral analysisMODEL PARAMETERSAΓA1N H———χ2/DOFwabs(pow)1.78+0.05−0.061.38+0.10−0.100.530+0.042−0.042———638.9/633BΓA1N H N H(z)——χ2/DOFwabs zwabs(pow)1.77+0.05−0.061.35+0.10−0.090.3000.420+0.083−0.078——641.6/633CΓA1N H EσA2χ2/DOFwabs(pow+gau)1.86+0.12−0.081.47+0.16−0.120.558+0.056−0.0465.09+0.44−0.380.65+0.81−0.362.1+4.3−1.3629.7/630DΓA1N H EθA2χ2/DOFwabs(pow+diskline)1.87+0.08−0.081.48+0.14−0.130.561+0.052−0.0466.4090+0.0−552.4+1.4−1.4630.0/631Notes:A summary of best-fit parameters and90per cent(∆χ2=2.71)confidence limits from the spectral analysis of the ASCA data.Results are shown for four different modelsfitted simultaneously to the data for all four ASCA detectors.Γis the photon index of the underlying power-law continuum from the source.A1is the normalization of the power law component in the S0detector in10−3photon keV−1cm−2s−1at1keV.N H is the equivalent hydrogen column density in1022atom cm−2at zero redshift.In Model B,N H(z)is the best-fit intrinsic column density at the source for an assumed Galactic column density of0.3×1022atom cm−2.In Model C,E is the energy of the Gaussian emission line in the frame of the observer,σis the one-sigma line width in keV,and A2is the line strength in10−5photon cm−2s−1.In Model D,E is the rest-energy of the line in the emitted frame,θis the inclination of the disk in degree,and A2is again the line strength in10−5photon cm−2s−1.be above5,suggesting a total line-of sight reddening to the BLR of E(B−V)∼>0.8.Thus,the BLR is likely to be intrin-sically reddened by E(B−V)∼>0.3.The optical emission line results are therefore consistent with the two-component absorber model(B),with the column density of the intrinsic absorber being comparable with the Galactic component.3C109is the most powerful object in which a strong broad iron line has been resolved to date.Several more lu-minous quasars observed with ASCA do not show any iron emission or reflection features(Nandra et al1995).The next most luminous object with a confirmed broad line is 3C390.3(Eracleous,Halpern&Livio1996)which is about 10times less luminous in both the X-ray and radio bands than3C109.The equivalent widths of the lines in both ob-jects are∼300eV and therefore similar to those observed in lower-luminosity Seyferts.This argues against any X-ray ‘Baldwin effect’(as proposed by Iwasawa&Taniguchi1993).The line emission from3C109is most plausibly due to fluorescence from the innermost regions of an accretion disc around a central black hole(Fabian et al1995).Our results constrain the inner radius of the accretion disk to be<70R s and the inclination of the disk to be>35degree.The strong iron line observed in3C109,and the lack of evidence for a synchrotron self-Compton continuum in the X-ray spectrum, both suggest that little radiation from the jet is beamed into our line of sight.The inclination determined from the ASCA data is larger than the angle proposed by Giovannini et al.(1994) based on the jet/coreflux ratio of the source(θ<34de-gree).However,the jet/coreflux arguments are based on simple assumptions about the average orientation angles for radio galaxies and neglect environmental effects.The con-flict with the X-ray results may indicate that the situation is more complicated.Giovannini et al.(1994)also present constraints on the inclination from VLBI observations of the jet/counterjet ratio,which requireθ<56degree.The VLBI constraint,together with the ASCA X-ray constraint, then suggests35<θ<56degree.Our results on3C109are in good agreement with the unification schemes for radio sources and illustrate the power of X-ray observations for examining such models.The pre-ferred,intermediate inclination angle for the disk in3C109 is in good agreement with the results on X-ray absorption, polarization and optical reddening of the source,all of which suggest that our line of sight to the nucleus passes closes to the edge of the surrounding molecular torus.The results on the broad iron line reveal a striking similarity between the X-ray properties of3C109and those of lower power,Seyfert 1galaxies(Mushotzky et al1995;Tanaka et al1995;Iwa-sawa et al1996).This is despite the fact that the X-ray power of3C109exceeds that of a typical Seyfert galaxy by ∼2orders of magnitude.5ACKNOWLEDGEMENTSWe thank K.Iwasawa,C.Reynolds and R.Johnstone for discussions and the annonymous referee for helpful and con-structive comments concerning the intrinsic reddening in 3C109.SW A and ACF thank the Royal Society for support.The ASCA X-ray spectrum of the powerful radio galaxy3C1097 REFERENCESAllen S.W.&Fabian A.C.,1992,MNRAS,258,29PAllen S.W.&Fabian A.C.,1996,MNRAS,in pressBarthel P.D.,1989,ApJ,336,606Bohlin R.C.,Savage B.D.,Drake J.F.,1978,ApJ,224,132Burke B.E.et al.1991,IEEE Trans.,ED-38,1069Day C.,Arnaud K.,Ebisawa K.,Gotthelf E.,Ingham J.,MukaiK.,White N.,1995,the ABC Guide 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I NSTITUTE OF P HYSICS P UBLISHING I NVERSE P ROBLEMS Inverse Problems20(2004)121–135PII:S0266-5611(04)60933-6Blind deconvolution of bar code signalsSelim EsedogluMathematics Department,University of California-Los Angeles,Box951555,Los Angeles,CA90095,USAReceived17March2003,infinal form9October2003Published21November2003Online at /IP/20/121(DOI: 10.1088/0266-5611/20/1/007)AbstractBar code reconstruction involves recovering a clean signal from an observedone that is corrupted by convolution with a kernel and additive noise.Theprecise form of the convolution kernel is also unknown,making reconstructionharder than in the case of standard deblurring.On the other hand,bar codes arefunctions that have a very special form—this makes reconstruction feasible.Wedevelop and analyse a total variation based variational model for the solutionof this problem.This new technique models systematically the interaction ofneighbouring bars in the bar code under convolution with a kernel,as well asthe estimation of the unknown parameters of the kernel from global informationcontained in the observed signal.1.IntroductionWe study the problem of recovering a bar code from the noisy signal detected by a bar code reader.Bar codes represent(finite)sequences of digits by(finite)sequences of dark parallel ‘bars’of varying thickness,separated by‘white spaces’of varying size.As such,they can be conveniently modelled as characteristic functions of measurable subsets of R(seefigure1). We therefore introduce the setS={u(x)∈L2(R):u(x)∈{0,1}a.e.x}.(1) The process that converts a given bar code from the set S to the signal that is actually detected by a bar code reader depends,among other things,on the distance of the reader(the detector)to the surface where the bar code appears[10,11,18].The longer the distance,the more blurred the observed signal.And depending on ambient illumination the optical sensor of the bar code reader introduces an unknown gain factor.This process has been modelled[10,11,18]as the convolution of the bar code u(x)with a Gaussian kernel of unknown amplitudeαand standard deviationσ,and is denoted by Tα,σ:Tα,σ:u(x)−→α·Gσ∗u(x)(2) whereαis a strictly positive constant,andGσ(x)=1σ√2πexp−x22σ2withσ>0.(3)0266-5611/04/010121+15$30.00©2004IOP Publishing Ltd Printed in the UK121122S EsedogluFigure1.Top to bottom:a bar code,the function u(x)∈S that represents it,and a typical observedsignal f(x)obtained from u(x)via convolution by a Gaussian kernel followed by the addition ofnoise.Furthermore,in any practical situation,the observed signal f(x)is further corrupted by noise,which is modelled to be additive:f(x)=Tα,σ(u)+n(x).(4) Therefore,in our model it is f(x)that represents the typical output of a bar code reader.The goal of bar code reconstruction is to recover the bar code u(x)from the observedsignal f(x),without any knowledge ofαandσ.The bar code reconstruction problem thus differs from standard denoising problems ofimage processing in that the convolution kernel is not completely known in advance.In thisregard,it is closer to the blind deconvolution problem.2.Previous work and our approachPrevious work on the bar code reconstruction problem is based onfinding local minima andmaxima in the derivative of f(x)(which we called the observed signal above)using edge detectorfilters,and trying to relate them to the structure of the bar code they must have comefrom:under favourable conditions,local extrema in the derivative of the convolved signalcorrespond approximately to locations of discontinuities in the original bar code,and so help locate the‘bars’in the code.A major difficulty with such an approach is sensitivity to noise.Moreover,locations of local maxima and minima in f (x)are difficult to relate to the true locations of edges of the‘bars’in the original bar code u(x)because the convolution operatorinvolved in the observation process tends to shift their positions depending on the configurationof neighbouring bars and the amount of blurring(which is another unknown of the problem);Blind deconvolution of bar code signals123 this is known as‘convolution distortion’in bar code literature[18].This effect is significant when the standard deviation of the convolution kernel becomes comparable to the smallest length scale of interest in the problem,namely the minimum of the thicknesses of bars and their distances to each other.Joseph and Pavlidis describe in[10,11]a modification of the traditional edge detection technique to take into account this issue,but we believe it can be addressed more systematically.Furthermore,when the standard deviation of the convolution kernel is large enough(which happens when,for example,the reader is held at a sufficiently large distance to the bar code),‘edges’of the bars that make up the bar code may have no corresponding local extrema in the derivative of the convolved signal.In this situation,a traditional approach based on locating extrema in the derivative of the convolved signal would be at a significant disadvantage even in the absence of any noise.We follow a completely different path based on the variational approach to image processing:we write down an energy whose minimizer is the candidate solution.These techniques are more robust than traditional edge detectors in the presence of noise:first,they are more global in that they utilize information from all over the image domain to detect transitions in the signal,and second they avoid working with the derivative of the signal which is always an error prone quantity.Moreover,unlike previous approaches,the technique we present systematically models interactions between neighbouring‘bars’under convolution with a Gaussian kernel.Indeed,our model takes into account the interactions between all‘bars’in the signal under convolution,and not just the neighbouring few(although of course the main contribution comes from the immediate neighbours).This is accomplished by explicitly modelling the convolution process using the‘fidelity’term in the energy that we propose to minimize.Another way the model presented here differs from previous approaches is in how the unknown parameterσis handled.Our technique provides a systematic way of determiningσfrom the global information contained in the observed signal and avoids having to estimate it from an isolated peak or valley.To be more specific,we introduce and study both analytically and numerically a version of the total variation based denoising/deblurring technique of Rudin and co-workers[16,17] that is adapted to minimizing over functions that take only two values.The resulting algorithm minimizes an energy functional via gradient descent,and is thus iterative.It does not require a priori knowledge of the number of‘bars’expected in the reconstructed bar code.This new algorithm does not require pronounced local extrema in the derivative of the convolved signal in order to successfully reconstruct bar codes.It is robust under noise,even at high blur.It is therefore a promising new approach to furthering the distance from which bar codes can be reliably reconstructed by readers.Moreover,it can be extended very naturally to two-dimensional signals.Although we describe all the details of the numerical implementation,our emphasis in this paper is not the speed of the algorithm but the accuracy of its reconstructions.In particular, we should point out that there are other techniques besides gradient descent for minimizing total variation based functionals that are potentially much more efficient;examples of other optimization approaches can be found in[3–6,9,12,14,19,20].Many previous authors studied total variation based regularization for denoising and deblurring(with a known kernel) in image processing and related applications[1,4,16,17,19].Furthermore,application of total variation based reconstruction to blind deconvolution was previously introduced by Chan and Wong[7];that work deals with the situation where,unlike our setting,there is no a priori information available about the unknown function u(x)and the convolution kernel.124S Esedoglu 3.Preliminary observationsWe start with a uniqueness result which shows that in the absence of any noise,the signal detected by a bar code reader contains enough information to determine the bar code it resulted from:Proposition1.Let u1,u2∈S be two bar codes such that Tα1,σ1(u1)=Tα2,σ2(u2)identically. Then u1=u2identically.Furthermore,if u1=u2does not vanish identically,thenα1=α2 andσ1=σ2.Proof.First,it is plain that Tα1,σ1(u1)=Tα2,σ2(u2)vanishes if and only if u1=u2=0.Solet us now assume that Tα1,σ1(u1)=0.Then,we can show thatσ1=σ2.To that end,supposenot and,with no loss of generality,assume thatσ1>σ2.The equalityα1Gσ1∗u1=α2Gσ2∗u2(5)implies:u2=α1α2Gσ∗u1whereσ=σ21−σ22.(6)That would mean u2∈C∞,which is a contradiction.It follows thatσ1=σ2.With that,we getα1u1=α2u2,and the conclusion of the proposition follows.Let us note,on the other hand,that in the presence of noise the equation Tα,σu(x)=f(x) cannot in general be solved forα,σ,u(x).Indeed,for any choice ofα,σ,u(x),the right-hand side either takes only two values(which happens ifσ=0,a value that we allow)or is smooth. Hence,when f(x)is any non-smooth function that takes more than two values,there is no corresponding solution.Remark.Proposition1has an obvious higher-dimensional analogue.On the other hand, there seems to be no clear way to adapt this argument to the discrete setting considered in the subsequent sections.4.Variational modelsWe will study a number of total variation based models for the solution of the bar code problem. In applications,it makes more sense to pose the problem on a bounded interval I,which we will take to be I=(0,1).We then define the subset S I of S asS I:={u∈S:u=0a.e.x∈R\I}.(7) We will assume that the observed signal f(x)satisfies f∈L2(R).Also,from here onwards it is more convenient to letα 0.Before considering total variation based models,let us note that the following natural variational approach to the bar code problem in general does not have a solution;in other words,the approach is not well-posed:inf u(x)∈S I α,σ 0E(u,α,σ)where E(u,α,σ)=R(α·Gσ∗u−f)2d x.(8)In fact,without some regularization on u(x),even the simpler minimization problem with α 0fixed has no solution in general.The following claim helps explain why.Blind deconvolution of bar code signals 125Proposition 2.Fix α>0,and take any f (x )∈L ∞(R )such thatf (x )=0for a.e.x ∈I c ,and f (x )∈[0,α]for a.e.x ∈I .(9)Then,inf u (x )∈S I σ>0E (u (x ),α,σ)=0.(10)Proof.First,we haveG σ∗f −→fin L 2(R )as σ→0+.(11)Also,there exists a sequence b n (x )∈S I such thatαb n (x )w −→f (x )weakly in L 2(R )as n →∞.(12)The last statement follows from a well-known generalization of the Riemann–Lebesgue lemma.By compactness of the convolution operator,αG σ∗b n −→G σ∗f strongly in L 2(R )as n →∞,(13)for any σ>0.Taking now a sequence {σj }∞j =1→0+,we can take a diagonal sequence{b n j (x )}such thatαG σj ∗b n j −→fin L 2(R )as j →∞,(14)which implies the desired conclusion.Combined with the uniqueness results of proposition 1,the last proposition shows that the infimum in (8)is in general not attained,and therefore the approach is not well-posed.As the foregoing discussion suggests,it is necessary to put some regularization on u (x ).With that in mind,we define the following energy:E λ(u ,α,σ)= R |∇u |+λR(α·G σ∗u −f )2d x (15)over functions u (x )∈S I ,and constants α,σ 0.Here,λis a positive constant.The regularization term,given by the first integral on the right-hand side is defined as R |∇u |=sup φ(x )∈C 1c (R )|φ(x )| 1∀x ∈Ru (x )φ (x )d x (16)and agrees with its ordinary sense whenever u (x )is smooth.A natural approach to recovering u (x )from f (x )would be to carry out the following minimization:inf u (x )∈S I α,σ 0E λ(u ,α,σ).(17)However,we have the following proposition.Proposition 3.In general,the infimum in (17)is not attained.Proof.Take f (x ):=G σ0(x −12)for some σ0>0,and find a λ>0large enough so that E λ(0,1,1)=λRf 2(x )d x >2.(18)On the other hand,any non-zero function u (x )∈S I has total variation at least 2,and as in the uniqueness result of proposition 1we can easily see thatR(f (x )−α·G σ∗u )2d x >0(19)126S Esedoglu for all u (x )∈S I and α>0,σ 0.Therefore,E λ(u ,α,σ)>2(20)for all u (x )∈S I and α,σ 0.Now letu j (x )=χ[−12j ,12j ](x −12)for j =1,2, (21)Consider the sequence {(u j ,j ,σ0)}∞j =1.We havej ·u j (x )j →∞−→δ12(x )(22)weakly in the sense of measures.In fact,j ·G σ0∗u j j →∞−→L 2G σ0(x )=f (x )(23)so that lim j →∞E λ(u j ,j ,σ0)=inf u (x )∈S I α,σ 0E λ(u ,α,σ)=2.(24)This establishes the proposition.Perhaps the variational problem (17)has solutions for most choices of the original signal f (x ).Nevertheless,the proposition given above makes a strong argument against using it to solve the bar code problem.We therefore look for alternative variational models.One possibility is to put restrictions on the constant α 0.To that end,let K be a compact subset of positive real numbers,and consider instead of (17)the following variational problem:inf u (x )∈S I α∈K and σ 0E λ(u ,α,σ).(25)We then have the following proposition.Proposition 4.Problem (25)has a solution (infimum is attained).Proof.Let {(u j ,αj ,σj )}j be a minimizing sequence for (25).The sequence {u j }j lies in S I and has bounded total variation.Therefore,by the standard compactness result (see e.g.[8])for functions with bounded variation,and the fact that αj all lie in a compact set K ,we can assume by passing to a subsequence if necessary that u j and αj converge to u ∞(x )and α∞∈K respectively.Since S I is a closed subset of L 2(R ),we have that u ∞(x )∈S I .If it happens that lim inf j →∞σj =∞,then one can easily see that (u ≡0,α=1,σ=1)is a minimizer.If lim inf j →∞σj <∞,we pass to a further subsequence so that σj →σ∞ 0.It is possible that σ∞=0,but no matter:in any case we haveαj G σj ∗u j −→α∞G σ∞∗u ∞in L 2(26)even when σ∞=0.Existence of a minimizer (u ∞,α∞,σ∞)follows from this continuity property,and the lower semicontinuity of the total variation norm (first term). Remark.We allow σ=0.This is to be interpreted to mean that inf u (x )∈S I α∈K and σ 0E λ(u ,α,σ)= R |∇v |+λR (αv −f )2d x (27)for some v(x )∈S I and α∈K .We now list some possible variational models whose well-posedness follows immediately from proposition 4.Which model among these is more applicable depends on what kind of additional information is available in practice.Blind deconvolution of bar code signals 127Corollary 1.The following minimization problems have solutions.(1)Given a fixed α0,inf u (x )∈S I σ 0E λ(u ,α0,σ).(28)(2)Given a continuous,strictly positive function ψ(x )such that ψ(x )→∞as |x |→∞,inf u (x )∈S I α,σ 0(E λ(u ,α,σ)+ψ(α)).(29)(3)Given ε>0,inf u (x )∈S εI α,σ 0E λ(u ,α,σ)(30)whereS εI :={u ∈S I :u (x )=1⇒u (y )=1∀y ∈[x −β1,x +β2]for some β1,β2 0with β1+β2 ε}.(31)(4)inf u (x )∈S I α,σ 0E λ(αu ,1,σ).Proof.Problem 1is the same as the problem given in (25)with K ={α0},so has a solution by proposition 4.To see that problem 2has a solution,observe that the minimum energy is bounded from above by M :=λ f 2d x +ψ(0);that means,in particular,we only consider αsuch that ψ(α) M .By hypothesis on ψ,that constrains αto a compact subset of R ,so that reasoning of proposition 4applies.For problem 3,the minimum energy is clearly bounded by λ f 2d x .For any u ∈S εI ,u ≡0this restricts relevant αto a compact set (independent of u )so that once again the reasoning of proposition 4can be applied to find a minimizer.Finally,in problem 4the energy bounds the total variation of the function αu (x )so that the compactness and continuity argument of proposition 4can be applied to a minimizing sequence of these functions. Remarks.(1)The first variational problem in the corollary above is useful when the amplitude of thekernel can be estimated a priori .We present a number of numerical experiments with this approach in the subsequent sections.(2)The third variational problem is over bar codes in which the thickness of each ‘bar’isbounded below by ε>0.This is indeed the case with bar code signals in practice.On the other hand,S εI can be described by a finite number of parameters,and penalizing the total variation of the signal might be unnecessary.We next consider whether solving the variational problem (25)indeed leads to the correct bar code if the observed signal is noise free.To be precise,fix a b (x )∈S I such that b (x )=0.Let f (x ),the observed signal,be given byf (x )=α0G σ0∗b (x )for some α0,σ0>0.(32)The following proposition shows that indeed for every large enough choice of the parameter λthe solution (minimizer)of the variational problem (25)recovers the correct bar code b (x )and the parameters α0,σ0from an observed signal of the form (32).128S Esedoglu Proposition 5.If α0∈K and f (x )is given by (32),then there exists a λ∗such that whenever λ λ∗the unique minimizer of (25)is precisely (b (x ),α0,σ0).Proof.Begin by noting thatE λ(b (x ),α0,σ0)= R |∇b |=2N (33)where N ∈N .Therefore,the claim is proved if we show that for any α,σ 0and any u (x )∈S I with |∇u | 2N and u (x )=b (x )we have E λ(u ,α,σ)>2N .Case 1: |∇u |=2N .Then,by the uniqueness result,(αG σ∗u −f )2d x =0only if (u (x ),α,σ)=(b (x ),α0,σ0).(34)Therefore,for any other u (x ),we have E λ(u ,α,σ)=2N +λ(αG σ∗u −f )2d x >2N .(35)Case 2: |∇u |<2N .The set of all such u (x )lie in a finite-dimensional space;indeed,any such u (x )can be written asu (x )=N −1 j =1χ(a j ,b j )(x )where a j b j <a j +1for all j ,(36)and a j ,b j ∈[0,1].The function F of 2N variables defined as F (a 1,...,a N −1;b 1,...,b N −1;α;σ)≡E λ j χ(a j ,b j )(x ),α,σ(37)is continuous for α∈K and σ 0.Moreover,lim σ→∞αG σ∗u =0in L 2(38)uniformly in u ∈S I and α∈K .Recalling once again that by the uniqueness result E λ(u ,α,σ)>0for all u that fall under this case,these implym ≡inf u ∈S I and |∇u |<2N α∈K and σ 0 αG σ∗u −f 2L 2>0.(39)Choosing λ∗=2N /m ,the conclusion of the proposition follows.putationWe start by describing a numerical technique for minimizing the following special instance of (25):inf u (x )∈S I σ 0E λ(u ,α,σ)(40)where α>0is kept fixed.Our approach is to approximate this problem by a ‘diffuse interface’model that involves a small parameter.This allows us,among other things,to impose the two-valuedness constraint on u (x )via a penalty term in the energy and minimize over all functions instead.To that end,we introduce the following energies:E ε,λ(u ,σ):= R ε(u (x ))2+1εW (u (x )) d x +λ R(αG σ∗u (x )−f (x ))2d x .(41)Blind deconvolution of bar code signals 129Here,εis the positive small parameter,and W (x )is the ‘double-well’function W (x )=x 2(1−x )2.Then,the following minimization problem:inf u (x )=0for a .e .x ∈I σ 0E ε,λ(u ,σ)(42)approximates (40)as ε→0+.The idea for this well-known approximation technique comes from the work of Modica and Mortola [13],which deals with the more interesting setting of (n −1)-dimensional interfaces in R n .(See [2]and [15]for other examples of such approximations in different contexts.)We propose to minimize the approximate energies E ε,λvia gradient descent,starting with an initial guess for u (x )and σ.In particular,we initialize u (x )so that it has as many interfaces as can be resolved,and let it coarsen as the descent progresses.The Euler–Lagrange equations for these energies lead to the following gradient descent equations:u t =2εu xx −1εW (u )−2λαG σ∗(αG σ∗u −f )(43)andσt =−α R (αG σ∗u −f ) ∂G σ∂σ ∗u d x .(44)If we minimize also over α,the optimal choice for it at any given t 0would be given by α(t )= f (x )(G σ∗u )d x (G σ∗u )2d x −1(45)for as long as α(t )∈K .Numerically,these equations are discretized and solved for a large value of t .The important feature is how the variable u is handled.Let u n (x )be the numerical solution at the n th time step (i.e.at t =n δt ,where δt is the time step size).The time discretization used for u is as follows:u n +1−2(δt ){εu n +1xx −λα2G σ∗G σ∗u n +1}=u n −(δt ) 1εW (u n )−2λαG σ∗f .(46)The right-hand side of this equation is completely in terms of u n ,while the left-hand side is given by a linear operator acting on u n +1.We discretize this equation also in space,and solve the resulting fully discrete equation via the fast Fourier transform.Note that the nonlocal term in the left-hand side of course has the pleasant expression(ˆGσ)2(ξ)ˆu n +1(ξ)(47)in terms of the Fourier transform of the quantities involved.6.Numerical resultsWe applied the numerical technique described in the previous section to a number of bar codes.One crucial point in such numerical experiments is that the constants involved (such as the fidelity weight constant λ)should be kept fixed;in other words,once a good value for the constants have been chosen,they should work for all (or at least a wide range of)test signals without any change.We therefore fixed the constants in table 1.These values were used verbatim for all our experiments.130S Esedoglu0.50.5010020030040050060070080090010000.5Figure 2.Top to bottom:the bar code,corresponding corrupted signal,and the reconstructionfound by the algorithm of this paper,under the assumption that the kernel amplitude αis known.Standard deviation of the kernel used to generate the corrupted signal was σ=0.0118.Thealgorithm found σ=0.0115.Root mean square signal to root mean square noise ratio was about19.3dB.Table 1.Values of variables adopted for experiments.VariableValue ε0.00107λ7500In each experiment,a ‘clean’bar code signal was corrupted by convolving it with a kernel of known standard deviation,followed by the addition of some noise.Then,the algorithm of this paper was carried out to see if it could recover the correct bar code and the correct standard deviation of the convolution kernel.In the experiment of figure 6,αwas also treated as an unknown and recovered by the algorithm.We experimented with three different choices of standard deviation for the kernel,which were approximately 0.012,0.013and 0.014.These values were chosen because σ=0.014seems to be about when the technique starts yielding erroneous results at signal to noise ratios of about 20dB;for values of the standard deviation much smaller than these,the reconstruction is almost perfect at moderate noise levels.Figures 2and 3present results from two of these experiments,where the former is an example of completely successful reconstruction,and the latter an example of how the algorithm begins to fail when the noise level and/or the blur factor get too high.The initial guess for the bar code (required by the gradient descent algorithm)was taken to be an alternating sequence of 1and 0.We made the following empirical observation concerning the initial guess for the variance:It is better to start with a low initial guess for the standard deviation of the convolution kernel.010020030040050060070080090010000.5010020030040050060070080090010000.50.5Figure 3.Top to bottom:the bar code,corresponding corrupted signal,and the reconstructionfound by the algorithm of this paper,under the assumption that the kernel amplitude αis known.Notice that it failed to reconstruct one of the bars,located at around the 800th grid point.Standarddeviation of the kernel used to generate the corrupted signal was σ=0.0129.The algorithm foundσ=0.0124.Root mean square signal to root mean square noise ratio was about 15.7dB.This prevents the initial guess for the signal from coarsening too rapidly and ending up with very few ‘bars’:presumably,there are local minima associated with large values of the standard deviation.In the experiments presented,we took 0.0079or 0.0088as our initial guess.Starting with even lower initial values seems to make no difference in the final result;it only takes the algorithm longer to reach it.Figure 4makes an important point.Its top row shows the derivative of the bar code signal used in figures 2and 3after convolution with a kernel of standard deviation σ=0.01414.Some of the discontinuities in the original bar code have no corresponding local extrema in the derivative of the convolved signal;for example,see the thin bars located near the 495th and 530th grid points.Hence,a traditional reconstruction technique that attempts to locate extrema of the signal’s derivative would be at a very significant disadvantage at this level of blur even in the absence of any noise.The middle row shows the observed signal,which is obtained from the convolved signal by adding a moderate amount of noise.The last (bottom)row shows the reconstruction obtained by the algorithm of this paper (under the assumption that αis known)from the corrupted signal shown in the middle row.Naturally,the level of noise that the algorithm can tolerate depends on the level of blur:as the standard deviation of the convolution kernel gets large,the amplitude of noise that can be tolerated for a reasonable reconstruction decreases.For example,when the parameters ε,λare casually selected to have the values quoted above,and when σis about 0.01,the algorithm yields accurate reconstructions at signal to noise ratios as low as 13dB.When σis about 0.013,the algorithm starts to fail,as shown in figure 3,at signal to noise ratios below0100200300400500600700800900100001002003004005006007008009001000Figure 4.Top to bottom:derivative of a convolved bar code signal,the convolved signal afteraddition of noise,and the bar code reconstructed by the algorithm,under the assumption thatαis known.Standard deviation of the kernel used was σ=0.01414.The algorithm found σ=0.01408.Root mean square signal to root mean square noise ratio was about 21.55dB.16dB.The failure in figure 3seems to be typical:one or more of the thinner bars do not get reconstructed.It is also possible to end up with extraneous thin bars.These are the types of error that would adversely affect recognition;otherwise,tiny discrepancies in the location of bars are inconsequential,since they are easy to compensate for by using additional a priori information about bar codes.At a blur level of about σ=0.014,a signal to noise ratio of about 21dB seems to be the threshold for reliable reconstructions.With a more careful tuning of the parameters ε,λ,we expect that the performance of the algorithm can be improved.Most of our numerical experiments correspond to model 1of corollary 1,where the amplitude αof the kernel is assumed known a priori ,and therefore is not minimized over (however,see figure 6).We chose this simplest model for the bulk of our experiments because at this stage we would like to leave open the issue of how to treat minimization over α,since this decision involves knowing what kind of additional information is available in practice about this parameter.Right now,it is not clear which model among models 2through 4of corollary 1would be the most appropriate,and so we do not wish to commit to any one in particular.In general,we of course cannot expect to have a perfect estimate for the kernel amplitude α(but it is easy to get some estimate:for instance,the amplitude of the observed signal).In figure 5we investigate the sensitivity of the results to errors in the assumed value of this parameter.When the width (standard deviation)of the convolution kernel and the noise level are moderate,we see that the results are quite stable under perturbations in α:the method seems to be resilient up to about 25%error.However,results get more sensitive to such perturbations if the original signal is corrupted by a wider kernel.This is to be expected.Once we allow αto be updated (i.e.minimize also with respect to α),we would expect these results to improve.。

基于Diviner热红外数据的Apollo 15登陆区元素含量反演马明;陈圣波;周超;李健;陆天启【摘要】月球元素含量的反演是了解月球物质成分的分布和月球矿产资源开发利用的依据.通过比较月球样品元素含量与不同粒径样品光谱CF值所建立模型的反演精度,确定10 ～20μm粒径样品最适用于月表元素含量反演.以Apollo 15登陆点附近为例,利用Diviner热红外数据得到了完整覆盖度和更高分辨率月球CF值影像,反演了月表Al、Fe、Mn、Mg和Ca元素相对含量.与月球样品实测值进行了对比,均方根误差均小于3,验证了利用红外数据反演月表元素相对含量的可行性,为月表元素含量反演提供了新的思路.【期刊名称】《岩石学报》【年(卷),期】2016(032)001【总页数】7页(P144-150)【关键词】Diviner;元素含量;热红外;CF值;Apollo 15登陆点【作者】马明;陈圣波;周超;李健;陆天启【作者单位】吉林大学地球探测科学与技术学院,长春130026;吉林建筑大学,长春130018;中国科学院国家天文台,北京100012;吉林大学地球探测科学与技术学院,长春130026;吉林大学地球探测科学与技术学院,长春130026;中国科学院国家天文台,北京100012;吉林大学地球探测科学与技术学院,长春130026;吉林大学地球探测科学与技术学院,长春130026【正文语种】中文【中图分类】P691月球元素的研究是探讨月球形成与演化过程的基础。

随着各种探测仪器对月探测及数据分析工作的展开及深入，对月球元素的遥感定量分析取得长足的进展，主要方法有X射线谱法(Narendranath et al., 2011; 班超等, 2014)、伽马射线能谱法(Lawrence et al., 1999; Hasebe et al., 2008)、中子能谱法(Feldman et al., 2000; Prettyman et al., 2002)、反射光谱法(Lucey et al., 2000; Korokhin et al., 2008)、发射光谱法(Greenhagen et al., 2010; Allen et al., 2012)和微波探测法(Spudis et al., 2005; Elphic et al., 2011; 连懿, 2014)。

ADC分类•直接转换模拟数字转换器〔Direct-conversion ADC〕,或称Flash模拟数字转换器〔Flash ADC〕•循续渐近式模拟数字转换器〔Successive approximation ADC〕•跃升-比较模拟数字转换器〔Ramp-pare ADC〕•威尔金森模拟数字转换器〔Wilkinson ADC•集成模拟数字转换器〔Integrating ADC〕•Delta编码模拟数字转换器〔Delta-encoded ADC〕•管道模拟数字转换器〔Pipeline ADC〕•Sigma-Delta模拟数字转换器〔Sigma-delta ADC〕•时间交织模拟数字转换器〔Time-interleaved ADC〕•带有即时FM段的模拟数字转换器•时间延伸模拟数字转换器〔Time stretch analog-to-digital converter, TS-ADC1、闪速型2、逐次逼近型3、Sigma-Delta型1. 闪速ADC闪速ADC是转换速率最快的一类ADC.闪速ADC在每个电压阶跃中使用一个比较器和一组电阻.2. 逐次逼近ADC逐次逼近转换器采用一个比较器和计数逻辑器件完成转换.转换的第一步是检验输入是否高于参考电压的一半,如果高于,将输出的最高有效位<MSB>置为1.然后输入值减去输出参考电压的一半,再检验得到的结果是否大于参考电压的1/4,依此类推直至所有的输出位均置"1"或清零.逐次逼近ADC所需的时钟周期与执行转换所需的输出位数相同.3. Sigma-delta ADCSigma-delta ADC采用1位DAC、滤波和附加采样来实现非常精确的转换,转换精度取决于参考输入和输入时钟频率.Sigma -delta转换器的主要优势在于其较高的分辨率.闪速和逐次逼近ADC采用并联电阻或串联电阻,这些方法的问题在于电阻的精确度将直接影响转换结果的精确度.尽管新式ADC采用非常精确的激光微调电阻网络,但在电阻并联中仍然不甚精确.sigma-delta转换器中不存在电阻并联,但通过若干次采样可得到收敛的结果.Sigma-delta转换器的主要劣势在于其转换速率.由于该转换器的工作机理是对输入进行附加采样,因此转换需要耗费更多的时钟周期.在给定的时钟速率条件下,Sigma-delta转换器的速率低于其它类型的转换器；或从另一角度而言,对于给定的转换速率,Sigma-delta转换器需要更高的时钟频率.Sigma-delta转换器的另一劣势在于将占空<duty cycle>信息转换为数字输出字的数字滤波器的结构很复杂,但Sigma-delta转换器因其具有在IC裸片上添加数字滤波器或DSP功能而日益得到广泛应用.Atmel AVR127: Understanding ADC ParametersThis application note is about the basic concepts of analog-to-digital converter <ADC> and the parameters that determine the performance of an ADC.These ADC parameters are of good importance since they determine the accuracy of the ADC’s output.The parameters can be broadly classified into static performance parameters and dynamic performance parameters.Static performance parameters are those parameters that are not relatedto ADC’s input signal.These parameters are measured and analyzed for all types of ADCs<ADCs integrated within the microcontroller or standalone ADCs whose operating frequency are usually higher>.Instead, dynamic performance parameters are related to ADC’s input signal and their effects are significant with higher frequencies.Major static parameters include gain error, offset error, full scale error and linearity errorswhereas some important dynamic parameters include signal-to-noise ratio <SNR>, total harmonic distortion <THD>,signal to noise and distortion <SINAD> and effective number of bits <ENOB>. Basic ConceptsAn ADC is an electronic system or a module that has analog input, reference voltage input and digital outputs.The ADC convert the analog input signal to a digital output value that represents the size of the analog input paring to the reference voltage.It basically samples the input analog voltage and produces an output digital code for each sample taken.Figure 1-1. Basic diagram of ADCTo get a better picture about the ADC concepts, let us first look into some basic ADC terms used.1.1 Input Voltage RangeThe input voltage range of an ADC is determined by the reference voltage<VREF> applied to the ADC.A reference voltage can be either internal voltage or external voltage by applying a voltage on an external pin of the microcontroller.Generally reference voltage can be selected by configuring the corresponding register’s bit field of the microcontroller.ADC will saturate with a analog voltage higher than the reference voltage,so the designer must make sure that the analog input voltage does not exceed the reference voltage.The input voltage range is also called as conversion range.If ADC runs in signed mode <the mode produces signed output codes>, it allows negative analog input voltages.In such cases the analog input range is from –VREF to +VREF.An ADC which accepts both positive and negative input voltages is calledas bipolar ADCwhereas an ADC that accepts only positive input voltage is called as unipolar ADC.1.2 ResolutionThe entire input voltage range <from 0V to VREF> is divided into a number of sub-ranges.Each sub range is assigned a single output digital code.A sub range is also called LSB <least significant bits> and the number of sub ranges is usually in powers of two.The total number of sub ranges is called the resolution of the ADC.For an example, an ADC with eight LSBs has the resolution of three bits <2^3 = 8>.If an ADC’s resolution is three bits then it also means that the code width of the output is three bits.1.3 QuantizationThe LSB is determined if input analog voltage lies in the lowest sub-range of the input voltage range.For example, consider an ADC with VREF as 2V and resolution as three bits.Now the 2V is divided into eight sub-ranges, so the LSB voltage is within250mV.Now an input voltage of0V as well as 250mV is assigned to the same output digital code000.This process is called as quantization.1.4 Conversion ModeA conversion mode determines how the ADC processes the input and performs the conversion operation.A standard ADC has basically two types of conversion modes.1. Single ended conversion mode.2. Differential conversion mode.1.4.1 Single Ended Conversion ModeIn single ended conversion, only one analog input is taken and the ADC sampling and conversion is done on that input.In single ended conversion ADC can be configured to operate in unsigned or signed mode.The analog is connected to ADC has non-inverting<+> input and inverting<-> inputwhich should be differently connected under signed or unsigned mode.For example in signed mode of operation, the single-ended input may begiven to the non-inverting input of the ADCand the inverting input of the ADC is grounded.This is depicted in Figure 1-2. In this case the reference voltage is from –VREF to + VREF,which means it allows negative input voltages.In unsigned single-ended mode, the single-ended input is given to the non-inverting input of the ADCas before and the inverting input of the ADC is supplied with some fixed voltage value VFIXEDwhich is usually half of the reference voltage minus a fixed offset> as shownin Figure 1-3.In this case the input voltage range is from 0V to VREF, which means it does not allows negative input voltages.1.4.2 Differential ConversionIn differential conversion mode, two analog inputs are taken and applied tothe inverting and non-inverting inputs of the ADC,either directly or after doing some amplification by selecting some programmable amplification stages <gain amplifier stage>.Differential conversions are usually operated in signed mode, wherethe MSB of the output code acts as the sign bit.Also the reference voltage is from - VREF to +VREF for signed mode. This is shown in the Figure 1-41.5 Ideal ADCAn ideal ADC is just a theoretical concept, and cannot be implemented in real life.It has infinite resolution, where every possible analog input value gives a unique digital outputfrom the ADC within the specified conversion range.An ideal ADC can be described mathematically by a linear transfer function,as shown in Figure 1-5 and Figure 1-6.1.6 Perfect ADCTo define a perfect ADC, the concept of quantization must be used.Due to the digital nature of an ADC, continuous output values are not possible.The perfect ADC performs the quantization process during conversion.This results in a staircase transfer function where each step represents one LSB.If the reference voltage is 2V, say, and the ADC resolution is three bits,then the step width bees 250mV <1LSB>.The input analog voltage range from 0V to 250mV will be assigned the digital output code 000and the input analog voltage range from 251mV to 500mV will be assignedthe digital code 001 and so on.This is depicted in Figure 1-7 which shows the transfer function of a perfect 3-bit ADC operating in single ended mode.Figure 1-8, given below, shows the transfer function of a perfect 3-bit ADC operating in differential mode.NOTE The reference voltage is from -1V to +1V in this case and the MSB acts as sign bit.From the Figure 1-7, it is obvious that an input voltage of 0V produces an output code 000.At the same time, an input voltage of 250mV also produces the same output code 000.This explains the quantization error due to the process of quantization.As the input voltage rises from 0V, the quantization error also rises from0LSBand reaches a maximum quantization error of 1LSB at 250mV.Again the quantization error increases from 0 to 1LSB as the input rises from 250mV to 500mV.This maximum quantization error of 1LSB can be reduced to ±0.5LSB by shifting the transfer function towards left through 0.5LSB.Figure 1-9 depicts the quantization adjusted perfect transfer function together with the ideal transfer function.As seen on the figure, the perfect ADC equals the ideal ADC on the exact midpoint of every step.This means that the perfect ADC essentially rounds input values to the nearest output step value.Similarly Figure 1-10 is for differential ADC.Quantization error is the only error when perfect ADC is considered.But in case of real ADC, there are several other errors other than quantization error as explained below.1.7 Offset ErrorThe offset error is defined as the deviation of the actual ADC’s transfer functionfrom the perfect ADC’s transfer function at the point of zero to the transition measured in the LSB bit.When the transition from output value 0 to 1 does not occur at an input value of 0.5LSB,then we say that there is an offset error.With positive offset errors, the output value is larger than 0 when the input voltage is less than 0.5LSB from below.With negative offset errors, the input value is larger than 0.5LSB when the first output value transition occurs.In other words, if the actual transfer function lies below the ideal line, there is a negative offset and vice versa.Positive and negative offsets are shown in Figure 1-11 and Figure 1-12 respectively measured with double ended arrows.In Figure 1-11, the first transition occurs at 0.5LSB and the transition is from 1 to 2.But 1 to 2 transitions should occur at 1.5LSB for perfect case.So the difference <Perfect – Real = 1.5LSB – 0.5LSB = +1LSB> is the offset error.Similarly in the Figure 1-12, the first transition occurs at 2LSB and the transition is from 0 to 1.But 0 to 1 transition should occur at 0.5LSB for perfect case.So the difference <Perfect – Real = 0.5LSB – 2LSB = -1.5LSB> is the offset error.It should be noted that offset errors limit the available range for the ADC.A large positive offset error causes the output value to saturate at maximum before the input voltage reaches maximum.A large negative offset error gives output value 0 for the smallest input voltages.1.8 Gain ErrorThe gain error is defined as the deviation of the last step’s midpoint of the actual ADC from the last step’s midpoint of the ideal ADC,after pensated for offset error.After pensating for offset errors, applying an input voltage of 0 always give an output value of 0.However, gain errors cause the actual transfer function slope to deviate from the ideal slope.This gain error can be measured and pensated for by scaling the output values.The example of a 3-bit ADC transfer function with gain errors is shown in Figure 1-13and Figure 1-14.If the transfer function of the actual ADC occurs above the ideal straight line, then it produces positive gain error and vice versa.The gain error is calculated as LSBs from a vertical straight line drawn between the midpoint of the last step of the actual transfer curve and the ideal straight line.In Figure 1-13, the output value saturates before the input voltage reaches its maximum.The vertical arrow shows the midpoint of the last output step.In Figure 1-14, the output value has only reached six when the input voltage is at its maximum.This results in a negative deviation for the actual transfer function.1.9 Full Scale ErrorFull scale error is the deviation of the last transition <full scale transition> of the actual ADCfrom the last transition of the perfect ADC, measured in LSB or volts.Full scale error is due to both gain and offset errors.In Figure 1-15, the deviation of the last transitions between the actual and ideal ADC is 1.5LSB.1.10 Non-linearityThe gain and offset errors of the ADC can be measured and pensated using some calibration procedures. When offset and gain errors are pensated for, the actual transfer function should now be equal to the transfer function of perfect ADC. However, non-linearity in the ADC may cause the actual curve to deviate slightly from the perfect curve, even if the two curves are equal around 0 and at the point where the gain error was measured. There are two major types of non-linearity that degrade the performance of ADC. They are differential non-linearity <DNL> and integral non-linearity <INL>.1.10.1 Differential non-linearity <DNL>Differential non-linearity <DNL> is defined as the maximum and minimum difference in the step width between actual transfer function and the perfect transfer function. Non-linearity produces quantization steps with varying widths, some narrower and some wider.For the case of ideal ADC, the step width should be 1LSB.But an ADC with DNL shows step widths which are not exactly 1LSB.In Figure 1-16, in a maximum case the width of the step with output value 101 is 1.5LSB which should be 1LSB.So the DNL in this case would be +0.5LSB. Whereas in a minimum case, the width of the step with output value 001 is only 0.5LSB which is 0.5LSB less than the expected width. So the DNL now would be ±0.5LSB.1.10.2 Missing codeThere are some special cases wherein the actual transfer function of the ADC would look as in the Figure 1-17.In the example below, the first code transition <from 000 to 001> is caused by an input change of 250mV. This is exactly as it should be. The second transition, from 001 to 010, has an input change that is 1.25LSB, so is too large by 0.25LSB. The input change for the third transition is exactly the right size. The digital output remains constant when the input voltage changes from 1000mV to 1500mV and the code 100 can never appear at the output. It is missing. the highter the resolution of the ADC is, of the less severity the missing code is. An ADC with DNL error less than ±1LSB guarantees no missing code.1.10.3 Integral non-linearity <INL>Integral non-linearity <INL> is defined as the maximum vertical difference between the actual and the ideal curve.It indicates the amount of deviation of the actual curve from the ideal transfer curve.INL can be interpreted as a sum of DNLs. For example several consecutive negative DNLs raise the actual curve above the ideal curve as shown in Figure 1-16 and the INL in this case would be positive. Negative INLs indicate that the actual curve is below the ideal curve. This means that the distribution of the DNLs determines the integral linearity of the ADC. The INL can be measured by connecting the midpoints of all output steps of actual ADC and finding the maximum deviation from the ideal curve in terms of LSBs. From the Figure 1-18, we can note that the maximum INL is +0.75LSB.1.11 Absolute errorAbsolute error or absolute accuracy is the total unpensated error and includes quantization error, offset error, gain error and non-linearity. So in a perfect case, the absolute error is 0.5LSB which is due to the quantization error. Gainand offset errors are more significant contributors of absolute error. The absolute error represents a reduction in the ADC range. So users should therefore consider keep some margins against the minimum and maximum input values to avoid the absolute error impact.1.12 Signal to noise ratio <SNR>SNR is defined as the ratio of the output signal voltage level to the output noise level. It is usually represented in decibels <dBs> and calculated with the following formula.For example if the output signal amplitude is 1V<RMS> and the output noise amplitude is 1mV<RMS>,then the SNR value would be 60dB. To achieve better performance, the SNR value should be higher.The above mentioned formula is a general definition for SNR. The SNR value of an ideal ADC is given by:SNR <dB> = 6.02N+1.76<dB>where N is the resolution <no. of bits> of the ADC.For example an ideal 10-bit ADC will have an SNR of approximately 62dB.1.13 Total harmonic distortion <THD>Whenever an input signal of a particular frequency passes through a non-linear device, additional content is added at the harmonics of the original frequency. For example, assume an input signal having frequency f. Then the harmonic frequencies are 2f, 3f, 4f, etc. So non-linearity in the converter will produce harmonics that were not present in the original signal. These harmonic frequencies usually distort the output which degrades the performance of the system. This effect can be measured using the term called total harmonic distortion <THD>. THD is defined as the ratio of the sum of powers of the harmonic frequency ponents to the power of thefundamental/original frequency ponent. In terms of RMS voltage, the THD is given by,The THD should have minimum value for less distortion. As the input signal amplitude increases, the distortion also increases. The THD value also increases with the increase in the frequency.1.14 Signal to noise and distortion <SINAD>Signal to noise and distortion <SINAD> is a bination of SNR and THD parameters. It is defined as the ratio of the RMS value of the signal amplitude to the RMS value of all other spectral ponents, including harmonics, but excluding DC. For representing the overall dynamic performance of an ADC, SINAD is a good choice since it includes both the noise and distortion ponents. SINAD can be calculated with SNR and THD as given below.1.15 ENOBEffective number of bits <ENOB> is the number of bits with which the ADC behaves like a perfect ADC.It is another way of representing the signal to noise ratio and distortion<SINAD> and is derived from the formula specified in Section 2.11 as given below:1.16 ADC timingsBasically an ADC takes some time for startup, sampling and holding and for conversion.Out of these, the startup time is more concerned with ADCs of high end microcontrollers that operate at higher frequencies.1.16.1 Startup timeStartup time contains the minimum time <in clock cycles> needed to guarantee the best converted valueafter the ADC has been enabled either for the first time or after a wake up from some of the sleep modes.1.16.2 Sample and hold timeUsually after giving a trigger to an ADC to start a conversion, it take some time <in clock cycles> to charge the internal capacitor to a stable value so that the conversion result is accurate. This time is called as sample time. This time must be considered carefully especially when multiple channels are used during conversion. In such case there is a minimum time <in clock cycles> needed to guarantee the best converted value between two ADC channel switching. After the sampling time, the number of clock cycles it takes to convert the charge or the voltage across the internal sampling capacitor into corresponding digital code is called the hold time.1.16.3 Settling timeWhen using multiple channels, there may be cases in which each channel may have different gain and offset configurations. Switching between these channels requires some amount of time, before beginning the sample and hold phase, in order to have good results. Especially care should be taken when switching between differential channels. Once a differential channel is selected, the ADC should wait for some amount of time for some of the analog circuits <for example the automatic offset cancellation circuitry> to stabilize to the new value. This time is called as settling time. So ADC conversion should not be started before this time. Doing so will produce an erroneous output. The same settling time should be observed for the first differential conversion after changing the ADC reference.1.16.4 Conversion timeConversion time is the bination of the sampling time and the hold time, usually represented in number of clock cycles. The conversion time is the main parameter in deciding the speed of the ADC. Also the startup time, sample and hold time and the settling time are all software configurable in ADC’s of some high end microcontrollers.1.17 Sampling rate, throughput rate and bandwidthSampling rate is defined as the number of samples in one second.Bandwidth represents the maximum frequency of the input analog signal that can be given to the ADC.Sampling rate and bandwidth followNyquist sampling theorem.为了不失真地恢复模拟信号,采样频率应该不小于模拟信号频谱中最高频率的2倍.Fs ≥ Fn = 2 Fh采样率越高,稍后恢复出的波形就越接近原信号,但是对系统的要求就更高,转换电路必须具有更快的转换速度.采样是将一个信号〔即时间或空间上的连续函数〕转换成一个数值序列〔即时间或空间上的离散函数〕.采样定理指出,如果信号是带限的,并且采样频率大于信号带宽的2倍,那么,原来的连续信号可以从采样样本中完全重建出来.从信号处理的角度来看,此采样定理描述了两个过程：其一是采样,这一过程将连续时间信号转换为离散时间信号；其二是信号的重建,这一过程离散信号还原成连续信号.从采样定理中,我们可以得出结论：如果已知信号的最高频率fH,采样定理给出了保证完全重建信号的最低采样频率.这一最低采样频率称为临界频率或奈奎斯特频率,通常表示为fN相反,如果已知采样频率,采样定理给出了保证完全重建信号所允许的最高信号频率.以上两种情况都说明,被采样的信号必须是带限的,即信号中高于某一给定值的频率成分必须是零,或至少非常接近于零,这样在重建信号中这些频率成分的影响可忽略不计.在第一种情况下,被采样信号的频率成分已知,比如声音信号,由人类发出的声音信号中,频率超过5 kHz的成分通常非常小,因此以10 kHz的频率来采样这样的音频信号就足够了. 在第二种情况下,我们得假设信号中频率高于采样频率一半的频率成分可忽略不计.这通常是用一个低通滤波器来实现的.According to this theorem, the sampling rate should be at least twice the bandwidth of the input signal.Consider the case of single ended conversion where one conversion takes 13 ADC clock cycles.Assuming the ADC clock frequency to be 1MHz, then approximately 77k samples will be converted in one second.That means the sampling rate is 77k.So according to Nyquist theorem,the maximum frequency of the analog input signal is limited to 38.5kHzwhich represents the bandwidth of the ADC in single ended mode.Taking the same case above, if 1MHz is the maximum clock frequencythat can be applied to an ADC which takes at least 13 ADC clock cycles for converting one sample,then 77k samples per second is said to be the maximum throughput rate of the ADC.When using differential mode, the bandwidth is also limited to the frequency of the internal differential amplifier.So before giving the analog input to the ADC, any frequency ponents above the mentioned bandwidthshould be filtered using external filter to avoid any non-linearity1.18 Impedances and capacitances of ADCInside the ADC, the sample and hold circuit of the ADC contains a resistance-capacitance <RADC & CADC> pair in a low pass filter arrangement.The CADC is also called as sampling capacitor. Whenever an ADC start conversion signal is issued, the sampling switch between the RADC – CADC pair is closed so that the analog input voltage charges the sampling capacitor through the resistance RADC. The input impedance of the ADC is the bination of RADC and the impedance of the capacitor.As the sampling capacitor gets charged to the input voltage, the current through RADC reduces and ends up with a minimum value when voltage across the sampling capacitor equals the input voltage. So the minimum input impedance of the ADC equals RADC.In the source side, the ideal source voltage is subject to some resistance called the source resistance <RSRC> and some capacitance called source capacitance <CSRC> present in the source module. Because of the presence of RSRC, the current entering the sample and hold circuit reduces.So this reduction in current increases the time to charge the sampling capacitance thereby reducing the speed of the ADC. Also the presence of CSRC makes the source to first charge it pletely before charging the sampling capacitor.This reduces the accuracy of the ADC since the sampling capacitor may not be pletely charged.1.19 OversamplingOversampling is a process of sampling the analog input signal at a sampling rate significantly higher than the Nyquist sampling rate.The main advantages of oversampling are:1. It avoids the aliasing problem, since the sampling rate is higher pared to the Nyquist sampling rate.2. It provides a way of increasing the resolution of the ADC. For example, to implement a 14-bit converter,it is enough to have a 10-bit converter which can run at 256 times the target sampling rate.Averaging a group of 256 consecutive 10-bit samples adds four bits to the resolution of the average,producing a single sample with 14-bit resolution.3. The number of samples required to get additional n bits is = 22n .4. It improves the SNR of the ADC.Understanding analog to digital converter specificationsConfused by analog-to-digital converter specifications?Here's a primer to help you decipher them and make theright decisions for your project.Although manufacturers use mon terms to describe analog-to-digital converters <ADCs>, the way ADC makers specify the performance of ADCs in data sheets can be confusing, especially for a newers. But to select the correct ADC for an application, it's essential to understand the specifications. This guide will help engineers to better understand the specifications monly posted in manufacturers' data sheets that describe the performance of successive approximation register <SAR> ADCs.ABCs of ADCsADCs convert an analog signal input to a digital output code. ADC measurements deviate from the ideal due to variations in the manufacturing process mon to all integrated circuits <ICs> and through various sources of inaccuracy in the analog-to-digital conversion process. The ADC performance specifications will quantify the errors that are caused by the ADC itself.ADC performance specifications are generally categorized in two ways: DC accuracy and dynamic performance. Most applications use ADCs to measure a relatively static, DC-like signal <for example, a temperature sensor or strain-gauge voltage> or a dynamic signal<such as processing of a voice signal or tone detection>. The application determines which specifications the designer will consider the most important.For example, a DTMF decoder samples a telephone signal to determine which button is depressed on a touchtone keypad. Here, the concern is the measurement of a signal's power <at a given set of frequencies> among other tones and noise generated by ADC measurement errors. In this design, the engineer will be most concerned with dynamic performance specifications such as signal-to-noise ratio and harmonic distortion. In another example, a system may measure a sensor output to determine the temperatureof a fluid. In this case, the DC accuracy of a measurement is prevalent so the offset, gain, and nonlinearities will be most important.DC accuracyMany signals remain relatively static, such as those from temperature sensors or pressure transducers. In such applications, the measured voltage is related to some physical measurement, and the absolute accuracy of the voltage measurement is important. The ADC specifications that describe this type of accuracy are offset error, full-scale error, differential nonlinearity <DNL>, and integral nonlinearity <INL>. These four specifications build a plete description of an ADC's absolute accuracy.Although not a specification, one of the fundamental errors in ADC measurement is a result of the data-conversion processitself: quantization error. This error cannot be avoided in ADC measurements. DC accuracy, and resulting absolute error are determined by four specs—offset, full-scale/gain error, INL, and DNL. Quantization error is an artifact of representing an analog signal with a digital number <in other words, an artifact of analog-to-digital conversion>. Maximum quantization error is determined by the resolution of the measurement <resolution of the ADC, or measurement if signal is oversampled>. Further, quantization error will appear as noise, referred to as quantization noise in the dynamic analysis. For example, quantization error will appear as the noise floor in an FFT plot of a measured signal input to an ADC, which I'll discuss later in the dynamic performance section>.The ideal transfer functionThe transfer function of an ADC is a plot of the voltage input to the ADC versus the code's output by the ADC. Such a plot is not continuous but is a plot of 2N codes, where N is the ADC's resolution in bits. If you were to connect the codes by lines <usually at code-transition boundaries>, the ideal transfer function would plot a straight line. A line drawn through the points at each code boundary would begin at the origin of the plot, and the slope of the plot for each supplied ADC would be the same as shown in Figure 1.Figure 1 depicts an ideal transfer function for a 3-bit ADC with reference points at code transition boundaries. The output code will be its lowest <000> at less than 1/8 of the full-scale <the size of this ADC's code width>. Also,。