Axis Alternation for Signal Propagation Over Polarization-Maintaining Fibers

MXA X-Series Signal AnalyzerN9020AConfiguration GuideThis MXA configuration guide will help you determine which performance options, measurement applications, accessories, and services to include with your new MXA or to add as upgrades to an existing MXA.This step-by-step process will help you configure your MXA. Capabilities that are listed as standard come with the instrument at no additional charge. Tailor the performance to meet your requirements.For detailed specifications, refer to the MXA signal analyzer specification guide (N9020-90113). For a summary of specifications, refer to the MXA signal analyzer data sheet (5989-4942EN).Portable configuration includes pivoting carrying handle and protectivecorner rubber guards (front protective cover comes standard) – N9020A-PRCMXA bench top configurationFor more information on accessories go to: /find/accessoriesUpgrades for analysis bandwidth in MXA depend on the vintage of the instrument and the options already installed. The upgrade options can be stacked up. Therefore, more than one option may be required to achieve desired wider analysis bandwidth. A web-based calculator at the following URL assists you in finding what upgrade options you may need:/selector/cdma2000®is a registered certification mark of the Telecommunications Industry Association.Bluetooth and the Bluetooth logos are trademarks owned by Bluetooth SIG, Inc., U.S.A. and licensed to Agilent Technologies, Inc.WiMAX™ is a trademark of the WiMAX Forum ®.LAN eXtensions for Instruments puts the power of Ethernet and the Web inside your test systems. Agilent is a founding member of the LXI consortium.Agilent Channel Partnersw w w /find/channelpartners Get the best of both worlds: Agilent’s measurement expertise and product breadth, combined with channel partner convenience./find/mxaRelated LiteratureAgilent MXA Signal Analyzers Brochure 5989-5047EN Data Sheet5989-4942ENX-Series Measurement 5989-8019ENFor more information on Agilent Technolo-gies’ products, applications or services, please contact your local Agilent office. The complete list is available at:/find/contactus Americas Canada (877) 894 4414 Brazil (11) 4197 3600Mexico 01800 5064 800 United States (800) 829 4444 Asia Pacific Australia 1 800 629 485China 800 810 0189Hong Kong 800 938 693India 1 800 112 929Japan 0120 (421) 345Korea 080 769 0800Malaysia 1 800 888 848Singapore 180****8100Taiwan 0800 047 866Other AP Countries (65) 375 8100 Europe & Middle East Belgium 32 (0) 2 404 93 40 Denmark 45 45 80 12 15Finland 358 (0) 10 855 2100France 0825 010 700**0.125 €/minuteGermany 49 (0) 7031 464 6333 Ireland 1890 924 204Israel 972-3-9288-504/544Italy 39 02 92 60 8484Netherlands 31 (0) 20 547 2111Spain 34 (91) 631 3300Sweden 0200-88 22 55United Kingdom 44 (0) 118 927 6201For other unlisted countries: /find/contactusRevised: January 6, 2012Product specifications and descriptions in this document subject to change without notice.© Agilent Technologies, Inc. 2013Published in USA, September 20, 20135989-4943EN/find/myagilent A personalized view into the information most relevant to you.myAgilentmy Agilent/quality/find/AdvantageServices Accurate measurements throughout the life of your instruments.Agilent Advantage ServicesThree-Year Warranty/find/ThreeYearWarranty Agilent’s combination of product reliability and three-year warranty coverage is another way we help you achieve your business goals: increased confidence in uptime, reduced cost of ownership and greater convenience.。

Background T ranscatheter aortic valve implantation (TAVI)requires assessment of gated CT images for accurate aortic annulus sizing.We investigated the accuracy of The Heart Navigator III software (Philips Healthcare,Netherlands)in performing fully automatic annulus measurements.Methods One-hundred and sixty patients underwent gated cardiac CT scans as pre-assessment for a TAVI procedure.The Heart Navigator III software (Philips Healthcare,Netherlands)performed automatic segmentation of the aortic root and measurement of the aortic annulus area in systole without operator intervention.These were compared with manual measurements made by an experienced CT operator during pre-procedural planning with commercially available CT soft-ware.We then evaluated whether the automated measurements would lead to the same valve size selected as the human-oper-ator utilising commonly used TAVI manufacturers.Results When Heart Navigator III automatic measurements of the aortic annulus size were compared to CT human-operator images,there was a bias of -1.48mm 2.95%limits of agree-ment were from -96.16to +93.21mm 2(see figure 1).Auto-matic measurements and CT human-operator measurements led to the same size Edwards Sapien valve in 71.3%of patients,Abbott Portico valve in 60.6%of patients,Medtronic Evolut in 71.3%of patients and NVT Allegra in 68.8%of patients.The Heart Navigator III selected valves within 1size of the human-operator choice in 97.1–99.4%of cases (table 1).Conclusion The Heart Navigator III software (Philips Health-care,Netherlands)is a promising technology allowing fully automated aortic annulus segmentation and sizing.However,at present the accuracy is not sufficient for clinical use and human-operator oversight is still required.Conflict of Interest None29GONE BUT NOT FORGOTTEN:A CONTEMPORARY IMAGING SERIES OF PATIENTS WITH A SYSTEMICRIGHT VENTRICLE AND A LV-PA CONDUIT FOR NATIVE OBSTRUCTION OF THE LEFT VENTRICULAR OUTFLOW TRACT.1Liam Corbett,1Sarah ElGamal,1Julia Jones,1Reza Ashrafi,2Ian Peart,1James Redfern,1Damien Cullington.1Liverpool Heart &Chest Hospital NHS Foundation Trust,Liverpool,UK ;2Alder Hey Children ’s Hospital NHS Foundation Trust 10.1136/heartjnl-2021-BCS.29Background In the UK,left ventricle to pulmonary artery (LV-PA)conduit implantation was utilised in two centres in the late 1980s to 1990s in very small numbers.The LV-PA con-duit bypassed native LV-PA outflow tract obstruction in patients with transposition of the great arteries (D-TGA)with an atrial-switch and congenitally corrected transposition of the great arteries (CCTGA,L-TGA).It is now generally appreci-ated that LV-PA obstruction offers some physiological advant-age for patients with an atrial-switch or CCTGA to ‘preserve ’interventricular septal conformation and to help lessen pro-gressive systemic tricuspid valve regurgitation –akin to ‘phys-iological ’repair with PA banding.The practice of LV-PA conduit implantation has essentially become extinct from clini-cal practice.Case Presentations We report of 5patients with native LV-PA obstruction that all underwent additional extra-cardiac LV-PA conduit implantation without resection of their native LV-PA obstruction.The operations were performed at the same surgi-cal centre between 1989and 1995(n=3CCTGA,n=2D-TGA with atrial-switch).During adulthood follow-up,imaging of the LV-PA conduit was missed or deemed non-diagnostic by echocardiography.Subsequent cross-sectional imaging found all conduits to be small in calibre with an unusual anterior course.Patient 1&2remained stable with preserved ventric-ular function,low sub-pulmonic left ventricular pressures and only mild gradients demonstrated through their LV-PA out-flows.Patients 3,4&5had preserved ventricular function in the context of severe native and extra-cardiac LV-PA conduit obstruction,with significant circumferential conduit calcifica-tion and adhesion to the retro-sternum.Patient 3underwent conduit excision and replacement after presenting with Staph Capitus endocarditis,which was confirmed with PET-CT,Abstract 28Table 1Edwards Sapien,Abbott Portico,Medtronic Evolut and NVT Allegra valve size choices using heart navigator III vs CThuman-operatorAbstract 28Figure 1Bland-Altman analysis demonstrating the difference between the heart navigator III measurements and CT operator measurements107 on December 24, 2023 by guest. Protected by copyright./Heart: first published as 10.1136/heartjnl-2021-BCS.29 on 4 June 2021. Downloaded fromwhilst Patient 4underwent balloon dilatation and stenting,as the primary stenosis was discrete at the distal anastomosis site.After 6-months follow-up,Patient 3&4recovered well with improved clinical status.Patient 5had complete LV-PA conduit adhesion to the retro-sternum and demonstrated sub-systemic sub-pulmonary pressures by diagnostic catheterisation.It was agreed that the intervention risk outweighed any potential benefit and conservative management with follow-up would be most appropriate.Discussion In our cases,despite knowing the exact anatomical location and conduit course,repeat echocardiography remained non-diagnostic.This surgical approach was first described in 1976,and there are case reports on only 15patients,whereby,direct LV-PA resection was not felt to be surgically feasible due to abnormal mitral valve chordal attach-ments and/or long fibromuscular tunnel-type obstruction.It remains technically challenging to directly relieve native LV-PA obstruction without having detrimental impact on systemic right ventricular function,tricuspid valvular competence and electro-physiologically.But as ACHD practice has evolved,it is now actually an anatomical problem which doesn ’t necessarily always need a ‘surgical-fix ’.Conclusion Awareness of this historical surgical approach to managing native LV-PA obstruction is important to understand-ing physiology and the potential long-term sequelae in these patients.They present a particular imaging challenge,especially via echocardiography ,but an important finding to be compre-hensively assessed through multimodal cross-sectional imaging.Although the technique is gone,it shouldn ’t be forgotten.Conflict of Interest None30SEVERE AORTIC STENOSIS MANAGEMENT IN A TERTIARY CARDIAC CENTRENorildin Al-Refaie,Waqas Jarral,Abhishek Shetye,Mark Cassar,Jim Newton.Oxford University Hospitals NHS Trust,Oxford,UK 10.1136/heartjnl-2021-BCS.30Introduction Aortic stenosis (AS)is the most common valvular heart disease in developed countries with an estimated preva-lence of 3%.According to ESC/EACTS guidelines,invasivemanagement is recommended in patients with severe sympto-matic AS,because of dismal spontaneous prognosis.It was reported that the average survival durations of patients with severe AS after developing symptoms such as angina,syncope,and shortness of breath were only 5,3and 2years respec-tively if managed conservatively.Management of asymptomatic severe AS remains controversial.Purpose Assess the prevalence of symptoms in patients with severe AS,and their management plans in relation with symp-toms and age.Method Retrospective data analysis of 259patients with severe AS in a tertiary cardiac centre.Clinic notes,operation sheets,procedure reports and discharge summaries were the main source of data.Results 199(76.8%)patients were symptomatic (shortness of breath,chest pain,dizziness or syncope).143(71.8%)of these underwent intervention (surgical aortic valve replacement (SAVR),transcatheter valve implantation (TAVI)or Valvulo-plasty).56(28.2%)were managed conservatively (reasons for this being high risk for intervention,technical inadequacy for TAVI and patient informed decision).9(4.5%)patients passed away during the study duration (all were managed conserva-tively).60(23.2%)patients were asymptomatic,of which 8(13.3%)underwent intervention.None of medically managed asymptomatic patients passed away during the study period.Average age for symptomatic patients who had surgical AVRAbstract 30Table1Abstract 30Figure 1107 on December 24, 2023 by guest. Protected by copyright./Heart: first published as 10.1136/heartjnl-2021-BCS.29 on 4 June 2021. Downloaded from。

Optimal signal timing for an oversaturated intersectionTang-Hsien Chang *,Jen-Ting LinDepartment of Transportation Science,Tamkang University,P.O.Box 7-876,Taipei 10617,Taiwan,ROCReceived 5September 1998;accepted 16June 1999AbstractTra c congestion occurs frequently at downtown intersections during rush hours,at road construction zones as well as at accident sites.Under such circumstances,tra c ¯ow exceeds intersection capacity causing queuing of automobiles that cannot be eliminated in one signal cycle.In this paper,we present a timing decision methodology which considers the whole oversaturation period.Discrete dynamic optimi-zation models are developed and an algorithm to solve them is presented.The optimal cycle length and the optimal assigned green time for each approach are determined for the case of two-phase control.The application of the performance index model to certain multi-phase signals in common use is also intro-duced.Evaluation results indicate that the proposed discrete type performance index model is a more appropriate design for congested tra c signal timing control.Ó2000Elsevier Science Ltd.All rights reserved.1.IntroductionMultilevel design strategies are a novel trend in tra c signal control (Gartner et al.,1995).Among the promising design features are included the ability to avoid and relieve congestion.Many basic signal theories have been studied in recent decades,including those developed by Webster (1958),May (1965)and Allsop (1972)and that described in the Highway Capacity Manual (1985).However,relatively few of those models have addressed congestion relief strat-egies.Neither control systems nor commonly used software such as SOAP (1985)and TRANSYT (1987)can adequately handle oversaturated tra c.The performance of these conventional signal systems deteriorates under heavy tra c conditions (Tarno and Parsonson,1981;Cronje,1983;Elahi et al.,1991).While addressing the limitations of conventional signal control systems,Cronje (1983)developed a model for optimizing ®xed-time signalized intersections that can be appliedtoTransportation Research Part B 34(2000)471±491/locate/trb*Corresponding author.Tel.:+886-2-2363-1004;fax:+886-2-2622-1135.E-mail address:thchang@.tw (T.-H.Chang).0191-2615/00/$-see front matter Ó2000Elsevier Science Ltd.All rights reserved.PII:S0191-2615(99)00034-X472T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491Nomenclaturea i the number of lanes on approach or movement iB the control gainc cycle lengthd the average delay per vehicle in a cycleD total delay in a cycleD k total delay in cycle state kD i k 1 delay per lane of approach or movement i in cycle state kF number of stopsg e ective green timeg max Y g min upper limit and lower limit of e ective green timeg k green time in cycle state kg i k e ective green time for approach or movement i in cycle state kg i max Y g i min upper limit and lower limit of e ective green time for approach or movement i G k green-time adjusted factor due to stop penalty in kG i k green-time adjusted factor due to stop penalty in k for approach or movement iH Hamiltonian formulak the pointer of a cycle state in a sequence of cycles during the saturation period K stop penalty factorl i queue length of approach or movement il k queue length at the beginning of cycle state kl i k 1 queue length of approach or movement i at the end of cycle state k,equal to the queue length of approach or movement i at the beginning of cycle state k 1 N terminative statePI performance indexPI k total performance index in state kPI i k performance index of approach or movement i in state kq input¯ow rateq k input¯ow rate in cycle state kq i k input¯ow rate of approach or movement i in cycle state ks saturated¯ow rate as de®ned by Webster(1958)s i saturated¯ow rate of approach or movement iu max Y u min upper and lower limit of control variablesu k control variables in state kW i k exogenous variable of approach or movement i in state kW k exogenous variables in state kY i k exogenous variable of approach or movement i in state kZ k exogenous variables in state kk k Lagrange multiplier in state k"k g/c,ratio of e ective green timeX Hessian matrixT.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491473 undersaturated and oversaturated conditions.That investigation also compared microscopic and macroscopic models to determine delay and the number of stops,indicating that the macroscopic approach is su ciently accurate for practical purposes.In a related work,Elahi et al.(1991) developed a knowledge-based system SCII.For near-and over-saturated conditions,SCII adopts the deterministic model proposed by Newell(1982),in which the e ects of random variations are neglected since arriving and queuing vehicles provide a steady source of inputs.Elahi et al.(1991) also indicated that the TEXAS model and NETSIM have no optimization capability.Although capable of providing optimal design,SOAP84heavily depends on Webster's(1958)approach. When searching for timing optimization,the above models only plan for the next single cycle after the executing one,not concurrently for the entire congestion period.The timing design of isolated signals is a prerequisite for tra c control.This paper presents a novel strategy for the timing decision of isolated signals during congestion or oversaturation.A macroscopic and deterministic model is developed.The underlying notion of the delay formula is derived from the interactive relationship between the delay in a signal cycle and the following cycle.This relationship lacks a conventional signal timing formula.Dispersing a whole queue in one cycle in oversaturated conditions is problematic owing to the maximum cycle length con-straint.The remaining automobiles in queues cause delay in each cycle stage,i.e.the delay in a cycle a ects the delay in the subsequent cycle.Conventional timing strategies consider only the optimization of a single cycle,commonly referred to as static systems,and are obviously unsat-isfactory.Optimal control timing should be designed to regulate the tra c for minimum delay during the entire oversaturated period.A dynamic theory of optimization has to be developed to resolve such a cycle-chaining problem.Regarding the one-by-one structure of cycle-chaining states,the conventional delay formula can be modi®ed into a state-dependent form called`state space equations'.An optimal control methodology can then be applied to determine optimal timing from the constructed state space equation of an intersection.Herein,we focus mainly on minimizing total intersection delay during the entire oversaturated period,not per cycle only.The proposed model is formulated as a discrete type operation.Gazis(1964),Gazis and Potts(1965),Green(1968),Burhardt(1971),Kaltenbach and Koivo(1974),Dans and Gazis(1976)and Michalopoulos and Stephanopolos(1977,1978) constructed similar models for oversaturation control.But their models are all continuous types and do not address the problem of optimizing cycle length.Gazis(1964)proposed that,during an oversaturated period,the queues in all approaches should be allowed to disperse completely and simultaneously,thereby minimizing the total delay(Green,1968).This method focuses on en-suring that the green time does not have any loss in any cycle during the oversaturated period. This type of control is terminated when completely dispersing the queues of all approaches. Michalopoulos and Stephanopolos(1977,1978)proposed an e cient two-stage timing method, termed`bang-bang control',for the controlled signal.Their method attempts to®nd an optimal switch-over point during the oversaturated period to interchange the timing of the approaches. For example,during the®rst stage,the procedure is as follows:set maximal green time to the approach having a maximal arrival rate and minimal green time to the minimal arrival rate ap-proach.At the optimal switch-over point,switch the maximal green time to the minimal arrival approach and the minimal green time to the maximal arrival approach.Continuous type models are limited in that the switch-over point does not necessarily occur at the end of a cycle,neither does the termination of the oversaturated period occur only at the endof the ®nal cycle.On the other hand,the switch-over points determined by a discrete model occur exactly at the termination of a cycle.Discrete operation provides a smooth,regular,and ordered transfer of control.Calculating delay is more reliable.In addition,the penalty level incurred by vehicle stops is easily incorporated.It is more suitable for calculating the optimal cycle length and setting the optimal green time for each approach.Details of the two-phase model are described below.Certain multi-phase signals in common use are introduced later.2.Two-phase timing plan for oversaturation control 2.1.Subjective function with state space representationThe following describes the two proposed models:one is a basic discrete minimal delay model,and the other a performance index model.The former is to manifest the complexity of the con-tinuous delay model developed by Michalopoulos and Stephanopolos (1977,1978),and dem-onstrate that pure delay models are ine ective in searching optimal cycle length.The latter is suggested to be more appropriate in studying oversaturation control.2.1.1.Discrete minimal delay modelFig.1illustrates the situation of queue during oversaturation.The graph there represents a queue l k 1 left when the green time terminates at a certain cycle state k .(`Cycle state'denotes the cycle in a sequence of cycles during a saturation period.)The delay in the graph can geo-metrically be calculated asD 122Ál k c  q k c 2Àsg 2k ÃX1 This equation meets the May's delay formula (May,1965)d c 1À"k2" 2 since "kg a c Y x qc a sg ,and D d Áqc ,the area of the graph in Fig.1.The continuous delay model developed by Michalopoulos and Stephanopolos (1977,1978)is also consistent with this approach.In the case of a cross intersection with a two-phase signal control as Fig.2illustrates,during oversaturation,the queue and dispersion situation is as indicated in Fig.3.Without lossofFig.1.Situation of the queue in a certain phase during oversaturation.474T.-H.Chang,J.-T.Lin /Transportation Research Part B 34(2000)471±491generality,it is assumed herein that the cumulative demand on all the approaches is a linear asymptotic function of time and that the cumulative output curves do not intersect the cumulative input curves for any of the approaches.This fact implies that no queue becomes negative or zero before the end of the oversaturated period.If a queue becomes negative while the signal is green,the designed green time becomes invalid due to the waste of control time.According to Fig.3,the relation of the queue lengths between state k and k 1can be rep-resented by the following equations:l 1 k 1 l 1 k q 1 k À1 g 2 k À1 q 1 k Às 1 Á c Àg 2 k Y 3a l 2 k 1 l 2 k q 2 k À1 g 2 k À1 q 2 k Às 2 Á c Àg 2 k Y3bFig.3.Queue and delay of a four-leg intersection with two-phasecontrol.Fig.2.Four-leg intersection with two-phase signal control.T.-H.Chang,J.-T.Lin /Transportation Research Part B 34(2000)471±491475l3 k 1 l3 k q3 k cÀs3g2 k Y 3cl4 k 1 l4 k q4 k cÀs4g2 k X 3d Also,from Fig.3,the delay of approach1can be stated asD1 k 1 122l1 k cÂ2q1 kÀ1 g2 kÀ1 c q1 k c2Às1c2 s1g22 kÃX 4Thus,D1 k 2 122l1 kÂ1 c 2q1 k g2 k c q1 k 1 c2Às1c2 s1g22 k 1ÃX 5Incorporate(3a)into(5);to obtainD1 k 2 D1 k 1 12s1g22 k 1 W1 k 1 6in which,W1 k 1 12q1 k c2ÂÀs1g22 k À2s1c2 2s1g2 k c q1 k 1 c2ÃX 7Similarly,for approach2,3,4which giveD2 k 2 D2 k 1 12s2g22 k 1 W2 k 1 Y 8D3 k 2 D3 k 1 À1s3g22 k 1 W3 k 1 Y 9D4 k 2 D4 k 1 À1s4g22 k 1 W4 k 1 Y 10whereW2 k 1 12q2 k c2ÂÀs2g22 k À2s2c2 2s2g2 k c q2 k 1 c2ÃY 11W3 k 1 12q3 k c2Âs3g22 k À2s3g2 k c q3 k 1 c2ÃY 12W4 k 1 12q4 k c2Âs4g22 k À2s4g2 k c q4 k 1 c2ÃX 13Suppose that approach1has a1lanes,approach2has a2lanes,approach3has a3lanes,and approach4has a4lanes,the total delay,summed from(6),(8),(9)and(10),should beD k 2 D k 1 12a1s1 a2s2Àa3s3Àa4s4 g22 k 1 a1W1 k 1a2W2 k 1 a3W3 k 1 a4W4 k 1 X14 The above equation can be equivalently restated as a state space expression476T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491D k 1 D k Bu k W k Y 15 where D k is the state variable;B the control gain;u k the control variable and W k is theexogenous variable completely known before triggering the stateD k a1D1 k a2D2 k a3D3 k a4D4 k Y 16B 12a1s1 a2s2Àa3s3Àa4s4 Y 17u k g22 k Y 18 W k a1W1 k a2W2 k a3W3 k a4W4 k X 19 2.1.2.Performance index modelDuring oversaturation,the number of stops and arrivals will increase.If the stop factor is considered in the utilization of penalty,the model becomes more reasonable(SOAP,1985; TRANSYT-7F,1987,1991).In general,the performance index of signal control is expressed as PI D KF X 20 Applying basic Eq.(20)with(6)and following the derivative procedure of the discrete minimal delay model,we havePI k 1 PI k Bu k Z k Y 21 wherePI k a1PI1 k a2PI2 k a3PI3 k a4PI4 k Y 22B 12a1s1 a2s2Àa3s3Àa4s4 Y 23u k g2 k G k 2Y 24Z k À12a1s1 a2s2Àa3s3Àa4s4 G2 k a1W1 k a2W2 k a3W3 k a4W4 kK a1Y1 k a2Y2 k a3Y3 k a4Y4 k 25 satisfying the relationships:PI1 k 1 PI1 k 12s1g22 k K s1Àq1 k g2 k W1 k KY1 k Y 26PI2 k 1 PI2 k 12s2g22 k K s2Àq2 k g2 k W2 k KY2 k Y 27PI3 k 1 PI3 k À12s3g22 k ÀKs3g2 k W3 k KY3 k Y 28PI4 k 1 PI4 k À12s4g22 k ÀKs4g2 k W4 k KY4 k Y 29T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491477Y1 k Àq1 kÀ1 g1 kÀ1 2q1 k cÀs1c Y 30 Y2 k Àq2 kÀ1 g1 kÀ1 2q2 k cÀs2c Y 31 Y3 k Àq3 kÀ1 c 2q3 k c Y 32 Y4 k Àq4 kÀ1 c q4 k c Y 33G k K a1s1 a2s2Àa3s3Àa4s4Àa1q1 k Àa2q2 k11223344X 342.2.Objective function and solution approachFirst,the objective function is set only to minimize the total delay of the entire oversaturated period.The function is assigned to be a quadratic form as below(Anderson and Moore,1990; Kuo,1991)MIN J 1D N 21 Nk 2D k 2 35in which,N is the terminative state of the oversaturated period.Minimizing(35)subjected to(15), based on the optimal control theory,involves equivalently to minimizing the Hamiltonian for-mula(Kuo,1991;Luenberger,1979).The Hamiltonian formula is de®ned asH 12D k 2 k k 1 D k Bu k W k Y 36where the adjoint variables,k k Y k 0Y1Y2Y F F F are functions of time.Now,the task is to®nd a satisfactory value of the control variable such that(36)is minimal in the subjection of(15). According to the optimal control theory,if an extreme in H exists,it must satisfy the following conditions:1X o 1a2 D2 No D Nk N A D N k N Y 372X o Hk k A D k k k 1 k k Y 383Xo Ho k k 1D k 1 A D k 1 D k Bu k W k Y 394Xo Ho u k0X 40Eq.(36)obviously indicates that only the single control variable u k can minimize H.In signal control,the control variable is related to the green time which should be taken as the value 478T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491479 between predetermined upper and lower limits,i.e.g min6g6g max.As de®ned in(18),g2 k is the only control variable hereu k f g22 k g2minj6g2 k 6g2max g X 41 Eq.(36)clearly reveals that the relation between H and the control variable u k is linear.This leads to o H a o u k k k 1 B 0.Thus,to minimize H,the control at each time point should be taken with u k g22min,(i.e.g2 k g2min,g1 k cÀg2min)when k k 1 B b0;u k g22max, (i.e.g2 k g2max,g1 k cÀg2max)when k k 1 B`0.This proposition is clearly a bang-bang control with a two-stage operation,from g2max switching to g2min or from g2min switching to g2max.The time at which the switching is required is termed the`switch-over'point.For example in Figs.2and3,at the®rst stage,the maximal green time g2max is set to approaches3and4which are associated with higher¯ow rates;then the green time for the other pair of approaches(with lower¯ow rates)is determined if the cycle length is given.When the switch-over point evaluated by the described above requirement is reached,the second stage begins,at which point the minimal green time g2min is switched to substitute g2max for the control of approaches3and4.The control is terminated at l i 0 i 1Y2Y3or4 XIf the objective function is to minimize the performance index previously described,the func-tion can also be constructed as(35)±(40),but previous D k should be replaced by PI k and W k be replaced by Z k ,respectively.This results in the control variableu k g2 k G k 2 42 and,which should be operated with the following two situations:(i)When k k 1 B b0,u k MIN g2 k G k 2.Since only green time g2can be con-trolled,MIN g2 k G k 2implies that g2 k ÀG k ifÀG k is located in the interval g2min Y g2max ;g2 k g2max ifÀG k P g2max;and g2 k g2min ifÀG k 6g2min.(ii)When k k 1 B`0,u k MAX g2 k G k 2.u k may be veri®ed as a concave curve by taking twice di erential of u k with g2 k .This implies that maximal u k ,g2 k should be at its boundary,g2 k g2min or g2 k g2max.IfÀG k is located in the interval g2min Y g2max ,the choice is dependent upon MAX f g2min G k 2Y g2max G k 2g,i.e.g2 k g2min when g2min G k 2b g2max G k 2g and g2 k g2max when g2max G k 2g b g2min G k 2.In addition,ifÀG k P g2max,g2 k g2min is selected.IfÀG k 6g2min,g2 k g2max.De®nitely, g1 k cÀg2 k .Obviously,the control by the performance index model di ers somewhat from that by the discrete minimal delay model.In condition(i),whenÀG k drops into the interval g2min Y g2max , there exists an otherwise condition from`bang-bang control',i.e.the optimal green time may not be at the assigned boundary.The fact that such an outcome is seldom but still possible during oversaturation(the outcome is much relying on the factor K)accounts for why a`bang-bang like control'is denoted as such a model's control to discriminate the real`bang-bang control'.3.Algorithm for solving the timing modelsBased on the solution approach and the conditions described in Section2.2,the algorithm for solving the discrete minimal delay timing model is arranged in the following steps:480T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491Step1.Let k 2Y and initiate k 2 with a positive value.Step2.When k k B b0,g2 kÀ1 g2min;when k k B`0,g2 kÀ1 g2max.Step3.Calculate D k ,l i k (i 1,2,3,4).Check the queue length of each approach,if spil-lover,adjust k 2 and back to step1.Step4.If l i k `0(i 1,2,3,4),go to step7.Step5.If l1 k `0,l2 k `0,l3 k b0and l4 k b0,next step;otherwise,employing Eq.(38) calculate k k 1 and reset k k 1Y then go to step2.Step6.Let g2 k g2 kÀ1 .Calculate l3 k 1 and l4 k 1 .If l3 k 1 `0and l4 k 1 `0,next step;otherwise,adjust k 2 then go to step1.Step7.Calculate total delay:sum of D j from j 2to kÀ1.Also,show g2 j j 1Y F F F Y kÀ1 ;then stop.Step1aims to give priority of dispersion with a maximal green time to the approaches with the maximum¯ow rate.In step6,if the calculation falls into`otherwise',this indicates that there is some green time loss,because the dispersal curve intersects the arrival curve before achieving the termination.Thus,k 2 should be adjusted.Based on Eq.(39),move D k to the right,and substitute k k by its elder generations till k 2Y then impliesk k k 2 À D 2 D 3 ÁÁÁ D kÀ1 X 43 Therefore,in order to make k k `0,k 2 should be reduced in the next iteration.As for the algorithm for solving the performance index model,except for step2needing to be replaced by(i)and(ii)described in Section2.2,the procedure is similar to that for solving the delay timing model.4.Evaluation with a caseBased on the complicated description above,a simpli®ed case is now presented to demonstrate how the model is employed.plexity of the continuous delay modelAs mentioned earlier,Michalopoulos and Stephanopolos(1977,1978)proposed a continuous signal timing model for oversaturated control.The model attempts to minimize the total delay of the entire oversaturated period.Its cycle length is®xed at150s c 150 .Also mentioned earlier was its de®ciency,i.e.the possible mis-timing of its switch-over point before a cycle is complete. To explain this phenomenon,the case in their paper is applied herein.Assume an intersection of two one-way streets with a two-phase signal control.One street,denoted as approach1,has two lanes;the other,denoted as approach2,has a single lane.No left-turn tra c is considered. Approach1is with s1 1400pcu/h,g1max 0X65c,g1min 0X4c,and approach2,s2 1000pcu/h, g2max 0X6c,g2min 0X35c.Table1lists the input volumes(extracted from Michalopoulos and Stephanopolos,1978).While corresponding to the previously described algorithm for the discrete minimal delay timing model,Table2summarizes those results.According to that table,at the eighth cycle,the control strategy is switched from g 2min to g 2max .Notably,the oversaturation control is terminated at the 16th cycle.The total delay summed from approaches 1and 2is 737,914veh-s,which is equivalent to 283.29s/veh in average delay.According to Michalopoulos and Stephanopolos (1978),the switch-over point of their con-tinuous delay model is at 994s,and termination at 2558s.However,in Table 2,the switch-overTable 2Queue length and control strategy by the discrete minimal delay model Cycle sequence k Queue length on approach 1l k 1 Queue length on approach 2l k 1 Green time on approach 2g 2 k 1262852.52485752.53597352.54638952.55609752.565410552.574310752.583810090.09389090.010358090.011326890.012275690.013224390.014153090.01591690.0161390.017)71190.0Total delay from 1st cycle to 16th402,624(s)335,290(s)Table 1Five-minute cumulative volumes Approach 1(veh/lane)Approach 2(veh/lane)Time (s)1218630020514760026819290031822712003592571500396283180043030721004623302400492352270052337330005523943300582415360061143639006404574200T.-H.Chang,J.-T.Lin /Transportation Research Part B 34(2000)471±491481482T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491point of the discrete delay model is at1050s and termination at2400s.The switch-over point and the termination of the continuous model are not located at the ends of their corresponding cycles. This means these two cycle lengths are probably not a constant at150s.Consequently,the op-eration would be problematic for a general signal controller.In addition,the oversaturation control time in the continuous model is longer than in the discrete model,indicating that the discrete model is better than the continuous model.4.2.Control of the performance index modelAlso,this study applies the case in Section4.1to discover the control(bang-bang like control) of the performance index model.The control is the same as the previous strategy for the discrete minimal delay model shown in Table2.The total delay is extended to1,046,886veh-s(equivalent to363.51s/veh in average)because the performance index model includes a stop-penalty item.parison of equal time-sharing control and bang-bang like controlAt oversaturation,in the bang-bang control,the basic strategy involves assigning the sequence of the maximal green time and minimal green time to a relevant approach.Thus,the tra c of the relevant approach is controlled in two stages:®rst with maximal green time and then with minimal green time,or vice versa.Regarding the bang-bang like control,results di er somewhat from the bang-bang control,as described in Section2.2.For nearly all conventional timing designs,the timing split is distributed with the Webster's frame,which maintains the green time ratio with respect to the following formula(Webster,1958):g a a g b q a a s a a q b a s b 44 in which g a Y q a and s a are the green time volume,and saturation¯ow rate of approach a,and g b Y q b and s b the green time,volume,and saturation¯ow rate of approach b.Obviously,at oversaturation,g a X g b should be1:1.With conventional control,the green time for each approach should be0.5c during oversaturation and equally distributed.Thus,the signal timing becomes equal time-sharing for oversaturation control.The case in Section4.1is applied to compare the two strategies.Also investigated herein are the results based on the performance index model and c 155s involving both the two strategies of equal time-sharing control and bang-bang like control.This study also determines the total delay arising from the conventional equal time-sharing control to be449.07s/veh;meanwhile,for bang-bang like control,it is only362.78s/veh. This observation con®rms Michalopoulos and Stephanopolos'hypothesis on applying bang-bang control(as well as the bang-bang like control proposed herein)to the oversaturation operation to be feasible.Clearly,conventional controls for congested intersections are invalid.In terms of robustness,bang-bang like control is superior to conventional equal time-sharing control.Providing aÆ5%detection or prediction error in tra c volume is acceptable,similar to the above case,we®nd no di erence in the switch-over point when applying bang-bang like control;but,it changes when applying equal time-sharing control.This indicates that bang-bang like control is more stable than equal time-sharing control.4.4.Optimal cycle lengthThe above discussion con®rms that the cycle length remains constant.In fact,the total inter-section delay is a function not only of green time g k ,but also of cycle length c.For other op-erational reasons,cycle lengths generally have upper and lower limits.Under normal conditions, the imposed cycle length ranges from60to180s.The previous case still applies to the analysis of the optimal cycle length.The left column in Table3lists the switch-over points,termination,and average delays with respect to the minimal delay model in each given cycle,varying from60to180s.This table reveals that the average delay decreases as the cycle length descends.This phenomenon resembles the model's®nding for an undersaturated situation,which can be veri®ed from the May's formula presented in Eq.(2).This observation con®rms that the delay in c 120is twice the delay in c 60.However,the de-scendent slope of the model's®nding applied for an undersaturated situation is steeper than in an oversaturated one.Obviously,the optimal cycle length in the minimal delay model should be as small as possible.This®nding implies that,at oversaturation,the cycle length is set in c 60.In fact,a short cycle causes more stops(including full stops and partial stops,see TRANSYT-7F User Guide,1991),resulting in increased operating cost,exhaust energy and pollution.Therefore, pertinent indicates that long cycle lengths are common in practice.Nevertheless,extremely long cycle lengths may also waste time and become unfair.To attain more reasonable control,exceptTable3Switch-over point,termination and average delay in each given cycleCycle length (s)Minimal delay model Performance index modelSwitch-overpoint(s)Termination(s)Averagedelay(s/veh)Switch-overpoint(s)Termination(s)Averagedelay(s/veh)18010802340292.8110802340365.40 17510502275295.7110502275370.29 17010202380294.7010202380370.34 1659902310299.399902310377.60 16011202240284.45±±±15510852325284.0410852325362.78 15010502400283.2910502400363.51 14510152320288.5310152320371.96 1409802380288.309802380373.65 13010402340280.1410402340368.47 12510002375279.7210002375370.40 11510352300274.4410352300369.50 1109902310277.929902310377.40 10510502310268.3310502310386.18 10010002400268.8810002400373.02 909902340268.569902340381.66 809602320269.409602320394.00 759752325265.439752325395.20 709802380259.589802380394.28 659752340260.769752340404.65 609602340260.429602340414.15 T.-H.Chang,J.-T.Lin/Transportation Research Part B34(2000)471±491483。

Optics and Lasers in Engineering35(2001)263–284Fourier transform profilometry:a reviewXianyu Su*,Wenjing ChenOpto-Electronics Department,Sichuan Uni v ersity,Chen g du610064,ChinaReceived1September2000;received in revised form20February2001;accepted28February2001AbstractFourier transform profilometry is one of the popular non-contact3-D measurement methods,where a Ronchi grating or sinusoidalgrating is projected onto a diffuse three-dimensionalsurface,and the resul ting deformed grating image is detected by a CCD camera and processed by a computer.This method requires only one frame(or two frames)of the deformed fringe pattern in some algorithms to retrieve the surface of measured object,so it has obvious advantage for realtime data acquisition and3-D measurement of dynamic process.I n this paper,we review some algorithms in FTP,discuss some important problems,including frequency spectra overlapping,phase unwrapping,sampling,and3-D measurement of dynamic process.With the development of computer hardware and software and availability of high-resolution image grabber,FTP method will be a promising one for acquiring3-D data of object,and more and more researchers pay attention to it.#2001Elsevier Science Ltd.All rights reserved.1.IntroductionOptical3-D non-contract profilometry has been widely used for3-D sensing, mechanical engineering,machine vision,intelligent robots control,industry monitoring,biomedicine,dressmaking,etc.Several3-D object profil ometry methods that use structured light pattern,including Moir!e technique(MT)[1,2],phase-measuring profilometry(PMP)[3–11],Fourier transformation profilometry(FTP) [12,13],modulation measurement profilometry(MMP)[14,15],spatial phase detection(SPD)[16–18],laser triangulation measurement[19–22],color-coded *Corresponding author.E-mail address:xianyusu@(X.Su).0143-8166/01/$-see front matter#2001Elsevier Science Ltd.All rights reserved.PII:S0143-8166(01)00023-9fringe projection [23],gray-coded binary fringe sequences [24]have been exhaustively studied.Among them,Fourier transform profilometry,by Takeda et al .is a popular one,because of following merits,only one (or two)fringe(s)needed,full field analysis,and high precision,etc.In FTP,a Ronchi grating or a sinusoidal grating is projected onto the object surface,the depth information of the object is encoded into a deformed fringe pattern recorded by an image acquisition sensor.The surface shape can be decoded by calculating Fourier transformation,filtering in spatial frequency domain,and calculating inverse Fourier pared withthe Moir !etopography (MT),FTP can accomplish fully automatic distinction between a depression and an evaluation of the object shape.It requires no fringe order assignments or fringe center determination,and it requires no interpolation between fringes because it gives height distribution at every pixelover the entire fipared with the phase-measuring profilometry (PMP)and modulation measurement profilometry (MMP),FTP requires only one or two images of the deformed fringe pattern,which makes real-time data processing and dynamic data processing possible.Whereas,PMP and MMP require many images with fixed phase variation between neighboring two images to retrieve the height distribution,and they take much time to finish phase-shifting procedure using mechanicaldevice.So it is impossible to use them to measure dynamic object.After Takeda et al.the FTP method has been extensively studied [25–41].A grating p phase shifting technique [28,29]can extend the measurable slope of height variation to nearly three times that of the unimproved FTP.Two-dimensional Fourier transform and 2-D hanning filtering are applied to provide a better separation of the height information from noise when speckle-like structures and discontinuities exist in the fringe pattern [31].FTP based on TDI camera can be used to measure 3608shape [33].The frequency-multiplex technology [35,36]permits the 3-D shape measurement of objects that have discontinues height step and/or spatially isolated surfaces.The phase error caused by sampling in FTP is discussed in detail[40].This paper reviews some of the devel opments in Fourier transform profilometry over the past years,including frequency spectra overlapping,phase unwrapping,sampling,and 3-D measurement of dynamic process,complex object phase unwrapping,3-D phase unwrapping,etc.With the availability of high resolving CCD and high frame rate grabber,FTP has become an effective method for 3-D shape measurement.2.PrincipalFTP was introduced by Takeda et al.The general geometry is shown in Fig.1,in which the opticalaxes P 1P 2of a projector lens crosses that of camera lens I 1I 2at point O on a reference plane R,which is a fictitious plane normal to I 1I 2and serves as a reference,from which object height h ðx ;y Þis measured.D expresses a tested point,A,C express points on R,d is the distance between P 2and I 2,and L 0is the distance between I 2and O.Ronchi grating G has its lines normal to the plane of the figure,and its image is projected onto the object surface.X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284264When the measured object is put on R,the deformed fringe pattern observed through a CCD can be expressed bygðx;yÞ¼rðx;yÞX1n¼À1A n expðið2p nf0xþn jðx;yÞÞÞ:ð1ÞWhen hðx;yÞ¼0,the deformed grating image is written asg0ðx;yÞ¼r0ðx;yÞX1n¼À1A n expðið2p nf0xþn j0ðx;yÞÞÞ;ð2Þwhere rðx;yÞand r0ðx;yÞare non-uniform distributions of reflectivity on the diffuse object and on the reference plane,respectively.A n is the weighting factors of Fourier series,f0is the fundamentalfrequency of the observed grating image,jðx;yÞand j0ðx;yÞare the phase modulations resulting from the object height distribution and originalphase modul ation(hðx;yÞ¼0),respectively.Compute the1-D Fourier transform of Eq.(1)and obtain the Fourier spectra,as shown in Fig.2.With a suitablefilter function,the spectra arefiltered to let only the fundamentalcomponent.The inverse Fourier transform is appl ied to the fundamentalcomponent,we obtain a compl ex signal#gðx;yÞ¼A1rðx;yÞexpði2p f0xþfðx;yÞÞ:ð3ÞThe same operation is applied to Eq.(2),we obtain#g0ðx;yÞ¼A1r0ðx;yÞexpði2p f0xþf0ðx;yÞÞ:ð4ÞThe core variable varied directly with the height distribution is the phase change D jðx;yÞ:D jðx;yÞ¼jðx;yÞÀj0ðx;yÞ¼2p f0%AC:ð5ÞD jðx;yÞcan be obtained by Eqs.(3)and(4)asD fðx;yÞ¼Im f log½#gðx;yÞ#g*0ðx;y Þg:ð6ÞThe phase calculation by computer gives principal values ranging from Àp to p ,and has discontinuities with 2p phase jumps.By phase unwrapping algorithm,we can obtain continuous phase distribution.Assuming the measuring system is perfect and the system parameters (L 0and d )have no error,then height distribution can be computed by the following formula:h ðx ;y Þ¼L 0D f ðx ;y ÞD f ðx ;y ÞÀ2p f 0d:ð7ÞSubstituting Eq.(6)into Eq.(7),h ðx ;y Þis obtained.When the measuring system is not perfect,how to solve the problems have been discussed [21,25].Since Fourier spectra of the deformed fringe pattern usually have multiple components,which can be expressed asf n ¼nf 0þn 2p @j ðx ;y Þ@x:ð8ÞIn order to restore the object surface correctly,the fundamental component must be separated from all other spectra,as shown in Fig.2,it is necessary thatðf 1Þmax 5ðf n Þmin ;n >1;ð9Þðf 1Þmin >f b :ð10ÞConsequently,the phase variation caused by height modulation must be limited in @f ðx ;y Þ@x max52p f 0=3:ð11ÞAssuming that L 04h ðx ;y Þ,we have approximatelyf ðx ;y Þ%D f ðx ;y Þ¼À2p f 0d L 0h ðx ;y Þ:ð12ÞSubstituting Eq.(12)into Eq.(11),we obtain @h ðx ;y Þ max 5L 0=3d :ð13ÞThat is:FTP can be used only for surfaces on which the slopes do not exceed this limitation.When the measurable slope of height variation extend the limitation,the fundamentalcomponents overl ap the zero component and other highcomponents.Fig.2.1-D spatialfrequency spectra of deformed grating pattern.X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284266Aliasing will influence the precision of FTP,even correct reconstruction cannot be obtained.In following section,we review the techniques used to reduce frequency overlapping and improve the measurement precision.3.Several improvements in FTP3.1.Quasi-sine projection and p phase shiftin g technique [28,29]In FTP,we apply quasi-sine projection technique and p phase shifting technique to merely make the fundamental component exist in spatial frequency domain.In this case,the lower frequency part of the fundamental component can extend to zero,and the higher part can extend to 2f 0without overlaps.FTP can measure the object with higher variation.The intensity distribution on the object surface can be expressed asg ðx ;y Þ¼a ðx ;y Þþb ðx ;y Þcos ð2p f 0x þf ðx ;y ÞÞ:ð14ÞTo eliminate the influence of background intensity a ðx ;y Þ,the opticalfiel d is sampled twice.At the second sampling,the grating is moved half of the grating period,and the other conditions remain unchanged.The difference between the two fringes isg ðx ;y Þ¼2b ðx ;y Þcos ð2p f 0x þf ðx ;y ÞÞð15Þwhere no zero component and higher components exist in frequency domain.So the fundamental component can be extended toward lower frequency,nearly to 0,and toward higher frequency,at least to nearly 2f 0in the spectraldomain.The results of quasi-sine projection and p phase shifting technique result in the larger range of the measurement,that is @f ðx ;y Þ@x max52p f 0;ð16Þ@h ðx ;y Þ@x max 5L 0=d :ð17ÞIt is obvious that the improved method can raise the measurable slope of the height variation nearly three times while other system parameters remain unchanged.A primary experiment is used to verify our demonstration.The measured object is a triangle,which base is 40mm,and the height is 60mm,the slopes of the triangle are 3and –3.The parameter of the system is L 0=d ¼5:2.Since L 0=3d 5@h ðx ;y Þ=@x max 5L 0=d ,Fig.3(a)shows the frequency spectra of the deformed fringe,the overlap is obvious.So the two sides of the triangle cannot be restored completely by unimproved FTP,as shown in Fig.3(b).Using quasi-sine projection and p phase shifting technique,the background intensity a ðx ;y Þand higher spectra are eliminated,as shown in Fig.3(c),the surface of the triangle can be completely restored,as shown in Fig.3(d).X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–2842673.2.Two-dimensional Fourier transform profilometry[31]To accomplish automatic measurement of a coarse object,on which there are discontinuities and speckle-like structures in the fringe pattern,for example,sand-body,two-dimensional Fourier transform profilometry is applied.In this case,the deformed fringe pattern with noise can be expressed asX1gðx;yÞ¼rðx;yÞb n expðið2p nf0xþn jðx;yÞÞÞþNðx;yÞ;ð18Þn¼À1where Nðx;yÞrepresents2-D noise distribution.The2-D Fourier transform is applied to compute the spectra of Eq.(18),then2-D hanningfilter function,which is expressed by Eq.(19),is used to reinforce the frequencies around the carrier frequency f0and attenuate the rest more as the distance from f0is increased.Thefrequencies caused by speckle-like structure and the discontinuity are eliminated,finally 2-D inverse Fourier transform is applied to the fundamental component.H ðf x ;f y Þ¼0:251þcos bp f x Àf 0f cx !1þcos bp f y f yx!:ð19ÞThe same operation is applied to the reference fringe.Applying the phase algorithm and phase unwrapping algorithm,we obtain the 2-D continuous phase distribution.Fig.4(a)shows the surface of a Chinese word ‘‘jiang’’written on a sand-body,on which a Ronchi grating pattern is projected.By 2-D FTP method,the shape of the object can be restored correctly,as shown in Fig.4(b).3.3.Fourier transform profilometry based on TDI camera [33]Time delay and integration (TDI)camera can be easily adapted for recording image in a high bined with TDI camera,Fourier transformprofilometry Fig.3.(Continued .)X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284269can be used for 3608shape measurement.When the object rotates for 3608,TDI camera records single stripe structured light recorded sequentially on one image.The finalimage contains the surface information of the 3608object.The fringe pattern is processed by 2-D Fourier transform profilometry to obtain the phase changecausedFig.4.(a)A Chinese word ‘‘jiang’’shape on the sand with a grating pattern projected onto it.(b)The restored surface of ‘‘jiang’’using 2-D FTP.X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284270by height distribution of the 3608object.Then it is easy to calculate the actual height distribution.Since the sampling and processing are separated,and only one image is needed,the speed of the method can be improved rapidly.The schematic of the 3608shape testing is given in Fig.5.Illumination is by a thin line of light from a laser diode.The TDI camera is mounted so that the scanning direction is perpendicular to the rotation axis of the test object.When the object has been rotated for 3608,a distorted fringe pattern is formed on a single image.As a demonstration,a mannequin head is used.The fringe pattern image of a 3608light stripe obtained by TDI camera is shown in Fig.6(a).Fig.6(b)is the contour map with gray scale presentation.Fig.6(c)is the reconstructed profile of the mannequin head.3.4.Frequency-multiplex Fourier transform profilometry [35,36]In 1997,Takeda et al.proposed frequency-multiplex Fourier transform profilometry based on spatial frequency multiplexing combined with the Gushov–Solodkin phase unwrapping algorithm.The technique permits the three-dimensional shape measurement of objects that have discontinuous height steps and/or spatially isolated surface,which has not possible by conventional FTP.An important feature of the technique is that it requires only a single fringe pattern.So it is suitable for instantaneous 3-D shape measurement of discontinuous objects in fast motion.4.The influence of sampling in FTP [40]Employing continuous Fourier transform analytical method,Takeda et al.analyzed the problems that existed in FTP,such as frequency aliasing,measurable range,etc.[13].But in practice,the deformed fringe pattern captured byCCD Fig.5.The schematic for the 3608profilometry.X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284271camera is discrete,and the discrete Fourier transform (DFT)is applied.The obvious shortcoming in theory analysis results in the inconsistency between theory and experience,especially if high-order spectra existed.To obtain the correct reconstruction of the measured object,the influence of sampling in FTP must be discussed.The deformed fringe pattern caused by CCD camera can be expressed asg ðx ;y Þ¼X 1n ¼À1q n ðx ;y Þexp ði2p nf 0x Þcomb x D x comb y D y ;ð20ÞFig.6.(a)Projected grating lines on unwrapped mannequin head.(b)The contour map with gray-scale presentation.(c)3-D display of the mannequin.X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284272whereq n ðx ;y Þ¼r ðx ;y Þb n exp ði n j ðx ;y ÞÞ:ð21ÞD x and D y denote sampling intervals in x ,y directions.For simplicity,we compute the 1-D Fourier transform of Eq.(20)for the variable x only,with y fixed,and obtain G s ðf ;y Þ¼X 1N ¼À1X 1n ¼À1Q n ðf Ànf 0ÀNmf 0;y Þcomb y D y ;ð22Þwhere Nmf 0¼N D f ¼N =D x ,Eq.(22)states that the function P 1n ¼À1Q n ðf Ànf 0;y Þappears in replica at intervals of mf 0in both directions along x -axis,which is called a general spectrum region.To eliminate the overlapping between spectral regions,m must be big enough.As shown in Fig.7,the dark lines correspond to the right-hand side of P 1n ¼À1Q n ðf Ànf 0;y Þ,the light lines correspond to the left-hand side of its adjacent frequency P 1n ¼À1Q n ðf Ànf 0Àmf 0;y Þ.According to the definition of a local spatial frequency f n for the n th spectrum component,shown as Eq.(8),and assuming the fringe pattern to be a band-limited signal,then ðf n Þmax corresponds to the cutofffrequency of the Fourier spectra.Only when ðf n Þmax does not exceed mf 0Àðf n Þmax ,does the frequency spectra determined by P 1n ¼À1Q n ðf Ànf 0;y Þnot overlap those determined by P 1n ¼À1Q n ðf Ànf 0Àmf 0;y Þ.In other words,ðf n Þmax 5mf 0Àðf n Þmax must be satisfied.In a word,in FTP,the following three inequations must be satisfied:ðf 1Þmax 5ðf n Þmin ;n >1;ð23Þðf 1Þmin >f b ;ð24Þðf 1Þmax 5mf 0Àðf n Þmax :ð25ÞSubstituting Eq.(8)into the above inequations,we obtain @h ðx ;y Þ@x max 5L 03d ;ð26Þ@h ðx ;y Þ@x max 5m Àn À1n þ1L 0d ;ð27Þwhere m ¼D f =f 0,and the bigger m results in the larger range of the measurement.Since the weighing factor of the second-order frequency spectrum is much bigger than that of other spectra,the phase error caused by overlapping bet-ween the fundamentalfrequency and the second-order spectrum in the same isl and is larger than that from the adjacent period.That is,only when Eq.(26)is satisfied,does increasing sampling frequency to decrease overlapping between periods have practicalmeaning for decreasing the phase errors.I t is necessary that13L 0d 5m Àn À1n þ1L 0d;ð28Þthat ism 54ðn þ1Þ:ð29ÞSo owing to the discrete nature of the DFT,in practicalmeasurement,we must ensure that the fundamentalcomponent does not overl ap the zero component and other higher-order spectra in the same Frequency Island.Furthermore,we must also ensure that the fundamentalcomponent does not overl ap the higher spectra from the adjacent frequency islands.A triangle is used in our experiment,its base line is 54mm and height is 27mm,@h =@x ¼1,L 0=d ¼4:5,@h =@x max 5L 0=3d .According to the theories proposed by previous authors [12,13],the triangle surface can be correctly restored by FTP.Buttaken into account the overlapping between adjacent frequency period caused by the third spectrum of Ronchi grating,m >163%5:3,according to Eq.(29).If the sampling frequency is 4f 0,correct reconstruction cannot be obtained.The frequency spectra and the restored surface are shown in Fig.8(a).If the sampling frequency is 7f 0,we can obtain the correct reconstruction.The frequency spectra and the restored surface are shown in Fig.8(b).5.Dynamic 3-D shape measurement method based on FTPNow we review the method based on Fourier transform profilometry for dynamic 3-D shape measurement.First,we record a fringe pattern for h ðx ;y Þ¼0:g 0ðx ;y Þ¼X1n ¼À1A n exp ði ð2p nf 0x þn j 0ðx ;y ÞÞÞ;ð30Þthen put a dynamic 3-D object in the opticalfiel d,and record and store a sequence of deformed fringe patterns rapidly.The intensity distributions of these fringe patternsX.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284274can be expressed asgðx;y;tÞ¼X1n¼À1A n rðx;y;tÞexpðið2p nf0xþn jðx;y;tÞÞÞðt¼1;2;...;sÞð31Þin Eqs.(30)and(31),rðx;y;tÞand jðx;y;tÞrepresent a non-uniform distribution of reflectivity and phase modulation resulting from the object height distribution at the time of t,respectively,which are a slowly varying function relating to position and time.s denotes the totalframe number of the patterns recorded by CCD.To obtain jðx;y;tÞseparately from the unwanted amplitude variation rðx;y;tÞcaused by non-uniform reflectively on object surface.We compute the Fourier transform of deformed fringes only for the variable x,with y beingfixedGðf;y;tÞ¼X1n¼À1Q nðfÀnf0;y;tÞ;ð32Þwhere Gðf;y;tÞand Q nðf;y;tÞare the1-D Fourier spectra of gðx;y;tÞand q nðx;y;tÞ,q nðx;y;tÞ¼b n rðx;y;tÞexpði n fðx;y;tÞÞ,respectively.If the fundamental component separates from the other spectra,using a suitablefilter function the spectra can befiltered to let only fundamental component through.The inverse Fourier transform is applied to the fundamental component,we get#gðx;y;tÞ¼A1rðx;y;tÞexpði2p f0xþfðx;y;tÞÞ:ð33ÞThe same operation is done on the reference fringe to obtain#g0ðx;yÞ¼A1r0ðx;yÞexpði2p f0xþf0ðx;yÞÞ:ð34ÞThere are two methods to obtain the dynamic phase change resulting from height distribution.5.1.Direct phase al g orithmCalculating the multiplication of the conjugation of the#g0ðx;yÞwith#gðx;y;tÞ,we obtain#gðx;y;tÞ#g*ðx;yÞ¼j A1j2rðx;y;tÞexpði D fðx;y;tÞÞ:ð35ÞThe phase change D jðx;y;tÞcan be obtained byD jðx;y;tÞ¼jðx;y;tÞÀj0ðx;yÞ¼arctg Im½#gðx;y;tÞ#g*ðx;yÞRe½#gðx;y;tÞ#g*ðx;yÞ;ð36Þwhere I m[]and Re[]represent the imaginary part and realpart,respectivel y.By this method,we can obtain a sequence of phase maps,which include thefluctuation information of dynamic object.X.Su,W.Chen/Optics and Lasers in Engineering35(2001)263–2842755.2.Phase difference al g orithmBy calculating the product of the #g*0ðx ;y Þwith #g ðx ;y ;1Þand that of #g *Âðx ;y ;t À1Þwith #gðx ;y ;t Þin neighboring time,we obtain #g ðx ;y ;1Þ#g *0ðx ;y Þ¼j A 1j 2r ðx ;y ;1Þexp ði D f 1ðx ;y ÞÞ;ð37Þ#gðx ;y ;t Þ#g *ðx ;y ;t À1Þ¼j A 1j 2r ðx ;y ;t Þr ðx ;y ;t À1Þexp ði D f t ðx ;y ÞÞ:ð38ÞD f t ðx ;y Þcan be expressed as D f t x ;y ðÞ¼f ðx ;y ;t ÞÀf 0ðx ;y Þ¼arctg Im #g ðx ;y ;1Þ#g *0ðx ;y ÞÂÃRe #g ðx ;y ;1Þ#g *0ðx ;y ÞÂÃðt ¼1Þf ðx ;y ;t ÞÀf 0ðx ;y ;t À1Þ¼arctg Im #g ðx ;y ;t Þ#g *ðx ;y ;t À1Þ½ Re gðx ;y ;t Þg *ðx ;y ;t À1Þ:ðt >1Þ8>>><>>>:ð39ÞBy computing the finite sum of Eq.(39),we getX t n ¼1D f n ðx ;y Þ¼j ðx ;y ;t ÞÀj 0ðx ;y Þ:ð40ÞComparing Eq.(36)to Eq.(40),we getD f ðx ;y ;t Þ¼X t n ¼1D f n ðx ;y Þ:ð41ÞThe phase distribution in any time computed by the two methods discussed above lies in (Àp p ).To obtain continuous phase distribution,we must unwrap the phase along x ,y coordinates and time dimension t .In evidence,the phase difference of f ðx ;y ;t ÞÀf ðx ;y ;t À1Þis always smaller than that of f ðx ;y ;t ÞÀf 0ðx ;y Þ,this provides a new approach for phase unwrapping.6.Phase unwrapping in FTP methodPhase unwrapping is a critical but challenging step in any grating projection profilometry,including Fourier transform profilometry.In recent years,phase unwrapping problem has been widely studied [42–56].In this paper,we will concentrate on the phase unwrapping based on the modulation ordering and extend 2-D phase unwrapping algorithm into 3-D phase space for dynamic 3-D measurement.6.1.Phase unwrappin g based on modulation for complex object [5,45–51]Since the phase calculation by any inverse trigonometric function provides the principalval ues ranging from Àp to p ,for phase data without noise,these discontinuities can be corrected easily by adding or subtracting 2p according to the phase jump ranging from Àp to p or vice versa.This is called the phase unwrapping X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284276procedure.If the wrapped phase is reliable everywhere and the maximum phase variation between neighboring pixels is less than p everywhere,the phase unwrapping procedure consists of adding multiples of2p to the phase when discontinuities appear.The unwrapped phase is correctly written asf uðx;yÞ¼fðx;yÞþ2k p:ð42ÞBut in practice,phase unwrapping is a difficult problem for complex shape measurement.Many factors,such as noise,local shadows,under-sampling,fringe discontinuities and irregular surface brightness make the actual unwrapping procedure complicated and path-dependent.Combined with modulation analysis technique,we propose a phase unwrapping algorithm suitable for complex3-D shape measurement.First,we define modulation function asmðx;yÞ¼j#gðx;yÞj¼A1rðx;yÞ;ð43Þwhich means the modulation is direct ratio to non-uniform distributions ofreflectivity rðx;yÞ,obviously,in the areas of local shadow and in the regions ofabrupt surface discontinuities,modulation is low,which means that the phase is uncertain.Therefore,the modulation function can be selected as one of the criteria of reliability.Phase unwrapping based on modulation has been successfully used in FTP for complex object [51].In FTP,filtering by the digital weighting filter in frequency domain is carried out to make modulation function contain information about fringe density.For example,by hanning filter function,we can reinforce the frequency components around carrier frequency,and attenuate the parts more as the distance from f 0is increased.This associates the modulation function with fringe density.The phase unwrapping based on modulation start from the pixel with higher intensity modulation.First,we produce a pixel queue by comparing the intensity modulation of each pixel in 3*3adjacent region of start point,so that the pixelwith the highest modulation is put on the top of the queue.Then,the top pixel is pulled out for unwrapping and meanwhile new pixels in 3*3adjacent region of the pixelare put on the queue according to the modulation ordering.When the phase unwrapped areas are more than one pixel,the ordering operation is done for all the pixels on outer layer of boundary of the phase unwrapped areas,so that the pixel with the highest modulation is put on the top of the queue.The advantage of this approach is that the path of phase unwrapping is always along the direction from the pixel with higher modulation to the pixel with lower modulation until phase is unwrapped.We have verified our algorithm by experiment.The measured object is face of a modelcat with an abrupt region around the mouth,so it is difficul t to obtain the correct reconstruction.Employing the phase unwrapping based on modulation yields a satisfactory result.Fig.9(a)shows an intermediate step of phase unwrapping,the bright region represents the unwrapped part with higher modulation,the dark region denotes that the part with lower modulation will be unwrapped later.The unwrapping path successfully goes round the shadows,fringe discontinuity and possible defects.Fig.9(b)is the result of the reconstruction of the complex 3-D object.6.2.3-D phase unwrappin g for dynamic object6.2.1.Direct 3-D phase unwrappin gIn dynamic 3-D surface measurement,the wrapped phase maps computed is a function about position (x ,y )and time (t ).If it is reliable everywhere and the phase difference is less than p between neighboring pixels in 3-D phase space,the unwrapping problem is trivial.The phase unwrapping can be carried out along any direction.Fig.10shows one of the possible unwrapping path.First,we select any pixel (i.e.point O)at initialtime (t ¼1)as the start point to be unwrapped.1-D phase unwrapping procedure is carried out along the t direction.Afterwards,columns from the unwrapped pixels in every phase map are selected to be unwrapped.At last,all rows from the unwrapped column in every phase map are unwrapped,and natural phases in the whole 3-D space are obtained.Of course,column and row operations X.Su,W.Chen /Optics and Lasers in Engineering 35(2001)263–284278。

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a r X i v :0711.1432v 2 [a s t r o -p h ] 23 N o v 2007Astrophysical J.Letters,v.671,pp 61-64,2007Preprint typeset using L A T E X style emulateapj v.10/09/06EXOPLANET HD209458B:INFLATED HYDROGEN ATMOSPHEREBUT NO SIGN OF EVAPORATIONLotfi Ben-JaffelInstitut Astrophysique de Paris,UPMC,CNRS,98bis Blvd Arago,75014Paris,France(Received 2007August 21;Accepted 2007October 18;Published 2007November 8)Astrophysical J.Letters,v.671,pp 61-64,2007ABSTRACTMany extrasolar planets orbit closely to their parent star.Their existence raises the fundamental problem of loss and gain in their mass.For exoplanet HD209458b,reports on an unusually extended hydrogen corona and a hot layer in the lower atmosphere seem to support the scenario of atmospheric inflation by the strong stellar irradiation.However,difficulties in reconciling evaporation models with observations call for a reassessment of the problem.Here,we use HST archive data to report a new absorption rate of ∼8.9%±2.1%by atomic hydrogen during the HD209458b transit,and show that no sign of evaporation could be detected for the exoplanet.We also report evidence of time variability in the HD209458Lyman-αflux,a variability that was not accounted for in previous studies,which corrupted their diagnostics.Mass loss rates thus far proposed in the literature in the range 5×1010−1011g s −1must induce a spectral signature in the Lyman-αline profile of HD209458that cannot be found in the present analysis.Either an unknown compensation effect is hiding the expected spectral feature or else the mass loss rate of neutrals from HD209458is modest.Subject headings:Stars:individual (HD209458)—Stars:planetary systems —Ultraviolet:stars —Line:profiles —Techniques:spectroscopic1.INTRODUCTIONOf all the planets discovered outside the realm of our solar system,some of the most dramatic new classes of objects are those in which the planet is a gas giant or-biting at merely a few stellar radii (∼0.02AU)from its parent star.These close-in extrasolar planets are Jupiter-like giants that are exposed to strong fluxes,magnetic fields,and plasma winds—a very harsh and active stellar environment.Because of their stars’proximity,gravity,through tidal effects,distorts the shape of their atmo-sphere while the continuous extreme ultraviolet (UV)energy deposition inflates it (Lammer et al.,(2003);Baraffe et al.,(2004);Lecavelier et al.,(2004);Yelle (2004);Jaritz et al.,(2005);Tian et al.,(2005);Munoz (2007);Villaver and Livio (2007)).Unfortunately,little is known about those regions that separate extrasolar gi-ant planets from their stars,particularly the immediate environment of the planet.One of the most extensively studied extrasolar systems is HD209458.For reference,HD209458b was first discov-ered transiting its parent star and covering 1.5%of its disk (Charbonneau et al.,(2000);Henry et al.,(2000)).Some of the first attempts to learn about the immediate environment of the planet were Lyman-α(121.6nm)ob-servations of the system using the Space Telescope Imag-ing Spectrometer (STIS)onboard the Hubble Space Tele-scope (HST).A first program of observation,obtained with the STIS/G140M grating and the 52”x0.1”slit,was implemented in 2001during HD209458planetary transit but no conclusions were reported (see Table 1).Soon after,a second program visited the target during three transits (Vidal-Madjar et al.,(2003)).An initial analysis of this data set concluded that a huge cloud of hydrogen is covering 15%±4%of the stellar disk (Vidal-Madjar et al.,(2003));it also claimed that spectral absorption dur-Electronic address:bjaffel@iap.fring transit is deeper on the blue side of the stellar line.Accordingly,the hydrogen cloud was required to extend beyond the planetary Roche limit where an intense es-cape of ∼1010g s −1of hydrogen is a priori operating.These results,along with other far UV low-resolution observations of heavy constituents,led to the conclu-sion that the upper atmosphere of HD209458b should be in a hydrodynamic blow-offstate (Vidal-Madjar et al.,(2003);Vidal-Madjar et al.(2004)).Numerous studies then followed on different mecha-nisms for hydrogen loss from hot exoplanets closely or-biting their stars (Lammer et al.,(2003);Baraffe et al.,(2004);Jaritz et al.,(2005);Lecavelier et al.,(2004);Yelle (2004,2006);Tian et al.,(2005);Munoz (2007)).As noted by Munoz (2007),all loss rates thus far proposed by theoretical models in the range 5×1010−1011g s −1exceed the lower limit provided by Vidal-Madjar et al.,(2003).Unfortunately,most studies neglected to quantitatively translate their loss rate to a spectral absorption in the Lyman-αline profile that could be tested with the HST observation.Independently,pointing out that the observed mass function distribution of extrasolar giant planets (EGPs)follows a trend M −1for mass range ∼0.2−5M J ,where M J is the Jovian mass,Hubbard et al.,(2007)derived the same mass function distribution for highly irradiated EGPs orbiting at dis-tances smaller than ∼0.07AU.Accordingly,Hubbard et al.,(2007)rejected substantial mass loss during EGPs’migration to smaller distances from their star,unless the loss mechanism is compensated by an unknown process.When combined with the unusual scales derived for the hydrogen extent and escape,all these studies then call for a careful reassessment of the HST Lyman-αobservations thus far obtained on HD209458,at least in order to pro-vide validated constraints on theoretical models.2.OBSERVATIONS AND DATA ANALYSIS2HD209458b:inflated but not evaporating In the following,we report a new analysis of archivedata obtained during the two HST/STIS programs de-scribed above.In total,we have four visits of the tar-get corresponding to three exposures of roughly∼2000s duration each,resulting in12exposures of the systems around the transit period(Table1).All observations were obtained in the time-tag mode,a technique that keeps track every125×10−6s of photon events during each exposure.The question,then,is:why is this mode of observation important in the present case?First,we stress that the transit effect is a weak variation of the stellar signal.As such,its trend is best represented by a dense time series.Second,chromospheric and coro-nal variabilities of the star are unknown in the Lyman-αspectral window considered here,and this may seri-ously corrupt any diagnostic.To properly handle time tagged data,we partition each time-tag exposure into a set of shorter sub-exposures, taking into account the heliocentric and barycentric time correction procedure in which ephemerides are retrieved from the archives before the IRAF/STSDAS”odelay-time”procedure is applied(Brown et al.,(2002)).After several trials,we found that300s sampling of the time-tag data is a good compromise between acceptable signal-to-noise ratio(S/N)and time coverage.Next,each sub-exposure is calibrated through the STIS pipeline.The emitting source(the star plus sky background)is pre-sumed extended,an option that allows efficient control of the subtraction of the sky background contamination. Time is then converted tofixed orbital phases measured from the transit central time(TCT),itself carefully taken from the most recent and accurate determination of the HD209458system parameters(Ballester et al.,(2007); Knutson et al.,(2007)).Sub-spectra of identical phase positions are accumulated from the initial twelve expo-sures,resulting in a unique53bins time series of the system versus the orbital phase angle(Fig??).Unex-pectedly,three gaps,lasting respectively312s,404s,and 406s,appear in the time series,for which no observa-tion is available.Because the three gaps are narrow and well-separated from each other,we determined thatfill-ing them has a negligible effect on ourfinal conclusions (Schneider(2001)).Errors due to photon counting have been propagated,taking into account the correlation be-tween the different phase positions relative to the initial sampling of sub-exposures time over the full observing time period.We next define the wavelength domain of contamina-tion by the sky background,including both the Earth’s geocorona and the interplanetary medium emissions. The difficulty comes from the uncertainty about the geo-corona’s strength when estimated from a detector sec-tor,along the STIS slit,different from the one where the stellar signal was recorded.First,we subtracted the dark noise of the detector following(Vidal-Madjar et al., (2003)and Ballester et al.,(2007))and then compared the sky background signal from different sectors along the slit and for different conditions of observation.Our conclusion is that the STIS MAMMA detector has an in-herent non-uniformity corresponding to an incompress-ible uncertainty of5%on extended sources.Coinciden-tally,this uncertainty is comparable to photon statistical errors.To ensure that such error will not corrupt the stellar signal per wavelength pixel at the1%level,weFig. 1.—Contours of equalflux for the HD209458time series vs wavelength(nm)and time from transit(or planetary orbital phase angle).Top axis shows velocities in the stellar rest frame (∼10km s−1)from heliocentric system).Horizontal dark bands are time gaps of∼300-400s for which no observation is available. These bands are linearly interpolated using nearby spectra for light curves analysis and in/out transit spectra comparison.Following the time evolution of the signal(from bottom to top),we observe the transit absorption as a slight dimming of the stellarflux start-ing∼5000s before TCT.The wide,vertical,light purple band corresponds to the spectral window of extinction of the stellar sig-nal by the interstellar gas along the line of sight(Wood et al., (2005)deduce that a void window[121.541,121.584]nm should be disregarded in any spectral analysis that requires high accuracy,such as for a transit event or short-term stellar variability.3.LIGHT CURVE TREND AND TIME VARIABILITY Next,to obtain the trend of the planetary transit in Lyman-α,we integrated the time series spectra in the range[121.483,121.536]nm on the blue wing and [121.589,121.643]nm on the red wing.These ranges were selected so that the stellar signal per wavelength pixel remains above the statistical noise(≥1σ).The resulting light curve is noisy,but a trend is apparent and can be efficiently extracted(Fig.2a).To dampen the signal noise while keeping a clear trend,the best compro-mise is to gather data by eight phase bins for a new bin of2400s.Accumulating the signal from three new bins (3×2400s)inside transit,we derive∼8.9±2.1%drop-offof the stellar Lyman-αintensity during the planetary transit(Fig.2a).Our absorption rate of∼8.9%±2.1% is much lower and accurate than reported in a previ-ous study(Vidal-Madjar et al.,(2003)),yet a marginal agreement could be found between our maximum rate (11%)and their bottom value.If this obscuration is con-verted directly to a planetary occulting disk,then one would obtain a hydrogen cloud of∼2.47±0.30R P ra-dius,much smaller than the Roche lobe limit of∼4.08 R P(Gu et al.,(2003)),where R P=1.32R J is the most recent estimate of the radius of HD209458b(Ballester et al.,(2007);Knutson et al.,(2007)),and R J is the Jo-vian one.Now,to capture the trend of the transit curve, we used a sophisticated2D model of planetary transit at Lyman-αthat accurately accounts for the atmospheric radial structure of the planet(Yelle(2004);Ben-Jaffel et al.,(2007))and properly estimates the atmospheric ob-scuration versus wavelength,including extinction by theL.Ben-Jaffel3TABLE 1HST/STIS Data Set on HD209458Used in This Study.All observations were obtained with the G140M grating and the 52”x0.1”long slit.Transit central time (TCT)is defined by 2,452,826.628521HJD (Ballester et al.,(2007);Knutson etal.,(2007)).Dataset name Program IDStart time -TCT (s)Duration (s)End time -TCT (s)O4ZEA40107508-7980.282600.-5380.12O4ZEA40207508-2202.292600.397.87O6E2010109064-8075.111780.-6295.02O6E2010209064-2246.122100.-145.96O6E20103090643531.892100.5631.98O6E2020109064-10167.671780.-8387.50O6E2020209064-4750.682100.-2650.52O6E20203090641025.312100.3125.46O6E2030109064-11258.451780.-9478.27O6E2030209064-5876.472100.-3776.29O6E2030309064-102.452100.1997.73Fig.2.—(a)Light curve (LC)obtained from our time series (as shown in Fig.1)by integration of the signal in the spectral windows [121.483,121.536]nm and [121.589,121.643]nm.Histogram and related errors (plotted every two bins for clarity)show the LC with a time bin of 300s,while filled circles with attached error bars represent the LC rebinned to a larger timescale of 8×300s =2400s.The solid curve is our best least square fit to the rebinned LC.A total obscuration of ∼8.9%±2.1%is derived during the planetary transit.(b)Ratio of LC (histogram)to best model fit (solid line)is shown with related statistical error bars.This ratio cancels the transit trend shown in (a ).The resulting signal is a good indicator of the variability of the HD209458Lyman-αintensity vs time.interstellar gas intervening along the line of sight (Wood et al.,(2005)).Our best least square fit is shown in Fig-ure 2a.For our purpose of time analysis,we remark that a functional fit could also be a good model to obtain the light curve’s trend.We can now determine the stellar signal time evolu-tion after we cancel the transit trend using our best fit to the observed light curve (Fig.2a).The resulting ra-tio shows a variable behavior with an average amplitude ∼8.6±5.6%of the stellar integrated intensity (Fig.2b).Using the Durbin-Watson statistical test (Durbin and Watson (1951)),we found no apparent serial correlation at the 1%confidence level in the corrected signal—a sig-nal that also shows no evident periodicity.HD209458was previously suspected to have a relatively moderatechromospheric activity from CaII H and K lines that were recorded over full orbits of the system (Shkolnik et al.,(2005)).Our finding of a time variation of 8.6%on aver-age in the stellar Lyman-αsignal,with peaks that may reach ∼20%(>3σ),seems to support a relatively active corona of the star,presumably up to the planet’s orbit.Such activity could be of common origin (flaring,non-uniformity of the stellar disc during transit,etc.)and/or related to an enhancement of magnetic activity on the star-planet line (Zarka (2007)).Also,one can speculate about the hydrogen cloud topology around the planet and its evolution with time.To that end,comparative studies with interacting binary stars may be useful in clarifying the different regimes of interaction between an exoplanet and its host star (Shore et al.,(1994)).Un-fortunately,the FUV observations thus far obtained do not cover a full orbit of the planet,thereby making it difficult to predict the exact configuration of the star-planet system.In any case,we believe that the unusual 15%obscuration previously reported (Vidal-Madjar et al.,(2003))was corrupted by this unaccounted-for vari-able component in the star-planet system signal.Here we can extract it because we are able to sample the transit period by a dense time series using the information gath-ered from the time tag mode of HST/STIS and ∼25%more observation time from the archives.4.PLANETARY MASS LOSS OR FLUX VARIABILITY?In the following,we compare the in/out of transit stel-lar line profiles.The impetus of this study is the need to determine the relevance of a blueshifted absorption in the stellar line profile that may occur during transit,as claimed in earlier studies (Vidal-Madjar et al.,(2003)).On the one hand,we derive an average unperturbed pro-file of the HD209458Lyman-αemission line by merging all sub-spectra of the time series that we correct for the transit trend with the best fit shown in Figure 2a.The resulting profile is a good reference that best represents the out-transit stellar line and for which time variability has been reduced to the 1%signal level (Fig.3a).On the other hand,the in-transit line profile,when corrected for the ∼8.9%drop-offduring transit,properly recov-ers the unperturbed line profile (Fig.3a),leaving no real possibility of extra absorption as claimed in prior studies (Vidal-Madjar et al.,(2003)).To further investigate how time variability of the HD209458Lyman-αemission line corrupts the diagnos-tic as it pertains to extra absorption or emission features4HD209458b:inflated but notevaporatingFig.3.—Comparison between Lyman-αline profiles in and out of transit period.The sky background spectral window is indicated by two dashed vertical lines.(a)The in-transit line profile (solid thin line)is accumulated for the time period starting ∼3900s before TCT and ending ∼3900s after it.To correct for the ∼8.9%obscuration derived in this study,the corresponding intensity is scaled by 1.098.The resulting line profile (dotted curve)properly recovers the unperturbed line profile (histogram).(b)The first in-transit line profile,B1(thin solid line),was accumulated over the time period starting ∼4000s before TCT and ending ∼600s after it.The second in-transit line profile,B2(dotted line),was accumulated over the time period starting ∼1800s before TCT and ending ∼3900s after it.that may appear in the stellar line during transit,we se-lected two phase windows inside the transit period for which we compared line profiles to the unperturbed stel-lar line.As shown in Figure 3b,a direct comparison would indicate that line peaks are equally absorbed for line profile B1,while for line profile B2,the red peak is the most absorbed.On the basis of line profile B2,the diagnostic would be just the opposite of that of (Vidal-Madjar et al.,(2003)),leading to escaping hydrogen toward the star,while for line profile B1,the diagnostic would be no H escape.The problem is that these inter-pretations of preferred blueshifted or redshifted absorp-tion do not account for the relatively strong modulation of the stellar signal evidenced in this study.Therefore,any claim of a preferred absorption during transit,either blue or redshifted,is not realistic,particularly at this rel-atively modest level of the signal to noise.It follows that the blueshifted absorption,advanced in previous studies (Vidal-Madjar et al.,(2003);Lecavelier et al.,(2004))as a signature of atmospheric evaporation in a cometary-like tail of HD209458b,has,unfortunately,no foundation in the HST/STIS data set as it was only the effect of the stellar signal variability with time that corrupted the di-agnostic.5.CONCLUSIONWe use HST archive observations of the Lyman-αemission of HD209458to report an absorption rate of ∼8.9%±2.1%by atomic hydrogen during the transit of the planetary companion.If the planet is sketched as a compact blocking body,our analysis requires an H cloud effective extent that does not exceed ∼2.5R P —a size that falls short of the Roche limit ∼4.08R P of HD209458b.In addition,time variability of the stel-lar flux is evidenced,but no sign of extra or Doppler-shifted absorption could be detected during transit.This absence of extra absorption during transit and the rel-atively small size of the effective area of the hydrogen cloud around the exoplanet make it difficult to conceive of significant atmospheric evaporation from the planet.Of course,we cannot rule out that a complex atmospheric distribution,related to a particular planet-star interac-tion scenario,may hide or compensate the loss signature during the observing time.Future HST (when repaired)FUV observation of the system during a full planetary orbit should help to disentangle the different processes in play.The author acknowledges support from Universit Pierre et Marie Curie (UPMC)and the Centre National de la Recherche Scientifique (CNRS)in France.This work is based on observations with the NASA/ESA Hub-ble Space Telescope,obtained at the Space Telescope Sci-ence Institute,which is operated by AURA,Inc.L.Ben-Jaffel5 REFERENCESBallester,G.,Sing,D.,Herbert,F.2007,Nature,445,511.Baraffe,I.,et al.2004,A&A,419,L13.Ben-Jaffel,L.,Kim,Y.,and Clarke,J.2007,Icarus,190,504. Brown,T.,et al.2002,in HST STIS Data Handbook,B.Mobasher, Ed.(Baltimore,STScI,v4),pp131-192.Charbonneau,D.,et al.2000,ApJ,529,L45.Durbin,J.,and Watson,G.S.1951,Biometrika38,159.Gu,P.,Lin,D.,and Bodenheimer,P.2003,ApJ,588,509. Henry,G.et al.2000,ApJ,529,L41.Hubbard,W.B.,et al.2007,ApJ,658,L59.Jaritz,G.,et al.2005,A&A,439,771.Knutson,H.,et al.2007,ApJ,655,564.Lammer,H.,et al.2003,ApJ,598,L121.Lecavelier des Etangs,A.,et al.2004,A&A,418,L1.Munoz,G.A.2007,Planet.Space Sci.,55,1426.Schneider,T.2001,J.Climate,14,853.Shkolnik,E.,et al.2005,ApJ,622,1075.Shore,S.,Livio,M.,and van den Heuvel,E.1994,in Interacting binaries,ed.Nussbaumer,H.,and Orr(Berlin:Springer),1 Tian,F.,Toon,O.B.,Pavlov,A.A.,and De Sterck,H.2005,ApJ, 621,1049.Vidal-Madjar,A.,et al.2003,Nature,442,143.Vidal-Madjar,A.,et al.2004,ApJ,604,L69.Villaver,E.,and Livio,M.2007,ApJ,661,1192.Wood,B.E.,et al.2005,ApJS,159,118.Yelle,R.2004,Icarus,170,167.Yelle,R.2006,Icarus,183,508.Zarka,P.2007,Planet.Space Sci.,55,598.。

专利名称：DEVICE AND METHOD FOR COMPENSATING FOR PROPAGATION DELAY发明人：SCHRÖDINGER, Karl申请号：DE2000003097申请日：20000904公开号：WO01/019044P1公开日：20010315专利内容由知识产权出版社提供摘要：The invention relates to a device for compensating propagation differences between n serial data streams (n = 2, 3,...), which are each transmitted over parallel optical lines (1.1 ... 1.n), whereby data (D01.1 ... D01.n) that can be transmitted via the n serial data streams is configured as m-bit words (m = 1, 2, ...). According to the invention, n regeneration devices (2.1 ... 2n) are provided, whereby data (D1.1 ... D1.n) and a clock pulse (C1.1 ... C1.n) of the data stream can be regenerated with the aid of the respective regeneration devices (2.1 ... 2n). A data output and a clock pulse output of the regeneration devices (2.1 ... 2n) are connected to a propagation time control device (5.1 ...5.n) so that the regenerated data (D1.1 ... D1.n) and the regenerated clock pulse (C1.1 ... C1.n) can be transmitted to a data input or to a clock pulse input of the propagation time control devices (7.1 ... 7.n). The propagation time control devices (7.1 ... 7.n) each comprise a demultiplexer for dividing the regenerated data (D1.1 ... D1.n) as well as the regenerated clock pulses (C1.1 ... C1.n) with a ratio of 1:(x•m) (x = 1, 2,...), and each comprise an alignment device for distributing the divided regenerated data (D2.1 ... D2.n) on x•m parallel data outputs (8.1 ... 8.m) of the propagation time control devices (7.1 ... 7.n).申请人：SCHRÖDINGER, Karl地址：DE,DE国籍：DE,DE代理机构：NINNEMANN, Detlef 更多信息请下载全文后查看。

Plant Signaling & Behavior 4:11, 1096-1098; November 2009; © 2009 Landes BiosciencearticLe addeNdum1096 Plant Signaling & Behavior Volume 4 issue 11Key words: Amorphophallus titanum , araceae, thermogenesis, infrared ther-mography, pollination Submitted: 08/18/09Accepted: 08/18/09Previously published online:/journals/psb/article/9872*Correspondence to:WilhelmBarthlott;Email:*********************Addendum to: Barthlott W, Szarzynski J, Vlek P, Lobin W, Korotkova N. A torch in the rain forest: thermogenesis of the Titan arum (Amorphophallus titanum ). Plant Biol 2009; 4:499–505; PMID: 19538388; DOI: 10.1111/j.1438-8677.2008.00147.xThe Titan arum (Araceae) produces the largest bloom of all flowering plants. Its flowering period of two days is divided into a female flowering phase in the first night and a male flowering phase in the second night. Recently, we have documented thermogenesis in the spa-dix of the Titan arum during the female flowering phase. Here, we document a second thermogenic phase in which the male florets are heated during the male flowering phase. Obviously the two noc-turnal thermogenic phases are linked with the two flowering periods. These observations now allow a more detailed understanding of the flowering behavior of the Titan arum.The Titan arum (Amorphophallus tita-num ) is one of the most spectacular flow-ering plants. It has drawn the attention of botanists and naturalists since its discov-ery in 1878. However, the species has been rare in cultivation and flowering events in botanical gardens were even rarer. Besides, flowering events observed in the plant’s nat-ural habitat are very few.1,2 Therefore, the knowledge on A. titanum that depended on exact observations and scientific exper-iments remained very limited. It was only in the late 90s when a monograph on the species, containing anatomical details and some first experimental hypotheses, has been published.1The Botanical Gardens of the University of Bonn (Germany) have been cultivating Amorphophallus titanum for more that 70 years and obtained 14 flow-erings between 1937 and 2009. These regular flowering events have been the prerequisite to study A. titanum in detail. Consequently the data and hypotheses in the monograph mentioned above were gained mainly from the A. titanum plantsin the Botanical Gardens Bonn. As a result of three flowering events in 2006, we have recently documented for the first time, that the inflorescence undergoes thermogen-esis in which the central column (spadix) heats up to 36°C. Meanwhile four addi-tional flowering events yielded additional insights into the flowering behavior of A. titanum .The inflorescence of A. titanum con-sists of a thickened unbranched inflo-rescence axis bearing hundreds of small female and male florets which are spatially separated (Fig. 1A ). The inflorescence axis is extended into an appendix (spadix) and enveloped by a large bract referred to as spathe. The spathe enclosing the florets forms the floral chamber. Since the whole inflorescence functions as a single unit in pollination is often referred to as a bloom or “flower”. A. titanum has two timely sep-arated flowering phases: a female flowering phase during the first evening and night after opening of the spathe and a male flowering phase in the following night.Thermogenesis plays an important role in the pollination ecology of Araceae 3,4 and therefore occurs in many genera.4-7 Similarly in A. titanum , we have reported the thermogenic spadix during the female flowering phase. Based on our observa-tions of now six inflorescences, the heat production is determined and begins around 20 h, the temperature maximum of 36–38°C being reached around mid-night. The duration of heat production differs between individual plants but usually stops between 2 h and 4 h in the morning. The spathe begins to close the next day in the early morning hours or in the forenoon. The opening and closing of the spathe seems to be influenced by the hours of daylight but these might be different in European countries from theOn the thermogenesis of the Titan arum (Amorphophallus titanum )Nadja Korotkova and Wilhelm Barthlott*Nees Institute for Biodiversity of Plants; Bonn, Germany Plant Signaling & Behavior 1097articLe addeNdumarticLe addeNdumambient air temperature (ca. 26°C) around midnight. To test whether the tempera-ture in the floral chamber around the male florets increases while they are heated, we recorded the temperature within the spathe of three intact inflorescences with data loggers (Tinytag, Gemini Data Loggers). However, no warming within the chamber in comparison with ambient air temperature could be measured, so the heated florets seem not to affect the tem-perature within the floral chamber.The flowering behavior of A. titanum is summarised in Figure 2. The carrion-like odor and the thermogenic spadix attract pollinators in the female flowering phase,this, the male florets were made visible by removing a part of the spathe of two flow-ering A. titanum and observed right after opening of the spathe. The beginning of the male flowering phase is easily to deter-mine since the pollen is shed in well visible string-like structures.The pollen dissemination began in the evening around 17:20 h. Thereupon we filmed the male florets with a thermo-graphic camera (Flexcam, GORATEC) taking an image every five minutes. The male florets were clearly thermogenic reaching a temperature maximum of 35.9°C between 18:40 h and 20:00 h (Fig. 1B ). They slowly cooled down to plants native habitat in the tropical rain-forests of Sumatra. The flowering events in Bonn usually take place in summer, the spathe opens during a daytime when it is still very bright and is fully opened when the daylight is decreasing while it is already dark then in the tropics.Some authors have observed heating of the male florets prior to appendix heating in other Araceae species.4,5,8,9 In A. titanum however, we could not find an evidence for this, as stated in our previous article. But a question that still remained open is: when exactly the male flowering phase begins and if there might be thermogenic activityduring the male flowering phase. To study (a) Flash-light photograph of an Amorphophallus titanum flowering zones showing part of the appendix, the male florets and the femaleflorets. (B) Thermographic image taken during the male flowering phase. The male florets are heated to the maximum temperature of 35.9°C whereas the other parts of the plant have largely ambient air temperature of 26°C.Figure 2. Scheme of the flowering behavior ofAmorphophallus titanum over its two-days flowering period. The scheme is idealised but represents observation of seven A. titanum inflorescences that all behave highly similar. Deviations in the time when opening and closing of the spathe begin in individual plants are indicated with a dashed line.1098 Plant Signaling & Behavior Volume 4 issue 11References1. Barthlott W, Lobin W, eds. Amorphophallus titanum .Stuttgart: Franz Steiner Verlag 1998.2. Lobin W, Neumann M, Radscheit M, BarthlottW. The cultivation of Titan arum (Amorphophallus titanum )—A flagship species for botanic gardens. Sibbaldia 2007; 5:69-86.3. Meeuse BJD, Raskin I. Sexual reproduction in thearum lily family, with emphasis on thermogenicity. Sex Plant Reproduct 1988; 1:3-15.4. Skubatz H, Nelson TA, Dong AM, Meeuse BJD,Bendich AJ. Infrared thermography of Arum lily inflorescences. Planta 1990; 182:432-6.5. Albre J, Quilichini A, Gibernau M. Pollination ecol-ogy of Arum italicum (Araceae). Bot J Linn Soc 2003; 141:205-14.6. Gibernau M, Barabe D. Thermogenesis in threePhilodendron species (Araceae) of French Guiana. Can J Bot 2000; 78:685-9.7. Skubatz H, Nelson TA, Meeuse BJD, Bendich AJ.Heat production in the Voodoo Lily (Sauromatum guttatum ) as monitored by infrared thermography. Plant Physiol 1991; 95:1084-8.8. Lamprecht I, Schmolz E, Blanco L, Romero CM.Flower ovens: thermal investigations on heat produc-ing plants. Thermochim Acta 2002; 391:107-18.9. Bermadinger-Stabentheiner E, Stabentheiner A.Dynamics of thermogenesis and structure of epi-dermal tissues in inflorescences of Arum maculatum . New Phytol 1995; 131:41-50.10. Hetterscheid W. Ecology and reproductive biology.In: Barthlott W, Lobin W, eds. Amorphophallus tita-num . Stuttgart: Franz Steiner Verlag 1998; 196-7.11. Seymour RS, White CR, Gibernau M. Heat rewardfor insect pollinators. Nature 2003; 426:243-4.12. Gibernau M. Pollinators and Visitors of AroidInflorescences. Aroideana 2003; 26:73-91.13. Giordano C. Observations on Amorphophallus tita-num (Becc.) Becc. ex Arcangeli in the forest of Sumatra. Aroideana 1999; 22:10-9.14. Dyer AG, Whitney HM, Arnold SEJ, Glover BJ,Chittka L. Behavioural ecology: Bees associate warmth with floral colour. Nature 2006; 442:525.15. Takács S, Bottomley H, Andreller I, Zaradnik T,Schwarz J, Bennett R, et al. Infrared radiation from hot cones on cool conifers attracts seed-feeding insects. Proc Royal Soc B: Biol Sci 2009; 276:649-55.their activity level.11,14 Both may also apply to A. titanum —the insects that have spent the day within the flower chamber may use the heated surface of the male florets to warm themselves up and by this collect pollen or feed on pollen. Still, a verifica-tion of these hypotheses could only come from field observations.To draw a conclusion, the new observa-tions reported here now allow us a good understanding of the flowering behavior of A. titanum . Its two thermogenic phases are clearly linked with the two flowering phases and the plant’s complex interaction with its pollinators.AcknowledgementsWe are grateful to the staff of the Botanical Gardens of the University of Bonn, espe-cially the curator W. Lobin and the gar-deners M. Neumann, A. Schulz and B. Reinken who care for the A. titanum plants with enthusiasm. We thank H. Schmitz (Institut für Zoologie, University of Bonn) for kindly lending us the ther-mographic camera and B.M. Möseler (INRES, University of Bonn) for provid-ing the data loggers. We thank some of our colleagues from the Nees Institute, Bonn for various kinds of assistance: A.-J. Schulte and H. Bohn helped much with the data recording and B.C. Ho provided valuable comments on the manuscript. Financial support from the Academy of Science and Literature, Mainz, Germany is acknowledged.during the first evening and night of the flowering period. Heating of the male florets occurs when no more odor is pro-duced and hence no olfactorical attraction of the pollinators can take place. As a con-sequence, there must be only one attrac-tion time period which is more or less restricted to the female flowering phase and to the nighttime where pollinators can be successfully attracted. The pollina-tors, although not exactly known,10 hence must be active only in these evening hours and at night. Once attracted, the pollina-tors stay inside the inflorescence and most likely use it as mating site or as a place to stay during the following day. It has already been hypothesised that Araceae inflorescences forming floral chambers may offer mating sites or places to rest for insects and rather keep their pollina-tors inside the floral chamber instead of a second attraction phase.11, 12 Numerous insects inside a A. titanum inflorescence have indeed been observed in its natural habitat,13 although the author did not explain these observations, it provides evi-dence for our hypothesis that pollinators spend some time inside the inflorescence.The male florets are heated while pollen is released. There is evidence that at least some insects are able to percept IR light and it has been hypothesised that infrared radiation itself could be an attractant for insects, most likely to locate food sources.15 Floral heat may also be a direct reward for pollinators, helping them increasing their body temperature and thus faster reaching。

文章标题：探索三维非均匀介质波动方程有限差分python开源代码1. 简介在地质勘探、医学成像和地震监测等领域，对三维非均匀介质波动方程的研究与应用日益重要。

而有限差分方法在数值求解波动方程中具有广泛的应用。

在本文中，我们将探讨如何利用Python编程语言实现三维非均匀介质波动方程的有限差分方法，并开源共享相应的代码，以便更多人能够深入理解和应用这一重要领域。

2. 三维非均匀介质波动方程简介三维非均匀介质波动方程描述了波在非均匀介质中的传播规律，是地震勘探、医学成像等领域中常见的数学模型之一。

该方程的数值求解通常采用有限差分方法，通过离散网格化空间和时间来逼近连续的微分方程，从而得到数值解。

3. 有限差分方法有限差分方法是数值求解微分方程的一种常见方法，其基本思想是将微分方程中的导数用差分近似代替，从而将连续的问题转化为离散的问题。

在三维非均匀介质波动方程中，有限差分方法可以有效地模拟波的传播过程，并得到波场的数值解。

4. Python编程实现利用Python编程语言实现三维非均匀介质波动方程的有限差分方法具有许多优势，如简洁易读的代码、丰富的科学计算库等。

在实现过程中，我们可以利用NumPy库进行数组操作，使用Matplotlib库进行波场可视化，并通过SciPy库进行数值求解等。

5. 开源代码共享在本文中，我们将共享我们编写的三维非均匀介质波动方程有限差分Python开源代码，包括空间离散化、时间离散化、边界条件处理、波场更新等关键部分。

我们也会附上详细的注释和使用说明，以便感兴趣的读者能够下载并运行我们的代码，深入理解和学习有限差分方法在波动方程中的应用。

6. 个人观点和理解通过编写三维非均匀介质波动方程的有限差分Python开源代码，我深刻体会到数值模拟在地质勘探、医学成像等领域中的重要作用。

Python作为一种强大的科学计算语言，为我们提供了丰富的工具和库，使得数值模拟变得更加高效和灵活。