The application of a rotating-wave-plate stokes polarimeter for measurement

The application of a rotating-wave-plate stokes polarimeter for measurementof the optical rotation angleJing-Fung Lin a,Ã,Jyh-Shyang Wu b,Cong-Hui Huang c,Te-Tan Liao d,Chih-Chao Chang da Department of Computer Application Engineering,Far East University,No.49,Jhonghua Road,Hsin-Shih Township,Tainan County744,Taiwanb Department of Energy Application Engineering,Far East University,No.49,Jhonghua Road,Hsin-Shih Township,Tainan County744,Taiwanc Department of Automation and Control Engineering,Far East University,No.49,Jhonghua Road,Hsin-Shih Township,Tainan County744,Taiwand Graduate School of Mechanical Engineering,Far East University,No.49,Jhonghua Road,Hsin-Shih Township,Tainan County744,Taiwana r t i c l e i n f oArticle history:Received16May2009Accepted2October2009Keywords:Chiral mediumCircular birefringenceOptical rotationStokes parametersa b s t r a c tAn optical scheme based on Stokes–Mueller formalism and rotating-wave-plate Stokes polarimeter issuccessfully developed to measure the optical rotation angle in a chiral medium.The average relative errorin the measured rotation angle of a half-wave plate is determined to be1.16%.The average relative error inthe measured rotation angles of glucose solutions with concentrations ranging from0to 1.2g/dl isdetermined to be3.78%.The correlation coefficient between the measured rotation angle and the glucoseconcentration is found to be0.99950,while the standard deviation is just0.003761.From the inspection ofmeasured rotation angle in the sol–gel materials containing C17H17ClO6with concentrations ranging from0to0.0665g/ml,the average relative error in the measured rotation angles is determined to be3.63%.Consequently,the derived algorithm for measuring the rotation angle of a chiral medium is feasible,and thedeveloped system is evaluated with a precision of5.4%approximately in rotation angle measurement.&2010Elsevier GmbH.All rights reserved.1.IntroductionCertain optical media are found to cause a rotation of the planeof polarization of linearly polarized light passing through them.This phenomenon is known as optical activity or circularbirefringence and wasfirst observed in quartz[1].It has beenknown that the circular birefringence(polarization rotation angle)arises from either individual molecules exhibiting chirality(handness)such as glucose in solution,or from a chiral structureof the material such as quartz crystal.Owing to development ofnanotechnology and diverse applications such as optical sensingof glucose concentration and chirality detection in nanograting,the precise measurement of circular birefringence is increasinglyimportant.In the past rotation angle measurement systems,a successfuloptical method and apparatus has been developed and names as ahigh accuracy universal polarimetry(HAUP).The apparatus isbased on a least-squares refinement of the transmitted lightintensity as a function of the azimuth angles of the polarizer andthe analyzer[2].It is has been known that the disadvantage of thetraditional polarimetric system is that the resolution and accuracyof the rotation measurement is limited by the polarizer and themechanical limitations of mounting stage.In1997,Cameronand Co´te[3]designed the glucose sensing digital closed-loopprocessing system.This measurement system is also based on thecommon-path heterodyne interference technique.It utilizesFaraday rotators(FR)for both modulation and compensation.This method uses a closed loop processing system and lock-inamplifier to obtain the rotation angle of the glucose.This systemrequires the use of a feedback mechanism in order to reduce thesystem instability of FR modulator.In2004,Lin et al.[4]proposed a heterodyne Mach–Zehnderinterferometer to enhance the measurement resolution about to6Â10À5degrees.However,Lin’s optical configuration and theassociated algorithm are more complicated.In2006,Lo and Yu[5]adopted a liquid-crystal(LC)modulator to modulate the azimuthof the linearly polarized light in a sinusoidal signal and developeda new signal-processing algorithm for the measurement ofglucose concentrations.The standard deviation in rotation anglelevel of0.005511has been obtained,with a0.998773correlationcoefficient between the reference and the measured values.Thesensing system is capable of measuring minimum glucoseconcentration of0.2g/dl.However,the LC modulator has thedrawback of slow frequency response[5].In2008,Lin[6]proposed a metrology system for simultaneously measuring theoptical rotation angle and retardance via a linearly probe lightspolarized at451.Further,Lin[7]presented a technique forobtaining concurrent measurements of the linear and circularbirefringence properties of an optical sample by using a rotating-wave-plate Stokes polarimeter to extract the2Â2centralContents lists available at ScienceDirectjournal homepage:www.elsevier.de/ijleoOptik0030-4026/$-see front matter&2010Elsevier GmbH.All rights reserved.doi:10.1016/j.ijleo.2009.10.003ÃCorresponding author.Fax:+88665977510.E-mail address:jacklin@.tw(J.-F.Lin).Optik122(2011)14–19elements of the corresponding Mueller matrix via two linearly polarized probe lights.Recently,Lin et al.[8]propose a new electro-optic modulated circular heterodyne interferometer and use a phase-lock technique to measure the rotation angle directly and precisely.In the proposed optical scheme for intentionally measuring the optical rotation angle,we use a linearly polarized input light of 451incident on the three measured samples,i.e.,a half-wave plate,glucose solutions,and specific sol–gel materials containing griseofulvin,respectively.The Stokes parameters of the output light are detected by a commercial rotating-wave-plate Stokes polarimeter.Consequently,the algorithm for obtaining the rotation angle is derived successfully,and the developed system using Stokes–Mueller formalism and rotating-wave-plate Stokes polarimeter is capable of measuring the optical rotation angle corresponding to the concentrations of glucose and griseofulvin in sol–gel samples,respectively.2.Methodology 2.1.Optical configurationThe optical configuration for measuring the optical rotation angle is shown in Fig.1.The measurement system consists of a light source,polarizer,sample,and a Stokes polarimeter.A He–Ne laser with wavelength 632.8nm is employed as the light source.The polarization condition of incident beam is controlled to be linear by a polarizer.After this initial beam passes through polarizer with 451to the horizontal plane and sample,it is given the change of polarization state.The change in the polarization condition of the transmitted beam from the sample is monitored by measuring the Stokes parameters with a rotating-wave-plate Stokes polarimeter (Thorlabs,PA510).Subsequently,the optical rotation angle is estimated by substituting the observed Stokes parameters of output light into the derived algorithm.2.2.PrincipleThe polarization state of light can be completely described by aStokes vector S ¼S 0;S 1;S 2;S 3ÈÉT(where T denotes transpo-sition).We can write the four Stokes components as S ¼S 0S 1S 2S 3266664377775¼I x þI y I x ÀI y I 453ÀI À453I L ÀI R266664377775;ð1Þwhere S 0is the total light intensity,S 1represents the intensity difference between horizontal and vertical linearly polarized components,S 2represents the intensity difference between linearly polarized components oriented at 7451angle,and S 3represents the intensity difference between right and left circular components.A polarizer oriented horizontally (x ),vertically (y ),or at 7451would let light pass through with intensity I x/y or I 451/À451,whereas a quarter-wave plate followed by a polarizer oriented at 7451with respect to the slow axis of the wave plate would transmitI L/R as the intensity of left and right components of circular polarization.An optic that changes the polarization state of light is modeled by a Mueller matrix (4Â4)such that the inner product of theStokes vector that models the polarization state of incident light ^Swith the Muller matrix that models that optics M results in a Stokes vector that represents the polarization state of light exiting the optic S [9].According to the Stokes–Mueller formalism,the output light S is calculated byS ¼S 0S 1S 2S 3266664377775¼m 1;1m 1;2m 1;3m 1;4m 2;1m 2;2m 2;3m 2;4m 3;1m 3;2m 3;3m 3;4m 4;1m 4;2m 4;3m 4;4266664377775^S 0^S 1^S 2^S 3266664377775¼M ^S:ð2ÞThe Mueller matrix for a sample with the optical rotation angle,g ,and the retardance,b ,such as a half-wave plate,is expressed as Eq.(3).When the retardance,b ,in a perfect half-wave plate is 1801,the half-wave plate can be considered as a kind of chiral medium,and hence the Mueller matrix for a half-wave plate seen as a chiral medium with undetermined rotation angle [10]is given as Eq.(4).It is noted that the Mueller matrix for a chiral medium is given as Eq.(5),which is different from Eq.(4)for a half-wave plate.andM l =2;b ¼1800¼10000cos ð2g Þsin ð2g Þ00sin ð2g ÞÀcos ð2g Þ00À12666437775;ð4ÞandM ch ¼10000cos ð2g Þsin ð2g Þ00Àsin ð2g Þcos ð2g Þ0012666437775:ð5ÞCalculating the right side of Eq.(2)using the expressions for M l =2;b ¼1800and M ch in Eqs.(4)and (5),respectively,and gives asS l =2¼S 0S 1S 2S 3266664377775l =2¼M l =2Àb ¼1800^S ¼10000cos ð2g Þsin ð2g Þ00sin ð2g ÞÀcos ð2g Þ0000À12666437775^S 0^S 1^S 2^S 3266664377775;ð6ÞHe-Ne LaserPolarizer 45oYZDetectorPolarimeter & PCGlucose or Griseofulvin`Fig.1.Experimental setup for measurement of the optical rotation angle.M l =2¼10cos ð2g Þsin 2ðb =2Þþcos 2ðb =2Þsin ð2g Þsin 2ðb =2ÞÀsin ðg Þsin ðb Þ0sin ð2g Þsin 2ðb =2ÞÀcos ð2g Þsin 2ðb =2Þþcos 2ðb =2Þcos ðg Þsin ðb Þ0sin ðg Þsin ðb ÞÀcos ðg Þsin ðb Þcos ðb Þ66664377775;ð3ÞJ.-F.Lin et al./Optik 122(2011)14–1915andS CB ¼S 0S 1S 2S 3266664377775CB¼M CB ^S ¼10000cos ð2g Þsin ð2g Þ00Àsin ð2g Þcos ð2g Þ0012666437775^S 0^S 1^S 2^S 3266664377775:ð7ÞFor input polarization condition is chosen a linear polarizationlight at 451direction,i.e.,^S 453¼1;0;1;0ÈÉT ,The Stokes parameters of the output light are expressed,respectively,as Eq.(8),and the optical rotation angle for a half-wave plate can be determined as Eq.(9)S 0¼1;S 1¼sin ð2g Þ;S 2¼Àcos ð2g Þ;S 3¼0;ð8Þandg ¼12tan À1ðS 1ÀS 2Þ:ð9ÞFurther,we can deliberately choose the output Stokes para-meters S 1and S 2for a chiral medium in Eq.(7),combine to give S 1S 2"#CB¼^S1^S 1À^S1^S 2"#sin 2g cos 2g "#;ð10Þwhich can be solved for tan(2g )by applying Cramer’s rule,and the optical rotation angle can be determined fromg ¼12ta n À1ðÀS 2^S1þS 1^S 2S 1^S1þS 2^S 2Þ:ð11ÞFor input polarization condition is chosen a linear polarizationlight at 451direction,i.e.,^S 453¼1;0;1;0ÈÉT ,the optical rotation angle can be determined asg ¼1tan À1S 12:ð12ÞTherefore,the expression in Eq.(12)can be applied to Stokes vectors measured with a Stokes polarimeter to determine the optical rotation angle of a chiral medium.Noted that the rotation angle can be determined from an arctangent function of the ratio of the Stokes parameter,S 1,to the Stokes parameter,S 2,and the measurement range can be Àp /2r g r p /2,and the measured rotation angle is independent of the actualStokes parameter,^S2,when the input linear polarization light is at 451.The correlation between the glucose concentration of a liquid solution and the rotation of the polarization plane of the measurement light beam as it passes through the sample is given by C ¼100gL ½g;ð13Þwhere C is the glucose concentration expressed in grams per deciliter of solution,g is the rotation angle of the polarization plane,L is the sample path length in decimeters,and [g ]is the specific rotation angle of glucose and is determined by the temperature under which the measurement process is performed,the wavelength of the measurement laser beam,and the pH level of the sample solution.2.3.Uncertainty analysisAccording to [11],using the Eq.(12)derived for the rotation angle measurement of a chiral medium,the measurement errord g in Eq.(12)is,d g ¼12ðS 1þS 2ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS 22d S 21þS 21d S 22q ¼12ð1ÀS 3ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS 22d S 21þS 21d S 22q ;ð14Þwhere d S 1and d S 2are the errors in the measurement of the Stokes parameters S 1and S 2of the output polarization state.SinceS 21þS 22þS 23¼1,the Stokes parameters S 1,S 2,and S 3in Eq.(14)correspond also to the output polarization state.Eq.(14)indicates us that the value measured for rotation angle,g ,grows unbounded and has a poor precision for light becoming circularly polarized when S 3¼71:ð15ÞThe Stokes polarimeter we used in this study is based on the rotating wave retarder technique,the simplest of a class of techniques for measuring the four-element of Stokes vector,in which the unknown polarization state of the radiation under measurement can be a time modulated [12].The classification of Stokes vector measurement technique and comparisons of performances between rotating polarizer and rotating retarder plate polarimeter is presented in Ref.[13].3.Experimental setup and results 3.1.Preparation of samplesIn this study,three kinds of samples such as a half-wave plate,glucose solutions,and sol–gel materials containing griseofulvin are prepared.The half-wave plate was available from market.The glucose samples were prepared from a 60mg/ml stock glucose solution produced by dissolving 6g of D-glucose (Merck Ltd.)in a total volume of 100ml of de-ionized water.Individual glucose samples with concentrations ranging from 0to 1.2g/dl in increments of 0.2g/dl were then prepared by diluting the stock solution with an appropriate volume of de-ionized water.The individual samples were injected into 50mm long sample cells and were then introduced into the optical measurement system one-by-one in order to measure their rotational angles.We use the sol–gel method to fabricate the chiral solid sample containing griseofulvin (C 17H 17ClO 6)according to the procedure of fabrication found in Ref.[14].Firstly,2g of griseofulvin (C 17H 17ClO 6)and 20ml N,N-dimethyl formamide dimethyl acetal (C 3H 7NO)are mixed and stirred for $30min with a magnetic power stirrer.Secondly,1g of benzoyl peroxide (C 14H 10O 4)and $10ml methyl methacrylate (CH 2C(CH 3)COOCH 3)are mixed and stirred for 10min.Thirdly,the two mixtures are mixed and stirred about 30min.The transparent chiral solution can be made.The solution is poured into a 52Â12.5Â45mm 3cell with lid,the transparent length of which is 50mm.They are sealed up and put in the oven at 401C for 1week.The procedure for fabricating the chiral solid sample is illustrated in Fig.2.3.2.Experimental setupThe experimental setup comprised a He–Ne laser (Spectra-Physics,Model 117A)with an output power of 1mW and a wavelength of 632.8nm,a Glan–Thompson-type polarizer with extinction ratios of 5Â10À6,and a Stokes polarimeter.The four Stokes parameters of output light were simultaneously measured by a rotating-wave-plate Stokes polarimeter (Thorlabs PA510)with accuracy of degree of polarization of 71%at a calibration wavelength.During the calibration routine various system parameters of Stokes polarimeter are characterized.Preparing input polarization states,including a linear state of polarization and an elliptical,J.-F.Lin et al./Optik 122(2011)14–1916near circular,state of polarization,and prior to initializing the calibration routine will facilitate the calibration process.Hence,these experimental parameters are as follows.The angle between the defined horizontal and the transmission axis of linear analyzer is À6.971,the angle between the defined horizontal and the fast axis of the quarter-wave plate is À6.971,the retardance of the quarter-wave plate at the operating wavelength is 89.551,and the electronic offset voltage of the detection circuit is À0.007V.Noted that calibration procedure is required to assure the initial angular position of quarter-wave plate,the procedure should be performed every time [13].3.3.Experimental resultsFirstly,the verification experiment was performed using a commercial half-wave plate (Casix Inc.,USA;Model WPF1225-633-l /2)as a chiral medium.In the verification experiment,the rotation angle was measured as the principal angle of the half-plate was rotated through a full 1801in increments of 51.The Stokes vector before the sample is [1,0.001,0.999,0]T .The corres-ponding results are presented in Fig.3,which are calculated by Eq.(9).The correlation coefficient of 0.999989confirms that the metrology system has a high linear response.Moreover,the average relative error in the measured optical rotation is determined to be just 1.16%[6].Secondly,the metrology system was employed to measure the optical rotation angles of glucose samples with known concentra-tions ranging from 0to 1.2g/dl in increments of 0.2g/dl.The Stokes vector after polarizer set at 451is measured as ^S453¼1;È0;0:997;0:001g T ,whereas the Stokes vector after sample cell (no glucose solutions)is measured as S cell ¼1;0;0:996;0:025ÈÉT .Fig.4presents the experimental results obtained for the relationship between the rotation angle and the glucose concentration at atemperature of 221C.From inspection,the correlation coefficient is found to be 0.99950,while the standard deviation is just 0.003761.According to Wang [15],a 0.2g/dl glucose solution has a rotation angle of 0.05271when at a temperature of 201C,the average relative error in the measured rotation angle is determined to be 3.78%.When compared with Refs.[5,8],the correlation coefficient is higher than those in Refs.[5,8],while the standard deviation is lower than those in Refs.[5,8].To verify the repeatability of the measurement system for measuring rotation angle,the rotation angle of a glucose sample with a concentration of 0.2g/dl was measured 10times.From the results of Fig.5,a standard deviation,s ,of 2.77Â10À5degrees and the average value of 0.05731are observed in g ,which leads to a 1s value of 0.05%of the average.The corresponding results presented in Fig.5confirm that the proposed system has high repeatability characteristics.According to Ref.[15],the average relative error in measured rotation angle of glucose sample with a concentration of 0.2g/dl is 8.80%.If the estimated uncertainty of Stokes parameters S 1ÀS 3is 0.0001,respectively,and substituting the parameters of the output Stokes vector,S ¼1;0;0:997;0:001ÈÉTregarding toglucose with a concentration of 0.2g/dl,into Eq.(14)for measured rotation angle error,the measurement error of rotation angle is determined to be 0.0028651.Therefore,the system has an estimated precision of 5.44%in rotation angle measurement.Considering the empirical precision requirement of 1/10–1/3,the developed system has excellent precision in rotation angle measurement.Thirdly,the metrology system was employed to measure the optical rotation angles of solid chiral samples with known concentrations of griseofulvin (C 17H 17ClO 6)molecule.The sol–gel samples containing C 17H 17ClO 6were fabricated according to Fig.2.Individual sol–gel samples containing C 17H 17ClO 6with concentrations ranging from 0to 0.0665g/ml in increments ofFig.2.Fabrication of the sol–gel material containinggriseofulvin.60120180240300360420Optical Rotation (deg.)M e a s u r e d O p t i c a l R o t a t i o n (d e g .)Fig.3.Variation of measured rotational angle (sample:half-waveplate).0.000.050.100.150.200.250.300.35Glucose Concentration (g/dl)M e a s u r e d R o t a t i o n A n g l e (d e g .)Fig.4.Variation of rotation angle with glucose concentration (sample:glucosesolution).0.057170.057220.057270.057320.057370.057420.05747Measurement TimesM e a s u r e d R o t a t i o n A n g l e (d e g .)Fig.5.Measurement repeatability test (sample:glucose solution with concentra-tion of 0.2g/dl).J.-F.Lin et al./Optik 122(2011)14–19170.0133g/ml were then prepared.The individual samples were filled into 50mm long sample cells and were then introduced into the optical measurement system one-by-one in order to measure their rotational angles.The Stokes vector after polarizer set at 451is measured as ^S 453¼1;0;0:999;0ÈÉT,whereas the Stokes vector after empty sample cell is measured as S cell ¼1;0;0:996;0:032ÈÉT .Fig.6presents the experimental results obtained for the relationship between the rotation angle and the griseofulvin concentration at a temperature of 221C.From inspection,the correlation coefficient is found to be 0.99965,while the standard deviation is 0.12681.According to Ref.[16],the specific rotation of the griseofulvin is 3521–3671when at a temperature of 201C,the average relative error in the measured rotation angle is determined to be 3.63%.Moreover,for the sample with minimum concentration of 0.0133g/ml,the average relative error in the measured rotation angle is determined to be 4.36%.The apparatus of Fig.7was used to measure the optical polarization property of the sol–gel material containing C 17H 17ClO 6with a concentration of 0.0665g/ml.The optical configuration of Fig.7is composed of a laser,sample,polarizer,and a powermeter.The polarizer is rotated from À20to 1601.The experimental results are illustrated in Fig.8.From inspection,the rotation angles shift more for the sample than without the sample,and the measured rotation angle is 111.Moreover,the same sample is measured to be 11.581by the optical configuration of Fig.1and derived algorithm.The measured rotation angle is close to 111measured by Fig.7.According to Ref.[16],a sol–gel material containing C 17H 17ClO 6of 0.0665g/ml has a rotation angle of 11.701when measured at a temperature of 201C using a laser beam with a wavelength of 633nm,therefore,the average relative error in measured rotation angle ofsol–gel24681012Griseofulvin Concentration (g/ml)M e a s u r e d R o t a t i o n A n g l e (d e g .)Fig.6.Variation of rotation angle with chiral griseofulvin concentration (sample:griseofulvin sol–gel).Analyzer0~180°YZIFig.7.The apparatus used to measure the optical polarization property of the sol–gelmaterial.20406080100-20020406080100120140160Polarizer Angle (deg.)I nt e n s i t y ( w )Fig.8.Experimental results of the optical polarization property of sol–gel material containing C 17H 17ClO 6with a concentration of 0.0665g/ml via a configuration composed of analyzer and powermeter.Fig.9.Infrared absorption spectra (a)sol–gel material matrix,(b)chiral sol–gel material containing C 17H 17ClO 6,and (c)the chiral molecule C 17H 17ClO 6.J.-F.Lin et al./Optik 122(2011)14–1918material containing C 17H 17ClO 6of 0.0665g/ml is 1.06%.Further,compared with Ref.[17],the measured rotation angle of 11.581is close to 81or 9.31measured by two optical configurations in Ref.[17].However,the difference might be resulted from that the two optical configurations in Ref.[17]are different from the developed system illustrated in Fig.1,and there is no information about temperature in Ref.[17].Furthermore,we use a Fourier transform infrared spectroscopy (Thermo,USA;NICOLET 5700)to measure infrared absorption spectra of sol–gel material matrix,chiral sol–gel material contain-ing C 17H 17ClO 6,and the chiral molecule C 17H 17ClO 6,respectively,and to find out which state the chiral molecule may be in organic glass.In Fig.9(a),a absorption peak can be found at 1450cm À1for sol–gel matrix,while in Fig.9(b),four absorption peaks can be found at 1610,1590,1470,and 1410cm À1for chiral sol–gel material containing C 17H 17ClO 6.In Fig.9(c),four absorption peaks can be found at 1620,1590,1430,and 1350cm À1for the chiral molecule C 17H 17ClO pared Fig.9(a)with (b),two absorption peaks at 1610and 1590cm À1are found in (b),while are not found in (a)in feature region (4000À1333cm À1).If compared Fig.9(b)with (c),their absorption peaks are close to each other and there is no obvious red shift or blue shift.Therefore,it can be found that the chiral molecules fill in the pore of network structure in organic glass and hardly link with host.It is noted that the experimental results are consistent with the relative results in Refs.[17,18].Finally,we use a UV–VIS spectrophotometer (Shimadzu,Japan;MPC-2200)to measure the absorbance spectrum of the sol–gel material matrix and the sol–gel material containing C 17H 17ClO 6,respectively.Experimental results of the absorbance spectrum are shown as in Fig.10.It can be found there is small absorbance for the sol–gel material containing C 17H 17ClO 6in wavelength range of 400–700nm.So,the so–gel material containing C 17H 17ClO 6is suitable for the use in this band of wavelength.4.ConclusionsAn optical scheme based on Stokes–Mueller formalism and rotating-wave-plate Stokes polarimeter is successfully developed to measure the optical rotation angle of a half-wave plate,glucose solutions,and sol–gel materials containing C 17H 17ClO 6,respectively.The optical structure is composed of a polarizer,sample,and a Stokes polarimeter.The incident linear polarized light is at 451,and the output Stokes vector is measured by a Stokes polarimeter (Thorlabs,PA510),which can measure four Stokes parameters of light simultaneously.Experimental results show that the average relative error in rotation angle of 1.16%has been determined for a half-wave plate,with a correlation coefficient of 0.999989indicates a good linearresponse.Besides,the standard deviation in rotation angle level of 0.003761has been obtained for glucose solutions with concentra-tions ranging from 0to 1.2g/dl,with a correlation coefficient of 0.99950between the measured rotation angle and the glucose concentration.The average relative error in the measured rotation angle is determined to be 3.78%.When compared with previous studies [5,8],the correlation coefficient is higher and the standard deviation is lower.Moreover,from the inspection of sol–gel materials containing C 17H 17ClO 6with concentrations ranging from 0to 0.0665g/ml,the average relative error in the measured rotation angles is determined to be 3.63%.The correlation coefficient between the measured rotation angle and the C 17H 17ClO 6concentration is found to be 0.99965,while the standard deviation is 0.12681.In conclusions,the derived algorithm for measuring the optical rotation angle of a chiral medium is feasible.The developed system is evaluated with an excellent precision of 5.4%approximately in rotation angle measurement.Above all,the proposed system could be an alternative in the rotation angle measurement.AcknowledgementThis research was partially supported by the National Science Council of Taiwan,Republic of China,under contract number 96-2221-E-269-026-CC3.References[1]A.Yariv,P.Yeh,Optical Waves in Crystal,John Wiley and Sons,New Jersey,2003,pp.94.[2]J.Kobayashi,Y.Uesu,A new optical method and apparatus HAUP formeasuring simultaneously optical activity and birefringence of crystals:principles and construction,Applied Crystallography 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