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Optical Rotation and Linear and Circular Depolarization Rates in Diffusively Scattered Light from Chiral, Racemic, and Achiral Turbid Media

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Optical Rotation and Linear and Circular Depolarization Rates in Diffusively Scattered Light from Chiral, Racemic, and Achiral Turbid Media Journal of Biomedical Optics 7(3), 291–299 (July 2002) Optical rotation and linear and circular depolarization rates in diffusively scattered light from chiral, racemic, and achiral turbid media Kevin C. Hadley Abstract. The polarization properties of light scattered in a lateral University of Waterloo direction from turbid media were studied. Polarization modulation Department of Chemistry and synchronous detection were used to measure, and Mueller calcu- Waterloo, Ontario N2L 3G1, Canada lus to model and derive, the degrees of surviving linear and circular I. Alex Vitkin polarization and the optical rotation induced by turbid samples. Poly- Ontario Cancer Institute/University of Toronto styrene microspheres were used as scatterers in water solutions con- Departments of Medical Biophysics and taining dissolved chiral, racemic, and achiral molecules. The preser- Radiation Oncology vation of circular polarization was found to exceed the linear Toronto, Ontario M5G 2M9, Canada polarization preservation for all samples examined. The optical rota- tion induced increased with the chiral molecule concentration only, whereas both linear and circular polarizations increased with an in- crease in the concentrations of chiral, racemic, and achiral molecules. This latter effect was shown to stem solely from the refractive index matching mechanism induced by the solute molecules, independent of their chiral nature. © 2002 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.1483880] Keywords: polarization; multiple scattering; chirality; polarization modulation. Paper JBO TP-14 received Mar. 8, 2002; revised manuscript received Mar. 14, 2002; accepted for publication Mar. 31, 2002. 1 Introduction Optical investigations of turbid media that contain chiral 23–31 Many natural and synthetic systems have disordered proper- components have also been reported. The interest in chi- ties that render them optically turbid. Examples abound in ral turbid media is driven by the attractive possibility of non- invasive optical monitoring of the glucose level in diabetic science, technology, medicine, and the natural environment, patients. This is a very difficult unresolved problem in clinical and include such diverse systems as interstellar gases, biologi- medicine and an active area of research that utilizes different cal tissues, turbulent flows, colloidal suspensions, and micro- biomedical optics approaches.32,33 For polarized light re- crystalline solids. Optical examinations of these random me- search, detection of glucose and quantification of its concen- dia are challenging due to extensive multiple light scattering tration rely on the molecule’s chirality that stems from its which scrambles potentially useful sample information en- asymmetric molecular structure, resulting in a number of coded in the light beam. For example, most biological tissues characteristic effects generically called optical activity.34 A ͑ ͒ are highly scattering at visible and near-infrared IR well-known manifestation of optical activity is the ability of a 1 wavelengths, so quantitative tissue spectroscopy and imaging glucose solution to rotate the plane of linearly polarized light are difficult. In recent investigations researchers have at- about the axis of propagation. The amount of rotation depends tempted to utilize the polarization properties of light to probe on the molecular concentration, the pathlength through the biological tissues and other random media, since diffusely medium, and the optical rotatory power at the interrogation scattered light is often partially polarized to an extent that can wavelength.35 This and other chiral asymmetries encoded in be experimentally detected. Several research groups are thus the polarization properties of light transmitted through largely investigating the response of turbid media to polarized light transparent ͑nonscattering͒ media enable very sensitive and by examining the polarization properties of multiply scattered accurate determination of glucose concentrations. With turbid light.2–19 These polarization methodologies have been devel- materials, however, the scattering effects dominate, loss of oped to study various aspects of polarized light interaction polarization information is significant, pathlengths get with turbid media, including the investigation of the depolar- scrambled, and chiral effects stemming from a small amount ization mechanisms, quantification of depolarization length of dissolved glucose are much more difficult to discern. scales, determination of system Mueller matrices, and deriva- We have previously developed polarization modulation tion of the Stokes parameters of scattered light. In several and synchronous detection methods to measure surviving po- recent publications polarization imaging studies of multiply larization fractions in diffusive scattering even in the presence scattering media were described.6,11,20–22 of large noisy depolarized backgrounds, such as in the case of synthetic turbid media25,27,28,30,31 and ex vivo28 and in vivo Address all correspondence to I. Alex Vitkin.Tel: 416-946-4501, Ext. 5742; Fax: 416-946-6529; E-mail: [email protected] 1083-3668/2002/$15.00 © 2002 SPIE Journal of Biomedical Optics ᭹ July 2002 ᭹ Vol. 7 No. 3 291 Hadley and Vitkin Fig. 1 Schematic of the apparatus for measuring degrees of polarization and optical rotation of scattered light. Arrangement B is shown. In arrangement A, the quarter wave plate is removed. biological tissues.31 Furthermore, we have experimentally ob- where the equality holds for fully polarized light, and the served chiral asymmetries due to the presence of glucose. inequality applies to partially polarized light. The total degree Both varied the level of polarization preservation and the ro- of polarization ͑DOP͒ is defined as tation of linearly polarized light fraction varied with glucose concentrations in the turbid samples.25,27,28,30 Q2ϩU2ϩV2 DOP ϭͱ . ͑3͒ In comparing turbid microsphere suspensions with and T I2 without chiral molecules, depolarization was diminished in the former case both in the lateral and backscattering direc- The linearly polarized fraction is represented by the degree of tions, although the mechanism responsible for this polariza- linear polarization, tion enhancement effect was not determined. In this paper, we 2 2 extend our methodology to perform this determination. Spe- Q ϩU DOP ϭͱ . ͑4͒ cifically, we analyze the polarization characteristics of later- L I2 ally scattered light from chiral, racemic ͑equal amounts of The degree of circular polarization is similarly defined as oppositely handed isomers͒, and achiral solutions that contain scattering polystyrene microspheres in an effort to determine V2 whether the chirality or the refractive index matching mecha- ϭͱ ͑ ͒ DOPT 2 . 5 nism is the dominant cause of preservation of the enhanced I polarization. We also develop methods to explicitly derive Of interest in the current study were the linear and circular linear and circular degrees of polarization, and compare these depolarizations that occurred due to multiple scattering within depolarization rates in microsphere suspensions. Finally, the the turbid sample and the optical rotation of the linearly po- dependence of optical rotation of the linearly polarized light larized light that may be induced by the chirality of the me- fraction on the chirality of the turbid medium is quantified. dium. The sample was thus illuminated with a polarized light beam whose incident polarization varied in a time-dependent, controlled fashion. Upon diffusive interactions with the scat- 2 Theory tering medium, the surviving polarization properties of the Light of any arbitrary polarization state may be represented light were detected at 90°, synchronously with the incident by a Stokes vector ͑S͒ of the form polarization modulation. The surviving linear and circular po- ␤ ␤ larization fractions, L and C , respectively, are defined in I terms of the incident ͑subscript i͒ and scattered ͑subscript s͒ Q polarization states as ͫ ͬ , ͑1͒ U DOP ␤ ϭ L,s ͑ ͒ V L , 6 DOPL,i where I represents the total light intensity, Q and U represent the linearly polarized components of the beam, and V repre- DOP ␤ ϭ C,s ͑ ͒ sents the circularly polarized component. The intensity I is C . 7 directly measurable with a photodetector. For an arbitrary DOPC,i light beam, these terms are related by The layout of optical elements is schematically presented in Figure 1. There were two experimental arrangements em- I2уQ2ϩU2ϩV2, ͑2͒ ployed for this study that differed in the analyzing elements 292 Journal of Biomedical Optics ᭹ July 2002 ᭹ Vol. 7 No. 3 Optical Rotation and Linear and Circular Depolarization Rates... placed between the sample and the detector. In arrangement the light incident on the sample has the following Stokes vec- A, the analyzing optics consisted of a linear polarizer ͑ana- tor lyzer͒ with pass axis ␪ ° to the horizontal plane. Positive angles indicate rotation of the analyzer counterclockwise as 1 one looks down the beam in the direction of its propagation. 0 ͫ ͬ , This arrangement was useful for determining the optical rota- cos ␦͑t͒ ␣ ␤ tion and the degree of linear polarization L . To extract the sin ␦͑t͒ degree of circular polarization ␤ , arrangement B was em- C ␦(t) is the retardation of the PEM as a function of time, ployed, which included a quarter wave plate with its fast axis where ␦ϭ␦ sin(2␲ft). ␦ is the maximum retardation im- 45° to the horizontal placed between the sample and the linear
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