Circular polarization memory effect in low-coherence enhanced backscattering of light

Exploring the evolution of circular polarized light backscattered from turbid tissue-like disperse medium utilizing generalized Monte Carlo modeling approach with a combined use of Jones and Stokes-Mueller formalisms

Significance

Phase retardation of circularly polarized light (CPL), backscattered by biological tissue, is used extensively for quantitative evaluation of cervical intraepithelial neoplasia, presence of senile Alzheimer's plaques, and characterization of biotissues with optical anisotropy. The Stokes polarimetry and Mueller matrix approaches demonstrate high potential in definitive non-invasive cancer diagnosis and tissue characterization. The ultimate understanding of CPL interaction with tissues is essential for advancing medical diagnostics, optical imaging, therapeutic applications, and the development of optical instruments and devices.

Aim

We investigate propagation of CPL within turbid tissue-like scattering medium utilizing a combination of Jones and Stokes-Mueller formalisms in a Monte Carlo (MC) modeling approach. We explore the fundamentals of CPL memory effect and depolarization formation.

Approach

The generalized MC computational approach developed for polarization tracking within turbid tissue-like scattering medium is based on the iterative solution of the Bethe-Salpeter equation. The approach handles helicity response of CPL scattered in turbid medium and provides explicit expressions for assessment of its polarization state.

Results

Evolution of CPL backscattered by tissue-like medium at different conditions of observation in terms of source-detector configuration is assessed quantitatively. The depolarization of light is presented in terms of the coherence matrix and Stokes-Mueller formalism. The obtained results reveal the origins of the helicity flip of CPL depending on the source-detector configuration and the properties of the medium and are in a good agreement with the experiment.

Conclusions

By integrating Jones and Stokes-Mueller formalisms, the combined MC approach allows for a more complete representation of polarization effects in complex optical systems. The developed model is suitable to imitate propagation of the light beams of different shape and profile, including Gaussian, Bessel, Hermite-Gaussian, and Laguerre-Gaussian beams, within tissue-like medium. Diverse configuration of the experimental conditions, coherent properties of light, and peculiarities of polarization can be also taken into account.

Discriminating turbid media by scatterer size and scattering coefficient using backscattered linearly and circularly polarized light

The effects of scatterer size and scattering coefficient on backscattered linearly and circularly polarized light are investigated through Stokes polarimetry. High-SNR polarization modulation/synchronous detection measurements are corroborated by polarization-sensitive Monte Carlo simulations. Circular degree of polarization (DOP) is found to be sensitive to scatterer size, but is equivocal at times due to helicity flipping effects; linear DOP appears to be mostly dependent on the medium scattering coefficient. We exploit these trends to generate a DOP_C - DOP_L response surface which clusters turbid samples based on these medium properties. This work may prove useful in biomedicine, for example in noninvasive assessment of epithelial precancer progression.

Role of scattering and birefringence in phase retardation revealed by locus of Stokes vector on Poincaré sphere

SIGNIFICANCE

Biological tissues are typically characterized by high anisotropic scattering and may also exhibit linear form birefringence. Both scattering and birefringence bias the phase shift between transverse electric field components of polarized light. These phase alterations are associated with particular structural malformations in the tissue. In fact, the majority of polarization-based techniques are unable to distinguish the nature of the phase shift induced by birefringence or scattering of light.

AIM

We explore the distinct contributions of scattering and birefringence in the phase retardation of circularly polarized light propagated in turbid tissue-like scattering medium.

APPROACH

The circularly polarized light in frame of Stokes polarimetry approach is used for the screening of biotissue phantoms and chicken skin samples. The change of optical properties in chicken skin is accomplished by optical clearing, which reduces scattering, and mechanical stretch, which induces birefringence. The change of optical properties of skin tissue is confirmed by spectrophotometric measurements and second-harmonic generation imaging.

RESULTS

The contributions of scattering and birefringence in the phase retardation of circularly polarized light propagated in biological tissues are distinguished by the locus of the Stokes vector mapped on the Poincaré sphere. The phase retardation of circularly polarized light due to scattering alterations is assessed. The value of birefringence in chicken skin is estimated as 0.3  ×  10^-3, which agrees with alternative studies. The change of birefringence of skin tissue due to mechanical stretch in the order of 10^-6 is detected.

CONCLUSIONS

While the polarimetric parameters on their own do not allow distinguishing the contributions of scattering and birefringence, the resultant Stokes vector trajectory on the Poincaré sphere reveals the role of scattering and birefringence in the total phase retardation. The described approach, applied independently or in combination with Mueller polarimetry, can be beneficial for the advanced characterization of various types of malformations within biological tissues.

Asymptotic theory of circular polarization memory

We establish a quantitative theory of circular polarization memory, which is the unexpected persistence of the incident circular polarization state in a strongly scattering medium. Using an asymptotic analysis of the three-dimensional vector radiative transfer equation (VRTE) in the limit of strong scattering, we find that circular polarization memory must occur in a boundary layer near the portion of the boundary on which polarized light is incident. The boundary layer solution satisfies a one-dimensional conservative scattering VRTE. Through a spectral analysis of this boundary layer problem, we introduce the dominant mode, which is the slowest-decaying mode in the boundary layer. To observe circular polarization memory for a particular set of optical parameters, we find that this dominant mode must pass three tests: (1) this dominant mode is given by the largest, discrete eigenvalue of a reduced problem that corresponds to Fourier mode k=0 in the azimuthal angle, and depends only on Stokes parameters U and V; (2) the polarization state of this dominant mode is largely circular polarized so that |V|≫|U|; and (3) the circular polarization of this dominant mode is maintained for all directions so that V is sign-definite. By applying these three tests to numerical calculations for monodisperse distributions of Mie scatterers, we determine the values of the size and relative refractive index when circular polarization memory occurs. In addition, we identify a reduced, scalar-like problem that provides an accurate approximation for the dominant mode when circular polarization memory occurs.

Depth-resolved measurements with elliptically polarized reflectance spectroscopy

The ability of elliptical polarized reflectance spectroscopy (EPRS) to detect spectroscopic alterations in tissue mimicking phantoms and in biological tissue in situ is demonstrated. It is shown that there is a linear relationship between light penetration depth and ellipticity. This dependence is used to demonstrate the feasibility of a depth-resolved spectroscopic imaging using EPRS. The advantages and drawbacks of EPRS in evaluation of biological tissue are analyzed and discussed.

Polarized light interaction with tissues

This tutorial-review introduces the fundamentals of polarized light interaction with biological tissues and presents some of the recent key polarization optical methods that have made possible the quantitative studies essential for biomedical diagnostics. Tissue structures and the corresponding models showing linear and circular birefringence, dichroism, and chirality are analyzed. As the basis for a quantitative description of the interaction of polarized light with tissues, the theory of polarization transfer in a random medium is used. This theory employs the modified transfer equation for Stokes parameters to predict the polarization properties of single- and multiple-scattered optical fields. The near-order of scatterers in tissues is accounted for to provide an adequate description of tissue polarization properties. Biomedical diagnostic techniques based on polarized light detection, including polarization imaging and spectroscopy, amplitude and intensity light scattering matrix measurements, and polarization-sensitive optical coherence tomography are described. Examples of biomedical applications of these techniques for early diagnostics of cataracts, detection of precancer, and prediction of skin disease are presented. The substantial reduction of light scattering multiplicity at tissue optical clearing that leads to a lesser influence of scattering on the measured intrinsic polarization properties of the tissue and allows for more precise quantification of these properties is demonstrated.

Circular polarization memory in polydisperse scattering media

We investigate the survival of circularly polarized light in random scattering media. The surprising persistence of this form of polarization has a known dependence on the size and refractive index of scattering particles, however a general description regarding polydisperse media is lacking. Through analysis of Mie theory, we present a means of calculating the magnitude of circular polarization memory in complex media, with total generality in the distribution of particle sizes and refractive indices. Quantification of this memory effect enables an alternate pathway toward recovering particle size distribution, based on measurements of diffusing circularly polarized light.

Propagation of coherent polarized light in turbid highly scattering medium

Within the framework of further development of unified Monte Carlo code for the needs of biomedical optics and biophotonics, we present an approach for modeling of coherent polarized light propagation in highly scattering turbid media, such as biological tissues. The temporal coherence of light, linear and circular polarization, interference, and the helicity flip of circularly polarized light due to reflection at the medium boundary and/or backscattering events are taken into account. To achieve higher accuracy in the results and to speed up the modeling, the implementation of the code utilizes parallel computing on NVIDIA graphics processing units using Compute Unified Device Architecture. The results of the simulation of coherent linearly and circularly polarized light are presented in comparison with the results of known theoretical studies and the results of alternative modelings.

Alternate formulation of enhanced backscattering as phase conjugation and diffraction: derivation and experimental observation

Enhanced backscattering (EBS), also known as weak localization of light, is derived using the Huygens-Fresnel principle and backscattering is generally shown to be the sum of an incoherent baseline and a phase conjugated portion of the incident wave that forms EBS. The phase conjugated portion is truncated by an effective aperture described by the probability function P(s) of coherent path-pair separations. P(s) is determined by the scattering properties of the medium and so characterization of EBS can be used for metrology of scattering materials. A three dimensional intensity peak is predicted in free space at a point conjugate to the source and is experimentally observed.

Numerical investigation on polarization characteristics of coherent enhanced backscattering using SLPSTD

We investigate the polarization characteristics of coherent enhanced backscattering (EBS) using the pseudo-spectral time domain method implemented on staggered grid and local Fourier basis (SLPSTD) [Opt. Express 18, 9236 (2010)]. The studies are focused on Mie scatterers with findings profound to the understanding of polarization evolution in the scattering process. For linear polarization studies, the low-order scattering component of EBS is azimuthally anisotropic. A relationship between the degree of anisotropy and the photon's penetration depth is established to characterize the depolarization progress. For circular polarization, exact numerical solutions disclose the origin of polarization memory effect and the helicity-flipping phenomenon. The region responsible for helicity-flipping is identified. Our numerical technique can be potentially applied to subsurface imaging that explores polarization memory effect.

Enhancement factor in low-coherence enhanced backscattering and its applications for characterizing experimental skin carcinogenesis

We experimentally study potential mechanisms by which the enhancement factor in low-coherence enhanced backscattering (LEBS) can probe subtle variations in radial intensity distribution in weakly scattering media. We use enhanced backscattering of light by implementing either (1) low spatial coherence illumination or (2) multiple spatially independent detections using a microlens array under spatially coherent illumination. We show that the enhancement factor in these configurations is a measure of the integrated intensity within the localized coherence or detection area, which can exhibit strong dependence on small perturbations in scattering properties. To further evaluate the utility of the LEBS enhancement factor, we use a well-established animal model of cutaneous two-stage chemical carcinogenesis. In this pilot study, we demonstrate that the LEBS enhancement factor can be substantially altered at a stage of preneoplasia. Our animal result supports the idea that early carcinogenesis can cause subtle alterations in the scattering properties that can be captured by the LEBS enhancement factor. Thus, the LEBS enhancement factor has the potential as an easily measurable biomarker in skin carcinogenesis.

Virtual pinhole-scanning spectroscopic imaging platform using low-coherence enhanced backscattering

We present that multiple mutually independent coherence areas can be used for simultaneous spatial filtering in an imaging platform as effective as pinhole scanning. In this imaging platform, the unique combination of low-spatial-coherence illumination and differential angle imaging allows us to take advantage of low-coherence enhanced-backscattering (LEBS) phenomenon to permit self-generated optical sectioning to the subsurface in a relatively large area. We further demonstrate that LEBS spectroscopic imaging substantially minimizes cross talk among adjacent pixels, rejects the background light caused by out-of-plane scattered light, and thereby enhances image contrast and resolution.

Diffuse light suppression of back-directional gating imaging in high anisotropic media

We experimentally demonstrate that back-directional gating in an imaging setup can potentially remove unwanted diffuse light to improve the contrast of an object embedded in a high anisotropic surrounding medium. In such back-directional gating, the high anisotropic property of the surrounding medium can serve as a waveguide to deliver the incident light to the embedded object and to isolate the ballistic or snake-like light backscattered from the object in a moderate depth. We further discuss the effects of back-directional gating in the image formation in terms of the image resolution and the depth of field. Although backscattering detections of biological tissue have recently received considerable attention, we, for the first time to our knowledge, show its potential advantage for the contrast improvement in high anisotropic media.