Double-pass imaging polarimetry in the human eye

Spatially Resolved Chiroptical Spectroscopies Emphasizing Recent Applications to Thin Films of Chiral Organic Dyes

Instrumental techniques able to identify and structurally characterize the aggregation states in thin films of chiral organic π-conjugated materials, from the first-order supramolecular arrangement up to the microscopic and mesoscopic scale, are very helpful for clarifying structure-property relationships. Chiroptical imaging is currently gaining a central role, for its ability of mapping local supramolecular structures in thin films. The present review gives an overview of electronic circular dichroism imaging (ECDi), circularly polarized luminescence imaging (CPLi), and vibrational circular dichroism imaging (VCDi), with a focus on their applications on thin films of chiral organic dyes as case studies.

Liquid-crystal based drift-free polarization modulators: Part II. Ultra-stable Stokes and Mueller polarimeters

We have previously reported a new design for drift-free liquid-crystal polarization modulators (LCMs) based on liquid-crystal variable retarders (LCVRs). Here, we study their performance on Stokes and Mueller polarimeters. LCMs have polarimetric responses similar to LCVRs and can be used as temperature-stable alternatives to many LCVR-based polarimeters. We have built an LCM-based polarization state analyzer (PSA) and compared its performance to an equivalent LCVR-based PSA. Our system parameters remained stable over a wide range of temperature, precisely from 25°C to 50°C. Accurate Stokes and Mueller measurements have been conducted, paving the way to calibration-free polarimeters for demanding applications.

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.

Characterization of retardance spatial variations over the aperture of liquid-crystal variable retarders

We present a comparison of two experimental methods to measure retardance as a function of applied voltage and as a function of position over the aperture of liquid-crystal variable retarders. These measurements are required for many applications, particularly in polarimetry. One method involves the scan of an unexpanded laser beam over the aperture, and the other uses an expanded beam from a LED and a CCD camera to measure the full aperture with a single measurement. The first method is time consuming, is limited in the measured spatial resolution, and requires more expensive equipment to perform the scan, whereas the second method is low cost, with the spatial resolution of the CCD, and fast, but in principle has variations of the incident beam over the aperture that affect the measured retardance values. The results obtained show good agreement for the average values of retardance for the two methods, but the expanded-beam method shows more noise, particularly close to the voltage values at which the variable-retarder retardance versus voltage curves are unwrapped. These retardance variations can be reduced by smoothing the retardance image, which makes the expanded-beam method an attractive method for polarimetry applications since it gives the complete information in the full aperture of the device with the additional advantages of low cost, simplicity, and being less time consuming.

Review on Complete Mueller Matrix Optical Scanning Microscopy Imaging

Optical scanning microscopy techniques based on the polarization control of the light have the capability of providing non invasive label-free contrast. By comparing the polarization states of the excitation light with its transformation after interaction with the sample, the full optical properties can be summarized in a single 4×4 Mueller matrix. The main challenge of such a technique is to encode and decode the polarized light in an optimal way pixel-by-pixel and take into account the polarimetric artifacts from the optical devices composing the instrument in a rigorous calibration step. In this review, we describe the different approaches for implementing such a technique into an optical scanning microscope, that requires a high speed rate polarization control. Thus, we explore the recent advances in term of technology from the industrial to the medical applications.

Full-polarization wavefront shaping for imaging through scattering media

The scattering effect occurring when light passes through inhomogeneous-refractive-index media such as atmosphere or biological tissues will scramble the light wavefront into speckles and impede optical imaging. Wavefront shaping is an emerging technique for imaging through scattering media that works by addressing correction of the disturbed wavefront. In addition to the phase and amplitude, the polarization of the output scattered light will also become spatially randomized in some cases. The recovered image quality and fidelity benefit from correcting as much distortion of the scattered light as possible. Liquid-crystal spatial light modulators (LC-SLMs) are widely used in the wavefront shaping technique, since they can provide a great number of controlled modes and thereby high-precision wavefront correction. However, due to the working principle of LC-SLMs, the wavefront correction is restricted to only one certain linear polarization state, resulting in retrieved image information in only the right polarization, while the information in the orthogonal polarization is lost. In this paper, we describe a full-polarization wavefront correction system for shaping the scattered light wavefront in two orthogonal polarizations with a single LC-SLM. The light speckles in both polarizations are corrected for retrieval of the full polarization information and faithful images of objects. As demonstrated in the experiments, the focusing intensity can be increased by full-polarization wavefront correction, images of objects in arbitrary polarization states can be retrieved, and the polarization state of the object's light can also be recognized.

Polarimeter for measuring the properties of birefringent media in reflective mode

This work presents a description of a polarimetric system for measuring the properties of birefringent media. In our reflection system the applied Stokes polarimeter acts both as a generator of the light's selected polarization states as well as a light analyzer leaving the examined medium. The method is based on six intensity distribution measurements realized in six different configurations of polarizers/analyzers: four linear and two circular ones. Thus, we have achieved parallel polariscope for linear polarizers and the crossed polariscope for circular polarizers. Such a setup can be easily applied for linearly birefringent media properties measurements including dichroic ones. This measurement setup and the measurement method were successfully tested in a homogeneous medium and a medium with variable phase difference.

Active compensation of extrinsic polarization errors using adaptive optics

We present a scheme for active compensation of complex extrinsic polarization perturbations introduced into an optical system. Imaging polarimeter is used to measure the polarization state across a beam profile and a liquid crystal spatial light modulator controls the polarization of the input beam. A sequence of measurements permits determination of the birefringence properties of a perturbing specimen. The necessary correction is calculated and fed back to the polarization modulator to compensate for the polarization perturbation. The system capabilities are demonstrated on a range of birefringent specimens.

Broadband ellipso-polarimetric camera utilizing tunable liquid crystal achromatic waveplate with improved field of view

An ellipso-polarimetric camera integrated with improved field of view tunable achromatic waveplate (AWP) over wide spectral band based on nematic liquid crystal retarders is presented. The AWP operates as half, quarter and full waveplate over a wide range of 430-780nm and wide field of view. The proposed analysis proved that capturing images at these modes is sufficient to extract the ellipsometric parameters: sin(2ψ), cos(Δ) and the Stokes parameters S₁ and S₃, besides showing the relations in between. Transmission and reflection modes setups are demonstrated in addition to an ellipso-polarimetric smartphone camera. The results show for the first time superiority of cos(Δ) images in which prominent contrast and fine details appear even with scattering objects and higher immunity to device errors. Biometric, remote sensing and archeological improved imaging applications are demonstrated.

Experimental limits for eigenvalue calibration in liquid-crystal Mueller-matrix polarimeters

A numerical study is carried out to find the experimental conditions necessary for the eigenvalue calibration procedure to work correctly in a liquid-crystal variable-retarder-based Mueller-matrix polarimeter. Using the error between the simulated experimental Mueller matrix in a polarimeter with errors and the expected ideal Mueller matrices for four calibration samples, the maximum experimental errors are estimated for a successful eigenvalue calibration. It is found that the retarder axes' orientations have smaller permitted errors than the retardation values.

Permitted experimental errors for optimized variable-retarder Mueller-matrix polarimeters

An optimized Mueller-matrix polarimeter is simulated. The polarimeter is optimized by finding the configurations of the polarization state generator and polarization state analyzer that give the minimum condition number. Noise is included in the measurement of the polarimeter intensities, and the eigenvalue calibration procedure is used to reduce the errors in the final Mueller matrix. Controlled errors are introduced to the polarimeter configuration, and the error in the final measured Mueller matrix is calculated as a function of these configuration errors. It is found that the alignment of the retarder axes in the polarimeter is much more important than the use of the ideal, optimized retardance values. In particular, the misalignment of the retarders farthest from the sample is the error source with the highest impact in the precision of the polarimeter.

Calibration and data extraction in nonoptimized Mueller matrix polarimeters

We present a method for calibration and data extraction for a nonoptimized Mueller matrix polarimeter. The advantage of this type of method is a reduction in measurement time for multiwavelength systems or in systems with slow response times. The calibration process requires the measurement of four known polarization devices. Here we use free-space transmission, a horizontal and a vertical linear polarizer, and a quarter-wave retarder with its fast axis at 30° to the horizontal. Experimental measurements of rotating quarter-wave and half-wave retarders show that accurate results can be obtained with the proposed method.

Intrinsic coincident linear polarimetry using stacked organic photovoltaics

Polarimetry has widespread applications within atmospheric sensing, telecommunications, biomedical imaging, and target detection. Several existing methods of imaging polarimetry trade off the sensor's spatial resolution for polarimetric resolution, and often have some form of spatial registration error. To mitigate these issues, we have developed a system using oriented polymer-based organic photovoltaics (OPVs) that can preferentially absorb linearly polarized light. Additionally, the OPV cells can be made semitransparent, enabling multiple detectors to be cascaded along the same optical axis. Since each device performs a partial polarization measurement of the same incident beam, high temporal resolution is maintained with the potential for inherent spatial registration. In this paper, a Mueller matrix model of the stacked OPV design is provided. Based on this model, a calibration technique is developed and presented. This calibration technique and model are validated with experimental data, taken with a cascaded three cell OPV Stokes polarimeter, capable of measuring incident linear polarization states. Our results indicate polarization measurement error of 1.2% RMS and an average absolute radiometric accuracy of 2.2% for the demonstrated polarimeter.

Snapshot retinal imaging Mueller matrix polarimeter

Early diagnosis of glaucoma, which is a leading cause for visual impairment, is critical for successful treatment. It has been shown that Imaging polarimetry has advantages in early detection of structural changes in the retina. Here, we theoretically and experimentally present a snapshot Mueller Matrix Polarimeter fundus camera, which has the potential to record the polarization-altering characteristics of retina with a single snapshot. It is made by incorporating polarization gratings into a fundus camera design. Complete Mueller Matrix data sets can be obtained by analyzing the polarization fringes projected onto the image plane. In this paper, we describe the experimental implementation of the snapshot retinal imaging Mueller matrix polarimeter (SRIMMP), highlight issues related to calibration, and provide preliminary images acquired from the camera.

Preflight calibration of the Imaging Magnetograph eXperiment polarization modulation package based on liquid-crystal variable retarders

We present the study, characterization, and calibration of the polarization modulation package (PMP) of the Imaging Magnetograph eXperiment (IMaX) instrument, a successful Stokes spectropolarimeter on board the SUNRISE balloon project within the NASA Long Duration Balloon program. IMaX was designed to measure the Stokes parameters of incoming light with a signal-to-noise ratio of at least 10³, using as polarization modulators two nematic liquid-crystal variable retarders (LCVRs). An ad hoc calibration system that reproduced the optical and environmental characteristics of IMaX was designed, assembled, and aligned. The system recreates the optical beam that IMaX receives from SUNRISE with known polarization across the image plane, as well as an optical system with the same characteristics of IMaX. The system was used to calibrate the IMaX PMP in vacuum and at different temperatures, with a thermal control resembling the in-flight one. The efficiencies obtained were very high, near theoretical maximum values: the total efficiency in vacuum calibration at nominal temperature was 0.972 (1 being the theoretical maximum). The condition number of the demodulation matrix of the same calibration was 0.522 (0.577 theoretical maximum). Some inhomogeneities of the LCVRs were clear during the pixel-by-pixel calibration of the PMP, but it can be concluded that the mere information of a pixel-per-pixel calibration is sufficient to maintain high efficiencies in spite of inhomogeneities of the LCVRs.

Imaging linear polarimetry using a single ferroelectric liquid crystal modulator

In the field of polarimetry, ferroelectric liquid crystal cells are mostly used as bistable polarization rotators suitable to analyze crossed polarizations. This paper shows that, provided such a cell is used at its nominal wavelength and correctly driven, its behavior is close to that of a tunable half-wave plate, and it can be used with much benefit in lightweight imaging polarimetric setups. A partial Stokes polarimeter using a single digital video camera and a single ferroelectric liquid crystal modulator is designed and implemented for linear polarization analysis. Polarization azimuthal angle and degree of linear polarization are available at 150 frames per second with a good accuracy.

Mueller matrix interpolation in polarization optics

The question of the physical significance of the Mueller matrix average is addressed by means of an analysis of interpolation processes. We draw a comparison between two interpolation processes. The first one is related to the classical Euclidean metrics and the second one is based on the log-Euclidean metrics. Both the associated interpolation procedures are depicted with their underlying physical models. Addressing the question of the physical meaning of the log-Euclidean process of interpolation is founded on a very similar approach to the layered-medium interpretation proposed by Jones [J. Opt. Soc. Am.38, 671 (1948)] in the seventh paper of his series. Based on the analysis of their respective properties, we eventually show that the choice between both these interpolation processes may depend on what statistical situation is considered or what underlying physical model is assumed.

Design and optimization of partial Mueller matrix polarimeters

Mueller matrix polarimeters (MMPs) are designed to probe the polarization properties of optical scattering processes. When using a MMP for a detection, discrimination, classification, or identification task, a user considers certain elements of the Mueller matrix. The usual way of performing this task is to measure the full Mueller matrix and discard the unused elements. For polarimeter designs with speed, miniaturization, or other constraints, it may be desirable to have a system with reduced dimensionality that measures only elements of the Mueller matrix that are important in a particular application as efficiently as possible. In this paper, we develop a framework that allows partial MMPs to be analyzed. Quantitative metrics are developed by considering geometrical relationships between the space spanned by a particular MMP and the space occupied by the scene components. The method is generalized to allow the effects of noise to be considered. The results are general and can also be used to optimize complete and overspecified MMPs for performing specific tasks, as well.

Rapid Mueller matrix polarimetry based on parallelized polarization state generation and detection

We present rapid Mueller matrix polarimetry that can extract twelve Muller matrix elements from a single intensity image in real time and with high spatial resolution. This is achieved by parallelizing the respective polarization state generation and polarization state detection processes, which in existing polarimeters is performed sequentially. Parallelization of the polarization state generation process is accomplished through the use of vector beams, for which this work represents a new application domain. Polarization state detection is parallelized by uniquely combining a microscope/array detector setup with a specialized algorithm that simultaneously utilizes information from multiple spatial regions of the array detector. Simulated results applying this technique to two anisotropic samples including metamaterial yield material parameters that are consistent with those reported in the literature.

Estimating the polarization degree of polarimetric images in coherent illumination using maximum likelihood methods

We address the problem of estimating the polarization degree of polarimetric images in coherent illumination. It has been recently shown that the degree of polarization associated with polarimetric images can be estimated by the method of moments applied to two or four images assuming fully developed speckle. We show that the estimation can also be conducted by using maximum likelihood methods. The maximum likelihood estimators of the polarization degree are derived from the joint distribution of the image intensities. We show that the joint distribution of polarimetric images is a multivariate gamma distribution whose marginals are univariate, bivariate, or trivariate gamma distributions. This property is used to derive maximum likelihood estimators of the polarization degree using two, three, or four images. The proposed estimators provide better performance than the estimators of moments. These results are illustrated by estimations conducted on synthetic and real images.

Mueller matrix retinal imager with optimized polarization conditions

A new Mueller matrix polarimeter was used to image the retinas of normal subjects. Light from a linearly polarized 780 nm laser was passed through a system of variable retarders and scanned across the retina. Light returned from the eye passed through a second system of retarders and a polarizing beamsplitter to two confocal detection channels. Optimization of the polarimetric data reduction matrix was via a condition number metric. The accuracy and repeatability of polarization parameter measurements were within +/- 5%. The magnitudes and orientations of retardance and diattenuation, plus depolarization, were measured over 15 degrees of retina for 15 normal eyes.

Transmission imaging polarimetry for a linear birefringent medium using a carrier fringe method

We present an imaging polarimeter in transmission mode that is based on a carrier frequency method and allows a spatially resolved polarimetric description of nondichroic linear birefringent media. The apparatus incorporates a generator of polarization states in the incoming pathway and a Wollaston prism and a linear polarizer as the analyzer unit. A series of two fringe pattern images of the birefringent sample under study, corresponding to two independent polarization states of the generator unit, were recorded. From these images and by using Fourier analysis, the 2D distribution of azimuth angle and retardation were calculated. Two alternative generator units were used: (i) a linear polarizer combined with a rotatory quarter-wave plate and (ii) a liquid-crystal variable retarder. A uniform quarter-wave plate at different orientations was measured with both generator units to demonstrate the effectiveness and the accuracy of the method. The mean absolute deviations were 1.8 degrees and 4.1 degrees for the azimuth and the retardation, respectively, with the first generator unit, and 2.9 degrees and 4.4 degrees for the second one. Moreover, some nonuniform birefringent samples presenting wider ranges of azimuth and retardation were also tested.

Polarimetric high-resolution confocal scanning laser ophthalmoscope

A polarimetric high-resolution confocal scanning laser ophthalmoscope has been developed. The system incorporates a fixed linear polarizer in the illumination path and a rotatory quarter-wave plate and another fixed linear polarizer in the registration path. Retinal areas that are smaller than those provided by commercial instruments can be imaged. Series of four fundus images for independent polarization states in the second pass were recorded for different eyes and retinal locations and the spatially resolved Stokes vectors calculated. From those images, the contrast across retinal blood vessels was maximized and the corresponding image was reconstructed. In terms of polarization, the analysis of small retinal areas might prove to be useful in the improvement of retinal imaging and the enhancement of structural details in the early diagnosis of ocular pathologies.

Degree of polarization as an objective method of estimating scattering

A new method of determining objectively the amount of scattered light in an optical system has been developed. It is based on measuring the degree of polarization of the light in images formed after a double pass through the system. A dual apparatus composed of a modified double-pass imaging polarimeter and a wave-front sensor was used to measure polarization properties and aberrations of the system under test. We studied the accuracy of the procedure in a system that included a lanthanum-modified lead zirconate titanate (PLZT) ceramic plate able to generate variable amounts of scattered light as a function of the applied voltage. Changes in the voltage applied to the ceramics plate modified significantly the scattering contribution while hardly altering the wave-front aberration. The degree of polarization was well correlated with the level of scattering in the system as determined by direct-intensity measurements at the tails of the double-pass images. This indicates that this polarimetric parameter provides accurate relative estimates of the amount of scattering generated in a system. The technique can be used in a number of applications, for example, to determine objectively the amount of scattered light in the human eye.

Mueller polarimetric imaging system with liquid crystals

We present a new polarimetric imaging system based on liquid-crystal modulators, a spectrally filtered white-light source, and a CCD camera. The whole Mueller matrix image of the sample is measured in approximately 5 s in the transmission mode. The instrument design, together with an original and easy-to-operate calibration procedure, provides high accuracy over a wide spectral range (500-700 nm). This accuracy has been assessed by measurement of a linear polarizer at different orientations and a thick wedged quartz plate as an example of a partially depolarized retarder. Polarimetric images of a stained hepatic biopsy with significant fibrosis have been taken at several wavelengths. The optical properties of Picrosirius Red stained collagen (diattenuation, retardance, and polarizance) have been measured independently from each other between 500 and 700 nm.

Clustering of Mueller matrix images for skeletonized structure detection

This paper extends and refines previous work on clustering of polarization-encoded images. The polarization-encoded images used in this work are considered as multidimensional parametric images where a clustering scheme based on Markovian Bayesian inference is applied. Hidden Markov Chains Model (HMCM) and Hidden Hierarchical Markovian Model (HHMM) show to handle effectively Mueller images and give very good results for biological tissues (vegetal leaves). Pretreatments attempting to reduce the image dimensionality based on the Principal Component Analysis (PCA) turns out to be useless for Mueller matrix images.

Clustering of polarization-encoded images

Polarization-encoded imaging consists of the distributed measurements of polarization parameters for each pixel of an image. We address clustering of multidimensional polarization-encoded images. The spatial coherence of polarization information is considered. Two methods of analysis are proposed: polarization contrast enhancement and a more-sophisticated image-processing algorithm based on a Markovian model. The proposed algorithms are applied and validated with two different Mueller images acquired by a fully polarimetric imaging system.

A Mueller matrix model of Haidinger's brushes

Stokes vectors and Mueller matrices are used to model the polarisation properties (birefringence, dichroism and depolarisation) of any optical system, in particular the human eye. An explanation of the form and behaviour of the entoptic phenomenon of Haidinger's brushes is derived that complements and expands upon a previous study. The relationship between the appearance of Haidinger's brushes and intrinsic ocular retardation is quantified and the model allows prediction of the effect of any retarder of any orientation placed between a source of polarised light and the eye. The simple relationship of minimum contrast of Haidinger's brushes to the cosine of total retardation is derived.

Aberro-polariscope for the human eye

We have developed an aberro-polariscope that simultaneously measures spatially resolved polarization properties and wave-front aberration in a living human eye. The setup consists of an infrared Hartmann-Shack sensor that incorporates a polariscope. A series of four Hartmann-Shack images corresponding to independent polarization states were recorded. The corresponding wave-front aberration was computed from each image. Moreover, from each set of four images spatially resolved (over the pupil plane) parameters of polarization were also determined. This instrument allows useful information on both the optical and the biomechanical properties of the eye to be obtained.

Linear birefringence measurements of the in vitro human cornea

This paper presents results of an in vitro investigation of the optical anisotropy of the human cornea. Computer controlled imaging polarimetry and the Jones formalism were used to investigate the distribution of the birefringence and the azimuth angle across the surface of 12 corneas taken from the corneal bank. Each map of the birefringence and the azimuth angle has no rotational symmetry and is different for each cornea. The minimal value of the birefringence always appears in the corneal centre and varies from 9 to 43 degrees for different corneas. Birefringence of the cornea increases monotonically more than one order in the direction of the corneal periphery. Close to the centre of the cornea the azimuth angle is almost constant and varies significantly away from the optical part of the cornea.

Optimized Mueller polarimeter with liquid crystals

We demonstrate a Mueller polarimeter in which the polarization-state generator and analyzer are both composed of a linear polarizer and two liquid-crystal variable retarders. The polarimeter is designed to optimize the accuracy of the final results by minimization of the condition numbers of the modulation and analysis matrices. The polarimeter calibration, a difficult task by conventional procedures, is achieved easily by use of the eigenvalue method of Compain et al. [Appl. Opt. 38, 3490 (1999)]. The overall polarimeter performance is tested with a linear polarizer at various angles and a compensator at various retardations.

Polarization properties of the in vitro old human crystalline lens

We have studied the spatially resolved polarization properties of the in vitro intact old human crystalline lens (from 56 to 88 years old) by using Mueller-matrix imaging polarimetry. Analysis was performed within an average of 54 h of death. Results show that the overall retardation is small (7 degrees on average) and decreases from the centre of the lens to the periphery. Lenticular birefringence is linear but has a spatial dependence, reducing outwards along the radius. The distribution of azimuthal angle of the birefringent structure of the crystalline lens changes depending on each individual lens. Diattenuation and polarizance were found to be small, however, depolarization was about 35% for the set of lenses studied here.

Ocular aberrations with ray tracing and Shack-Hartmann wave-front sensors: does polarization play a role?

Ocular aberrations were measured in 71 eyes by using two reflectometric aberrometers, employing laser ray tracing (LRT) (60 eyes) and a Shack-Hartmann wave-front sensor (S-H) (11 eyes). In both techniques a point source is imaged on the retina (through different pupil positions in the LRT or a single position in the S-H). The aberrations are estimated by measuring the deviations of the retinal spot from the reference as the pupil is sampled (in LRT) or the deviations of a wave front as it emerges from the eye by means of a lenslet array (in the S-H). In this paper we studied the effect of different polarization configurations in the aberration measurements, including linearly polarized light and circularly polarized light in the illuminating channel and sampling light in the crossed or parallel orientations. In addition, completely depolarized light in the imaging channel was obtained from retinal lipofuscin autofluorescence. The intensity distribution of the retinal spots as a function of entry (for LRT) or exit pupil (for S-H) depends on the polarization configuration. These intensity patterns show bright corners and a dark area at the pupil center for crossed polarization, an approximately Gaussian distribution for parallel polarization and a homogeneous distribution for the autofluorescence case. However, the measured aberrations are independent of the polarization states. These results indicate that the differences in retardation across the pupil imposed by corneal birefringence do not produce significant phase delays compared with those produced by aberrations, at least within the accuracy of these techniques. In addition, differences in the recorded aerial images due to changes in polarization do not affect the aberration measurements in these reflectometric aberrometers.

Effect of the polarization on ocular wave aberration measurements

Measurement of the eye's wave aberrations has become fairly standard in recent years. However, most studies have not taken into account the possible influence of the polarization state of light on the wave aberration measurements. The birefringence properties of the eye's optical components, in particular corneal birefringence, can be expected to have an effect on the wave aberration estimates obtained under different states of polarization for the measurement light. In the work described, we used a psychophysical aberrometer (the spatially resolved refractometer) to measure the effect of changes in the polarization state of the illumination light on the eye's wave aberration estimates obtained in a single pass. We find, contrary to our initial expectation, that the polarization state of the measurement light has little influence on the measured wave aberration. For each subject, the differences in wave aberrations across polarization states were of the same order as the variability in aberrations across consecutive estimates of the wave front for the same polarization conditions.

Measurements of the corneal birefringence with a liquid-crystal imaging polariscope

An imaging polariscope has been used to analyze the spatially resolved polarization properties of living human corneas. The apparatus is a modified double-pass setup, incorporating a liquid-crystal modulator in the analyzer pathway. Keeping the incident polarization state fixed (first passage), we recorded a series of three images of the pupil's plane corresponding to independent polarization states of the analyzer unit. Azimuth and retardation at each point of the cornea were calculated from those images. Results show that the magnitude of retardation increases along the radius toward the periphery of the cornea. Left-right eye symmetry in retardation was also found. Maps of azimuth indicate that the direction of the corneal slow axis is nasally downward.

Depolarization effects in the human eye

We have studied the effects of depolarization in the living human eye by using a spatially resolved Mueller-matrix polarimeter [Opt. Lett. 24 (1999) 64]. Results show that the degree of polarization for the central part of double-pass images is about 0.85 and 0.70 for 2 mm and 5 mm of pupil, respectively. This parameter decreases towards the tails of the image. In the plane of the pupil, the degree of polarization also depends on the analyzed area, and it has been related to the different components of the light coming back from the retina. Values of polarizance suggest that the eye presents a slight polarizing power mainly due to the existence of both circular birefringence and dichroic properties. Polarizance is also larger at the central part of double-pass images (about 0.25 on average) and decreases along the radius. In addition, it has been shown that the major retinal layer where the light is reflected does not depend on the state of polarization of the incident light.

Polarization and retinal image quality estimates in the human eye

We have previously studied how polarization affects the double-pass estimates of the retinal image quality by using an imaging polarimeter [Opt. Lett. 24, 64 (1999)]. A series of 16 images for independent combinations of polarization states in the polarimeter were recorded to obtain the spatially resolved Mueller matrices of the eye. From these matrices, double-pass images of a point source for light with different combinations of incoming (first-pass) and outcoming (second-pass) polarization states were reconstructed and their corresponding modulation transfer functions were calculated. We found that the retinal image or, alternatively, the ocular aberrations, are nearly independent of the state of polarization of the incident light (in the first pass). This means that a significant improvement in the ocular optics by using a specific type of polarized light could not be achieved. However, quite different estimates of the retinal image quality are obtained for combinations of polarization states in both the first and the second passes in the double-pass apparatus.

Measurement of parameters of polarization in the living human eye using imaging polarimetry

An imaging polarimeter using liquid-crystal variable retarders (Bueno, J. M., Artal, P. (1999). Double-pass imaging polarimetry in the human eye. Optics Letters, 24, 64-66) has been used to study the parameters of polarization in the living human eye. Retardation introduced by birefringent structures of the eye has been calculated by using a spatially resolved collection of Mueller matrices obtained from series of 16 double-pass retinal images. Results for images with a 2-mm pupil diameter show that although the retardation introduced by the eye in a double-pass varies among individuals, at the central cornea the slow axis is directed along the upper-temporal to lower-nasal line and the ellipticity is close to zero, which indicates the presence of linear birefringence. As pupil size increased, the measured retardation also increased, while ocular birefringence remained linear and azimuthal angle changed without a clear tendency.