Broadband extended source imaging Mueller-matrix polarimeter.

An imaging Mueller matrix polarimeter, named the red-green-blue (RGB)950, takes images of medium-sized (tens of centimeters) objects by using a very bright source, large polarization state generator, and high-quality camera. Its broadband extended light source switches between red, green, blue, and near-infrared light to allow taking polarimetric images for comparison with RGB camera images. The large diffuse source makes shadow transitions gradual and spreads out the specular reflected spot into a larger less conspicuous area.

Calibration and validation of Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) polarization measurements.

The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI), a precursor to the future Multi-Angle Imager for Aerosols satellite instrument, is a remote-sensing instrument for the characterization of atmospheric aerosols and clouds. To help discriminate between different aerosol particle types, which is crucial to improve our understanding of their impact on climate and air quality, AirMSPI acquires imagery over multiple view angles in the ultraviolet, visible, and near-infrared, and it employs dual photoelastic modulators (PEMs) to target an uncertainty requirement of ±0.005 in the degree of linear polarization (DoLP) at selected wavelengths. Laboratory polarimetric calibrations using a second-generation Polarization State Generator-2 (PSG-2) and validation measurements at 0

Spectral density response functions for modulated polarimeters.

Conventional imaging devices are often compared using their optical transfer functions (OTFs) in space and their impulse responses in time. Modulated polarimeters cannot be directly compared this way, since they are frequency multiplexed. Here we define a spectral density response function that describes how the spectral density matrix of the Stokes parameters for an object transfers through a modulated polarimeter. This response function facilitates the objective comparison of polarimeters in a way that is analogous to the OTF for conventional imaging systems. The spectral density response is used to calculate a Wiener filter for a rotating analyzer polarimeter as an example of filter optimization for modulated polarimetry.

Liquid crystal polymer full-stokes division of focal plane polarimeter.

A division-of-focal-plane polarimeter based on a dichroic dye and liquid crystal polymer guest-host system is presented. Two Stokes polarimeters are demonstrated: a linear Stokes and the first ever Full-Stokes division-of-focal-plane polarimeter. The fabrication, packaging, and characterization of the systems are presented. Finally, optimized polarimeter designs are discussed for future works.

Role of the null space of the DRM in the performance of modulated polarimeters.

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.

Mueller matrix roots depolarization parameters.

The Mueller matrix roots decomposition recently proposed by Chipman in [1] and its three associated families of depolarization (amplitude depolarization, phase depolarization, and diagonal depolarization) are explored. Degree of polarization maps are used to differentiate among the three families and demonstrate the unity between phase and diagonal depolarization, while amplitude depolarization remains a distinct class. Three families of depolarization are generated via the averaging of different forms of two nondepolarizing Mueller matrices. The orientation of the resulting depolarization follows the cyclic permutations of the Pauli spin matrices. The depolarization forms of Mueller matrices from two scattering measurements are analyzed with the matrix roots decomposition-a sample of ground glass and a graphite and wood pencil tip.

Band limited data reconstruction in modulated polarimeters.

Data processing for sequential in time polarimeters based on the Data Reduction Matrix technique yield polarization artifacts in the presence of time varying signals. To overcome these artifacts, polarimeters are designed to operate at higher and higher speeds. In this paper we describe a band limited reconstruction algorithm that allows the measurement and processing of temporally varying Stokes parameters without artifacts. An example polarimeter consisting of a rotating retarder and polarizer is considered, and conventional processing methods are compared to a band limited reconstruction algorithm for the example polarimeter. We demonstrate that a significant reduction in error is possible using these methods.

Skew aberration: a form of polarization aberration.

We define a new class of aberration, skew aberration, which is a component of polarization aberration. Skew aberration is an intrinsic rotation of polarization states due to the geometric transformation of local coordinates, independent of coatings and interface polarization. Skew aberration in a radially symmetric system has the form of a circular retardance tilt plus coma aberration. Skew aberration causes undesired polarization distribution in the exit pupil. We demonstrate statistics on skew aberration of 2383 optical systems described in Code V's U.S. patent library [Code V Version 10.3 (Synopsys, 2011), pp. 22-24]; the mean skew aberration is 0.89° and the standard deviation is 1.37°. The maximum skew aberration found is 17.45° and the minimum is -11.33°. U.S. patent 2,896,506, which has ±7.01° of skew aberration, is analyzed in detail. Skew aberration should be of concern in microlithography optics and other high NA and large field of view optical systems.

Formulation of rigorous coupled-wave theory for gratings in bianisotropic media.

A formulation of rigorous coupled-wave theory for diffraction gratings in bianisotropic media that exhibit linear birefringence and/or optical activity is presented. The symmetric constitutive relations for bianisotropic materials are adopted. All of the incident, exiting, and grating materials can be isotropic, uniaxial, or biaxial, with or without optical activity. The principal values of the electric permittivity tensor, the magnetic permeability tensor, and the gyrotropic tensor of the media can take arbitrary values, and the principal axes may be arbitrarily and independently oriented. Procedures for Fourier expansion of Maxwell's equations are described. Distinctive polarization coupling effects due to optical activity are observed in sample calculations.

Polarization state generator: a polarimeter calibration standard.

A polarization state generator (PSG) was built to generate light having a degree of linear polarization (DoLP) varying from 0.0005 to 0.4 with 0.0005 uncertainty. The PSG operates by tilting a plane parallel SF11 glass plate in a nearly unpolarized beam. The DoLP of collimated, unpolarized light passing through a plane parallel plate over a defined range of field angles can be calculated from theory, and the PSG was intended to act as a calibration standard based on this calculation. Several effects make the DoLP distribution as a function of field and tilt plate difficult to model to the desired 0.0005 uncertainty: source DoLP and intensity nonuniformity, lens surface diattenuation, and errors in optical alignment. Because of these effects, modeled DoLP was not used as a standard. Instead, DoLP was characterized with repeatability of 0.0005.

Three-dimensional polarization ray-tracing calculus I: definition and diattenuation.

A three-by-three polarization ray-tracing matrix method for polarization ray tracing in optical systems is presented for calculating the polarization transformations associated with ray paths through optical systems. The method is a three-dimensional generalization of the Jones calculus. Reflection and refraction algorithms are provided. Diattenuation of the optical system is calculated via singular value decomposition. Two numerical examples, a three fold-mirror system and a hollow corner cube, demonstrate the method.

Three-dimensional polarization ray-tracing calculus II: retardance.

The concept of retardance is critically analyzed for ray paths through optical systems described by a three-by-three polarization ray-tracing matrix. Algorithms are presented to separate the effects of retardance from geometric transformations. The geometric transformation described by a "parallel transport matrix" characterizes nonpolarizing propagation through an optical system, and also provides a proper relationship between sets of local coordinates along the ray path. The proper retardance is calculated by removing this geometric transformation from the three-by-three polarization ray-tracing matrix. Two rays with different ray paths through an optical system can have the same polarization ray-tracing matrix but different retardances. The retardance and diattenuation of an aluminum-coated three fold-mirror system are analyzed as an example.

Analysis of static and time-varying polarization errors in the multiangle spectropolarimetric imager.

Multiangle Spectropolarimetric Imager (MSPI) sensitivity to static and time-varying polarization errors is examined. For a system without noise, static polarization errors are accurately represented by the calibration coefficients, and therefore do not impede correct mapping of measured to input Stokes vectors. But noise is invariably introduced during the detection process, and static polarization errors reduce the system's signal-to-noise ratio (SNR) by increasing noise sensitivity. Noise sensitivity is minimized by minimizing the condition number of the system data reduction matrix [Appl. Opt.41, 619 (2002)]. The sensitivity of condition numbers to static polarization errors is presented. The condition number of the nominal MSPI data reduction matrix is approximately 1.1 or less for all fields. The increase in the condition number above 1 results primarily from a quarter wave plate and mirror coating retardance magnitude errors. Sensitivity of the degree of linear polarization (DoLP) error with respect to time-varying diattenuation and retardance error was used to set a time-varying diattenuation magnitude tolerance of 0.005 and a time-varying retardance magnitude tolerance of ±0.2°. A Monte Carlo simulation of the calibration and measurements using anticipated static and time-varying errors indicates that MSPI has a probability of 0.9 of meeting its 0.005 DoLP uncertainty requirement.

First results from a dual photoelastic-modulator-based polarimetric camera.

We report on the construction and calibration of a dual photoelastic-modulator (PEM)-based polarimetric camera operating at 660?nm. This camera is our first prototype for a multispectral system being developed for airborne and spaceborne remote sensing of atmospheric aerosols. The camera includes a dual-PEM assembly integrated into a three-element, low-polarization reflective telescope and provides both intensity and polarization imaging. A miniaturized focal-plane assembly consisting of spectral filters and patterned wire-grid polarizers provides wavelength and polarimetric selection. A custom push-broom detector array with specialized signal acquisition, readout, and processing electronics captures the radiometric and polarimetric information. Focal-plane polarizers at orientations of 0 degrees and -45 degrees yield the normalized Stokes parameters q=Q/I and u=U/I respectively, which are then coregistered to obtain degree of linear polarization (DOLP) and angle of linear polarization. Laboratory test data, calibration results, and outdoor imagery acquired with the camera are presented. The results show that, over a wide range of DOLP, our challenging objective of uncertainty within +/-0.005 has been achieved.

Vortex retarders produced from photo-aligned liquid crystal polymers.

We present developments using photo-aligned liquid crystal polymers for creating vortex retarders, halfwave retarders with a continuously variable fast axis. Polarization properties of components designed to create different polarization vortex modes are presented. We assess the viability of these components using the theoretical and experimental point spread functions and optical transfer functions in Mueller matrix format, point spread matrix (PSM) and optical transfer matrix (OTM). The measured PSM and OTM of these components in an optical system is very close to the theoretically predicted values thus showing that these components should provide excellent performance in applications utilizing polarized optical vortices. The impact of aberrations and of vortex retarder misalignment on the PSM and OTM are presented.

Diffuse spectral fundus reflectance measured using subretinally placed spectralon.

The diffuse fundus reflectance and the spectral transmittance of the swine sensory retina was measured in vivo using intravitreal illumination. Pars plana vitrectomy and intravitreal manipulations were performed on a female American Yorkshire domestic swine. Light from a scanning monochromator was coupled into a fiber optic intraocular illuminator inserted into the vitreous. A 1.93-mm(2) region of the illuminated fundus was imaged from an oblique illumination angle. Multispectral retinal images were acquired for four experimental conditions: the eye (1) prior to vitrectomy, (2) after vitrectomy, (3) after insertion of a Spectralon disk super-retinally, and (4) after subretinal insertion of the disk. The absorption of melanin and hemoglobin in the red wavelengths was used to convert relative spectral reflectance to absolute reflectance. The flux scattered from the super-retinal Spectralon was used to correct for scattering in the globe. The transmittance of the sensory retina was measured in vivo using the scatter corrected subretinal Spectralon disk reflectance. The hemoglobin and melanin components of the spectrum due to scattered light were removed from the retinal transmission spectrum. The in vivo spectral transmittance of the sensory retina in this swine was essentially flat across the visible spectrum, with an average transmittance >90%.

Blue-green spectral minimum correlates with oxyhemoglobin saturation in vivo.

An imaging multi-spectral retinal oximeter with intravitrial illumination is used to perform the first in vivo test of the blue-green minima shift oximetry method (BGO) in swine eyes [K. R. Dennighoff, R. A. Chipman, and L. W. Hillman, Opt. Lett. 31, 924-926 (2006); J. Biomed. Opt. 12, 034020 (2007).] A fiber optic intravitreal illuminator inserted through the pars plana was coupled to a monochromator and used to illuminate the retina from an angle. A camera viewing through the cornea recorded a series of images at each wavelength. This intravitreal light source moves the specular vessel glint away from the center of the vessel and directly illuminates the fundus behind most blood vessels. These two conditions combine to provide accurate measurements of vessel and perivascular reflectance. Equations describing these different light paths are solved, and BGO is used to evaluate large retinal vessels. In order to test BGO calibration in vivo, data were acquired from swine with varied retinal arterial oxyhemoglobin saturations (60-100% saturation.). The arterial saturations determined using BGO to analyze the multispectral image sets showed excellent correlation with co-oximeter data (r2=0.98, and residual error +/-3.4% saturation) and are similar to results when hemoglobin and blood were analyzed using this technique.

Blood oxyhemoglobin saturation measurements by blue-green spectral shift.

Previous work describing a resilient method for measuring oxyhemoglobin saturation using the blue-green spectral shift was performed using cell free hemoglobin solutions. Hemoglobin solution and whole blood sample spectra measured under similar conditions in a spectrophotometer are used here to begin evaluating the impact of cellular scattering on this method. The blue-green spectral shift with changing oxyhemoglobin saturation was preserved in these blood samples and the blue-green spectral shift was relatively unaffected by physiological changes in blood pH (6.6, 7.1, and 7.4), path length through blood (100 and 200 microm), and blood hematocrit (19 to 48%). The packaging of hemoglobin in red blood cells leads to a decreased apparent path length through hemoglobin, and an overall decrease in scattering loss with increasing wavelength from 450 to 850 nm. The negative slope of the scattering loss in the 476 to 516-nm range leads to a +3.0 nm shift in the oxyhemoglobin saturation calibration line when the blue-green spectral minimum in these blood samples was compared to cell free hemoglobin. Further research is needed to fully evaluate the blue green spectral shift method in cellular systems including in vivo testing.

Retinal oximetry using intravitreal illumination.

PURPOSE: To demonstrate spectroscopic retinal oximetry measurements on arteries and veins in swine using intravitreal illumination. Retinal arterial and venous saturations are measured for a range of inspired O2 levels after pars plana vitrectomy. METHODS: Pars plana vitrectomy and intravitreal manipulations were performed on two female American Yorkshire domestic swine. Light from a scanning monochromator was coupled into a fiberoptic intraocular illuminator inserted into the vitreous. The retinal vessels were illuminated obliquely, minimizing vessel glints. Multispectral images of the retinal vasculature were obtained as the swine's arterial blood oxygen saturation was decreased from 100% to 67% in decrements of approximately 10%. Retinal vessel spectra were used to calculate oxygen saturation in selected arteries and veins. Arterial oxygen saturations were calibrated using blood gas analysis on blood drawn from a Swan-Ganz catheter placed in the femoral artery. RESULTS: Oblique illumination of retinal vessels using an intravitreal fiberoptic illuminator provided a substantial reduction in the central vessel glint usually seen in fundus images, thus simplifying the analysis of spectral data. The vessel shadows were displaced from the vessel image simplifying the light paths in the eye. Using a full spectral analysis simplified by the light path reductions, we calculated retinal vessel saturations. The reduction of glint allowed for increased accuracy in measuring retinal vessel spectral optical density. Abnormally low retinal venous oxygen saturations were observed shortly after pars plana vitrectomy. CONCLUSIONS: Retinal oximetry using intravitreal illumination has been demonstrated. As a research tool, intravitreal illumination addresses several difficulties encountered when performing retinal oximetry with transcorneal illumination.

Retinal oximeter for the blue-green oximetry technique.

Retinal oximetry offers potential for noninvasive assessment of central venous oxyhemoglobin saturation (SO(2)) via the retinal vessels but requires a calibrated accuracy of ±3% saturation in order to be clinically useful. Prior oximeter designs have been hampered by poor saturation calibration accuracy. We demonstrate that the blue-green oximetry (BGO) technique can provide accuracy within ±3% in swine when multiply scattered light from blood within a retinal vessel is isolated. A noninvasive on-axis scanning retinal oximeter (ROx-3) is constructed that generates a multiwavelength image in the range required for BGO. A field stop in the detection pathway is used in conjunction with an anticonfocal bisecting wire to remove specular vessel reflections and isolate multiply backscattered light from the blood column within a retinal vessel. This design is tested on an enucleated swine eye vessel and a retinal vein in a human volunteer with retinal SO(2) measurements of ∼1 and ∼65%, respectively. These saturations, calculated using the calibration line from earlier work, are internally consistent with a standard error of the mean of ±2% SO(2). The absolute measures are well within the expected saturation range for the site (-1 and 63%). This is the first demonstration of noninvasive on-axis BGO retinal oximetry.