Polarized pulse waves in random discrete scatterers

Polarimetric LiDAR backscattering contrast of linearly and circularly polarized pulses for ideal depolarizing targets in generic water fogs

In this paper, we investigate the backscattering depolarization of linearly and circularly polarized laser sources propagating in dense water fogs. We limit our investigation to a simple case where an active LiDAR system is pointed toward a white depolarizing Lambertian solid target. The receiver captures the reflected signal in the orthogonal channel so as to remove most of the backscattering from the water fog. It is shown that in the studied cases, a circularly polarized signal is depolarized faster than a linearly polarized signal and thus produces less contrast. We show that in the cases that can be described by the small angle approximation, the Rubenson degree of polarization (DoP) of a circularly polarized beam can be predicted by the DoP of a linearly polarized beam as DoP_cir=2DoP_lin-1, even for low-order multiple scattering events. In these conditions, since the linear DoP is always stronger, the contrast is expected to be better in linear polarization for ideal depolarizing targets.

Square pulse effects on polarized radiative transfer in an atmosphere-ocean model

Based on our previously proposed modified Monte Carlo method, which is efficient to simulate the time-dependent polarized radiative transfer problem in an atmosphere-ocean model with a reflective/refractive interface, we further investigate the square pulse effect on the polarized radiative transfer in an atmosphere-ocean model. A short square pulse, with a duration of nanoseconds, is assumed to be incident at the top of the atmosphere. The polarized signals varying with time and directions are presented for the locations just above and below the atmosphere-water interface and at the bottom of the ocean, and effects of the incidence and disappearance of the external pulse on the Stokes vector components are analyzed. Results in this paper present the general distribution of square-pulse induced polarized signals and they are important for signal analysis in the field of remote sensing using nanosecond pulses.

Study of polarization memory's impact on detection range in natural water fogs

The influence of the initial polarization state of a source on the detection range of a system probing through natural dense water fog is analyzed. Information about the source is conveyed by ballistic, snake, and highly scattered photons. During propagation, the polarization state of ballistic and snake photons is not altered. It is shown that though circular polarization is not altered by simple direction changes during scattering, and has thus a tendency to be preserved longer in the highly scattered photons, it does not necessarily convey more useful information about the source than linear polarization or even an unpolarized beam. It is also shown that in any forward propagating system that can be described by the small-angle approximation the impact of polarization memory can be neglected.

Forward transmission characteristics in polystyrene solution with different concentrations by use of circularly and linearly polarized light

Polarized light forward propagation in scattering environments is important basic research. Polystyrene microspheres in water are common scattering environments that can be helpful to investigate in existing literature research. In this paper, we investigated the polarization state persistence of both linearly and circularly polarized light. We used a single active source with a wavelength of 532 nm to illuminate 1 μm diameter polystyrene spheres immersed in water. To evaluate the polarization state persistence of linearly and circularly polarized light, a parameter change of polarization state was used to replace the Stokes parameters. In the setting environments of different concentrations, circularly polarized light has superior polarization state persistence to that of linearly polarized light.

Time-dependent polarized radiative transfer in an atmosphere-ocean system exposed to external illumination

Time-dependent polarized radiative transfer in an atmosphere-ocean system exposed to external illumination is numerically investigated. The specular reflection and transmission effects based on the relative refractive index between the atmosphere and water are considered. A modified Monte Carlo (MMC) algorithm combined with time shift and superposition principle, which significantly improves the computational efficiency of the traditional Monte Carlo (TMC) method, is developed to simulate the time-dependent polarized radiative transfer process. The accuracy and computational superiority of the MMC for polarized radiative transfer in the atmosphere-ocean system are validated, and the time-resolved polarized radiative signals are discussed.

Transient polarized radiative transfer in cloud layers: numerical simulation of imaging lidar returns

In this paper, we investigate the time-dependent backscattering halo of a pulsed light beam in a layer of scattering medium. We start from numerical simulations of polarized radiative transfer in the layer, which immediately reveals the effect under investigation. Then we analyze time-dependent structure of the light field using the simulation results. From the radiation field, we extract two principal components, immediately forming the halo structure. For each diffuse and ballistic component, we use the proper theoretical model, yielding a convenient analytic description of the time-dependent behavior of the radiation field. From the theory developed by us, we derive a simple numerical criterion of visibility of the halo. Finally, we validate our theory against Monte Carlo radiative transfer simulations. Thus, we propose a quantitative explanation of the studied effect.

Superior signal persistence of circularly polarized light in polydisperse, real-world fog environments

We present simulation results quantitatively showing that circularly polarized light persists in transmission through several real-world and model fog environments better than linearly polarized light over broad wavelength ranges from the visible through the infrared. We present results for polydisperse particle distributions from realistic and measured fog environments, comparing the polarization persistence of linear and circular polarization. Using a polarization-tracking Monte Carlo program, we simulate polarized light propagation through four MODTRAN fog models (moderate and heavy radiation fog and moderate and heavy advection fog) and four real-world measured fog particle distributions (Garland measured radiation and advection fogs, Kunkel measured advection fog, and Sandia National Laboratories' Fog Facility's fog). Simulations were performed for each fog environment with wavelengths ranging from 0.4 to 12 µm for increasing optical thicknesses of 5, 10, and 15 (increasing fog density or sensing range). Circular polarization persists superiorly for all optical wavelength bands from the visible to the long-wave infrared in nearly all fog types for all optical thicknesses. Throughout our analysis, we show that if even a small percentage of a fog's particle size distribution is made up of large particles, those particles dominate the scattering process. In nearly all real-world fog situations, these large particles and their dominant scattering characteristics are present. Larger particles are predominantly forward-scattering and contribute to circular polarization's persistence superiority over broad wavelength ranges and optical thicknesses/range. Circularly polarized light can transmit over 30% more signal in its intended state compared to linearly polarized light through real-world fog environments. This work broadens the understanding of how circular polarization persists through natural fog particle distributions with natural variations in mode particle radius and single or bimodal characteristics.

Transient/time-dependent radiative transfer in a two-dimensional scattering medium considering the polarization effect

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method

Transient (time-dependent) polarized radiative transfer in a scattering medium exposed to an external collimated beam illumination is conducted based on the time-dependent polarized radiative transfer theory. The transient term, which persists the nanosecond order time and cannot be ignored for the time-dependent radiative transfer problems induced by a short-pulsed beam, is considered as well as the polarization effect of the radiation. A discontinuous finite element method (DFEM) is developed for the transient vector radiative transfer problem and the derivation of the discrete form of the governing equation is presented. The correctness of the developed DFEM is first verified by comparing the DFEM solutions with the results from the literature. The DFEM is then applied to study the transient polarized radiative transfer induced by a pulsed beam. The time-dependent Stokes vector components are calculated, plotted and analyzed as functions of the axis coordinate and discrete direction. Effects of the diffuse/specular boundary and the incident beam polarization state with respect to the Stokes vector components are further analyzed for cases of different boundary reflection modes and incident beam illuminations.

Design of a circular polarization imager for contrast enhancement in rainy conditions

We present the design of a circular polarization imager for imaging in rainy conditions, which is free from image calibration and correction before obtaining the orthogonal-state contrast image. The system employed a quarter wave plate in front of two Wollaston Prisms (WPs) to capture circularly polarized information and to acquire two orthogonally polarized images simultaneously on the charge coupled device (CCD). Along with the WPs, a reimaging part with multiaperture structure composed of two separate specialized reimaging modules, were implemented to make sure the two orthogonally polarized intensity images are exactly indicating the same scene. Exploiting circularly polarized information provides advantages over a linear polarization imaging system when considering the turbulence of media and illumination. Substantial data have demonstrated the effects of the novel designed polarization imaging system.

Evolution of circular and linear polarization in scattering environments

This work quantifies the polarization persistence and memory of circularly polarized light in forward-scattering and isotropic (Rayleigh regime) environments; and for the first time, details the evolution of both circularly and linearly polarized states through scattering environments. Circularly polarized light persists through a larger number of scattering events longer than linearly polarized light for all forward-scattering environments; but not for scattering in the Rayleigh regime. Circular polarization's increased persistence occurs for both forward and backscattered light. The simulated environments model polystyrene microspheres in water with particle diameters of 0.1 μm, 2.0 μm, and 3.0 μm. The evolution of the polarization states as they scatter throughout the various environments are illustrated on the Poincaré sphere after one, two, and ten scattering events.

Detection range enhancement using circularly polarized light in scattering environments for infrared wavelengths

We find for infrared wavelengths that there are broad ranges of particle sizes and refractive indices that represent fog and rain, where circular polarization can persist to longer ranges than linear polarization. Using polarization tracking Monte Carlo simulations for varying particle size, wavelength, and refractive index, we show that, for specific scene parameters, circular polarization outperforms linear polarization in maintaining the illuminating polarization state for large optical depths. This enhancement with circular polarization can be exploited to improve range and target detection in obscurant environments that are important in many critical sensing applications. Initially, researchers employed polarization-discriminating schemes, often using linearly polarized active illumination, to further distinguish target signals from the background noise. More recently, researchers have investigated circular polarization as a means to separate signal from noise even more. Specifically, we quantify both linearly and circularly polarized active illumination and show here that circular polarization persists better than linear for radiation fog in the short-wave infrared, for advection fog in the short-wave and long-wave infrared, and large particle sizes of Sahara dust around the 4 μm wavelength. Conversely, we quantify where linear polarization persists better than circular polarization for some limited particle sizes of radiation fog in the long-wave infrared, small particle sizes of Sahara dust for wavelengths of 9-10.5 μm, and large particle sizes of Sahara dust through the 8-11 μm wavelength range in the long-wave infrared.

Depolarization coefficients of light in multiply scattering media

The depolarization coefficients are calculated for multiply scattered linearly and circularly polarized light. For a number of media (aqueous suspension of polystyrene particles, water droplets in air), the calculations are carried out both numerically, with solving the vector radiative transfer equation and analytically, within the polarization mode approximation. In the latter case the depolarization coefficients are expressed explicitly in terms of the scattering and absorption coefficients, and the scattering matrix elements of the medium. The range of applicability of the polarization mode approximation is established. For most practically important cases, this method is shown to provide a satisfactory degree of accuracy. We also find the fundamental values of the depolarization coefficients for a Rayleigh medium.

Transient radiative transfer in a scattering slab considering polarization

The characteristics of the transient and polarization must be considered for a complete and correct description of short-pulse laser transfer in a scattering medium. A Monte Carlo (MC) method combined with a time shift and superposition principle is developed to simulate transient vector (polarized) radiative transfer in a scattering medium. The transient vector radiative transfer matrix (TVRTM) is defined to describe the transient polarization behavior of short-pulse laser propagating in the scattering medium. According to the definition of reflectivity, a new criterion of reflection at Fresnel surface is presented. In order to improve the computational efficiency and accuracy, a time shift and superposition principle is applied to the MC model for transient vector radiative transfer. The results for transient scalar radiative transfer and steady-state vector radiative transfer are compared with those in published literatures, respectively, and an excellent agreement between them is observed, which validates the correctness of the present model. Finally, transient radiative transfer is simulated considering the polarization effect of short-pulse laser in a scattering medium, and the distributions of Stokes vector in angular and temporal space are presented.

Truncated Fourier-series approximation of the time-domain radiative transfer equation using finite elements

The radiative transfer equation (RTE) is widely accepted to accurately describe light transport in a medium with scattering particles, and it has been successfully applied as a light-transport model, for example, in diffuse optical tomography. Due to the computationally expensive nature of the RTE, most of these applications have been in the frequency domain. In this paper, an efficient solution method for the time-domain RTE is proposed. The method is based on solving the frequency-domain RTE at multiple modulation frequencies and using the Fourier-series representation of the radiance to obtain approximation of the time-domain solution. The approach is tested with simulations. The results show that the method can be used to obtain the solution of the time-domain RTE with good accuracy and with significantly fewer computational resources than are needed in the direct time-domain solution.

Selective polarization imager for contrast enhancements in remote scattering media

Conventional intensity imaging through turbid media suffers from rapid loss of image contrast due to light scattering from particles or random variations of refractive index. This paper features the development of an active imaging, snapshot, system design and postprocessing algorithms that differentiate between radiation that scatters or reflects from remote, obscured objects and the radiation from the scattering media itself through a combination of polarization difference imaging, channel blurring, and Fourier spatial filtering. The produced sensor acquires and processes image data in real time, yielding improved image contrasts by factors of 10 or greater for dense water vapor obscurants.

Depolarization of light in turbid media: a scattering event resolved Monte Carlo study

Details of light depolarization in turbid media were investigated using polarization-sensitive Monte Carlo simulations. The surviving linear and circular polarization fractions of photons undergoing a particular number of scattering events were studied for different optical properties of the turbid media. It was found that the threshold number of photon scattering interactions that fully randomize the incident polarization (defined here as <1% surviving polarization fraction) is not a constant, but varies with the photon detection angle. Larger detection angles, close to backscattering direction, show lower full depolarization threshold number for a given set of sample's optical properties. The Monte Carlo simulations also confirm that depolarization is not only controlled by the number of scattering events and detection geometry, but is also strongly influenced by other factors such as anisotropy g, medium linear birefringence, and the polarization state of the incident light.

Towards skin polarization characterization using polarimetric technique

Measurement of optical properties of skin is an expanding and growing field of research. Recent studies have shown that the biological tissue, especially skin, changes the polarization state of the incident light. Using this property will enable the study of abnormalities and diseases that alter not only the light intensity but also its polarization state. In this paper we report an experimental study for measuring changes of polarization state of the light scattered from a phantom similar to a sample model of scattering skin. Using the notation of Stokes vector for the polarized light and Mueller matrix for the sample with its polarization properties, we have shown that some elements of the matrix were particularly sensitive to the changes of the polarization-altering physical properties of the scatterers within the phantom.

Investigation of multilevel amplitude modulation for a dual-wavelength free-space optical communications system using realistic channel estimation and minimum mean-squared-error linear equalization

Fog is a highly dispersive medium at optical wavelengths, and the received pulse waveform may suffer significant distortion. Thus it is desirable to have the impulse response of the propagation channel to recover data transmitted through fog. The fog particle density and the particle size distribution both strongly influence the channel impulse response, yet it is difficult to estimate these parameters. We present a method using a dual-wavelength free-space optical system for estimating the average particle diameter and the particle number density and for approximating the particle distribution function. These parameters serve as inputs to estimate the atmospheric channel impulse response using simulation based on the modified vector radiative transfer theory. The estimated channel response is used to design a minimum mean-square-error equalization filter to improve the bit error rate by correcting distortion in the received signal waveform due to intersymbol interference and additive white Gaussian noise.

Quantification of scattering changes using polarization-sensitive optical coherence tomography

We demonstrate that changes in the degree of polarization (DOP) depend on changes in the scattering coefficient, and they can be quantified by using a polarization-sensitive optical coherence tomography (PS-OCT) system. We test our hypothesis using liquid and solid phantoms made from Intralipid suspensions and gelatin, respectively. We also quantify the DOP changes with depth caused by changes in the concentration of scatterers in the liquid and solid phantoms. It is clearly shown that the DOP change has a linear relationship with the scattering change. In our previous study, we showed that the axial slope of the DOP is different between normal and pathologic cervical tissues. Our results demonstrate that the quantification of the axial DOP slope can be used for the systematic diagnosis of certain tissue pathology.

Polarized temporal impulse response for scattering media from third-order frequency correlations of speckle intensity patterns

Second- and third-order frequency correlations of speckle intensity patterns are used to characterize scattering media for multiple polarization states. The polarized temporal responses thus obtained are sensitive to the degree of scatter, with results being predictable by a diffusion model with sufficiently strong scatter. Experimental data are used to reconstruct various transfer functions.

Analytical cumulant solution of the vector radiative transfer equation investigates backscattering of circularly polarized light from turbid media

The backscattering of circularly polarized light pulses from an infinite uniform scattering medium is studied as a function of helicity of the incident light and size of scatterers in the medium. The approach considers a polarized short pulse of light incident on the scattering medium, and uses an analytical cumulant solution of the vector radiative transfer equation with the phase matrix obtained from the Mie theory to calculate the temporal profile of scattered polarized photons for any position and any angle of detection. The general expression for the scattered photon distribution function is an expansion in spatial cumulants up to an arbitrary high order. Truncating the expansion at the second-order cumulant, a Gaussian analytical approximate expression for the temporal profile of scattered polarized photons is obtained, whose average center position and half width are always exact. The components of scattered light copolarized and cross polarized with that of the incident light can be calculated and used for determining the degree of polarization of the scattered light. The results show that circularly polarized light of the same helicity dominates the backscattered signal when scatterer size is larger than the wavelength of light. For the scatterers smaller than the wavelength, the light of opposite helicity makes the dominant contribution to the backscattered signal. The theoretical estimates are in good agreement with our experimental results.

Polarized light-pulse transport through scattering media

The propagation of a polarized pulse in random media is investigated using the discrete-ordinates method to solve the transient vector radiative transfer. The angular analysis of the transient polarized features of scattering fluxes makes it possible to investigate subtle details of the polarization flip encountered for circularly polarized waves. We found that, depending on the geometry, the state of polarization, and the angle of detection, the degree of polarization decays at either a slower or faster rate when the beam is impinging at an angle far from the normal incidence. At normal incidence, our results confirm that, for large particles, the circular polarization maintains a greater degree of polarization.

Frequency-resolved interferometer measurements of polarized wave propagation in scattering media

An interferometric technique is utilized to measure both the time- and frequency-domain optical fields scattered by a random medium. The method uses a tunable continuous-wave laser source to make frequency-resolved measurements within a fixed-path-length interferometer. Measured frequency-domain field statistics, with a linearly polarized input, are shown to be zero-mean, circular complex Gaussian for both co- and cross-polarization states. With decreasing scatter, the extracted average impulse responses for co- and cross-polarized states show distinct differences, thereby providing insight into the scattering domain.

Simulation of sea surface wave influence on small target detection with airborne laser depth sounding

A theoretical model for simulation of airborne depth-sounding lidar is presented with the purpose of analyzing the influence from water surface waves on the ability to detect 1-m3 targets placed on the sea bottom. Although water clarity is the main limitation, sea surface waves can significantly affect the detectability. The detection probability for a target at a 9-m depth can be above 90% at 1-m/s wind and below 80% at 6-m/s wind for the same water clarity. The simulation model contains both numerical and analytical components. Simulated data are compared with measured data and give realistic results for bottom depths between 3 and 10 m.

Numerical studies on time-domain responses of on-off-keyed modulated optical signals through a dense fog

We present a numerical technique to simulate the propagation characteristics of an on-off-keyed modulated optical signal through fog. The on-off-keyed modulated light (a square wave) is decomposed into a finite number of harmonic components, and a numerical solution for the vector radiative transfer equation is obtained for each harmonic that corresponds to the modulation frequency. With this method we study the distortion and the pulse spread in the received signal due to attenuation and scattering. We investigate the propagation characteristic of the modulated signal with different communication system parameters. This information can be used to study communication channel reliability.

Backscattering of circularly polarized pulses

Using numerical simulations of vector radiative transport, we examine time-resolved backscattering of circularly polarized plane waves normally incident upon a slab containing a random distribution of latex spheres in water. For large spheres the effect of polarization memory occurs a short time after first-order scattering and before depolarization. It is the result of successive near-forward-scattering events that maintain the incident wave's helicity. For moderately large scatterers it exhibits a simple dependence on the anisotropy factor. For larger spheres or those with higher refractive indices, it also depends on complicated angular and polarization characteristics of backscattering given by Mie theory.