Estimation of the degree of polarization in active coherent imagery by using the natural representation

We address the problem of degree of polarization estimation in polarization diversity images. We consider active imaging techniques with laser illumination, which have the appealing feature of revealing contrasts that do not appear in conventional intensity images. These techniques provide two images of the same scene that are perturbed with speckle noise. Because of the presence of nonhomogeneity in the reflected intensity, it can be preferable to perform image analysis of the orthogonal-state contrast image, which is a measure of the degree of polarization of the reflected light when the coherency matrix is diagonal. It has been shown that a simple nonlinear transformation of this orthogonal-state contrast image leads to an image perturbed with additive symmetrical noise on which simple and efficient estimation and detection techniques can be applied. We propose to precisely analyze estimation properties of the degree of polarization using this natural representation. In particular, we determine the Cramer-Rao bound of the polarization degree estimation and the variance of the proposed estimator, and we study the estimator's efficiency as a function of the speckle order for different measurement strategies.     

Degree of polarization in Young's double-slit interference experiment formed by stochastic electromagnetic beams

We analyze the behavior of the degree of polarization in the interference field of Young's double-slit experiment. We analyze the degree of polarization in Young's double-slit interference experiment illuminated by stochastic electromagnetic beams. The distribution of the degree of polarization in the interference field for different correlation lengths and different slit widths is investigated. Furthermore, it is shown that the degree of polarization for a fixed observation point may take on values different from those it takes in the slits, depending not only on the value of the correlation length but also on the width of the slit.     

Polarization changes of partially coherent pulses propagating in optical fibers

We consider polarization changes of partially coherent pulses propagating through birefringent dispersive fibers in the linear regime. We show that the evolution of the degree of polarization across such pulses is determined not only by the coherence properties of the pulse in the source plane, but also by the spatial walk-off introduced by the group-velocity mismatch between the two polarization components. The interplay between these two factors determines the asymptotic value of the degree of polarization of an initially unpolarized statistical pulse. We compare our results with previously discussed coherence-induced polarization changes of partially coherent beams propagating in free space.     

Polarization of skylight in the O(2)A band: effects of aerosol properties

Motivated by several observations of the degree of linear polarization of skylight in the oxygen A (O(2)A) band that do not yet have a quantitative explanation, we analyze the influence of aerosol altitude, microphysics, and optical thickness on the degree of linear polarization of the zenith skylight in the spectral region of the O(2)A band, between 755 to 775 nm. It is shown that the degree of linear polarization inside the O(2)A band is particularly sensitive to aerosol altitude. The sensitivity is strongest for aerosols within the troposphere and depends also on their microphysical properties and optical thickness. The polarization of the O(2)A band can be larger than the polarization of the continuum, which typically occurs for strongly polarizing aerosols in an elevated layer, or smaller, which typically occurs for depolarizing aerosols or cirrus clouds in an elevated layer. We show that in the case of a single aerosol layer in the atmosphere a determination of the aerosol layer altitude may be obtained. Furthermore, we show limitations of the aerosol layer altitude determination in case of multiple aerosol layers. To perform these simulations we developed a fast method for multiple scattering radiative transfer calculations in gaseous absorption bands including polarization. The method is a combination of doubling-adding and k-binning methods. We present an error estimation of this method by comparing with accurate line-by-line radiative transfer simulations. For the Motivated by several observations of the degree of linear polarization of skylight in the oxygen A (O(2)A) band that do not yet have a quantitative explanation, we analyze the influence of aerosol altitude, microphysics, and optical thickness on the degree of linear polarization of the zenith skylight in the spectral region of the O(2)A band, between 755 to 775 nm. It is shown that the degree of linear polarization inside the O(2)A band is particularly sensitive to aerosol altitude. The sensitivity is strongest for aerosols within the troposphere and depends also on their microphysical properties and optical thickness. The polarization of the O(2)A band can be larger than the polarization of the continuum, which typically occurs for strongly polarizing aerosols in an elevated layer, or smaller, which typically occurs for depolarizing aerosols or cirrus clouds in an elevated layer. We show that in the case of a single aerosol layer in the atmosphere a determination of the aerosol layer altitude may be obtained. Furthermore, we show limitations of the aerosol layer altitude determination in case of multiple aerosol layers. To perform these simulations we developed a fast method for multiple scattering radiative transfer calculations in gaseous absorption bands including polarization. The method is a combination of doubling-adding and k-binning methods. We present an error estimation of this method by comparing with accurate line-by-line radiative transfer simulations. For the O(2)A band, the errors in the degree of linear polarization are less than 0.11% for transmitted light, and less than 0.31% for reflected light. band, the errors in the degree of linear polarization are less than 0.11% for transmitted light, and less than 0.31% for reflected light.     

Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths

Techniques for modeling an object through observation are very important in object recognition and virtual reality. A wide variety of techniques have been developed for modeling objects with opaque surfaces, whereas less attention has been paid to objects with transparent surfaces. A transparent surface has only surface reflection; it has little body reflection. We present a new method for obtaining surface orientations of transparent surfaces through analysis of the degree of polarization in surface reflection and emission in visible and far-infrared wavelengths, respectively. This parameter, the polarization degree of reflected light at the visible wavelengths, is used for determining the surface orientation at a surface point. The polarization degree at visible wavelengths provides two possible solutions, and the proposed method uses the polarization degree at far-infrared wavelengths to resolve this ambiguity.     

Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmosphere

We study the changes in the degree of polarization of an electromagnetic Gaussian Schell-model beam, as the beam propagates through the turbulent atmosphere. We demonstrate that, within the framework of the Tatarskii model of the turbulent atmosphere, the degree of polarization of the beam changes appreciably at relatively short propagation distances in the atmosphere. In the long-propagation distance limit, however, we find that the degree of polarization of the beam tends to the value that it has in the source plane.     

Measurement of the polarization degree of accelerated polarized electrons at the 2.5 GeV synchrotron in Bonn for energies between 0.85 and 2 GeV

The polarization degree of accelerated longitudinally polarized electrons has been measured employing the spin dependence of the elastic electron-electron cross section. We observe strong depolarization as well as polarization flips in the neighbourhood of imperfection and intrinsic resonances.

Measures to maintain the initial polarization degree up to the highest available energies are discussed.     

Generalized Stokes parameters of a stochastic electromagnetic beam propagating through a paraxial ABCD optical system

On the basis of the generalized diffraction integral formula for an ABCD optical system in the spatial domain, a propagation law for the generalized Stokes parameters of a stochastic electromagnetic beam passing through an ABCD optical system is obtained. We describe the Stokes parameters of the source as linear combinations of the elements of the cross-spectral density matrix, and study the changes in the spectral degree of polarization and in the state of the polarization ellipse of a stochastic electromagnetic Gaussian Schell-model beam propagating through a gradient-index fiber with the help of generalized Stokes parameters and the cross-spectral density matrix. The medium has significant effect on the change of the spectral degree of polarization. However, when the correlation coefficients of the source satisfy the relation delta(xx)=delta(yy)=delta(xy)=delta(yx), the medium does not influence the spectral degree of polarization.     

Degree of polarization in tightly focused optical fields

We analyze the degree of polarization of random, statistically stationary electromagnetic fields in the focal region of a high-numerical-aperture imaging system. The Richards-Wolf theory for focusing is employed to compute the full 3 x 3 electric coherence matrix, from which the degree of polarization is obtained by using a recent definition for general three-dimensional electromagnetic waves. Significant changes in the state of partial polarization, compared with that of the incident illumination, are observed. For example, a wave consisting of two orthogonal and uncorrelated incident-electric-field components produces rings of full polarization in the focal plane. These effects are explained by considering the distribution of the spectral densities of the three electric field components as well as the correlations between them.     

Passive single-mode fiber depolarizer

We analyze and demonstrate a passive single-mode fiber depolarizer by using cascaded 2 x 2 couplers, recirculating delay lines, and a commercial laser diode. Design criteria and principles are discussed. We reduced the degree of polarization (DOP) to less than 20 dB by using ten cascaded couplers. The DOP can be reduced even further with more couplers. Experiments illustrate that this depolarizer is insensitive to the input polarization state and can eliminate polarization noise in a polarization-sensitive fiber-optic system.     

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.     

Polarization changes in a partially coherent radially polarized doughnut beam through turbulent ocean

On the basis of the extended Huygens–Fresnel integral principle and unified theory of coherence and polarization of light, we studied the effects of oceanic turbulence on polarization properties of a partially coherent radially polarized doughnut (PCRPD) beam. The ocean-induced fluctuations in the refractive index are assumed be driven by temperature and salinity fluctuations. Numerical examples of changes in polarization properties, such as the degree of polarization, the degree of ellipticity, and the orientation angle in the oceanic turbulence for the PCRPD beam, are given. Our analysis demonstrates how polarization of the PCRPD beam is affected by statistical properties of the source and by several parameters of oceanic turbulence. We find that the propagation of the PCRPD beam is different from that of stochastic beams in oceanic turbulence. The degree of polarization for the PCRPD beam approaches a certain steady value, and the elliptical polarized state of the fully polarized portion of the beam will become fully linear in the far field.     

Changes in the polarization and coherence of a random electromagnetic beam propagating through a misaligned optical system

On the basis of the generalized diffraction integral formula for misaligned optical systems in the spatial domain, an analytical propagation expression for the elements of the cross-spectral density matrix of a random electromagnetic beam passing through a misaligned optical system is derived. Some analyses are illustrated by numerical examples relating to changes in the spectral degree of polarization and in the spectral degree of coherence of an electromagnetic Gaussian-Schell-model beam propagating through such an optical system. We find that the degree of polarization in the neighboring areas of the focal plane is oscillating, and the effect of misalignment on coherence is not so evident as that on polarization.     

Polarization distribution control of anisotropic electromagnetic Gaussian-Schell model beams on free propagation by exploiting correlation properties at the source plane

When propagating in free space, the transversal distribution of the degree of polarization of an anisotropic electromagnetic Gaussian-Schell model (AEGSM) beam will generally undergo a complex evolution process. We find that this transversal distribution of the degree of polarization of an AEGSM beam can be controlled by exploiting the partial correlation properties of the source. The main research of our paper falls into two parts. First, the concept of analogical propagation of the transversal distribution of the degree of polarization is proposed, and the condition for an AEGSM beam having an analogical propagation is obtained. When an AEGSM beam is on analogical propagation, the distribution of the degree of polarization on any cross section of the beam is always similar to that on the source plane, except that the size of the distribution pattern will expand continuously as the propagation distance increases. Second, the far-field transversal distribution of the degree of polarization is considered, and the condition for the far-field transversal polarization distribution of an AEGSM beam to be always of circularly symmetric shape, no matter how complicated it is on the source, is obtained. Our research is expected to find applications in areas that make use of the polarization properties of random electromagnetic beams.     

Partial spatial coherence and partial polarization in random evanescent fields on lossless interfaces

We consider partial spatial coherence and partial polarization of purely evanescent optical fields generated in total internal reflection at an interface of two dielectric (lossless) media. Making use of the electromagnetic degree of coherence, we show that, in such fields, the coherence length can be notably shorter than the light's vacuum wavelength, especially at a high-index-contrast interface. Physical explanation for this behavior, analogous to the generation of incoherent light in a multimode laser, is provided. We also analyze the degree of polarization by using a recent three-dimensional formulation and show that the field may be partially polarized at a subwavelength distance from the surface even though it is fully polarized farther away. The degree of polarization can assume values unattainable by beamlike fields, indicating that electromagnetic evanescent waves generally are genuine three-dimensional fields. The results can find applications in near-field optics and nanophotonics.     

Twilight polarization and optical depth of stratospheric aerosols over Beijing after the Pinatubo volcanic eruption

After the volcanic eruption of Mt. Pinatubo the degree of polarization of skylight during twilight over Beijing was monitored with a polarimeter aimed at the local zenith. We analyze the effect of changes in the scattering coefficient of atmospheric aerosols for the case of multiple scattering on skylight polarization at the zenith and then discuss the evolution of skylight polarization over Beijing during the posteruption period. As a reference and for comparison we also discuss the evolution of the aerosol optical depth retrieved from the combination of skylight polarization and backscattering ratio measured by the polarimeter and a lidar for the period beginning with the eruption of Mt. Pinatubo through the end of 1993. The contributions of atmospheric aerosols at different altitudes to the ground-observed twilight polarization depend on the solar zenith angle. For larger solar zenith angles, the skylight polarization is mostly sensitive to aerosol variations in the upper layer that range from 15 to 30 km. The twilight polarization at the zenith from June 1991 to mid-1994 shows different features for three periods: (1) From October 1991 to February 1992, volcanic dust traveled to mid-latitudes, and the degree of polarization decreased substantially. (2) From February 1992 to November 1993, volcanic dust was dispersed the minimum degree of polarization at the solar zenith angle of 93.5 degrees disappeared and the maximum increased. In addition, polarization for solar zenith angles less than 90 degrees also increased. (3) From November 1993 to May 1994, most of the volcanic dust had fallen off, the atmosphere was restored to the background state, and the skylight polarization approached the preeruption condition.     

Orthogonal planar laser polarization spectroscopy

Planar laser polarization spectroscopy has recently been used to image the hydroxyl radical in combustion for small intersection angles of pump and probe beams. We report an experimental configuration that allows planar laser polarization imaging for perpendicular intersection of pump and probe beams. We demonstrate what to our knowledge is the first planar laser polarization spectroscopy imaging at a 90 degree intersection of pump and probe beams for both linearly and circularly polarized pump beams.     

Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements

We analyze the sensitivity of the degree of linear polarization in the Sun's principal plane as a function of aerosol microphysical parameters: the real and imaginary parts of the refractive index, the median radius and geometric standard deviation of the bimodal size distribution (both fine and coarse modes), and the relative number weight of the fine mode at a wavelength of 675 nm. We use Mie theory for single-scattering simulations and the doubling-adding method with the inclusion of polarization for multiple scattering. It is shown that the behavior of the degree of linear polarization is highly sensitive to both the small mode of the bimodal size distribution and the real part of the refractive index of aerosols, as well as to the aerosol optical thickness; whereas not all parameters influence the polarization equally. A classification of the importance of the input parameters is given. This sensitivity study is applied to an analysis of ground-based polarization measurements. For the passive remote sensing of microphysical and optical properties of aerosols, a ground-based spectral polarization measuring system was built, which aims to measure the Stokes parameters I, Q, and U in the visible (from 410 to 789 nm) and near-infrared (from 674 to 995 nm) spectral range with a spectral resolution of 7 nm in the visible and 2.4 nm in the near infrared. We compare polarization measurements taken with radiative transfer simulations under both clear- and hazy-sky conditions in an urban area (Cabauw, The Netherlands, 51.58 degrees N, 4.56 degrees E). Conclusions about the microphysical properties of aerosol are drawn from the comparison.     

Polarization discrimination of coherently propagating light in turbid media

We describe the use of degree of polarization to discriminate unscattered and weakly scattered light from multiply scattered light in an optically turbid material. We use spatially resolved measurements of the degree of polarization to compare how well linearly and circularly polarized light survives in a sample. Experiments were performed on common tissue phantoms consisting of polystyrene and Intralipid microsphere suspensions and on adipose and arterial tissue. The results indicate that polarization is maintained even after unpolarized irradiance through each sample has been extinguished by several orders of magnitude. The results also show that polarized light propagation in common tissue phantoms is distinctly different from polarized light propagation in the two tissues investigated. Further, these experiments illustrate when polarization is an effective discrimination criterion and when it is not. The potential of a polarization-based discrimination scheme to image through the biological and nonbiological samples investigated here is also discussed.     

Dependence on temperature of circular polarization and relaxation time in InAlAs/AlGaAs quantum dots

We have studied the variation of photoluminescence circular polarization as a function of temperature in self-organized InAlAs/AlGaAs quantum dots. We have found that the circular polarization depends on temperature. The relaxation time τ_s is deduced from the circular polarization degree. It decreases from 2 ns at 40 K to 100 ps at 85 K.