We revisit the theoretical model for emission polarization from rough surfaces to improve previous models.
Previous models treat the directional emissivity σ<sub>s</sub> as 1- r<sub>s</sub> where r<sub>s</sub> is directional reflectivity and s stands for
perpendicular or parallel component to the incident surface. The directional emissivity is based on the Kirchhoff's law
and the energy conservation between incident, reflected and transmitted light. This emission model considers only linear
polarization as it does not allow the cross term of parallel and perpendicular components of Fresnel reflection
In this paper, we formulate the four emission Stokes parameters with emission wave amplitudes to describe the
complete emission polarization content of dielectric as well as conduction media. The emission wave amplitudes are
derived from the energy conservation and are functions of Fresnel transmission coefficients and incident and refraction
angles. For a conducting medium which has a complex indices of refraction, the refraction angle is redefined to avoid the
physically unreasonable complex angle. The emission Stokes parameters are averaged over time and then over the
roughness of the surface. The time average of the cross terms of the perpendicular and parallel emission electric fields is
assumed to be zero as the emission is an incoherent process.
It is found that the emission S2 is zero for a smooth surface or a surface with isotropic roughness and S3 is zero
regardless of surface roughness if the time average of the cross terms is assumed to be zero. Our results are compared
with previous theoretical models and lab measurements and reasonable agreement is found.
Monostatic Mueller matrix measurements of aluminum plates of various roughnesses are presented using a Mueller matrix polarimeter with a dual rotating retarder. The measurements are compared with a theoretical Mueller matrix model derived from the vector Kirchhoff diffraction equation. The wavelength of the laser is 1.55 μm. The rms roughness depths are provided by surface profilometer measurements and the roughness correlation length is estimated by finding the best match between the measured and the model reflectance for varying roughness correlation length. Except one smooth surface, all other aluminum samples studied have roughness ratio ( = roughness correlation length/rms roughness depth) less than 5. We compare the Mueller matrices between the lab measurement and the theoretical model. The model results show that the off-diagonal elements of the matrix have a symmetry relation and the magnitudes of diagonal elements are nearly 1, implying negligible depolarization for angles less than 30°. The lab measurements show that the off-diagonal elements have a symmetry relation for a smooth sample but the symmetry relation is weaker for rougher samples (lower roughness ratios). The lab data also show that depolarization is about 2% for the smooth sample but larger than 25% for the rougher samples for angles near 0°. The smooth surface shows reasonable agreement between the lab data and the model result except higher depolarization shown by the lab data for angles larger than 30°. On the other hand, the rough samples do not show similar agreement as the smooth surface shows. Possible causes of discrepancies are discussed and improvements for the lab measurement and model are suggested.
We have developed a scattering and emission polarization model. The scattering model is based on the vector Kirchhoff diffraction equation. For the emission polarization model, we use the Kirchhoff law for opaque materials, where the directional emissivity is assumed to be the same as Fresnel parallel and perpendicular transmittance. It is assumed that the emitted radiation from each facet has no relation with the radiation from neighboring facets. The roughness of the surface is treated statistically using the rms roughness height and the autocorrelation length. A Gaussian distribution is assumed for the roughness facet normal vectors. Shadowing by neighboring facets is also included in the model. We compute look-up tables for the scattering Mueller matrix and emission Stokes parameters for all incident and scattering (or emission) angles. The look-up tables are used for simulating the scattering and emission polarization signatures of objects. Polarization images of scattering, self-emission, and combination of scattering and emission are studied for Aluminum objects of various roughnesses and for various wavebands. The results show that the surface roughness is an important factor to determine the intensity and polarization. Our simulation results agree with polarization field data in that solar reflection has larger cancellation effect on MW IR polarization signatures than LW IR.
Current simulations of optical polarization scattering and emission for remote sensing applications employ geometric optics. The approach is mathematically simple but lacks soundness of physics as it relies upon artificial adjustment of polarized specular and unpolarized diffuse components in the scattered radiation to match experiments. In order to improve the current polarization scattering model, we are developing a model based on the vector Kirchhoff diffraction integral. The vector Kirchhoff diffraction model will simulate a main lobe and a diffraction pattern for each rough surface facet of a material. Predictioins of measurable polarization states will result through calculating the diffraction lobes of different facet orientations. The Kirchhoff approach will produce specular and diffuse components solely depending on surface characteristics and incident/scattering angles. Our mathematical model is an extension of Beckmann’s scalar rough surface scattering model. The roughness of the surface is treated statistically using the rms roughness height and the autocorrelation length and a Gaussian distribution is used for the roughness slope and facet normal. The shadowing by neighboring rough surface facets is also taken into account in the model. The results of the model are to be compared with published results of polarization scattering experiment.
Recent industry efforts have focused on the Balanced Tree Clustering (BTC) approach to speed up the encoding process for fractal image compression. Since the BTC algorithm compares intensity pixel by pixel for blocks in a mother cluster, clocks are divided into different clusters when they have different orientations or when they have different amplitudes of intensity offset with the averaged values but otherwise the same intensity distribution, causing poor clustering. In this paper we present and discuss the improvement of the original BTC algorithm by devising a method to include all 8 isometric versions of a block without enlarging the size of the domain pool and without sacrificing the encoding time. The results of compression are compared using the BTC algorithm based on the three different pixel values, intensity, intensity offset by the average value, and intensity variance, with and without considering 8 isometries of each block. For a sample image of 256 X 256 X 8 with 4 X 4 block size and with about 10 blocks in each cluster, the BTC using intensity variance and considering the 8 isometries the encoding speed about 200 times while decreases PSNR less than 8 percent over the ordered quadrant intensity classification into three classes. The BTC based on intensity variance also improves the encoding time and the fidelity of compression over the BTC based on the other two pixel values. The BTC algorithm based on the three different pixel values also generate different fractal code books which may affect the utility of the code books for image classification and image matching.
The on- and off-axis polarizing properties of asymmetric retroreflectors are studied in detail for various angles of incidence and for various incident linear polarization states. An analytic model is developed by applying Fresnel law to the incident and reflecting radiation on each facet of the retroreflector. It is shown that the polarization state of retroreflected radiation is a sensitive function of incident angle, incident polarization rate, and retroreflector material. These characteristics may be applicable to the determination of the relative angular position between the retroreflector and the analyzer.