Vimal Thilak, David G. Voelz, and Charles D. Creusere, "Polarization-based index of refraction and reflection angle estimation for remote sensing applications," Appl. Opt. 46, 7527-7536 (2007)
A passive-polarization-based imaging system records the polarization state of light reflected by objects that are illuminated with an unpolarized and generally uncontrolled source. Such systems can be useful in many remote sensing applications including target detection, object segmentation, and material classification. We present a method to jointly estimate the complex index of refraction and the reflection angle (reflected zenith angle)
of a target from multiple measurements collected by a passive polarimeter.
An expression for the degree of polarization is derived from the microfacet polarimetric bidirectional reflectance model for the case of scattering in the plane of incidence. Using this expression, we develop a nonlinear least-squares estimation algorithm for extracting an apparent index of refraction and the reflection angle from a set of polarization measurements collected from multiple source positions. Computer simulation results show that the estimation accuracy generally improves with an increasing number of source position measurements. Laboratory results indicate that the proposed method is effective for recovering the reflection angle and that the estimated index of refraction provides a feature vector that is robust to the reflection angle.
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The true index of refraction (n) is 1.5 and the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. The variance of the Gaussian noise is 0.1% of the maximum DOP value, which is 1.0 for this case. The results are obtained from 500 Monte Carlo trials.
The true index of refraction (n) is 1.5 and the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. The variance of the Gaussian noise is 1% of the maximum DOP value, which is 1.0 for this case. The results are obtained from 200 Monte Carlo trials.
The true index of refraction is n = 0.314 and k = 3.544 while the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. The variance of the Gaussian noise is 0.1% of the maximum DOP value, which is 0.082 for this case. The results are obtained from 500 Monte Carlo trials.
The true index of refraction is n = 0.314 and k = 3.544 while the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. Note that the step size reduces to 2.5° for the case of 19 measurements (see text for explanation). The variance of the Gaussian noise is 1% of the maximum DOP value, which is 0.082 for this case. The results are obtained from 200 Monte Carlo trials.
The true index of refraction (n) is 1.5 and the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. The variance of the Gaussian noise is 0.1% of the maximum DOP value, which is 1.0 for this case. The results are obtained from 500 Monte Carlo trials.
The true index of refraction (n) is 1.5 and the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. The variance of the Gaussian noise is 1% of the maximum DOP value, which is 1.0 for this case. The results are obtained from 200 Monte Carlo trials.
The true index of refraction is n = 0.314 and k = 3.544 while the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. The variance of the Gaussian noise is 0.1% of the maximum DOP value, which is 0.082 for this case. The results are obtained from 500 Monte Carlo trials.
The true index of refraction is n = 0.314 and k = 3.544 while the true reflection angle is 60°. The range of the angle of incidence is noted and is varied in steps of 5°. Note that the step size reduces to 2.5° for the case of 19 measurements (see text for explanation). The variance of the Gaussian noise is 1% of the maximum DOP value, which is 0.082 for this case. The results are obtained from 200 Monte Carlo trials.