It is well known that underwater objects become more readily visible when viewed through a vertical polarizer that suppresses horizontally polarized reflections from the air-water interface. However, quantitative measurements of the contrast enhancement achieved with a polarizer do not seem to have been reported in the literature. To measure the polarization-enabled contrast enhancement, we placed white and black tiles next to each other, immersed in water, then measured the optical contrast between them as a function of viewing angle (relative to the surface normal) with a polarization camera that simultaneously recorded images with linear polarization oriented 0°, 90°, and 45°from horizontal. Images were recorded with an RGB polarization camera through approximately 45 cm of water at Bozeman Pond and with a monochrome polarization camera through approximately 5 cm of water at Bozeman Beach. Images also were recorded with the monochrome camera and a filter to isolate the near infrared band of approximately 750 to 1000 nm. Indoor laboratory measurements also were recorded to verify the role of the color of the reflecting background. All experiments used carefully calibrated division-of-focal-plane polarization cameras. The observed contrast decreased with viewing angle, but less so for the vertically polarized images. The contrast enhancement, represented by the ratio of vertically polarized to unpolarized contrast, increased with viewing angle, even past the Brewster angle (approx. 53°). The contrast enhancement only began decreasing for viewing angles larger than 70°. In outdoor experiments with a mostly clear sky, the highest contrast enhancement was in the blue spectral band. The contrast was essentially the same for red, green, and blue bands with a white background. In all measurements, the black tile exhibited much larger degree of linear polarization, which is an example of the Umov effect. In this paper we describe the experiments, show and explain polarization images, and show and explain plots of contrast and contrast enhancement as a function of viewing angle.
Optical science and engineering education and practice make frequent use of the concepts of Lambertian surfaces, Lambertian reflectance, or Lambertian emission. These are all based on Lambert’s cosine law, which states that the radiant or luminous intensity [W/sr] reflected or emitted from a Lambertian surface varies as the cosine of the angle between the direction of incident (or emitted) radiation and the surface normal. However, a simpler definition is a Lambertian source produces radiance [W/(m2 sr)] that is constant with angle. This definition helps avoid common errors and confusion that arise when a Lambertian source is viewed in different geometries in which the field-of-view (FOV) solid angle is over- or under-filled by the source. In this paper we describe the theory of Lambertian reflection and emission for under- and over filled FOV situations and show measurements from a simple set of reflection experiments that help to prove these theories in practice by demonstrating that flux measured with an under-filled FOV varies as the cosine of the viewing angle, while flux measured with an over-filled FOV does not. We also show how to set up and conduct experiments to illustrate these different situations using a simple halogen lamp, lens, photodiode, and Lambertian panel.
While Spectralon panels are largely assumed to be ideal Lambertian surfaces, their actual polarized reflective responses deviate from the ideal by at least a small amount at illumination and viewing angles off surface normal. The Mueller matrix response of four different panels between 10% and 99% reflectance were measured and the radiometric response from two distinct monostatic or nearmonostatic polarimeter systems are compared, one at Montana State University and one at the Air Force Research Lab. The deviations from an assumed ideal Lambertian surface are reported.
A near-monostatic laser polarimeter has been designed, built, and used to measure angular Mueller matrices characterizing the polarization-dependent reflectance of materials in support of research into polarization lidar. Here we explain the system, show that it has qualitatively similar results as previous complex systems, and show example measurements for red brick, concrete, sheetrock, tar shingles, milled aluminum, and plain steel.
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