Optical EngineeringImaging of retroreflective objects under highly nonuniform illumination
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The answers to two common questions are attempted. The first is the mathematical representation of the visibility characteristics of a retroreflector. The second question concerns the construction of the necessary viewing criterion under highly nonuniform illumination. The problem of viewing a retroreflective object is discussed from the general viewpoint of the optical reciprocity theorem. Nonuniform illumination leads to peculiarities in calculating the contrast because the absence of any reference image region that usually serves as a background. For this reason, an optical sensor focuses its attention on the maximal brightness gradient of an image to compare the radiances of two adjacent resolution elements. In such a case, the valid signal is shown to be determined only by the radiance of direct light from a dummy source having an angular pattern of radiation that is the same as the angular pattern of the real receiver sensitivity, whereas optical interferences are obtained by taking multiply scattered light into account. The calculations are made under the small-angle diffusion approximation with the direct light isolated. One interesting example of observing retroreflective and Lambertian objects is presented. In particular, the case of viewing a retroreflector on a Lambertian background with the same albedos is considered. Here, the observation is possible only due to the different angular patterns of reflection.