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Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to the cosine-fourth-power radiometric law, image and pupil aberrations, and light vignetting also count. In this paper, we use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing.
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Dmitry Reshidko, Jose Sasian, "The role of aberrations in the relative illumination of a lens system," Proc. SPIE 9948, Novel Optical Systems Design and Optimization XIX, 994806 (30 September 2016); https://doi.org/10.1117/12.2237204