Role of aberrations in the relative illumination of a lens system

Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to cosine-fourth-power radiometric law, image and pupil aberrations and light vignetting also count. 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.