Image irradiance in the absence of aplanatism and isoplanatism

Abstract

Textbook chapters on the subject of optical radiometry often impose the condition of aplanatism when deriving a well-known expression for image irradiance in optical systems, yet at least two authors (including this author) have shown that this condition is unnecessary for the expression to hold. In this paper, theories and computer-aided ray-tracing analyses are provided to support the validity of the expression for even wider cases, where stigmatism, aplanatism, and isoplanatism are all not assumed. Further, it is shown that when both diffraction and aberrations are involved, one may apply a fusion of the expression with the fundamentals of image formation by convolution (if the image is isoplanatic) or superposition (if the image is not isoplanatic) in Fourier optics. To highlight how graduate students and researchers in the laboratory may benefit from the concepts presented here, a practical application is discussed involving signal detection.