Accurate calculation of the irradiance of optical images

Abstract

Accurate knowledge of the relative image irradiance is important in the design of some optical instruments, e.g., IR systems, where it determines the apparent temperature of the object, and camera systems employing irregular-shaped aperture stops or light-absorbing elements. We review the quick Hopkins method for calculating the relative image irradiance of systems with circular or elliptical stops and then describe a modification that enables it to be used for the less conventional systems mentioned. The new method is used to calculate the relative irradiance of a camera objective that includes a neutral density wedge. We also present a brief discussion of the often misunderstood cos4 law, which is of some importance in the design of optical instruments.