Accurate knowledge of the relative image irradiance is important in th
e design of some optical instruments, e.g., IR systems, where it deter
mines the apparent temperature of the object, and camera systems emplo
ying irregular-shaped aperture stops or light-absorbing elements. We r
eview the quick Hopkins method for calculating the relative image irra
diance of systems with circular or elliptical stops and then describe
a modification that enables it to be used for the less conventional sy
stems mentioned. The new method is used to calculate the relative irra
diance of a camera objective that includes a neutral density wedge. We
also present a brief discussion of the often misunderstood cos(4) law
, which is of some importance in the design of optical instruments. (C
) 1998 Society of Photo-Optical Instrumentation Engineers. [S0091-3286
(98)00910-6].