Abstract

Coded apertures are useful for imaging sources of x rays and gamma rays in nuclear medicine, x-ray astronomy, laser fusion studies, and nuclear reactor safety research. While conventional apertures such as a pinhole or multibore collimator provide only two-dimensional (2D) projections of a three-dimensional (3D) source, coded apertures give some information about the 3D structure of the source. The easiest way to see this is by considering a point source some finite distance from the aperture plane. The coded image in this case is merely an enlarged shadow of the aperture transmission function. This shadow contains all the necessary information to fully characterize the source. The scale of the shadow gives the longitudinal coordinate of the point (i.e., its distance from the aperture plane), and the lateral position of the shadow on the detector is simply related to the lateral position of the point in a plane parallel to the aperture. The strength of the source is related to the number of recorded photons in the coded image. Thus the shadow uniquely determines the 3D location of the source and its strength if we know a priori that it is a point source. Of course, we are usually interested in more complicated sources, and the central problem of coded-aperture imaging may be stated as follows: Given one or more 2D coded images and possibly some a priori information about the source, estimate the 3D distribution of the source.

© 1983 Optical Society of America