Abstract

This paper presents a study of the piecewise isoplanatic approximation (PIA) applicable to the representation of space-variant linear systems. The approximation employed here divides the input plane into isoplanatic patches to which corresponding impulse responses are assigned. The resulting PIA output is an approximate representation of the true system output. A new measure of the degree of invariance is developed as an aid to classifying linear systems and applying the PIA model. This new measure seems to predict the relationships between the true and PIA system outputs better than the Lohmann and Paris measure.¹ A comparison of both measures is described. Several examples are presented to explain the relationships between the degree of invariance and the PIA system output. With the aid of the new measure, we can find the optimal size of each isoplanatic patch in the input plane and the optimal corresponding impulse response in each patch. The relationship of the variation bandwidth to the new measure of invariance is also mentioned in supporting the validity of the new measure.

© 1985 Optical Society of America