EXTENSION OF THE FRESNEL TRANSFORM TO ABCD SYSTEMS

An extension of the Fresnel transform to first-order optical systems t hat can be represented by an ABCD matrix is analyzed. We present and d iscuss a definition of the generalized transform, which is recognized to belong to the class of linear canonical transforms. A general mathe matical characterization is performed by listing a number of meaningfu l theorems that hold for this operation and can be exploited for simpl yfying the analysis of optical systems. The relevance to physics of th is transform and of the theorems is stressed. Finally, a comprehensive number of possible decompositions of the generalized transform in ter ms of elementary optical transforms is discussed to obtain further ins ight into this operation. (C) 1997 Optical Society of America.