An extension of the Fresnel transform to first-order optical systems that can be represented by an ABCD matrix is analyzed. We present and discuss a definition of the generalized transform, which is recognized to belong to the class of linear canonical transforms. A general mathematical characterization is performed by listing a number of meaningful theorems that hold for this operation and can be exploited for simplyfying the analysis of optical systems. The relevance to physics of this transform and of the theorems is stressed. Finally, a comprehensive number of possible decompositions of the generalized transform in terms of elementary optical transforms is discussed to obtain further insight into this operation.
© 1997 Optical Society of America
Original Manuscript: August 1, 1996
Revised Manuscript: December 2, 1996
Manuscript Accepted: December 2, 1996
Published: August 1, 1997
C. Palma and V. Bagini, "Extension of the Fresnel transform to ABCD systems," J. Opt. Soc. Am. A 14, 1774-1779 (1997)