Imaging in first-order optical systems

A general analysis of imaging phenomena based on the properties of the canonical integral transform has been carried out for first-order (ABCD) optical systems. It is shown that under some conditions the effect of the canonical integral transform on an input complex amplitude, being the eigenfunction of another canonical operator, generates its scaled replica with an additional quadratic phase shift. As particular examples, the imaging of a periodic input complex amplitude and a self-fractional Fourier function are considered. For imaging of a transparency the additional quadratic phase shift vanishes with use of a wave with a spherocylindrical phase front for illumination. (C) 1996 Optical Society of America.