Calculation and Analysis of the Pulse Response of Spatially Non-Invariant Projection Systems

Abstract

Characteristics of spatially non-invariant telecentric projection systems, which are widely used in practice, are considered within the framework of wave optics. In the class of the Fresnel functions, the pulse response of the system is precisely calculated for various values of the projection objective and filter apertures. It is found that the response consists of two components, which determine the invariant and non-invariant properties of the system, respectively. Based on the approximation of the Fresnel function by elementary functions proposed previously by the author, an analytical expression for the pulse response is derived for the first time, and the response behavior is studied for various relationships of the objective and filter apertures. The correctness of choosing the parameters of the known quasi-invariant optical systems is analyzed. Recommendations on choosing the filter aperture are given to improve their spatially invariant characteristics. In contrast to available optical and geometrical methods, the proposed approach allows one to obtain reliable information about the character of wave field transformations in the considered systems.