Spatial Frequency Filtering Characteristics of Three-Phase and Two-Phase Two-Dimensional Gratings

Spatial frequency filtering by three phase and two phase gratings was theoretically analyzed. The 3-phase grating is a two-dimensional extrapolation of a one-dimensional binary phase grating, and the two phase grating has a phase structure which is simplified into two phases. Their optical transfer functions (OTF) were derived from the Fourier transform of their Fraunhofer diffraction patterns for various phase steps and widths. The most remarkable point is that their on-axis OTF graphs consist of only straight-line segments. Since this graph exhibits a trend for the changes in phase difference and width, we can express the on-axis OTF as an analytic function. By expanding in a Fourier series, the analytic function is proved to be the OTF of these gratings with arbitrary phase difference and width. We also proved that the two types of gratings have the same on-axis OTF graph.