Abstract

It is often desired to generate a 2-D bandlimited function f (x,y), which when thresholded has specified edges. This is the case, for example, in generating binary masks through diffraction-limited systems. It has been shown in the past that bandlimited images can be constructed from slices which are themselves generated using 1-D methods. No emphasis, however, was placed on where the slices should be made. If an exact solution exists, and the slices are produced at distances separated by 1/2B (B being the required bandwidth in the y direction), f(x,y) can be found by simply low pass filtering the slices. If, however, an exact solution does not exist, which is often the case in image construction, such construction only guarantees the exact zero crossings along the slices. Our results indicate that uneven sampling can improve resolution. Samples are taken closer together in a finite region where greater resolution is required and farther apart elsewhere. The desired image is then formed using interpolating functions which are determined, depending on the desired sampling locations, by properly inserting and deleting zeros in a known bandlimited function. The resulting image can thus be forced to have the desired zero crossings at more places than in regular sampling, and hence greater accuracy is achieved.

© 1987 Optical Society of America