Abstract

An iterative algorithm for reconstructing an image from partial Fresnel zone information is discussed. With the standard 4-F canonical optical processor, processing is done midway between the two lenses in the Fourier transform plane. While others have studied reconstruction from partial Fourier plane information, we have investigated methods of reconstructing an object from partial information in the Fresnel region of an optical processor. Efficient digital calculation for integrations with a Fresnel-zone type of kernel are described. Iterative algorithms for reconstructing an object from either the phase or magnitude of the Fresnel zone transform are discussed. In the case of reconstructing an image from the Fresnel zone magnitude, we obtain good images in fewer iterations at locations which are farther from the Fourier plane. Reconstructing an image from the Fresnel zone phase is fairly insensitive to this shift out of the Fourier plane. In another investigation, we start with the assumption that the object has been coded into an unknown location in the Fresnel region. We describe an iterative searching technique that locates this position; thereafter we reconstruct the image.

© 1985 Optical Society of America