Karen M. Nashold

Image construction through diffraction-limited high-contrast imaging systems: an iterative approach

It is desired to preprocess an input image so that, when it is distorted by an imaging system, a prescribed output image is produced. The system of interest is a linear, shift-invariant, band-limited system followed by a hard limiter. Such a system is found, for example, in microphotography, when a camera that is band limited by diffraction effects is used to print on very-high-contrast film. In this paper, an iterative solution that employs alternating projections is presented. Two valiations of the procedure, which is similar to the Gerchberg-Papoulis algorithm, are applied to several examples having different space-bandwidth products. Also, a method of overrelaxing the projections to improve convergence is studied.

Synthesis of binary images from band-limited functions

Binary images usually are produced by clipping band-limited images generated through physical systems. We examine the conditions under which a prescribed image can be formed by this process. Obviously, when the desired image has infinitely sharp isolated corners, it cannot be formed by clipping a band-limited image. We show, however, that any desired binary image can be approximated arbitrarily closely. To make this approximation one must find a band-limited function that has approximately the desired level crossings, i.e., contours where the function is equal to the threshold value of the clipping operation. This can be done by defining a band-limited function in terms of a product of functions that define the function’s zero-crossing contours. In a finite region, these zero crossings are defined strictly in terms of the zeros of a two-dimensional polynomial.

Synthesis of two-dimensional binary images through band-limited systems: a slicing method

A method is presented for solving the problem of synthesis of a two-dimensional (2-D) band limited function with prescribed level crossing. This method relies on decomposing a 2-D band limited function into the sum of products of one-dimensional (1-D) band limited functions along two orthogonal directions. The 1-D functions in one direction represent slices of the desired 2-D function and have zero crossings at the desired locations. They are produced by inserting and deleting zeros in a known band limited function (a sinc function). The orthogonal 1-D functions are used as interslice interpolation functions. The generated 2-D function is band-limited and has correct zeros at the slices. Its zeros between slices may not be correct, but the interslice distance can be made arbitrarily small. Nonuniform slicing can be used to improve the resolution of the approximations. Interpolation functions for the nonuniform slices are generated by the same method used to produce the slices. >