Abstract

We show that a band-limited function that has zeros at a prescribed finite number of points within an interval of finite extent can always be found, regardless of how small the bandwidth is. This means that a one-dimensional image that crosses a given level at a number of prescribed points can always be constructed at the output of a diffraction-limited system, regardless of how close the points are, i.e., superresolution in image construction is feasible.

© 1985 Optical Society of America

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

Karen M. Nashold and Bahaa E. A. Saleh
J. Opt. Soc. Am. A 2(5) 635-643 (1985)

Synthesis of binary images from band-limited functions

Karen M. Nashold, James A. Bucklew, Walter Rudin, and Bahaa E. A. Saleh
J. Opt. Soc. Am. A 6(6) 852-858 (1989)

Fingerprints theorems for zero crossings

A. L. Yuille and T. Poggio
J. Opt. Soc. Am. A 2(5) 683-692 (1985)

New one-dimensional iterative approach to restoring two-dimensional circularly band-limited images

G. Gregori and S. Wabnitz
J. Opt. Soc. Am. A 2(11) 2046-2053 (1985)

Image construction: optimum amplitude and phase masks in photolithography

Bahaa E. A. Saleh and Karen M. Nashold
Appl. Opt. 24(10) 1432-1437 (1985)