Reconstructed Wavefronts and Communication Theory*

TLDR

Gabor’s two‑step imaging process records a Fresnel diffraction pattern as a hologram to reconstruct an object, and generalized holograms extend this concept beyond Fresnel patterns. The study reinterprets this holographic process through the lens of communication theory. Reconstruction applies an inverse‑frequency‑dispersion operation, and the authors propose and experimentally test techniques to improve the process. The hologram formation is a modulation, frequency dispersion, and square‑law detection sequence, yielding a reconstruction with unit signal‑to‑noise ratio, but the introduced techniques successfully enhance the signal‑to‑noise ratio.

Abstract

A two-step imaging process discovered by Gabor involves photographing the Fresnel diffraction pattern of an object and using this recorded pattern, called a hologram, to construct an image of this object. Here, the process is described from a communication-theory viewpoint. It is shown that construction of the hologram constitutes a sequence of three well-known operations: a modulation, a frequency dispersion, and a square-law detection. In the reconstruction process, the inverse-frequency-dispersion operation is carried out. The process as normally carried out results in a reconstruction in which the signal-to-noise ratio is unity. Techniques which correct this shortcoming are described and experimentally tested. Generalized holograms are discussed, in which the hologram is other than a Fresnel diffraction pattern.