Criteria for objects suitable for reconstruction from holograms and diffraction patterns

TL;DR

This paper establishes quantitative criteria for reconstructing objects from holograms and diffraction patterns, clarifying conditions under which amplitude and phase objects can be successfully reconstructed, and revisiting classical criteria with modern analysis.

Contribution

It revises and simplifies Gabor's classical criteria for holographic reconstruction, providing new quantitative bounds and extending applicability to iterative reconstruction methods.

Findings

Objects smaller than 0.5% of the illuminated area can achieve high SNR in holography.

Both amplitude-only and phase-only objects are reconstructible if they occupy less than 1% of the imaged area.

Iterative algorithms allow larger objects, up to half the field of view, to be reconstructed successfully.

Abstract

In this study, quantitative criteria for reconstruction of objects from their hologram and diffraction patterns, and in particular for the phase objects in digital holography, are derived. The criteria that allow distinguishing the hologram and diffraction pattern are outlined. Gabor derived his criterion for objects suitable for holography based on the condition that the background in the reconstructed object's distribution should be nearly flat so that its intensity contrast does not exceed 0.05. According to Gabor, an opaque object is suitable for holographic reconstruction if it occupies no more than one percent of the imaged area, and a phase-shifting object cannot be reconstructed in principle. We revisit these criteria and show that both amplitude-only and phase-only objects can be reconstructed when the object occupies less than one percent of the total illuminated area. In addition, a simplified derivation of the criteria is provided that is based on Parseval's theorem. It is shown that for objects (including amplitude-only and phase-only) reconstructed from their holograms and the twin image treated as noise, the signal-to-noise ratio of 10 or higher can be achieved provided the object occupies less than 0.5 percent of the total illuminated area. When a hologram is reconstructed by applying iterative algorithms, the requirement for the object size is much more generous and identical to that applied in coherent diffraction imaging: any type of object (amplitude-only, phase-only, or amplitude-and-phase mixed properties) is suitable for holography when the object's size in each dimension is less than half of the probed region's extent (or the field of view).