Gabor Holography Reinvented

Abstract

This paper presents a "reinvention" of Gabor Holography that does not suffer optically from the inherent twin-image problem originating back to Gabor's original Nobel Prize awarded invention. In-line or on-axis holography was ironically abandoned by its inventor Dennis Gabor himself and was effectively completely "re-placed" by so-called off-axis holography at the time when Gabor received the Nobel Prize in Physics in 1971. However, Gabor Holography is today the method of choice in modern digital holography due to its inherent on-axis, common-path robustness, lower requirements to resolution of the image sensor (or recording material), shorter exposure time, relaxed mechanical stability and temporal coherence requirements. However, it still inherently suffers from the aforementioned twin-image problem and, hence, one will find an abundance of papers trying to overcome this challenge by iterative phase retrieval or machine learning based approaches. Gabor Holography Reinvented overcomes this long-lasting twin-image problem for the first time by optical means.

Figures (7)

• Figure 1: Generalized recording and reconstruction process of holography. $\mathcal{H}$ and its conjugate $\mathcal{H}^*$ describe the optical system.
• Figure 2: Schematic of hologram recording and reconstruction processes. (a, d) Optical holography (OH), (b, e) computer-generated holography (CGH), (c, f) digital holography (DH). $\mathcal{H}$ and its conjugate $\mathcal{H}^*$ describe any operation between the input object and its output.
• Figure 3: Various axicon modalities. Top row: refractive axicons, bottom row: diffractive axicons. Left column: 4F-based, center column: single imaging lens, right column: combination of free-space propagation and axicon modulation.
• Figure 4: Image sensor read-out and reconstruction. (a) Object imaged without axicon placed in spatial frequency domain, (b) with axicon placed in spatial frequency domain. Holographic terms co-located in bands of characteristic width $r_{obj}$, (c) reconstructed object with twin-image term in band with radius $2r_0$.
• Figure 5: Numerical reconstructions of amplitude and phase of a complex-valued object. The two sides of an old Danish coin are encoded as amplitude and phase, respectively. (Left) reconstruction using Gabor Holography, (right) reconstruction using Gabor Holography Reinvented.