On the single point resolution of on-axis digital holography
Spotlight summary: Digital holography (DH) as an imaging modality has evolved and become increasingly popular over the past couple of decades, with improvements in digital array detectors (e.g., CCD arrays) and the simultaneous availability of computational power. We are all aware of the transition from film-based to digital cameras and the overall effect this has had. This transition has played an equally important role in the area of holographic imaging, with ever-increasing applications. When an object to be imaged is illuminated by spatially coherent light, the scattered wavefront from the object carries information about its structure in the form of amplitude and phase variations. A digital hologram is an interference pattern between the scattered waves and a reference wave derived from the same source (and obeying certain other conditions) that encodes the amplitude and phase variations in the scattered waves. This interference pattern is recorded on a digital array detector. The digital record of amplitude and phase of the scattered wavefront as in DH is very important because it allows one to perform the 3D imaging task computationally. Beyond real-time 3D display applications, DH has now matured enough to be used in quantitative imaging applications--most important, metrological applications in mechanics, biological imaging, imaging of fluid flow, etc.
When using any technology for quantitative or metrological applications, it is vital to understand the limits on the achievable accuracy. The paper by Fournier, Dennis, and Fournel addresses this problem for the single-point resolution estimate in case of DH. Given an experimentally recorded digital hologram for such a point object, the problem of finding its exact location is a statistical estimation task. In particular, the authors start with a model for a digitally recorded hologram for a single-point object and calculate the Cramér–Rao bound for the problem. The Cramér–Rao inequality is a general framework that gives the lower bound on the error in a statistical estimation task–this lower bound being achievable asymptotically. The analysis in the paper considers various practical parameters, such as the overall detector size, effect of pixel dimensions, signal-to-noise ratio, and on-axis versus off-axis point object in an experimental setting. The analysis may provide guidelines to the practitioners of DH metrological applications for analyzing the performance of their current systems or to design future systems with specified resolution requirements.
-- Kedar Khare
Technical Division: Optical Design and Instrumentation
ToC Category: Holography
|OCIS Codes:||(100.3010) Image processing : Image reconstruction techniques|
|(100.3190) Image processing : Inverse problems|
|(090.1995) Holography : Digital holography|
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