Abstract
A hologram is a recording of the interference between an unknown object wave and a coherent reference wave. Providing the object and reference waves are sufficiently separated in some region of space and the reference beam is known, a high-fidelity reconstruction of the object wave is possible. In traditional optical holography, high-quality reconstruction is achieved by careful reillumination of the holographic plate with the exact same reference wave that was used at the recording stage. To reconstruct high-quality digital holograms the exact parameters of the reference wave must be known mathematically. This paper discusses a technique that obtains the mathematical parameters that characterize a strongly divergent reference wave that originates from a fiber source in a new compact digital holographic camera. This is a lensless design that is similar in principle to a Fourier hologram, but because of the large numerical aperture, the usual paraxial approximations cannot be applied and the Fourier relationship is inexact. To characterize the reference wave, recordings of quasi-planar object waves are made at various angles of incidence using a Dammann grating. An optimization process is then used to find the reference wave that reconstructs a stigmatic image of the object wave regardless of the angle of incidence.
Highlights
Digital holography is a coherent imaging technique that, in contrast with conventional incoherent imaging methods, provides both phase and amplitude information that can be exploited in microscopy, vibration analysis, and shape and deformation measurements [1,2,3,4,5]
Holograms were taken at each of extremes of the scan region with another taken at the center of Dammann grating is used to define a set of object plane waves defined by a regular grid in frequency space, additional information concerning the relative position of the peaks is made available and, if required, this can be incorporated into the merit function
We have shown that it is possible to retrieve the reference wave parameters for a high numerical aperture (NA), large field of view compact digital holographic camera
Summary
Digital holography is a coherent imaging technique that, in contrast with conventional incoherent imaging methods, provides both phase and amplitude information that can be exploited in microscopy, vibration analysis, and shape and deformation measurements [1,2,3,4,5]. For the case of an inline (Gabor) geometry at large NA, characterization of the illumination wave (that may be considered as the reference) has been discussed by Riesenberg and Kanka [14] In this case, the diverging wave from a pinhole was assumed to be spherical and the pinhole position was found by an iterative method according to the magnification of a known transmissive test object. The reference wave used in the camera originates from a pinhole, reflection from the beam splitter means that a spherical wavefront is not guaranteed, and it is necessary to measure the deviation from this nominal form For these reasons, we have developed a variation on the method of Hillman et al [12]. Before discussing this method in detail, we will begin by discussing our compact camera design
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