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Chapter 6:
Digital Holographic Tomography
The book has thus discussed both Gabor and Leith–Upatneiks digital holography with applications in digital holographic interferometry. While it is true that holography yields the 3D shape of the object, it is only possible to deduce this information from the surface of the object that is illuminated in order to produce the “object” beam. If a 360-deg 3D profile of the object is desired, illumination of the object from all angles is required; this can be achieved by illuminating the object from different angles, as in tomography, and recording multiple holograms. The example provided here digitally reconstructs 3D profiles of amplitude and/or phase objects, such as lenses, water droplets, and dandelions, from recorded holograms formed from the illumination of the objects from multiple angles. This procedure is called digital holographic tomography (DHT). For experimental simplicity, only transmissive holograms (typically inline and Gabor) are considered. Lenslets, like water droplets, are also translucent objects with large curvatures that can scatter light at very large angles. The use of traditional DH to determine the 3D shape by using the light transmitted through the lenslets or water droplets results in thousands of fringes per millimeter, which may easily exceed the resolution of CCD cameras. A novel single-beam holographic tomography (SHOT) technique was developed to record and reconstruct the 3D shapes of water droplets and lenslets, and their distribution. Because the beamwidth is larger than several water droplets, the light that is transmitted between the droplets acts as the reference beam, which interferes with the “object” beam to record an inline Gabor hologram. In this case, the “object” beam comprises light scattered from the edges of the object because light passing through the droplet or lenslet converges and then diverges rapidly, and it is virtually absent on the recording plane. As stated earlier, single-beam (inline) holography reduces system complexity and allows us to determine the shape of the droplets or lenslets, albeit without details of the interior structure.
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