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“A Treatise on Cascaded Computer Generated Holograms”
by Ali Alkan Gulses
May 2014
In diffractive optics and computer holography, generally, a common and well-studied scenario is using one hologram plane to generate a single image plane. As a continuation, in this work, cascaded phase only holograms are presented for single and multi-plane image formation. Traditional design methods, such as deterministic iterative and stochastic simulated annealing algorithms, for the one planar hologram case have been expanded and enriched to handle cascaded computer generated holograms. This special arrangement of holograms demonstrates interesting attributes in the reconstruction of classical 2D images. When it comes to 3D images, on the other hand, the performance of these cascaded-holograms is found to follow a trend and is even more remarkable: in order to facilitate the system, 3D images may be conceived to consist of successive 2D image planes; after application of the cascaded holograms for reconstruction, numerical results from computer experiments show that increasing the number of holograms for input, decreases the error in all output image planes for 3D setup. In addition, the cascaded holograms technique can be combined with the classical method of noise window which is achieved by planar extension of a single hologram by forfeiting some resolution. Thus when cascaded holograms are also expanded in the lateral domain, the results are even more promising. Specifically, it is observed that, while lateral extension of holograms as an application of the classical noise window concept is responsible for noise removal phenomena up to some degree in a general sense, longitudinal extension as a form of cascades may especially become a remedy for apparent incompatibility between image planes appearing in multi focal systems, which is another remarkable outcome. As a continuation of the work, instead of cascaded phase only holograms, amplitude modulation is taken into account and phase plus amplitude modulation with a certain distance between them, is analyzed. This configuration shows some interesting properties and some significant superiority with respect to traditional techniques although some limitations, such as requirement of larger pixel sizes which is on the boundary of diffractive optics, exist. The proposed schemes in this work may be applicable to a formation of a simple and light-weight setup. Therefore, by using the techniques, results and algorithms here, especially on the cascaded phase only holograms, a functional static micro-holographic 3D display may be realizable. In addition, phase and amplitude modulating setup can be used on applications requiring large pixel size, such as on devices with large area electronics. Additionally, methods to overcome possible hurdles in both computational design and physical application stages of the novel displays whose properties are mentioned above are briefly discussed. Although the work up to now is concentrated on algorithms and computation, experimental techniques for fabrication and error consideration coming from physical misalignment are also proposed. We believe that this work will be not only useful and functional in the analysis of cascaded phase elements but also a thorough examination on algorithms, noise removal or some other issues on computer holography and computational optics.