| Holographic video display can convey all three dimension (3D) scene depth information of human perception; it is the ultimate goal of 3D imaging and display. A video imaging system has many functional modules, such as acquisition, compression, transmission and display unit; obviously, the acquisition is an important one. Compared with interference method, computer generated hologram or diffraction light field calculation reduces the optical device requirement, it also can express virtual scene, with some advantages like repeatability, low environmental requirements and high flexibility. But calculation of diffraction field still faces many challenges, such as discretization criterion, calculation methods and so on; this thesis will devote a preliminary study to this topic.There are two different views about whether a digital holographic image is sufficient to give a 3D image. C. J. R. Sheppard argues that 2D-hologram (two dimension wavefront representation) only is sufficient to record the surface height of a bulk 3D object, but not the detail inside of 3D object, unless object is very sparse, such as particles. On the other hand, D. J. Brady gives a different opinion, holography is an amazingly simple and effective encoder for compressive sampling, and it is possible getting 3D tomography from a single 2D digital hologram. It is important to discuss above two viewpoints for holographic video calculation. There is a variety of methods for calculation of 3D scene, such as triangular patches, surface patches and point cloud. This thesis will use point cloud method to calculate diffraction light field of 3D scene, because it is not only the basis of other calculation methods, also facilitates the discussion on the problem about the two perspectives above mentioned.Another key issue of diffraction light field calculation is sampling problem, the most influence is Nyquist, Shannon and Whittaker sampling theorem, this theorem states that a signal sampling frequency (it has a limited bandwidth) is at least twice of signal bandwidth. This relates to optical theory and fundamental problem of signal processing, also is hot topic on theoretical and numerical calculation for diffraction field. The thesis discusses sampling criteria for diffraction light field, specifically for the Fresnel diffraction light field.The main research and innovative work are as follows:(1)A fast algorithm for calculating diffraction field based on point cloud method is proposed, the main idea is using separability of Fresnel integral algorithm, making two-dimensional diffraction light field calculation to be decomposed into one-dimensional. By scaling the diffraction light field with a pre-computed to obtain fast calculation on different depth and proving 3D tomogram can be obtained by 2D digital hologram on calculating multi-plane diffraction intensity distribution of different depth. Comparing with calculation based on iteration method for each of separate plans, the point cloud method can effectively reduce difference between original scenes and computed light field as well as the complexity of calculations because it can handle well the mutual impact between the 3D points at different depth. Also it is very handy to prove the view putting forward by D. J. Brady is acceptable.(2) Sampling issues on horizontal and vertical of diffraction light field calculation is derived. According to Fourier transform algorithm and convolution algorithm for Fresnel diffraction, the lateral sampling criterion in calculation of Fresnel diffraction light field is given, which sampling interval is proportional with spread distance, and inversely proportional with product of pixel number and sampling interval. For longitudinal sample problem, also the sampling criterion is given:longitudinal interval is proportional with the square of pixel number and inversely proportional with square of sampling interval of spatial frequency. The numerical verification is done for calculation of diffraction light field by point cloud method of sampling criteria. |
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