Research On Computer-generated Holography

Based on computing generated hologram, this thesis addresses the theory, numerical computing and technology of holographic display. As we know, holographic display could provide all view points and perception of the three dimension, and so it is an ideal 3D display mechanism. However, traditional optical holography is realized by two independent courses of optical holographic recording and reconstruction, which prohibit it from being an applicable display medium. Scientists proposed to use the avenue of Computer Generated Holography(CGH), which simulates the physical process of holograhphic record by computing method and so make holographic display go a step toward practicality. For many years, a great deal of researches were carried out in the aspects of CGH because of large amount of data, complicated calculation and delay. Unfortunately, current computing method still could not be performed in real time by using present hard softwares. This thesis makes researches under above background.By analyzing many 3D display techniques, we think that holographic stereogram is an important one. Holographic stereogram approximates the continuous 3D optical field of the surface of object using 2D images, and it reduce the information needed to store. Also, the images could be captured by camera. It is known that the classical physical process that directly simulates optical holographic record could be described by communication theory and Fourier transformation. But holographic stereogram includes continuous and discrete optical forms, and there is not an unified and well-developed mathematical tools and model for it.After reviewing the Fourier transformation and the description of Fresnel diffraction, we propose an optical field description method of fractional Fourier transformation. Fractional Fourier transformation is a generalized form of the Fourier transformation, and it closely relates to Fresnel diffraction. Based on the theory of Fourier transformation, we re-consider holograph and can develop a new holograph method which is different from both the Fourier transformation holograph and the Fresnel holograph.Although Fourier transformation could transform a signal from space field to frequency field, it could only provide the frequency distribution, but could not determine the corresponding spacial position. Therefore, a unified optical model could not be established. However, Wigner distribution function is capable of describing the same signal in space and frequency field simultaneously and converting the 4D optical field that describes images into diffraction-specific light wavefront distribution no matter it is derived via using Fourier transformation. So, we propose a new method of computing generated hologram by employing Wigner transformation as a mathematicla tool describing the optical field.The topic we have tackled are as follows:(1) Numerical simulation for light propagation and visualization of light-field distribution of Fourier Transform , Fresnal diffraction with hologram recording and reconstruction.(2) Discuess CGH of Fractional fourier transformation and computer simulation make use of it' s character.(3) Discuess relation of Wigner distribution function and Fractional fourier transformation, simulate Wigner distribution of one-dimension signal.(4) Computation Wigner distribution function of different direction of circle, circularity.(5) Display hologram by Wigner distribution function as virtue describe field of optics, carry out a new CGH.