Theory and applications of Fourier optics and computer-generated holograms

Ping-Tai Sun, Marquette University


This dissertation discusses the theory of Fourier Optics and its application to Computer Generated Holograms (CGH); it goes on to simulate the process for producing CGH and also describes how the rectangular plotting method can be extended to the circular plotting method. Finally, it describes how these techniques and processes can be applied to Fuzzy Enhancement, Pattern recognition and Inverse of matrices. Furthermore, this dissertation describes how the Detour Phase Method can be applied to coding and plotting and how the FFT, TELL-A-GRAF, DISSPLA and PC-MATLAB software programs were utilized in the production of CGH. It is shown that, based on the Detour Phase Theory, the rectangular method can be extended to the circular method; this is desirable because the circular method is superior because a circle is continuous rather than angular and is therefore easier and smoother to plot. The developed theory for the circular method and the computer simulation are presented. This thesis presents a new algorithm which is proposed to be known as FFFT (Fuzzy Fast Fourier Transform). The advantages of using the FFFT method are: the image of the CGH is enhanced; the noise of the process is reduced; it provides simplicity; it provides convenience and high speed; it lowers the cost of designing lenses and filters, and the end result is improved. In the future, robots will become more and more intelligent; the ability to recognize patterns will be the main aspect of this greater intelligence. Matched spatial filters are the center of pattern recognition. In this thesis, the theory of pattern recognition after rotation will be discussed and the application of CGH to pattern recognition will be presented. A thin phase hologram, recorded under a weak reference condition is capable of inverting complex eigenvalues. By applying the CGH method to inversion of matrix, the amplitude and phase of the eigenvalues of the input matrix, the inverse of the eigenvalues of the input matrix, and the inverse of eigenvalues can be shown. A computer simulation of this type of CGH is presented. (Abstract shortened with permission of author.)

Recommended Citation

Sun, Ping-Tai, "Theory and applications of Fourier optics and computer-generated holograms" (1991). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. AAI9226223.