A fractional fourier transform algorithm for holographic display

Kaifeng Liu
Anhui university, Anhui, China
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In theory ,the diffraction efficiencies of kinoforms that have properly graded surface relief gratings can reach 100%.When the amplitude of object function are known and its phase are unknown , an iterative Fourier transform process of error-reduction algorithm is usually adopted to retrieval its phase spectrum. When the amplitude of result is a constant, it is so called kinoform type or phase-only hologram. The phase spectrum reserves not only phase information but also amplitude information of original object function. In this paper, a specific fractional Fourier transform for Digital Micromirror Device (DMD) is presented instead of Fourier transform and the typical constrain of the error-reduction. There are several advantages of the proposed method. Firstly, a fast simulated algorithm of fractional Fourier transform based on FFT are used to more flexible express the propagation of optical wavefields and improve convergence speed in iterative process . Based on the flexible expression for the propagation, a fast shifted Fresnel or fraunhofer transform can be used in a uniform equation to develop a tiling approach to hologram construction and reconstruction, which computes the propagation of different distances between parallel planes having different resolutions. Secondly, a combinational optimal constrains for DMD is used; they include of the microstructure of the element, Phase Modulation Properties and switched blazed grating Properties.The binary coding and the results of numerical and optical experiments are presented the results given is improved obviously in image quality and diffraction efficiency. Keywords: Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education , Anhui University, Hefei , Anhui 230039, China 

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