Abstract

Computer-generated hologram (CGH) is the method of making holograms with computer. A CGH can be made without preparing and instructing the exclusive optical tool. Therefore, we can make holograms easily and economically compared to the optical method. There are several calculating methods for a CGH such as Fourier transform, Fresnel diffraction and etc. In this study, we discuss on the angular spectrum method which is not limited by the diffraction distance. The Kirchhoff integral has the advantage of making reconstructions similar to optical experiment. However, the angular spectrum method has the disadvantage of accruing an error without proper conditions. These conditions are related to the transfer phase function. Moreover, the transfer phase function is related to the sampling interval and the number of sampling points. Therefore, it is necessary to investigate the relationship about these conditions and reconstruction errors. This study reports on the reconstruction using the angular spectrum method under different conditions about the transfer phase function. Simulation results will be shown on the relationship under these conditions.

Highlights

  • This study reports on the reconstruction using the angular spectrum method under different conditions about the transfer phase function

  • Formula (2) is complex amplitude distribution of hologram made of angular spectrum method

  • Formula (8) is discretize the complex amplitude distribution of the hologram made of angular spectrum method

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Summary

Transfer phase function

Angular spectrum method uses discrete Fourier transform. In this method, hologram is made as follows. Multiplying the transfer phase function and this image. This image is inverse discrete Fourier transform. The formula about transfer phase function is written as (1). In this formula, z is distance between the original image and the hologram. The spatial frequency is inverse proportion to the sampling interval. Transfer phase function depends on z and the sampling interval. Formula (2) is complex amplitude distribution of hologram made of angular spectrum method

Discretization
Comparing angular spectrum method and Kirchhoff integral
The error depending on distance
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