The resolution of images is increasing year by year. High-definition images have a large amount of data so that high calculation cost is required for image processing. For example, when original data is restored from non-clear high-definition two dimensional coded images, it is necessary to improve the image quality. A volume holographic optical element works as a multiple lens for each pixel in an image so that spreading pixel patterns can be individually focused. Then, each pixel becomes clear and original data can be easily restored. However, it is difficult to analytically express the function of volume holographic optical elements. In our previous study, reconstructed images from a volume hologram, in which some data pages were recorded in multiple, were expressed by analytic function. The analytic function was called pixel amplitude function. In this study, the pixel amplitude function is used for an input image to a volume holographic optical element. Then, output image is analytically expressed.
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