Computing the diffraction pattern (hologram) that generates a given image at a precise location does not have a unique, exact solution. Nonetheless, the signal-to-noise ratio (SNR) of the image can be optimized by a clever algorithm. One of the most well known examples of such an algorithm is the Gerberg-Saxton (G-S) iterative Fourier transform. In this article, Alejandro Velez-Zea noted that when multiple images are formed at different distances by a single hologram, the G-S does not fare particularly well due to the noise introduced to each plane. In order to improve upon this method, the researcher introduces a mixed constraint parameter that uses the intensity distribution of the previous image, rather than the initial homogeneous illumination. By optimizing this parameter, Velez-Zea improved the image correlation coefficient (related to the SNR) as well as the diffraction efficiency of the hologram. In addition, the article demonstrates how the same algorithm can be used to encrypt the hologram with an initial phase key, so the images can only be retrieved if the input phase is identical to the key.

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