为了提高数字全息图的重建速度和精度，本文提出了一种基于同态信号处理的数字全息广义线性重建算法。首先利用预放大数字全息显微系统并结合同态信号处理原理进行了理论分析，得到了广义线性重建算法的实现条件及重建步骤，并对该算法的优点进行了分析；然后利用计算机模拟和实验相结合的方法对理论分析进行了验证。结果表明：数字全息广义线性重建算法不仅可以有效的消除全息图频谱中零级项的干扰，实现高精度再现，而且由于采用一个完整象限的固定区域滤波，避免了常规线性算法的手动滤波操作，极大地提高了重建速度，同时最大限度地保留了原始像中的高频成分，实现全息图的高分辨重建。%In order to improve the accuracy and the speed of reconstructing an image, the digital holographic generalized linear reconstructing algorithm based on homomorphic signal processing is proposed. By using the pre-magnification digital holographic imaging system and the principle of homomorphic signal processing, the proposed algorithm is analyzed theoretically. The achieving condition for and reconstructing process of the proposed algorithm is presented. Then the theoretical results are demonstrated by simulations and experimental data. Results show that the zero-order term of digital hologram frequency spectrum can be eliminated effectively by the proposed algorithm so as to realize the high-precision reconstruction of the digital hologram. Because a whole quadrant is chosen as the filtered area, the manual frequency filtering operation needed in common linear reconstructing algorithm is avoided and then the reconstructing speed is improved greatly. Meanwhile, the high-frequency component of the reconstructed original image can be reserved up to the hilt so that the high resolution image can be achieved.
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