We examine the nature of the reconstructed 3D image as obtained by replay (or back-propagation) of the object wave from the hologram recording plane to the original object volume. While recording of a hologram involves transferring information from a 3D volume to a 2D detector, the replay of the hologram involves creating information in a set of 3D voxels from a much smaller number of 2D detector pixels, which on a first look appears to be surprising. We point out that the hologram replay process is a Hermitian transpose (and not inverse) of the hologram formation process and therefore only provides an approximation to the original 3D object function. With the knowledge of this Hermitian transpose property, we show how one may realize true 3D image reconstruction via a regularized optimization algorithm. The numerical illustrations of this optimization approach as presented here show excellent slice-by-slice tomographic 3D reconstruction of the original object under the weak sca...

中文翻译：

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数字全息术中的真正3D重建

我们检查了通过从全息图记录平面到原始对象体积的物波重播（或反向传播）获得的重建3D图像的性质。全息图的记录涉及将信息从3D体积传输到2D检测器，而全息图的重放涉及从数量少得多的2D检测器像素中在一组3D体素中创建信息，乍一看似乎令人惊讶。我们指出，全息图重放过程是全息图形成过程的厄密转置（而不是逆过程），因此仅提供了原始3D对象函数的近似值。借助这种Hermitian转置属性的知识，我们展示了如何通过正则化优化算法实现真正​​的3D图像重建。