The stochastic gradient descent (SGD) method is useful in the phase-only hologram optimization process and can achieve a high-quality holographic display. However, for the current SGD solution in multi-depth hologram generation, the optimization time increases dramatically as the number of depth layers of object increases, leading to the SGD method nearly impractical in hologram generation of the complicated three-dimensional object. In this paper, the proposed method uses a complex loss function instead of an amplitude-only loss function in the SGD optimization process. This substitution ensures that the total loss function can be obtained through only one calculation, and the optimization time can be reduced hugely. Moreover, since both the amplitude and phase parts of the object are optimized, the proposed method can obtain a relatively accurate complex amplitude distribution. The defocus blur effect is therefore matched with the result from the complex amplitude reconstruction. Numerical simulations and optical experiments have validated the effectiveness of the proposed method.

中文翻译：

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使用具有复杂损失函数的随机梯度下降算法生成多深度全息图

随机梯度下降（SGD）方法在仅相位全息图优化过程中很有用，并且可以实现高质量的全息显示。然而，对于当前在多深度全息图生成中的SGD解决方案，优化时间随着对象的深度层数的增加而急剧增加，从而导致SGD方法在复杂的三维对象的全息图生成中几乎是不切实际的。在本文中，所提出的方法在SGD优化过程中使用了复数损失函数，而不是仅振幅损失函数。这种替换确保了仅通过一次计算就可以获得总损失函数，并且可以大大减少优化时间。此外，由于对象的振幅和相位部分都得到了优化，所提出的方法可以获得相对准确的复振幅分布。因此，散焦模糊效果与复杂幅度重建的结果相匹配。数值模拟和光学实验已经验证了该方法的有效性。