We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex circle, and it can take a large gradient while diverging from the origin. This characteristic contributes to accelerating the gradient descent. Meanwhile, at the final stage of optimization, each element evolves along a complex circle, similar to previous state-of-the-art gradient methods. The experimental results demonstrate that our method outperforms previous methods, primarily due to the optimization of the amplitude.

翻译：我们提出了一种新的全息梯度方法，其中纯相位全息图不仅由相位参数化，还由振幅参数化。该方法的核心思想是利用辅助振幅对纯相位全息图进行建模。我们基于Wirtinger流算法在笛卡尔域内优化参数，该算法是一种基于Wirtinger微分的梯度方法。在优化初期，全息图的每个元素位于复圆内部，能够在远离原点时获取大梯度，这一特性有助于加速梯度下降。而在优化末期，每个元素沿复圆演化，与先前最先进的梯度方法类似。实验结果表明，由于振幅的优化，我们的方法在性能上优于现有方法。