In this paper, we demonstrate a method for random phase optimization in the Fresnel domain that enables the fast generation of phase-only holograms (POHs). Our proposal consists of applying the iterative Fresnel transform algorithm (IFrTA) to optimize a random phase with the parameters of a given holographic projection system. Then, the resulting optimized Fresnel random phase is used for the generation of POHs of several objects. We compare the performance of our proposed method to the direct generation of holograms using IFrTA, and quantitatively study the quality of the reconstructed object varying the generation parameters. Our results show significantly improved computation speed and minor loss of accuracy compared with the direct application of the IFrTA. We present both numerical and optical reconstructions obtained with a holographic projection scheme based on a phase-only spatial light modulator to verify the validity and effectiveness of our proposal.

在本文中，我们展示了一种在菲涅耳域中进行随机相位优化的方法，该方法能够快速生成仅相位全息图 (POH)。我们的建议包括应用迭代菲涅耳变换算法 (IFrTA) 来优化具有给定全息投影系统参数的随机相位。然后，所得优化的菲涅耳随机相位用于生成多个对象的 POH。我们将我们提出的方法的性能与使用 IFrTA 直接生成全息图进行比较，并定量研究不同生成参数的重建对象的质量。我们的结果表明，与直接应用 IFrTA 相比，计算速度显着提高，精度损失较小。