Digital holography is a three-dimensional (3D) measurement technique that can be used to quantitatively determine the size and 3D location of the objects inside a field-of-view. However, in systems where refractive index gradients are present, variations in optical phase due to high-speed shock-waves or low-speed thermal gradients can cause distortions that obscure objects. While techniques like phase-conjugate digital in-line holography and iterative phase measurement techniques have been developed in the past for phase removal or phase measurement, they require either nonlinear four-wave-mixing or iterative algorithms to operate. In this paper, we demonstrate a novel recalculated intensity propagation phase holography (RIPPH) method that captures distorted holograms using low-power continuous lasers, refocuses the hologram to the plane of the distortion, and cancels the phase distortion numerically in a single post-processing step. The resulting hologram can be numerically refocused to provide distortion-free 3D information describing objects that absorb or scatter light. In RIPPH, only the approximate $z$-locations of the phase distortions are needed, making this method significantly faster to compute than phase retrieval methods. Theoretical simulations are first used to describe and assess the distortion removal process. Experiments are then conducted to demonstrate at least $3\times$ lower edge distortion for RIPPH compared to traditional digital in-line holography. We demonstrate, for the first time, how phase distortions from supersonic air jets, particle-laden spherically expanding shock-waves, and convectively-driven thermal gradients are numerically cancelled and show how objects of interest are accurately recovered.

数字全息是一种三维 (3D) 测量技术，可用于定量确定视场内物体的大小和 3D 位置。然而，在存在折射率梯度的系统中，由于高速冲击波或低速热梯度引起的光学相位变化会导致物体失真。虽然过去已经开发了相位共轭数字在线全息术和迭代相位测量技术等技术，用于相位去除或相位测量，但它们需要非线性四波混合或迭代算法才能运行。在本文中，我们展示了一种新的重新计算强度传播相位全息 (RIPPH) 方法，该方法使用低功率连续激光器捕获扭曲的全息图，将全息图重新聚焦到失真平面，并在单个后处理步骤中以数字方式消除相位失真。生成的全息图可以在数值上重新聚焦，以提供描述吸收或散射光的物体的无失真 3D 信息。在 RIPPH 中，只有大约$z$- 需要相位失真的位置，这使得该方法的计算速度明显快于相位检索方法。首先使用理论模拟来描述和评估失真消除过程。然后进行实验以证明至少$3\times$与传统的数字在线全息相比，RIPPH 的边缘失真更低。我们首次展示了超音速空气喷射、载有粒子的球形膨胀冲击波和对流驱动的热梯度的相位失真是如何在数值上抵消的，并展示了如何准确地恢复感兴趣的物体。