Abstract The transport of intensity equation (TIE) is an ideal candidate for phase imaging with partially coherent illuminations. TIE has the advantages of simplicity in phase calculation due to its closed-form solution and no requirement for a reference beam and phase unwrapping due to its non-interferometric nature. However, TIE requires multiple through-focus intensity images, and is very sensitive to image boundaries and noise. Thus, in this paper, we combine deep learning with TIE, abbreviated as dTIE. After being trained by TIE phase results, the dTIE retains the advantages of TIE, and overcomes the shortcomings of TIE as follows: (i) only one de-focus intensity image is required for phase imaging while the result is very close to the TIE result with SSIM index reaches 0.95, enabling more efficient phase imaging; (ii) the boundary problem automatically disappears due to the translation invariance of the convolutional networks; (iii) it is insensitive to noise even with very heavy noise. All these enhancements are verified in the application of dTIE for phase imaging of real cells.

中文翻译：

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通过深度学习从单个强度图像传输强度方程

摘要 强度方程输运（TIE）是部分相干照明相位成像的理想候选方法。TIE 具有封闭形式的解决方案，因此具有相位计算简单的优点，并且由于其非干涉性质，不需要参考光束和相位展开。然而，TIE 需要多个离焦强度图像，并且对图像边界和噪声非常敏感。因此，在本文中，我们将深度学习与 TIE（缩写为 dTIE）相结合。经过TIE相位结果训练后，dTIE保留了TIE的优点，克服了TIE的缺点如下：（i）相位成像只需要一张散焦强度图像，而结果非常接近TIE结果SSIM指数达到0.95，实现更高效的相位成像；(ii) 由于卷积网络的平移不变性，边界问题自动消失；(iii) 即使噪音很大，它对噪音也不敏感。所有这些增强都在 dTIE 用于真实细胞相位成像的应用中得到验证。