Over the past three decades, defocus has consistently provided groundbreaking depth information in scene images. However, accurately estimating depth from 2D images continues to be a persistent and fundamental challenge in the field of 3D recovery. Heuristic approaches involve with the ill-posed problem for inferring the spatial variant defocusing blur, as the desired blur cannot be distinguished from the inherent blur. Given a prior knowledge of the defocus model, the problem become well-posed with an analytic solution for the relative blur between two images, taken at the same viewpoint with different camera settings for the focus. The Gaussian model stands out as an optimal choice for real-time applications, due to its mathematical simplicity and computational efficiency. And theoretically, it is the only model can be applied at the same time to both the absolute blur caused by depth in a single image and the relative blur resulting from depth differences between two images. This paper introduces the settings, for conventional imaging devices, to ensure that the defocusing operator adheres to the Gaussian model. Defocus analysis begins within the framework of geometric optics and is conducted by defocus aberration theory in diffraction-limited optics to obtain the accuracy of fitting the actual model to its Gaussian approximation. The results for a typical set of focused depths between $1$ and $100$ meters, with a maximum depth variation of $10\%$ at the focused depth, confirm the Gaussian model's applicability for defocus operators in most imaging devices. The findings demonstrate a maximum Mean Absolute Error $(\!M\!A\!E)$ of less than $1\%$, underscoring the model's accuracy and reliability.

翻译：过去三十年间，离焦现象持续为场景图像提供突破性的深度信息。然而，从二维图像中精确估计深度仍然是三维重建领域一个长期存在的基础性挑战。启发式方法需要处理推断空间变化离焦模糊这一不适定问题，因为目标模糊与固有模糊难以区分。在已知离焦模型先验知识的情况下，该问题可通过解析解转化为适定问题，该解描述了同一视角下采用不同对焦设置的相机所拍摄两幅图像间的相对模糊。高斯模型因其数学简洁性和计算高效性，成为实时应用中的最优选择。理论上，该模型是唯一能同时适用于单幅图像中由深度引起的绝对模糊和两幅图像间由深度差异产生的相对模糊的模型。本文针对传统成像设备提出了确保离焦算子符合高斯模型的参数设置。首先在几何光学框架下开展离焦分析，继而通过衍射极限光学中的离焦像差理论，评估实际模型与其高斯近似的拟合精度。针对典型对焦深度范围（1至100米）且最大深度变化不超过对焦深度10%的实验结果表明，高斯模型适用于大多数成像设备的离焦算子。研究数据显示最大平均绝对误差（MAE）小于1%，充分验证了该模型的准确性与可靠性。