快速自动对焦是机器视觉和数字视频系统中的关键技术。根据光学离焦成像模型，提出了一种基于微分图像自相关的快速自动对焦方法。首先利用拉普拉斯算子对离焦图像进行无方向二阶微分并求微分图像的自相关，然后从自相关图的环形槽鉴别出光学系统点扩展函数的半径，即离焦图像的弥散斑半径，最后依据离焦图像弥散斑半径与离焦量的几何光学关系推导出光学系统正确的对焦位置。实验结果显示该方法适用了任何目标，能够以较高的精度估计出弥散斑半径，并推导出离焦量，从而实现快速自动对焦。这种算法仅需要2幅离焦图像，相对于传统的基于图像清晰度评价函数的对焦方法，减少了计算量，提高了速度，降低了系统复杂度。

Fast auto-focusing technology is a crucial technology in computer vision and digital video system. A novel rapid auto-focusing method is proposed according to the model of optical defocusing system by using autocorrelation of derivative image. Firstly, a Laplacian operator is used to search an isotropic second-order differential to the defocused image and get the autocorrelation of the derivative image. Then, the radius of point spread function, that equals the blur′s radius of the defocused image, can be obtained from the annular groove of the autocorrelation. Finally, the right focus position can be deduced from the geometric relation between the radius of blurred spot and the defocusing value. The experimental results show that this proposed method can accurately estimate the radius of blurred spot and the right focus position for any target. Compared with the traditional methods based on focus criteria functions, this method only needs 2 defocused images that reduce the computation quantity and simplify the system to meet the fast auto focusing requirement.