调焦评价函数对离焦图像的灵敏度直接影响着自动调焦的精度。许多对调焦函数性能研究中,都只是对各个不同函数的灵敏度相互比较,忽略了调焦评价函数的灵敏度不仅和函数本身有关,还和调焦选择区域大小以及图像的空间频率等参量有关的问题。从成像原理基本公式推导出调焦评价函数灵敏度的数学模型。然后根据公式得出在光学系统的焦点附近,调焦评价函数的灵敏度与图像的空间频率成高次正比关系,与调焦区域的面积成线性正比关系,与照明光源的波长和光学系统空间截止频率成二次反比关系。最后实验证明理论分析的正确性。从而为实践中的自动调焦系统设计提供理论指导,以便有目的地选择和控制调焦系统的各个参量进一步提高自动调焦精度。

The precision of auto-focus system has been affected directly by the sensitivity of focus criteria function. In many researches about performance of focus criteria functions, the sensitivity of each different function is commonly compared, but ignoring that the sensitivity of focus criteria function is not only connected with the function itself but also with the parameters, such as area size selected by focus and the spatial frequency of image. Sensitivity of focus criteria function is firstly deduced from the basic function of the imaging theory. Then according to the function, conclusion is drawed near by focus of optical system that the sensitivity of focus criteria function is directly high-order proportional to relation with the spatial frequency of image and linear with the size of focus-area, and inversely proportional to the wavelength of the lighting power and spatial cutoff frequency of optics system. The experiments demonstrated that the theoretical analysis is correct. To some purpose it can provide theoretical guide to the design of auto-focus system and select clearly and control each parameter of focus system to further enhance the precision of autofocus.