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.