A new definition of potential field distribution function of image was proposed, and the characteristics of the distribution function were analyzed. Distribution function of potential field represents whole fluctuant information of image. So it can be used to analyze the image characteristics. Potential field of image background is weak and correspond to Gaussian distribution. Low stage of potential field distribution function can be used to evaluate noise level of image. Inflection point of the amplitude distribution function of potential field represented the transition point between the background and the actual edge in potential field image. So value of this point can be used as the threshold value to identify edge. When object distance of microscope changes, the edge comes more and more clear, and the edge area judged by the method above will be bigger and bigger. This character can be used to instruct auto-focus process.