The modulation transfer function of an optical system with a rotationally symmetric circle of confusion

The relationship between an optical system's circle of confusion and the quality of the image it forms is not specified by any universally accepted criterion. However, a simple geometric theory helps place the problem in perspective. As a first-order approximation, the circle of confusion is considered to be a uniformly illuminated disk. Then the illumination at a point in the image is the average of the illumination which would occur in the geometric image within an aperture of finite diameter centered at this point in the image plane. If the circle of confusion has a more complex radial illumination distribution, the image-forming process can be considered as the combined operation of a number of concentric averaging apertures of varying radii. If the circle of confusion has a Gaussian radial illumination distribution, a solution for the modulation transfer function can be obtained in closed form.