The Influence of Aberration and Detector Response on Optical Images

The optical-frequency response function is used to obtain the intensity distribution in the image of a step function of intensity, and from this the image intensity distributions for strips and Cobb test units are obtained. Detectors having a Gaussian type response function of different equivalent bandwidths s o are assumed. The treatment is applied to systems having secondary spherical aberration of amounts w 60 = - 6λ, - 9λ, - 12λ, with different amounts of primary spherical aberration and several planes of focus in each case, and for a range of values of s o , the equivalent bandwidth of the detector. From these calculations the edge gradient in the image of a step function of intensity, the limit of detection and the limit of resolution, using a criterion of 0.2 for the necessary image contrast, are found; these different methods for the assessment of optical systems are then intercompared. It is shown for example that if two systems are assessed by two different test methods the order of the figure of merit for the two systems can be significantly different, and furthermore the order of merit in which the two systems are placed depends strongly on the response function of the detector employed. The differences are large enough to be of real significance in practice. It is generally known from qualitative considerations of optical image formation that when the detector employed has a narrow bandwidth the shape of the frequency response function is of greater importance for low values of the spatial frequency s , the response function for higher spatial frequencies having little influence on the image quality, while for a system employing a detector of wide bandwidth the shape of the frequency response function for the higher frequencies is important, as these frequencies can now contribute to the formation of the image. An attempt has been made to study quantitatively the effect of detector bandwidth on the formation of the images of some standard test objects.