Modulation transfer function is the predominant measure of the performance of image-forming lenses and systems. It can be measured objectively and calculated from lens design data, enabling manufacturers to compare the quality of lenseswith design expectations and to detect errors in production. It can characterize not only traditional lenses, but also photonic systems such as video cameras, image intensifiers and film scanners. The image that a lens forms always differs from the original object. In general, there is a loss of detail, a blurring or smoothing of the original scene. This happens because a point in the object is not imaged as a perfect point in the image, but instead as a "blur spot." The shape of this blur spot, or point spread function, changes with position in the field of view: Near the center of the field, the spot tends to be relatively small and circular, whereas in the corner of the field it can become surprisingly large and take on bizarre and beautiful shapes. The reasons for the size and shape of the spot are…