Point Spread-Function, Line Spread-Function, and Modulation Transfer Function

IN linear, invariant communication systems has been of increasing usefulness in the study of radiographic imaging systems (1–4). Indeed, its application is not confined to the imaging systems themselves but can be extended to the analysis of the entire radiological process involving exposing, imaging, and visual detection operations (5). This analysis will eventually result in quantitative descriptions of the inherent limitations of present radiological processes and, hopefully, in the development of improved processes yielding increased diagnostic certainty. At present the number of investigators working in this field is very small-too small, in fact, to insure a satisfactory rate of progress toward the important goal. This is partly due to the fact that the physics and mathematics involved are highly specialized and cannot readily be assimilated from the existing literature. Any author in this field is faced with the dilemma of writing lucidly for readers having diverse backgrounds of scientific training, since meaningful investigations in this field cannot be carried out by physicists alone but must be made in cooperation with radiologists who are the only ones, after all, who fully appreciate the operational aspects of the radiological process. In this co-operation each investigator will tend to contribute most in the field for which he was trained. On the other hand, it is helpful if all investigators develop a common language and an understanding of basic concepts. With this in mind, the present discussion of some important concepts of optical communication theory is presented in nonmathematical form. A brief mathematical derivation is given in the APPENDIX. General Description Of Basic Concepts The Point Spread-Function In the analysis of a physical system, methods of communication theory are used to determine the performance of the system as a transducer in converting a system input to an output. It is not the aim of communication theory to investigate in detail the interior of a system but rather to characterize a system terminally by establishing a general dependence of the output on the input. As indicated in Figure 1, the problem can be stated as follows: Given a black box (the system), determine its transfer characteristics so that the output resulting from any conceivable input can be uniquely predicted. The practical importance of knowing the system transfer characteristics is obvious. For example, if the system is a sound transmitter the “fidelity” of the output can be predicted; in the case of imaging systems the image deterioration introduced for any given object can be predetermined. The present discussion will be confined to imaging systems. In the general case, this system analysis is extremely complicated.