Resolution in Terms of the Impulse Response
DOI: 10.1117/3.2303.ch6
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6.1 INTRODUCTION

The problem of the definition and the determination of an image quality criterion has long been and still is a major one in the field of image evaluation and assessment. A large variety of measures have been used, from a two-point resolution criterion to fidelity defect, etc. None of these measures is, however, completely satisfactory. In this chapter, we wish to discuss some of the simple criteria in terms of the intensity impulse response of the optical system. This allows us a preliminary look at the image assessment problem and also allows us to follow through further examples on the use of the intensity impulse response. We concern ourselves only with the Rayleigh and Sparrow criteria for two-point resolution; more sophisticated image quality criteria will be discussed in Chapter 19.

6.2 TWO-POINT RESOLUTION

Historically, one of the first measures established for the evaluation of optical systems was to specify how well the system could resolve a two-point object. The two objects were incoherent with respect to each other. Idealized point objects are, of course, not essential; all we require is that the individual objects are not themselves resolved, i.e., the intensity impulse response of the system is much broader than the geometrical image of the object. Clearly, two objects which are themselves resolved would be observable as two individual objects for all separations. What we are trying to establish now is a criterion that will allow us to determine the presence of two objects when the objects themselves are not resolved. Under these circumstances, the image will consist of the sum of the intensity impulse response of the optical system located at each image pointâin general, these two intensity distributions will overlap. What is the separation of the centers of the impulse responses and hence the separation of the objects that will allow us to distinguish them as two separate impulse responses and hence conclude that the object consisted of two distinct parts? Naturally, this type of discussion is only applicable if indeed the object to be imaged did consist of two equally bright unresolved objects.

© 1989 Society of Photo-Optical Instrumentation Engineers

## Topics

Image analysis; Image quality; Optical systems

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