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In Chapter 1 we applied a transfer-function-based analysis to describe image quality in classical optical systems - €”that is, systems with glass components only. In this chapter we will examine the MTF of electro-optical systems - €”that is, systems that use a combination of optics, scanners, detectors, electronics, signal processors, and displays. To apply MTF concepts in the analysis of electro-optical systems, we must modify our assumptions about MTF. Electro-optical systems typically include detectors or detector arrays for which the size of the detectors and the spatial sampling interval are both finite. We will therefore develop an expression for the MTF impact of irradiance averaging over the finite sensor size. Also, because of the shift-variant nature of the impulse response for sampled-data systems, we will develop the concept of an average impulse response obtained over a statistical ensemble of source positions. Perhaps most important, one cannot amplify an arbitrarily small signal and obtain a useful result. The classical MTF theory presented in Chapter 1 does not account for the effects of noise. Noise is inherent in any system with electronics. We will demonstrate how to broaden the MTF concept to include this important issue. We often think about the object as being imaged onto the detectors, but it is also useful to consider where the detectors are imaged. The footprint of a particular detector, called the instantaneous field of view (IFOV), is the projection of that detector into object space. We consider a scanned imaging system in Fig. 2.1, and a staring focal-plane-array (FPA) imaging system in Fig. 2.2. In each case, the flux falling onto an individual detector produces a single output. Inherent in the finite size of the detector elements is some spatial averaging of the image irradiance. For the configurations shown, we have two closely spaced point sources in the object plane that fall within one detector footprint. The signal output from the sensor will not distinguish the fact that there are two sources. Our first task is to quantify the spatial-frequency filtering inherent in an imaging system with finite-sized detectors.
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