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In this chapter we discuss a result stated earlier, Eq. (11.28). This result was obtained from coherence theory and justifies solving coherent imaging problems using a single complex wave equation even though all optical detectors are square law devices. We first review the square law property of detectors which results in losing the optical phase. We obtain several of the same results described in Chapter 11 using this simplified approach. In the usual circumstances of image formation, the object is illuminated incoherently and the image is formed by an addition of intensity of the light reaching the image plane. The characteristics of the image can be described if the intensity impulse response of the imaging system is known (see Chapter 4). Recall that the intensity impulse response is the distribution of intensity in the image plane produced by a point object. Hence, the image of an extended object is formed by a summation of the individual impulse responses suitably weighted by the intensity at the various points. In Chapter 7, an intensity transfer function was defined as the Fourier transform of the intensity impulse response, and it was seen that image formation could be discussed equally well in terms of this intensity transfer function. Note that above we have used the terminology intensity impulse response and intensity transfer function. This is to distinguish them from the impulse response and transfer functions required for describing image formation in coherent light, i.e., the amplitude impulse response and the amplitude transfer function. The words incoherent and coherent are sometimes used to replace intensity and amplitude in the above terms.
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