In the previous chapter, we showed that a stationary linear optical system using incoherent light could be completely described in terms of a convolution integral relating the object distribution Iobj(xâ²) to the image distribution Iim(x). In such a description, the optical system is characterized by its impulse response, i.e., the point image. Mathematically, these statements are summarized in the following integral [see Eq. (4.14)]: I im (x)=â«I obj (x â² )S(xâx â² )dx â² .
In this chapter, several relatively simple imaging problems will be analyzed with the aid of Eq. (5.1). In general, this approach to the imaging problem is too cumbersome to be used for detailed calculations and a more generally useful technique will be introduced in another chapter. However, it is instructive to carry out the convolution process for a few simple examples in order to develop some insight into the physical limitations on image quality which are introduced by the diffraction theory. To keep the computational difficulty to a minimum, the examples in this chapter are limited to a one-dimensional optical system. The concepts are readily generalized to two dimensions; however, details of the calculations become unwieldy.
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