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In this chapter, the response function for a sampled imager is derived. The sampled imager response function quantifies the transfer response of the sampled system; that is, it describes how well the desirable scene content is preserved within the image. The response function also quantifies the sampling artifacts which will be visible in the image.
The procedure for finding the sampled imager response function exactly parallels the procedure described in Chapter 2 for finding the transfer response for a non-sampled imager. The sampled imager response function is the Fourier transform of the imager point spread function. As discussed in Chapter 1, the point spread function of a sampled imager is not shift-invariant; it varies depending on position within the field of view of the sensor. The sampled imager response function is more complicated than the transfer function for a non-sampled system. This is because it contains information about both the transfer response of the system plus information about the sampling artifacts.
The sampled imager response function depends on the sensor pre-sample MTF, the sample spacing, and the post-sample or display MTF. These sensor characteristics are known to the design engineer or system's analyst. The sampled imager response function does not depend on the image samples, but rather on the process by which the samples are taken and displayed.
Since the sampling artifacts produced by an imager depend on the scene being imaged, one might question a mathematical process which quantifies sampling artifacts without including an explicit description of the scene. In that regard, we rely on assumptions identical to those used for non-sampled imagers.
As discussed in Chapter 2, MTF is used to characterize a non-sampled imager. MTF is the Fourier transform of the displayed point spread function. It describes the blur produced in the image by a point in the scene. In actual usage, the importance of a good MTF response at high frequency cannot be established until the high frequency content of the scene is established. The real impact or importance of the sensor blur is not known until the scene content is known. Nonetheless, MTF has proven to be a good indicator of the overall utility of the sensor. The ability of a non-sampled imager to resolve high frequency content in the scene is generally important when using the imager.
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