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Chapter 1:
The Sampling Process
Abstract

This chapter provides an introduction to several topics. First, the physical processes involved in sampling and displaying an image are discussed. In a staring sensor, the image is blurred by the optics, and then the detector array both blurs and samples the image. The detector samples are used to construct the displayed picture. The physical processes that occur in a sampled imager are described.

When analyzing sampled systems, it is convenient to conceptually separate the preblur, sampling, and postblur (display blur) attributes of the system. These three steps in the generic sampling process are described, and the importance of each step discussed.

Next, the system properties known as linearity and shift invariance are described. Systems that are both linear and shift invariant can be characterized by a transfer function. Circuits and optical systems, for example, are characterized by their modulation transfer functions (MTFs). This chapter describes the transfer function concept using an electrical low-pass filter as an example. For linear shift-invariant systems, the transfer function provides a quantitative way of characterizing system behavior.

Sampled systems are linear, so Fourier transform theory can be used to analyze sampled systems. However, sampled systems are not shift invariant. It is the lack of the shift-invariance property that differentiates sampled systems from other systems and makes sampled systems more difficult to analyze. The lack of shift invariance in a sampled system is illustrated. Also, the reasons that a sampled system cannot be assigned a transfer function are explained.

At the end of this chapter, three different mathematical ways of representing the sampling processes are presented. These three derivations correspond to three different physical views of the sampling process. The physical basis of the mathematical techniques used in Chapter 3 is described, and the role of the display in a sampled system is put into perspective. For simplicity, many of the examples in this chapter are one-dimensional, but the discussion and conclusions apply to two-dimensional imagery.