Optical Imaging and Spectroscopy

SAMPLING

If a function f(t) contains no frequencies higher than W cps, it is completely determined by giving its ordinates at a series of points spaced 1/2 W seconds apart. This is a fact which is common knowledge in the communication art.

—C. Shannon [219]

7.1 SAMPLES AND PIXELS

“Sampling” refers to both the process of drawing discrete measurements from a signal and the representation of a signal using discrete numbers. It is helpful in computational sensor design and analysis to articulate distinctions between the various roles of sampling:

• Measurement sampling refers to the generation of discrete digital values from physical systems. A measurement sample may consist, for example, of the current or voltage returned from a CCD pixel.
• Analysis sampling refers to the generation of an array of digital values describing a signal. An analysis sample may consist, for example, of an estimated wavelet coefficient for the object signal.
• Display sampling refers to the generation of discrete pixel values for display of the estimated image or spectrum.

Hard separations between sampling categories are difficult and unnecessary. For example, there is no magic transition point between measurement and analysis samples in the train of signal filtering, digitization, and readout. Similarly, analysis samples themselves are often presented in raw form as display samples. In the context of system ...