Shannon's sampling theorem (also called the Shannon-Whittaker-Kotel'nikov theorem) was developed for the
digitization and reconstruction of sinusoids. Strict adherence is required when frequency preservation is important. Three
conditions must be met to satisfy the sampling theorem: (1) The signal must be band-limited, (2) the digitizer must
sample the signal at an adequate rate, and (3) a low-pass reconstruction filter must be present.
In an imaging system, the signal is band-limited by the optics. For most imaging systems, the signal is not adequately
sampled resulting in aliasing. While the aliasing seems excessive mathematically, it does not significantly affect the
perceived image. The human visual system detects intensity differences, spatial differences (shapes), and color
differences. The eye is less sensitive to frequency effects and therefore sampling artifacts have become quite acceptable.
Indeed, we love our television even though it is significantly undersampled.
The reconstruction filter, although absolutely essential, is rarely discussed. It converts digital data (which we cannot see)
into a viewable analog signal. There are several reconstruction filters: electronic low-pass filters, the display media
(monitor, laser printer), and your eye. These are often used in combination to create a perceived continuous image. Each
filter modifies the MTF in a unique manner. Therefore image quality and system performance depends upon the
reconstruction filter(s) used. The selection depends upon the application.