Nyquist Sampling Theorem

Sampling a sound (using a microphone) or image (using a CCD camera) can introduce a distortion into the signal called ”aliasing.” Aliasing takes many forms; for example the apparent backward motion of wagon wheels in western movies, which occurs because the movie is actually a sequence of still frames. Nyquist showed that if the sampling rate is twice the highest frequency component, then the original information can be reconstructed without aliasing. In the case of a CCD image, you need to have a pixel density twice the highest spatial frequency in the image. In practice 2.5X is used to compensate for the distance across the diagonal of the pixel. Note that proper display of a ”critically sampled” image requires a reconstruction filter - interpolation to a higher sample rate - for proper image display. Also oversampling may be desirable because interpolation during image alignment can degrade resolution. Oversampling is also required if you intend to use deconvolution to increase resolution; the final deconvolved image must also meet the Nyquist Sampling Criterion.