Sampling: A technique used to record analog information by recording periodic snapshots. If the sampling rate is fast enough, the eye cannot discern the gaps between each snapshot when they are played back. This is the principle behind motion pictures. Sampling is the key technique used to digitize analog information such as sound, photographs, and images.
Sampling and the Nyquist Theorem
Nyquist sampling (f) = d/2, where d=the smallest object, or highest frequency, you wish to record.
The Nyquist Theorem states that in order to adequately reproduce a signal it should be periodically sampled at a rate that is 2X the highest frequency you wish to record. With images, frequency is related to structure size. Small structures are said to have a high frequency. Thus, the imaging sample rate (or pixel) size should be 1/2 the size of the smallest object you wish to record.
A High Sampling Rate = much greater than 2X the highest frequency. This is 'Oversampling' that, while not "bad" will take time and create a large digital file.
Nyquist Sampling Rate = The minimum sample rate that captures the "essence" of the analog information. Note that while Nyquist is appropriate for sampling, it may not capture nuances in information. But, of course, those nuances are higher frequency, and thus would require a higher Nyquist sample rate.
Undersampled: low sampling rate produces results that report false information about the analog data; which does not represent the original. This phenomenon is called aliasing.