Practical Electron Microscopy and Database

The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system. It is sometimes known as the folding frequency of a sampling system. This frequency represents the highest spatial frequency that can be accurately resolved without aliasing, a phenomenon where higher frequencies are misrepresented in the sampled signal. Fraction of Nyquist refers to the spatial frequency expressed as a fraction of the Nyquist frequency, which is a key concept in digital imaging and signal processing. Note that spatial frequency is a measure of how often features, like changes in brightness or color, occur per unit of distance in an image. In terms of image analysis and detectors, spatial frequency is essential because it affects how much detail a detector can capture. Higher spatial frequencies require finer pixel grids (higher resolution) to be accurately represented, as coarser grids may miss these details or introduce artifacts (like aliasing).

The sampling theorem shows that aliasing can be avoided if the Nyquist frequency is greater than the bandwidth, or maximum component frequency, of the signal being sampled.

Note that, to avoid having the overall CTF dampened too much by spatial coherence envelopes, temporal coherence envelope function and detector envelope function, it is important to find and use an optimum magnification (the highest useful magnification) since it is impossible in a pixel image to detect spatial frequencies less than the Nyquist limit (also called reciprocal pixel size). In other words, it is impossible to separate two objects in an image if they are closer than one pixel away from each other.