1. Optical Transfer Function
Optical transfer function (OTF)
Fourier transform of the PSF function
characterizes frequencies transmitted by the optical system
in real optical systems OTF domain is finite (image is band-limited)
the largest transmitted frequency is called cut-off frequency

2. Sampling theorem: Nyquist criterion
Nyquist criterion (Nyquistovo pravidlo)
sampling frequency  2 · cut-off frequency
Nyquist rate, Nyquist frequency (Nyquistova frekvence)
= 2 · cut-off frequency
Sampling theorem (vzorkovací teorém)
Band-limited signal should be sampled at a rate of at least twice its highest-frequency component (i.e. the sampling frequency should be equal at least to the Nyquist rate). If the band-limited signal is sampled at the Nyquist rate, it is possible to reconstruct it exactly.
Undersampling (podvzorkování)
sampling frequency < Nyquist rate
Oversampling (převzorkování)
sampling frequency > Nyquist rate

3. Alias
Alias (alias)
a new low-frequency information (not present in the original image) obtained during undersampling
the new information (the artifacts) is also called moiré effects or moiré patterns

4. Alias Reasons Elimination of alias: Suppression of alias:
original image is not band-limited (cut-off frequency does not exist)
original image is band-limited but sampling rate < Nyquist rate
Elimination of alias:
elimination of high frequencies in the continuos original image
unfortunately not possible
Suppression of alias:
oversampling k times
division of the oversampled image into k x k clusters (superpixels)
computation of average values within superpixels
creation of a new image with a normal sampling frequency such that each pixel of the new image is equal to the average of the pixels within the corresponding superpixel