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

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

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

Alias

• Reasons– 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