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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