Optical Transfer Function

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Presentation transcript:

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 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