Butterworth Low-Pass Filter in image processing

Transfer function of a Butterworth lowpass filter (BLPF) of order n, and with cutoff frequency at a distance D0 from the origin, is defined as

Transfer function does not have sharp discontinuity establishing cutoff between passed and filtered frequencies.

Cut off frequency D0 defines point at which H(u,v) = 0.5

BUTTERWORTH LOW-PASS FILTER