|One simple example to illustrate the notion of resolution: black segment|
The image we consider now is a simple black rectangle on a white background; in practice this can also be obtained in optics with a black line drawn on a transparent slide illuminated with a laser beam:
Initial image Fourier transform of the black segment
If one performs an inverse Fourier transform on the modified Fourier transform of the original segment by, for example, erasing the high resolution coefficients only in the vertical direction, the resulting image looks like a segment:
• which edges are sharp in the horizontal direction (its Fourier Transform in this direction is not modified)
• which edges in the vertical direction are blurred (sharp edges are replaced by oscillations), because the high resolution Fourier coefficients (coding for details) in this direction were set to zero.
Fourier Transform without the high resolution in the vertical direction Its inverse Fourier transform