Strioscopy (zero-order-filtering), bright field / dark field

    The Fourier coefficient 1/N2.F(0,0) is the average value of the intensity of the image I(n,m) pixels and contributes to the same amount to the amplitude of each pixel. The contrast of the image can then be modified in order to increase details visibility if this particular coefficient is set to zero, as shown by the two following images:

Initial image Image reconstructed from the FT of the original image, the Fourier coefficient F(0,0) being zeroed

    One can see that some areas have there relative gray level inverted (bright becomes dark and vice versa), for example the zone between the statue foot, or the forest background. In such a way some details are more visible (e.g. the branches of the trees).

    If a pixel is initially black (pixel value at 0 or close to zero), this corresponds to a situation where the interference of all the Fourier coefficients is destructive; if F(0,0) is zeroed, then the sum is no more null and the pixel has now a significant value:

Argand scheme showing the destructive interference, leading to a black pixel If the contribution of F(0,0) is eliminated, the resultant of the intensity of the pixel initially black becomes significative, leading to a contrast inversion

    This principle is used in electron microscopy: in bright field, all diffracted beams (corresponding to the Fourier coefficients of the electrostatic potential of the object under study) are included to construct the image and the background of this image where the electron beam is not shaded by any obstacle appears white (e.g. an hole in the sample); in dark field, the direct beam corresponding to F(0,0) is eliminated, and then the background of the image appears black, since no substance was present to diffract the electron beam (this area in the sample plan contributes only to F(0,0)).