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The formation and the contrast of Fourier images of a periodic object, especially a sinusoidally transparent object, are investigated under partially coherent illumination. It becomes apparent that the spatial coherence of light affects seriously the contrast of Fourier images and the positions of the Fourier image planes.

Fourier-imaging phenomenon is applied to grid coding image subtraction scheme. Double exposure and real time arrangements using complementary grating implementation techniques based on the grating self-imaging properties in coherent light are proposed. The simplicity, experimental ease and quality of the processed images prove the effectivness of the proposed technique.

Optical alignment operations and Fourier imaging phenomena have the common property that both occur in space along a straight line. The self-imaging property of a circular grating is applied to centring-error detection and to alignment in space. Moire fringes due to the interaction of Fourier (or Fresnel) images with a detecting grating provide an indicator of the alignment state. The merit of this approach is that it is easy and comfortable to make visual observations. Various applications of the method depending on the choice of the reference points used are discussed and some experimental data are presented.

Two techniques are proposed for beam collimation with the Talbot interferometer. One is called the mismatch method in which two gratings with slightly different periods are used. In the other method (called the grating shift method), one of two gratings of the same period is shifted in its plane in the direction perpendicular to the grating lines.

The moire effect is very sensitive in detecting small differences between two similar gratings. These differences might be caused by an object with phase gradient placed between the two gratings. The performance of such an instrument can be understood in terms of the “Talbot effect” (also called “Fourier imaging” or “self-imaging”). Slight modifications provide shearing interferences and the second derivative of the object.