Self-imaging in polar coordinates

This paper deals with the phenomenon of self-imaging. Starting from the results presented by Montgomery [ J. Opt. Soc. Am.55, 373 ( 1965)], the general shape of the function describing the object that self-images (under coherent illumination) is derived. Based on the obtained results, a new kind of Talbot interferometer, which displays the azimuthal derivative as well as the radial derivative in polar coordinates, has been proposed. The setup described, consisting of two evolute gratings, creates the required Talbot interferometer system. However, it has an important drawback: the shear value in the azimuthal direction decreases linearly along the radius of the investigated field.