Further analysis of the interference patterns in cross-grating Interferometers

The fringe characteristics in cross-grating interferometers, illuminated by a source at finite distance, are analyzed. From the measurements of the fringe visibilities and the fringe shifts on discrete planes, the spatial irradiance distribution of the illuminating source, which is separable in two orthogonal directions, can be synthesized. To recover a general 2-D source structure, a line-grating interferometer and the technique of computed tomography should be used. When the line structures of the two cross gratings are not parallel, the fringe pattern has lower contrast, which suggests that four-line gratings should be used to replace the second cross grating to have high contrast fringes. The possibility of forming cross-gratinglike patterns using either the combination of one cross grating and two line gratings or the combination of two line-grating interferometers is discussed. Finally, moire interferometry using a cross-grating interferometer (a line-grating interferometer when only two beams of light are used) is analyzed. Experimental results are given.