Reconstruction of Interfering Waves from Three Dimensional Analysis of Their Interference Pattern

Optical interferometry is being used as an efficient tool to analyse smooth surfaces for more than a century. Although, due to introduction of novel computer assisted analyzing techniques and array detectors, like CCD, the speed and the precision of processing have been increased tremendously, but the main equation involved is not changed. The main equation is the intensity distribution in the interference pattern of a plane reference wave and the required wave. In the paper it is shown that by analysis of the interference pattern of two unknown waves in three dimension (which is possible for coherent waves) it is possible to reconstruct each wave separately. This approach has several useful applications, namely, on can do without reference plane wave in the interferometric surface analysis and, it is possible to reconstruct an unknown wave by making it to interfere with itself. This is very useful in determining the profile of laser beams and erasing the effect of atmospheric disturbances on observing astronomical objects.