Analysis of fringe formation and localization in optical interferometry using optical coherence

Fringe formation and localization in holographic interferometry, speckle interferometry, and Michelson interferometry is very important to understand the nature of interfering waves and the perturbation involved in one of the waves. The fringes of optical interferometry [1] can be classified into two parts and they are i) Localized and ii) Non localized. The localized fringes are obtained in Michelson interferometer, irrespective of coherence of sources, if the two mirrors are tilted with respect to each other. On the other hand if they are parallel, then fringes never localize at any plane. The non localized fringes will be formed, if the interfering beams from two arms of the interferometer have path length variation within the coherence length of source. Unlike fringe formations in classical interferometric systems, localization of fringes in holographic interferometry, speckle interferometry depends on the reflected or transmitted object waves as the other interfering waves could be plane laser beam. In such cases the fringes localize only at planes where the phases remain constant and the plane is normal to the direction of interference. This condition can not be satisfied for most of the interferometric experiments which in turn may introduce error in measuring the cause of interference. For example if, we want to measure the tilt of an object or any other motion of an object in holographic interfreometry, it will not be possible to accurately compute the amount of motion without the fringes being localized at a particular plane. The fringe formation and localization also depends upon coherence of optical waves, interfering medium, polarization etc. In this paper we report detailed analysis about the formation and localization of interferometric fringes under various conditions.