Michelson interferometry

In a Michelson interferometer, the test beam and the reference beam develop a phase difference, not due to changes in refractive index along the path of light propagation but because of movement of one of the active surfaces. If the reference beam reflects off a fixed surface, the test beam, reflecting off a moving surface will interfere with the reference beam and produce an interference pattern. The simplest configuration of a Michelson interferometer is shown in Figure 4.68.

For definiteness, the application to Michelson interferometer to a crystal growth experiment is described below. Here, a seed crystal is immersed in its aqueous solution, supersaturated at the temperature considered. The excess salt deposits on the crystal introduced and the concerned surface grows with time. If this surface is taken as one off which the test beam is reflected, the growth rate can be monitored as a function of the position along the crystal and with time.

Consider a Michelson interferometer based experiment which is set-up for on-line monitoring of the microtopography of the growing face of a crystal. In this interferometry, one of the interfering beams is reflected from the surface of a growing crystal to get the microtopographic details of the growing surface. Since interferometry through the solution requires reflection of the light beam from the solution-crystal interface, it is a difficult task. Clear fringes can be recorded when the difference in refractive index between the solution and the crystal is sufficiently large. In spite of the inherent difficulties in working with this technique, it can be effectively used for studies in growth kinetics of crystals from their aqueous solution.

The basic principle of the Michelson interferometry in the context of crystal growth is that the phase variation due to growth or dissolution of the crystal surface manifests itself in the form of change in the fringe pattern. For example, if a crystal face has a growth hillock originating from a screw dislocation, the corresponding interference pattern consists of concentric fringes of equal thickness. Figure 4.68 shows schematically the process of fringe formation from a surface having a hillock generated from a dislocation. With every change in the crystal thickness by , one fringe shift takes place. Here is the wavelength of the laser used, and n is the refractive index of the solution. From such an interferogram the geographical description of the crystal face is obtained. Quantitative analysis of the interferogram yields the growth-kinetic parameters such as normal growth rate , slope of the dislocation growth hillock , and tangential growth velocity of the steps.