Interferometry - Basic Principles

Basic Principles

Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same frequency combine, the resulting pattern is determined by the phase difference between the two waves—waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Most interferometers use light or some other form of electromagnetic wave.

Typically (see Fig. 1, the well-known Michelson configuration) a single incoming beam of coherent light will be split into two identical beams by a beam splitter (a partially reflecting mirror). Each of these beams travels a different route, called a path, and are recombined before arriving at a detector. The path difference, the difference in the distance traveled by each beam, creates a phase difference between them. It is this introduced phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths, then the phase difference is diagnostic of anything that changes the phase along the paths. This could be a physical change in the path length itself or a change in the refractive index along the path.

As seen in Fig. 2a and 2b, the observer has a direct view of mirror M₁ seen through the beam splitter, and sees a reflected image M'₂ of mirror M₂. The fringes can be interpreted as the result of interference between light coming from the two virtual images S'₁ and S'₂ of the original source S. The characteristics of the interference pattern depend on the nature of the light source and the precise orientation of the mirrors and beam splitter. In Fig. 2a, the optical elements are oriented so that S'₁ and S'₂ are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to M₁ and M'₂. If, as in Fig. 2b, M₁ and M'₂ are tilted with respect to each other, the interference fringes will generally take the shape of conic sections (hyperbolas), but if M₁ and M'₂ overlap, the fringes near the axis will be straight, parallel, and equally spaced. If S is an extended source rather than a point source as illustrated, the fringes of Fig. 2a must be observed with a telescope set at infinity, while the fringes of Fig. 2b will be localized on the mirrors.

Use of white light will result in a pattern of colored fringes (see Fig. 3). The central fringe representing equal path length may be light or dark depending on the number of phase inversions experienced by the two beams as they traverse the optical system. (See Michelson interferometer for a discussion of this.)