Michelson Interferometer - Configuration

Configuration

A Michelson interferometer consists of two highly polished mirrors M₁ & M₂. In Fig 2, a source S emits light that hits a beam splitter (in this case, a half-silvered mirror), surface M, at point C. M is partially reflective, so one beam is transmitted through to point B while the other is reflected in the direction of A. Both beams recombine at point C' to produce an interference pattern (assuming proper alignment) visible to the observer at point E. To the observer at point E, the effects observed would be the same as those produced by placing surfaces A and B' (the image of B on the surface M) on top of each other. Fig. 2 shows use of a monochromatic source. White light can also be used, provided that the path lengths are carefully equalized, a requirement due to the short coherence length of white light (on the order of a micron).

Energy is conserved, because there is a redistribution of energy at the central beam-splitter in which the energy at the destructive sites is re-distributed to the constructive sites. The effect of the interference is to alter the share of the reflected light which heads for the detector, the part which misses the detector, and the part which reflected back to the source.

As seen in Fig. 3a and 3b, 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. 3a, 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 (fringes of equal inclination). If, as in Fig. 3b, 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 (fringes of equal thickness). If S is an extended source rather than a point source as illustrated, the fringes of Fig. 3a must be observed with a telescope set at infinity, while the fringes of Fig. 3b will be localized on the mirrors.

White light has only a very limited coherence length. When using a white light source, the two optical paths must be equal for all wavelengths. To meet this requirement, both the longitudinal and transverse light paths must cross an equal thickness of glass of the same dispersion. In Fig. 4a, the longitudinal beam crosses the beam splitter three times, while the transverse beam crosses the beam splitter once. To equalize the path lengths, a compensating plate identical to the beam splitter, but without the semireflective coat, is inserted into the path of the transverse beam. In Fig. 4b, we see that a cube beam splitter is self-compensating.

The extent of the fringes depends on the coherence length of the source. In Fig. 3b, the yellow sodium light used for the fringe illustration consists of a pair of closely spaced lines, D₁ and D₂, implying that the interference pattern will blur after several hundred fringes. Highly monochromatic sources, such as lasers, yield interference patterns that can remain distinct over many millions of fringes. In Fig. 4, the central fringes are sharp, but the fringe patterns rapidly become indistinct.

If one uses a half-silvered mirror as the beam splitter, as in Fig. 4a, the horizontally traveling beam will undergo a front-surface reflection at the mirror, and a rear-surface reflection at the beam splitter. The vertically traveling beam will undergo two front surface reflections at the beam splitter and the mirror. At each front-surface reflection, the light will undergo a phase inversion. Since light traveling the two paths will undergo a different number of phase inversions, when the two paths differ by a whole number (including 0) of wavelengths, there will be destructive interference and a weak signal at the detector. If they differ by a whole number and a half wavelengths (e.g., 0.5, 1.5, 2.5 ...) there will be constructive interference and a strong signal. Results will differ if a cube beam-splitter is employed, as in Fig. 4b, since a cube beam-splitter makes no distinction between a front- and rear-surface reflection. In Fig. 4a, the central fringe representing equal path length is dark, while in Fig. 4b, the central fringe is bright.