A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.
Double-path interferometers are highly sensitive to phase shifts or length changes between the reference and sample arms. Because of this, double-path interferometers have found wide use in science and industry for the measurement of small displacements, refractive-index changes, surface irregularities and the like. There are applications, however, in which sensitivity to relative displacement or refractive-index differences between reference and sample paths is not desirable; alternatively, one may be interested in the measurement of some other property.
Selected examples
Sagnac
Sagnac interferometers are totally unsuited for measuring lengths or length changes. In a Sagnac interferometer, both beams emerging from the beamsplitter simultaneously go around all four sides of a rectangle in opposite directions and recombine at the original beamsplitter. The result is that a Sagnac interferometer is, to first order, completely insensitive to any movement of its optical components. Indeed, in order to make the Sagnac interferometer useful for measuring phase changes, the beams of the interferometer must be separated slightly so that they no longer follow a perfectly common path. Even with a slight beam separation, Sagnac interferometers offer excellent contrast and fringe stability. Two basic topologies of the Sagnac interferometer are possible, differing in whether there are an even or odd number of reflections in each path. In a Sagnac interferometer with an odd number of reflections, such as the one illustrated, the wavefronts of the oppositely traveling beams are laterally inverted with respect to each other over most of the light path, so the topology is not strictly common-path.
The best known use of the Sagnac interferometer lies in its sensitivity to rotation. The first accounts of the effects of rotation on this form of interferometer were published in 1913 by Georges Sagnac, who mistakenly believed that his ability to detect a "whirling of the ether" disproved relativity theory. The sensitivity of present-day Sagnac interferometers far exceeds that of Sagnac's original arrangement. The sensitivity to rotation is proportional to the area circumscribed by the counter-rotating beams, and fibre optic gyroscopes, present-day descendants of the Sagnac interferometer, use thousands of loops of optical fibre rather than mirrors, such that even small to medium-sized units easily detect the rotation of the Earth. Ring laser gyroscopes (not illustrated) are another form of Sagnac rotation sensor that have important applications in inertial guidance systems.
Because of their exceptional contrast and fringe stability, interferometers using the Sagnac configuration played an important role in experiments leading to Einstein's discovery of special relativity, and in the subsequent defense of relativity against theoretical and experimental challenges. For example, one year before their famous experiment of 1887, Michelson and Morley (1886) performed a repeat of the Fizeau experiment of 1851, replacing Fizeau's setup with an even-reflection Sagnac interferometer of such high stability, that even placing a lighted match in the light path did not cause artifactual fringe displacement. In 1935, Gustaf Wilhelm Hammar disproved a theoretical challenge to special relativity that attempted to explain away the null results of Michelson–Morley–type experiments as being mere artifact of aether-dragging, using an odd-reflection Sagnac interferometer. He could operate this interferometer in the open, on a high hilltop with no temperature control, yet still achieve readings of 1/10 fringe accuracy.