Common-path interferometer
Because of this, double-path interferometers have found wide use in science and industry for the measurement of small displacements,[2] refractive-index changes,[3] 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.
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 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.
[7] Ring laser gyroscopes (not illustrated) are another form of Sagnac rotation sensor that have important applications in inertial guidance systems.
[8] 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.
[11][12] The reference beam is generated by diffraction from a small pinhole, about half the diameter of the Airy disk, in a semitransparent plate.
This advantage can be very important in large interferometric setups such as in wind tunnels that have long optical paths through turbulent media.
The illustrated plane parallel plate interferometer has unequal path lengths for the test and reference beams; because of this, it must be used with highly monochromatic (laser) light.
Newton, after all, had observed what are now recognized as diffraction phenomena, and wrote on them in his Third Book of Optics,[22] interpreting them in terms of his corpuscular theory of light.
Young's contemporaries raised objections that his results could simply represent diffraction effects from the edges of the slits, no different in principle than the fringes that Newton had previously observed.
Augustin Fresnel, who supported the wave theory, performed a series of experiments to demonstrate interference effects that could not be simply explained away as being the result of edge diffraction.
The electron biprism consists of a fine, positively charged electric filament (represented as a dot in the figure) bracketed by two plate electrodes at ground potential.
As noted above, Sagnac interferometers are, to first order, insensitive to any static or low-frequency displacement of their optical components, nor are the fringes affected by minor frequency variation in the lasers or birefringence.
This variant of the Sagnac interferometer is hence insensitive to rotation or low frequency drift of its optical components, while maintaining a high sensitivity to transient events of astronomical interest.
It usually consists of a beam splitter, an optical flat, a biconvex diverger of short focal length and a light source such as a semiconductor laser.
Common-path interferometers have proven useful in a wide variety of applications including optical coherence tomography,[1] digital holography,[35] and the measurement of phase delays.
[36] Their relative resilience to environmental vibration is a common outstanding feature, and they can sometimes be used when no reference beam is available; however, depending on their topology, their interference patterns may be more complicated to interpret than those generated by double path interferometers.
