A Common Path Interferometer is a type of interferometer in which the sample beam and reference beam uses a common optical path to interfere. 

In some interferometers like a Michelson interferometer, the optical beams take different geometrical paths and interfere. In this case, the obtained signal after interference will be highly sensitive to misalignments, and the path length difference will be affected by mechanical noise such as vibrations and shocks. The common path interferometer is a solution to this problem. These interferometers do not require perfect optical components with dimensions equal to those of the systems under test to produce the reference beam. Also, the path difference between the two beams in the center of the field of view is generally zero which makes the use of white light possible. In some common path interferometers, the reference beam travels through a small area of the optical system under test and is unaffected by the system aberrations. When this reference beam interferes with the test beam that travels through the full aperture of the optical system, explicit information about the system defects is obtained.

The common path interferometer setup is very simple and compact. The alignment of this setup is less critical and they do not require special measures to reduce mechanical noise. There are different types of common path interferometers such as sagnac interferometers, scatterplate interferometers, lateral shear interferometers, bath interferometers, point diffraction interferometers, etc.

Types of Interferometers

Sagnac Interferometer

Figure 1: Sagnac Interferometer

Sagnac Interferometer is a type of interferometer that uses the concept of sagnac effect to measure rotation using optical interferometry. A sagnac interferometer uses counter-propagating beams in a ring path, realized with multiple mirrors or with an optical fiber. In sagnac effect, if the whole interferometer is rotated e.g. around an axis that is perpendicular to the drawing plane, a relative phase shift is introduced to the counter-propagating beams. The sensitivity of rotations depends on the area covered by the ring multiplied by the number of round trips. This can be large when using many turns in an optical fiber. It is also possible to obtain a sensitivity that is sufficient for measuring the rotation of the Earth around its axis.

The Sagnac interferometer has a ring architecture. Figure 1 depicts the schematic of a sagnac interferometer. A light beam from a light source is split into two beams using a beam splitter and both these beams follow the same path but in opposite directions. While returning to the entry point, both these beams are allowed to exit the ring and undergo interference. According to the apparatus's angular velocity, the interference fringes' position, and the relative phases of the two outgoing beams are shifted. That is, when the interferometer is at rest with respect to the earth, the light travels at a constant speed. When the interferometer system is spun, one of the light beams will slow down with respect to the other light beam.

Scatterplate Interferometer

Figure 2: Scatterplate Interferometer

A Scatterplate Interferometer is an instrument used to measure the wavefront aberrations in optical systems. It is used for testing the quality of optical systems such as lenses, mirrors, and telescopes. This interferometer works by analyzing the scatter patterns produced when a wavefront from an optical source is passed through a diffusing plate, and these patterns are used to reconstruct the wavefront and determine its aberrations.

The reference path and test path are matched automatically in the scatterplate interferometer so that a zero-order fringe can be easily obtained with white light. The quality of auxiliary optics is not important for these interferometers since it is a common path interferometer. Lasers are used as light sources in these interferometers, but spectrally filtered white light sources or arc lamps are preferred. The fringe contrast is lower for these interferometers. It is mainly used for the optical testing of concave mirrors.

The scatterplate interferometer setup to test a spherical mirror is shown in figure 2. The scatterplate is placed close to the centre of curvature of the test surface (mirror under test), and this plate contains a pattern of tiny opaque patches that are distributed randomly and arranged on the plate with inversion symmetry. The spatially filtered light source is imaged onto the test part. This causes the scatterplate to be reimaged on itself (inverted). 

Four types of light are identified by the scatterplate's second transmission of light:

• A portion of the light enters the scatterplate directly, is reflected by the mirror, and then scatters when it encounters the scatterplate a second time. The reference beam is created by this direct-scattered light.
• A portion of the light is scattered when it first passes through the scatterplate, is reflected by the mirror, and then passes through the scatterplate unchanged when it encounters it a second time. The test beam, which is formed of this scattered-direct light, interacts with the reference beam to create interference fringes.
• A certain portion of the light directly passes through the scatterplate on both of its encounters. A tiny, undesirable hotspot is produced by this direct-direct light.
• On both encounters with the scatterplate, a specific portion of the light is scattered. The overall contrast of the interference pattern is decreased by this scattered-scattered light.

Lateral Shear Interferometer

Figure 3: Lateral Shear Interferometer

A Lateral Shear Interferometer is an optical interferometer used to measure the lateral displacement of an object. It works by shining a light onto the object and analyzing the interference patterns created by the light that reflects off of the object and a reference surface. The lateral displacement of the object can be determined by analyzing the phase shift in the interference pattern, which is proportional to the lateral displacement. Lateral shear interferometers are commonly used in metrology and metrological research, as well as in applications such as the measurement of surface roughness and the characterization of mechanical vibrations.

In the lateral shear interferometer, the wavefront under study is duplicated by laterally displacing it by a small amount and then the interference pattern is obtained between the original and the displaced wavefront. The wavefronts can be planar or spherical. If the wavefront is almost planar, the lateral shear is obtained by displacing the wavefront in its own plane. And if it is a spherical wavefront, the lateral shear is obtained by sliding the wavefront along itself by rotation about an axis passing through the center of curvature of the spherical wavefront. It is ideal for the testing of optical components & systems, the study of flow and diffusion phenomena in gases & liquids applications. Figure 3 shows the schematic of a lateral shear interferometer.

Bath Interferometer

Figure 4: Bath Interferometer

A Bath Interferometer is a type of interferometer used to measure the changes in the optical path length of a light beam as it passes through a liquid sample. Bath interferometers are often used in applications such as measuring the refractive index and density of liquids, as well as for detecting changes in the physical and chemical properties of liquids due to temperature, pressure, and other factors.

The bath interferometer usually consists of a light source such as a semiconductor laser with low coherence, a beam splitter, a plano-convex lens, and a fold mirror. It is mainly used to test telescope mirrors. 

The schematic of a bath interferometer is shown in figure 4. The lens is glued directly onto the beam splitter to eliminate two surfaces that might get dust and it is very convenient to mount a lens. The light from the laser is split into two beams, a reference beam, and a test beam. The test beam in blue goes straight through and comes to a focus and then diverges to fill out the aperture of the test mirror. The reference beam in red is reflected up and bounces off the fold mirror and goes out as the collimated beam. On the return path, the test beam reflects out the fold mirror and comes out of the bottom side of the beam-splitting cube where it is combined with the reference beam coming back through the plano-convex lens, there the interferogram appears with the camera lens or eyes.

Point Diffraction Interferometer

Figure 5: Point Diffraction Interferometer

The Point Diffraction Interferometer (PDI) is an interferometer used for measuring the phase variations in a beam caused by a point discontinuity in the path of the reference wave. PDI is based on the principle of diffraction and can be used to measure the properties of objects that are smaller than the wavelength of light used in the measurement. It works by illuminating an object with a small diffraction-limited spot of light, which creates an interference pattern in the far field that provides information about the object.

In a point diffraction interferometer, a pinhole etched onto a semi-transparent film generates the reference beam. The light beam from the light source is focused on a semi-transparent mask. There is a hole in the center of the mask about the size of an airy disc. The light beam is focused using a Fourier transforming lens onto this hole. The zeroth order light beam which is the test beam passes through the hole and interferes with the rest of the diffracted light beam (reference beam) and forms interference fringes. Figure 5 shows a point diffraction interferometer.

Applications of Common Path Interferometers

A common path interferometer is used for applications such as gyroscopes, femtosecond time-resolved interferometry, Fourier transform spectroscopy, wavefront sensing, and pulse characterization. This interferometer is more compact and stable than the commonly used dual-arm interferometer and is well suited for frequency-domain optical coherence tomography of biological samples. It is used for label-free protein sensing and for exemplary application in antibiotic guidance and opens possibilities for detecting further clinically or environmentally relevant small molecules with an intrinsically simple and robust sensing modality. A common-path interferometer using the modified Michelson system with a reflective grating is used for quantitative phase imaging. The point diffraction interferometers are used for adaptive optics applications.