Interferometers

An interferometer is an optical device which utilizes the effect of interference. That can be done with different kinds of radiation, but this article specifically deals with optical interferometers, i.e., interferometer for light. Typically, such a device is based on the following operation principle: it starts with some input beam, splits it into two separate beams with some kind of beam splitter (a partially transmissive mirror), possibly exposes some of these beams to some external influences (e.g. some length changes or refractive index changes in a transparent medium), and recombines the beams on another beam splitter. The power or the spatial shape of the resulting beam can then be used e.g. for a measurement.

Interferometers frequently need to be made from high-quality optical elements. For example, one often uses mirrors and optical flats with a high degree of surface flatness.

There are also substantially different principles of using interferometers. For example, Michelson interferometers are used in very different ways, using different types of light sources and photodetectors:

• When a light source with low optical bandwidth is used (perhaps even a single-frequency laser), the detector signal varies periodically when the difference in arm lengths is changed. Such a signal makes it possible to do measurements with a depth resolution well below the wavelength, but there is an ambiguity. For example, a monotonic increase or decrease of the arm length difference leads to the same variation of the detected signal. This problem may be solved by modulating the arm length difference e.g. with a vibrating mirror (or with an optical modulator) and by monitoring the resulting modulation on the detector in addition to the average signal power. Simultaneous operation of an interferometer with two wavelengths is another way of removing the ambiguity.
• If the detector is a kind of camera (e.g. a CCD chip) and the surfaces monitored are fairly smooth, the phase profile (and thus the profile of optical path length) can be reconstructed by recording several images with different overall phase shifts (phase-shifting interferometry). A phase-unwrapping algorithm can be used to retrieve unambiguously surface maps extending over more than a wavelength. However, such methods may not work for rough surfaces or for surfaces with steep steps.
• A white-light interferometer uses a broadband light source (e.g., a superluminescent diode), so that interference fringes are observed only in a narrow range around the point of zero arm length difference. In that way, the above-mentioned ambiguity is effectively removed.
• A wavelength-tunable laser can be used to record the detector signal for different optical frequencies. From such signals, the arm length difference can be unambiguously retrieved. This works also with two-dimensional detectors (e.g. CCD cameras).
• If one of the mirrors is intentionally tilted, an interference fringe pattern is obtained. Any change in arm length difference will then move the fringe pattern. This method makes it possible to measure phase changes sensitively and also to measure position-dependent phase changes, e.g. in some optical element.
• Instead of measuring distances, one can use interferometers for characterizing light. For example, the optical spectrum can be obtained by measuring the detector signal vs. arm length difference and applying a Fourier transform (Fourier transform spectroscopy). One can also retrieve wavelength-dependent phase shifts, for example for measuring chromatic dispersion of optical elements.

Another class of interferometric methods is named spectral phase interferometry. Here, interference in the spectral domain is exploited. The spectral modulation period is essentially determined by a time delay.

Interferometers can be used for many different purposes — by far not only for length measurements. Some examples are:

• for the measurement of a distance (or changes in a distance or a position, i.e., a displacement) with an accuracy of better than an optical wavelength (in extreme cases, e.g. for gravitational wave detection, with a sensitivity many orders of magnitude below the wavelength)
• for measuring the wavelength e.g. of a laser beam (→ wavemeter), or for measuring the full optical spectrum
• for monitoring slight changes in an optical wavelength or frequency (typically using the transmittance curve of a Fabry–Pérot interferometer) (frequency discriminators)
• for measuring rotations (with a Sagnac interferometer)
• for measuring slight deviations of an optical surface from perfect flatness (or from some other shape)
• for measuring the linewidth of a laser (→ self-heterodyne linewidth measurement, frequency discriminator)
• for revealing tiny refractive index variations or induced index changes in a transparent medium
• for modulating the power or phase of a laser beam, e.g. with a Mach–Zehnder modulator in an optical fiber communication system
• for measurements of the chromatic dispersion of optical components
• as an optical filter
• for the full characterization of ultrashort pulses via spectral phase interferometry

The first very prominent interferometer-based scientific experiment was the Michelson–Morley experiment in the context of the search for an ether wind. The most recent large discovery based on measurements with interferometers was the detection of gravitational waves [15]. Interferometers played vital roles also in many other scientific discoveries, e.g. in quantum optics.

Depending on the application, the demands on the light source in an interferometer can be very different. In many cases, a spectrally very pure source, e.g. a single-frequency laser is required. Sometimes, the laser has to be wavelength-tunable. In other cases (e.g. for dispersion measurements with white-light interferometers), a light source with a very broad and smooth optical spectrum is required.

While the underlying physical principles are universal, commercial interferometers are typically specialized for specific tasks:

• Laser interferometers for displacement: These are widely used in machine shops and lithography systems for measuring linear positions with nanometer precision over distances of meters. They often employ heterodyne detection (using two slightly different optical frequencies) to determine the direction of motion and improve noise immunity.
• Fizeau interferometers: The standard tool in optical workshops for testing the surface flatness of mirrors or the transmitted wavefront quality of lens systems. They require high-quality reference optics (transmission flats or spheres).
• White-light interferometers: Also known as coherence scanning interferometers, these are used for 3D surface profiling. By utilizing a broadband light source with low temporal coherence, they can measure rough surfaces and step heights without the phase ambiguity issues common to monochromatic interferometers.
• Fiber-optic interferometers: These compact systems, often based on Sagnac or Mach–Zehnder configurations, serve as sensors for temperature, strain, or rotation (gyroscopes) in environments where bulk optics are impractical.

Interferometric measurements can be subject to various types of noise:

• Mechanical noise (vibrations, shocks etc.) can affect measurements; one often needs to employ sophisticated mechanical means for suppressing such influences.
• There can be technical noise from light sources, e.g. laser noise, but also quantum noise influences. Typically, vacuum noise entering the open input port at a beamsplitter defines the standard quantum limit (shot noise limit) for the sensitivity [2, 5]. A noise level below that limit can sometimes be achieved by injecting squeezed states of light into an interferometer [2, 4, 12].