# Interferometry

Interferometry is the technique of using the pattern of interference created by the superposition of two or more waves to diagnose the properties of the aforementioned waves. The instrument used to interfere the waves together is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, quantum mechanics and plasma physics.

## Basic Principle

Interferometry makes use of the principal of superposition to combine separate waves together in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same frequency combine the resulting pattern is determined by the phase difference between the two waves -- waves that are in phase will undergo constructive inference while waves that are out of phase will undergo destructive interference. Most interferometers use light or some other form of electromagnetic wave.

Typically a single incoming beam of light will be split into two identical beams by a grating or a partial mirror. Each of these beams will travel a different route, called a path, before they are recombined at a detector. The path difference, the difference in the distance travelled by each beam, creates a phase difference between them. It is this introduced phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths then the phase difference is diagnostic of anything that changes the phase along the paths. This could be a physical change in the path length itself or a change in the refractive index along the path.

## Imaging Interferometry

The pattern of radiation across a region can be represented as a function of position i(x,y), i.e. an image. The pattern of incoming radiation i(x,y) can be transformed into the fourier domain f(u,v). A single detector measures information from a single point in x,y space. An interferometer measures the difference in phase between two points in the x,y domain. This corresponds to a single point in the u,v domain. The signals from each set of detectors is combined in a device called a correlator. A single detector builds up a full image by scanning through the x,y coordinates. An interferometry builds up a full picture by measuring multiple points in u,v space. The image i(x,y) can then be restored by preforming a fourier transform on the measured f(u,v) data. This technique is called aperture synthesis.

## Applications

### Astronomical Interferometry

The angular resolution that a telescope can achieve is determined by its diffraction limit (which is proportional to its diameter). The larger the telescope, the better its resolution. However, the cost of building a telescope also scales with its size. The purpose of astronomical interferometry is to achieve high-resolution observations using a cost-effective cluster of comparatively small telescopes rather than a single very expensive monolithic telescope. The basic unit of an astronomical interferometry is a pair of telescopes. Each pair of telescopes is a basic interferometer. Their position in u,v space is referred to as a baseline.

Early astronomical interferometry was involved with a single baseline being used to measure the amount of power on a particular small angular scale. Later astronomical interferometers were telescope arrays comprised of a set of, usually identical, telescopes arranged in a pattern on the ground. A limited number of baselines will result in insufficient coverage in u,v space. This can be alleviated by using the rotation of the earth to rotate the array relative to the sky. This causes the points in u,v space that each baseline points at to change with time. Thus, a single baseline can measure information along a track in u,v space just by taking repeated measurements. This technique is called earth-rotation synthesis. It is even possible to have baseline of tens, hundreds, or even thousands of kilometers by using a technique called very long baseline interferometry.

The longer the wavelength of incoming radiation the easier it is to measure its phase information. For this reason early imaging interferometry was almost exclusively done with long wavelength radio telescopes. Examples of radio interferometers include the VLA and MERLIN. As the speed of correlators and associated technologies have improved the wavelength of radiation usable with interferometry has decreased. There have been several submillimeter inferometers with the largest, the Atacama Large Millimeter Array, currently under construction. Optical astronomical interferometers have traditionally been specialised instruments, but recent developments have broadened their capabilities.