Aperture synthesis

# Aperture synthesis

Discussion

Encyclopedia
Aperture synthesis or synthesis imaging is a type of interferometry
Interferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...

that mixes signals from a collection of telescopes to produce images having the same angular resolution
Angular resolution
Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...

as an instrument the size of the entire collection. At each separation and orientation, the lobe-pattern of the interferometer produces an output which is one component of the Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

of the spatial distribution of the brightness of the observed object. The image (or "map") of the source is produced from these measurements. Astronomical interferometer
Astronomical interferometer
An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution by means of interferometry....

s are commonly used for high-resolution optical, infrared
Infrared astronomy
Infrared astronomy is the branch of astronomy and astrophysics that studies astronomical objects visible in infrared radiation. The wavelength of infrared light ranges from 0.75 to 300 micrometers...

, submillimetre
Submillimetre astronomy
Submillimetre astronomy or submillimeter astronomy is the branch of observational astronomy that is conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands, typically taken to be between a...

Radio astronomy is a subfield of astronomy that studies celestial objects at radio frequencies. The initial detection of radio waves from an astronomical object was made in the 1930s, when Karl Jansky observed radiation coming from the Milky Way. Subsequent observations have identified a number of...

observations.

## Technical issues

Aperture synthesis is possible only if both the amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

and the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

of the incoming signal is measured by each telescope. For radio frequencies, this is possible by electronics, while for optical lights, the elecromagnetic field cannot be measured directly and correlated in software, but must be propagated by sensitive optics and interfered optically. Accurate optical delay and atmospheric wavefront aberration correction is required, a very demanding technology which became possible only in the 1990s
1990s
File:1990s decade montage.png|From left, clockwise: The Hubble Space Telescope floats in space after it was taken up in 1990; American F-16s and F-15s fly over burning oil fields and the USA Lexie in Operation Desert Storm, also known as the 1991 Gulf War; The signing of the Oslo Accords on...

. This is why imaging with aperture synthesis has been used successfully in radio astronomy since the 1950s
1950s
The 1950s or The Fifties was the decade that began on January 1, 1950 and ended on December 31, 1959. The decade was the sixth decade of the 20th century...

and in optical/infrared astronomy only since the 2000 decade. See astronomical interferometer
Astronomical interferometer
An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution by means of interferometry....

In order to produce a high quality image, a large number of different separations between different telescopes are required (the projected separation between any two telescopes as seen from the radio source is called a baseline) - as many different baselines as possible are required in order to get a good quality image. The number of baselines (nb) for an array of n telescopes is given by nb=(n2- n)/2. For example the Very Large Array
Very Large Array
The Very Large Array is a radio astronomy observatory located on the Plains of San Agustin, between the towns of Magdalena and Datil, some fifty miles west of Socorro, New Mexico, USA...

has 27 telescopes giving 351 independent baselines at once, and can give high quality images.

## Differences

In contrast to radio arrays, the largest optical arrays currently have only 6 telescopes, giving poorer image quality from the 15 baselines between the telescopes. Most aperture synthesis interferometers use the rotation of the Earth to increase the number of different baselines included in an observation (see diagram on right).

Taking data at different times provides measurements with different telescope separations and angles without the need for buying additional telescopes or moving the telescopes manually, as the rotation of the Earth moves the telescopes to new baselines.

The use of Earth rotation was discussed in detail in the 1950 paper A preliminary survey of the radio stars in the Northern Hemisphere. Some instruments use artificial rotation of the interferometer array instead of Earth rotation, such as in aperture masking interferometry
Aperture Masking Interferometry is a form of speckle interferometry, allowing diffraction limited imaging from ground-based telescopes. This technique allows ground based telescopes to reach the maximum possible resolution, allowing ground-based telescopes with large diameters to produce far...

.

## History

Aperture synthesis imaging was first developed at radio wavelengths by Martin Ryle
Martin Ryle
Sir Martin Ryle was an English radio astronomer who developed revolutionary radio telescope systems and used them for accurate location and imaging of weak radio sources...

and coworkers from the Radio Astronomy Group
Cavendish Astrophysics Group
The Cavendish Astrophysics Group is based at the Cavendish Laboratory at the University of Cambridge. The group operates all of the telescopes at the Mullard Radio Astronomy Observatory except for the 32m MERLIN telescope, which is operated by Jodrell Bank.The group is the second largest of three...

at Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

. Martin Ryle and Tony Hewish
Antony Hewish
Antony Hewish FRS is a British radio astronomer who won the Nobel Prize for Physics in 1974 for his work on the development of radio aperture synthesis and its role in the discovery of pulsars...

Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

for this and other contributions to the development of radio interferometry.

The radio astronomy group in Cambridge went on to found the Mullard Radio Astronomy Observatory
Mullard Radio Astronomy Observatory is home to a number of large aperture synthesis radio telescopes, including the One-Mile Telescope, 5-km Ryle Telescope, and the Arcminute Microkelvin Imager...

near Cambridge in the 1950s. During the late 1960s and early 70s, as computers (such as the Titan
Titan (computer)
Titan was the prototype of the Atlas 2 computer developed by Ferranti and the University of Cambridge Mathematical Laboratory in Cambridge, England...

) became capable of handling the computationally intensive Fourier Transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

inversions required, they used aperture synthesis to create a 'One-Mile' and later a '5 km' effective aperture using the One-Mile
One-Mile Telescope
The One-Mile Telescope at the Mullard Radio Astronomy Observatory is an array of radio telescopes designed to perform aperture synthesis interferometry.- History :The One Mile Telescope was completed by the Radio Astronomy Group of Cambridge...

and Ryle
Ryle Telescope
The Ryle Telescope was a linear east-west radio telescope array at the Mullard Radio Astronomy Observatory. In 2004 three of the telescopes were moved to create a compact two-dimensional array of telescopes at the east end of the interferometer. The remaining five antennas were switched off on 19...

telescopes, respectively.

The technique was subsequently further developed in Very Long Baseline Interferometry
Very Long Baseline Interferometry
Very Long Baseline Interferometry is a type of astronomical interferometry used in radio astronomy. It allows observations of an object that are made simultaneously by many telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.Data...

to obtain baselines of thousands of km. Aperture synthesis is also used by a type of radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

system known as synthetic aperture radar
Synthetic-aperture radar is a form of radar whose defining characteristic is its use of relative motion between an antenna and its target region to provide distinctive long-term coherent-signal variations that are exploited to obtain finer spatial resolution than is possible with conventional...

, and even in optical telescopes
Optical interferometry
Optical interferometry combines two or more light waves in an opticalinstrument in such a way that interference occurs between them.Early interferometers used white light sources and also monochromatic light from atomic sources...

.

Originally it was thought necessary to make measurements at essentially every baseline length and orientation out to some maximum: such a fully sampled Fourier transform formally contains the information exactly equivalent to the image from a conventional telescope with an aperture diameter equal to the maximum baseline, hence the name aperture synthesis.

It was rapidly discovered that in many cases useful images could be made with a relatively sparse and irregular set of baselines, especially with the help of non-linear deconvolution
Deconvolution
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data. The concept of deconvolution is widely used in the techniques of signal processing and image processing...

algorithms such as the maximum entropy method. The alternative name synthesis imaging acknowledges the shift in emphasis from trying to synthesise the complete aperture (allowing image reconstruction by Fourier transform) to trying to synthesise the image from whatever data available, using powerful but computationally expensive algorithms.

## Other wavelengths

Aperture synthesis imaging has been demonstrated in the optical and infrared, first using aperture masking interferometry
Aperture Masking Interferometry is a form of speckle interferometry, allowing diffraction limited imaging from ground-based telescopes. This technique allows ground based telescopes to reach the maximum possible resolution, allowing ground-based telescopes with large diameters to produce far...

and later using arrays of separated telescopes. As of 2006 four optical/infrared interferometer arrays have released aperture synthesis images (COAST
Cambridge Optical Aperture Synthesis Telescope
COAST, the Cambridge Optical Aperture Synthesis Telescope, is a multi-element optical astronomical interferometer with baselines of up to 100 metres, which uses aperture synthesis to observe stars with angular resolution as high as one thousandth of one arcsecond COAST, the Cambridge Optical...

, NPOI
Navy Prototype Optical Interferometer
The Navy Prototype Optical Interferometer , is an astronomical interferometer operated by the United States Naval Observatory Flagstaff Station, in collaboration with the Naval Research Laboratory and The Lowell Observatory...

, IOTA
Infrared Optical Telescope Array
The Infrared Optical Telescope Array began with an agreement in 1988 among five Institutions, the Smithsonian Astrophysical Observatory, Harvard University, the University of Massachusetts, the University of Wyoming, and MIT/Lincoln Laboratory, to build a two-telescope stellar interferometer for...

and ISI
Infrared Spatial Interferometer
The Infrared Spatial Interferometer is an astronomical interferometer array of three 65 inch telescopes operating in the mid-infrared. The telescopes are fully mobile and their current site on Mount Wilson allows for placements as far as 70 m apart, giving the resolution of a telescope of that...

).

• Synthetic array heterodyne detection (SAHD)
Interferometric synthetic aperture radar, also abbreviated InSAR or IfSAR, is a radar technique used in geodesy and remote sensing. This geodetic method uses two or more synthetic aperture radar images to generate maps of surface deformation or digital elevation, using differences in the phase of...

(IfSAR or InSAR)
Synthetic-aperture radar is a form of radar whose defining characteristic is its use of relative motion between an antenna and its target region to provide distinctive long-term coherent-signal variations that are exploited to obtain finer spatial resolution than is possible with conventional...

(SAR) and Inverse synthetic aperture radar
Inverse synthetic aperture radar is a technique to generate a two-dimensional high resolution image of a target.ISAR technology utilizes the movement of the target rather than the emitter to create the synthetic aperture...

(ISAR)
• Synthetic aperture sonar
Synthetic aperture sonar
Synthetic aperture sonar is a form of sonar in which sophisticated post-processing of sonar data are used in ways closely analogous to synthetic aperture radar. Synthetic aperture sonars combine a number of acoustic pings to form an image with much higher resolution than conventional sonars,...

• Beamforming
Beamforming
Beamforming is a signal processing technique used in sensor arrays for directional signal transmission or reception. This is achieved by combining elements in the array in a way where signals at particular angles experience constructive interference and while others experience destructive...

• Synthetic Aperture Magnetometry
Synthetic Aperture Magnetometry
Synthetic-aperture magnetometry is a method for analysis of data obtained from magnetoencephalography and electroencephalography . SAM is a nonlinear beamforming approach which can be thought of as a spatial filter....