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Speckle imaging describes a range of high-resolution
astronomical imaging Astrophotography, also known as astronomical imaging, is the photography or imaging of astronomical objects, celestial events, or areas of the night sky. The first photograph of an astronomical object (the Moon) was taken in 1840, but it was no ...
techniques based on the analysis of large numbers of short exposures that freeze the variation of
atmospheric turbulence An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
. They can be divided into the
shift-and-add Speckle imaging describes a range of high-resolution Astrophotography, astronomical imaging techniques based on the analysis of large numbers of short Exposure (photography), exposures that freeze the variation of Astronomical seeing, atmospheri ...
("''image stacking''") method and the speckle interferometry methods. These techniques can dramatically increase the
resolution Resolution(s) may refer to: Common meanings * Resolution (debate), the statement which is debated in policy debate * Resolution (law), a written motion adopted by a deliberative body * New Year's resolution, a commitment that an individual mak ...
of ground-based
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
s, but are limited to bright targets.


Explanation

The principle of all the techniques is to take very short exposure images of astronomical targets, and then process those so as to remove the effects of
astronomical seeing In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing v ...
. Use of these techniques led to a number of discoveries, including thousands of
binary star A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in wh ...
s that would otherwise appear as a single star to a visual observer working with a similar-sized telescope, and the first images of
sunspot Sunspots are phenomena on the Sun's photosphere that appear as temporary spots that are darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. Sun ...
-like phenomena on other stars. Many of the techniques remain in wide use today, notably when imaging relatively bright targets. The resolution of a telescope is limited by the size of the main mirror, due to the effects of
Fraunhofer diffraction In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer ...
. This results in images of distant objects being spread out to a small spot known as the
Airy disk In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
. A group of objects whose images are closer together than this limit appear as a single object. Thus larger telescopes can image not only dimmer objects (because they collect more light), but resolve objects that are closer together as well. This improvement of resolution breaks down due to the practical limits imposed by the
atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
, whose random nature disrupts the single spot of the Airy disk into a pattern of similarly-sized spots scattered over a much larger area (see the adjacent image of a binary). For typical seeing, the practical resolution limits are at mirror sizes much less than the mechanical limits for the size of mirrors, namely at a mirror diameter equal to the
astronomical seeing In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing v ...
parameter ''r''0 – about 20 cm in diameter for observations with visible light under good conditions. For many years telescope performance was limited by this effect, until the introduction of speckle interferometry and
adaptive optics Adaptive optics (AO) is a technology used to improve the performance of optical systems by reducing the effect of incoming wavefront distortions by deforming a mirror in order to compensate for the distortion. It is used in astronomical tele ...
provided a means of removing this limitation. Speckle imaging recreates the original image through
image processing An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
techniques. The key to the technique, found by the American astronomer
David L. Fried David L. Fried (April 13, 1933 – May 5, 2022) was an American scientist, best known for his contributions to optics. Fried described what has come to be known as the Fried Parameter, or r0 (often pronounced ''r-naught'', but also ''r-zero''). Th ...
in 1966, was to take very fast images in which case the atmosphere is effectively "frozen" in place. At
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
wavelengths, coherence times τ0 are on the order of 100 ms, but for the
visible region The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye will respond to wav ...
they drop to as little as 10 ms. When exposure times are shorter than τ0, the movement of the atmosphere is too sluggish to have an effect; the speckles recorded in the image are a snapshot of the atmospheric seeing at that instant. Coherence tim
τ0 = ''r''0/''v''
is a function of wavelength, because ''r''0 is a function of wavelength. Of course there is a downside: taking images at this short an exposure is difficult, and if the object is too dim, not enough light will be captured to make analysis possible. Early uses of the technique in the early 1970s were made on a limited scale using photographic techniques, but since photographic film captures only about 7% of the incoming light, only the brightest of objects could be viewed in this way. The introduction of the CCD into astronomy, which captures more than 70% of the light, lowered the bar on practical applications by an order of magnitude, and today the technique is widely used on bright astronomical objects (e.g. stars and star systems). Many of the simpler speckle imaging methods have multiple names, largely from amateur astronomers re-inventing existing speckle imaging techniques and giving them new names. Another use of the technique is in industry. By shining a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
(whose smooth wavefront is an excellent simulation of the light from a distant star) on a surface, the resulting speckle pattern can be processed to give detailed images of flaws in the material.


Types


Shift-and-add method

The shift-and-add method (more recently "image-stacking" method) is a form of speckle imaging commonly used for obtaining high quality images from a number of short exposures with varying image shifts. It has been used in astronomy for several decades, and is the basis for the
image stabilisation Image stabilization (IS) is a family of techniques that reduce motion blur, blurring associated with the motion of a camera or other imaging device during exposure (photography), exposure. Generally, it compensates for panning (camera), pan an ...
feature on some cameras. The short exposure images are aligned by using the brightest speckle and averaged to give a single output image. The method involves calculation of the differential shifts of the images. This is easily accomplished in astronomical images since they can be aligned with the stars. Once the images are aligned they are averaged together. It is a basic principle of statistics that variation in a sample can be reduced by averaging together the individual values. In fact, when using an average, the signal-to-noise ratio should be increased by a factor of the square root of the number of images. A number of software packages exist for performing this, including
IRAF IRAF (Image Reduction and Analysis Facility) is a collection of software written at the National Optical Astronomy Observatory (NOAO) geared towards the reduction of astronomical images and spectra in pixel array form. This is primarily data take ...
,
RegiStax RegiStax is image processing software for Astrophotography#Amateur astrophotography, amateur astrophotographers, released as freeware, designed to run under Windows, but which also runs on Linux, under Wine (software), wine. Its purpose is to p ...
, Autostakkert, Keiths Image Stacker,
Hugin Hugin may refer to: * Bob Hugin (born 1954), American politician and businessman * Hugin (longship), a Danish reconstruction of a Viking longship on display in Ramsgate, England * HUGIN, a widely used tool for uncertain reasoning using Bayesian net ...
, and
Iris Iris most often refers to: *Iris (anatomy), part of the eye *Iris (mythology), a Greek goddess * ''Iris'' (plant), a genus of flowering plants *Iris (color), an ambiguous color term Iris or IRIS may also refer to: Arts and media Fictional enti ...
. In the
lucky imaging Lucky imaging (also called lucky exposures) is one form of speckle imaging used for astrophotography. Speckle imaging techniques use a high-speed camera with exposure times short enough (100 ms or less) so that the changes in the Earth's atm ...
approach, only the best short exposures are selected for averaging. Early shift-and-add techniques aligned images according to the image
centroid In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any ob ...
, giving a lower overall
Strehl ratio The Strehl ratio is a measure of the quality of optical image formation, originally proposed by Karl Strehl, after whom the term is named. Used variously in situations where optical resolution is compromised due to lens aberrations or due to imagi ...
.


Speckle interferometry

In 1970, the
French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...
astronomer
Antoine Labeyrie Antoine is a French given name (from the Latin ''Antonius'' meaning 'highly praise-worthy') that is a variant of Danton, Titouan, D'Anton and Antonin. The name is used in France, Switzerland, Belgium, Canada, West Greenland, Haiti, French Guiana, ...
showed that
Fourier analysis In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...
(''speckle interferometry'') can obtain information about the high-resolution structure of the object from the statistical properties of the speckle patterns. Methods developed in the 1980s allowed simple images to be reconstructed from this power spectrum information. One more recent type of speckle interferometry called '' speckle masking involves calculation of the ''
bispectrum In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions. Definitions The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional po ...
'' or ''
closure phase The closure phase is an observable quantity in imaging astronomical interferometry, which allowed the use of interferometry with very long baselines. It forms the basis of the self-calibration approach to interferometric imaging. The observable ...
s'' from each of the short exposures. The "average bispectrum" can then be calculated and then inverted to obtain an image. This works particularly well using aperture masks. In this arrangement the telescope aperture is blocked except for a few holes which allow light through, creating a small
optical interferometer Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opti ...
with better resolving power than the telescope would otherwise have. This aperture masking technique was pioneered by the
Cavendish Astrophysics Group The Cavendish Astrophysics Group (formerly the Radio Astronomy 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 MERLI ...
. One limitation of the technique is that it requires extensive computer processing of the image, which was hard to come by when the technique was first developed. This limitation has faded away over the years as computing power has increased, and nowadays desktop computers have more than enough power to make such processing a trivial task.


Biology

Speckle imaging in biology refers to the underlabeling of periodic cellular components (such as filaments and fibers) so that instead of appearing as a continuous and uniform structure, it appears as a discrete set of speckles. This is due to statistical distribution of the labeled component within unlabeled components. The technique, also known as
dynamic speckle In physics, dynamic speckle is a result of the temporal evolution of a speckle pattern where variations in the scattering elements responsible for the formation of the interference pattern in the static situation produce the changes that are seen i ...
enables real-time monitoring of dynamical systems and video image analysis to understand biological processes.


See also

*
Astronomical interferometer An astronomical interferometer or telescope array is a set of separate telescopes, mirror segments, or radio telescope antenna (radio), antennas that work together as a single telescope to provide higher resolution images of astronomical objects ...
*
Holographic interferometry Holographic interferometry (HI)Powell RL & Stetson KA, 1965, J. Opt. Soc. Am., 55, 1593-8 is a technique which enables static and dynamic displacements of objects with optically rough surfaces to be measured to optical interferometric precision (i.e ...
*
Electronic Speckle Pattern Interferometry Electronic speckle pattern interferometry (ESPI), also known as TV holography, is a technique that uses laser light, together with video detection, recording and processing, to visualise static and dynamic displacements of components with optic ...
*
Focus stacking Focus stacking (also known as focal plane merging and z-stacking or focus blending) is a digital image processing technique which combines multiple images taken at different focus distances to give a resulting image with a greater depth of fiel ...
* Bispectral analysis *
Optical interferometry Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opti ...
*
Aperture synthesis Aperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection. At each separation an ...
* Aperture Masking Interferometry *
Diffraction-limited system The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to th ...
*
Lucky Imaging Lucky imaging (also called lucky exposures) is one form of speckle imaging used for astrophotography. Speckle imaging techniques use a high-speed camera with exposure times short enough (100 ms or less) so that the changes in the Earth's atm ...
*
Super-resolution Super-resolution imaging (SR) is a class of techniques that enhance (increase) the resolution of an imaging system. In optical SR the diffraction limit of systems is transcended, while in geometrical SR the resolution of digital imaging sensors i ...


Example images

All of these were obtained using infrared AO or IR interferometry (not speckle imaging) and have higher resolution than can be obtained with e.g. the
Hubble Space Telescope The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most versa ...
. Speckle imaging can produce images with four times better resolution than these.
WR 104







Betelgeuse


References


External links


Hugin
- open source image software with shift-and-add "image-stacking"

- freeware astronomical images processing software
Autostakkert
- alignment and stacking of image sequences, minimizing the influence of atmospheric distortions {{DEFAULTSORT:Speckle Imaging