Physics:Speckle imaging

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  Typical short-exposure image of a binary star (Zeta Bootis in this case) as seen through atmospheric seeing. Each star should appear as a single point, but the atmosphere causes the images of the two stars to break up into two patterns of speckles (one pattern above left, the other below right). The speckles are a little difficult to make out in this image due to the coarse pixel size on the camera used. The speckles move around rapidly, so that each star appears as a single fuzzy blob in long exposure images. The telescope used had a diameter of about 7r₀ (see definition of r₀ under astronomical seeing, and the example simulated image through a 7r₀ telescope).

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  Slow-motion speckle imaging movie, showing what you see through a telescope when you look at a star at high magnification (negative images). The telescope used had a diameter of about 7r₀. Notice how the star breaks up into multiple blobs (speckles) -- entirely an atmospheric effect. Speckle imaging techniques attempt to recreate the image of the object as it was before being corrupted by the atmosphere. Some telescope vibration is also noticeable in this movie.

Speckle imaging describes a range of high-resolution astronomical imaging techniques based on the analysis of large numbers of short exposures that freeze the variation of atmospheric turbulence. They can be divided into the shift-and-add ("image stacking") method and the speckle interferometry methods. These techniques can dramatically increase the resolution of ground-based telescopes, 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. Use of these techniques led to a number of discoveries, including thousands of binary stars that would otherwise appear as a single star to a visual observer working with a similar-sized telescope, and the first images of sunspot-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. This results in images of distant objects being spread out to a small spot known as the Airy disk. 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, 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 parameter r₀ – 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 provided a means of removing this limitation.

Speckle imaging recreates the original image through image processing techniques. The key to the technique, found by the American astronomer David L. Fried in 1966, was to take very fast images in which case the atmosphere is effectively "frozen" in place. For infrared images, exposure times are on the order of 100 ms, but for the visible region they drop to as little as 10 ms. In images at this time scale, or smaller, 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.

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.

More recently, another use of the technique has developed for industrial applications. By shining a laser (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

Techniques based on the shift-and-add method

In one technique called shift-and-add (also called image stacking), the short exposure images are aligned by using the brightest speckle and averaged to give a single output image. In the lucky imaging approach, only the best short exposures are selected for averaging. Early shift-and-add techniques aligned images according to the image centroid, giving a lower overall Strehl ratio.

Techniques based on speckle interferometry

In 1970, the France astronomer Antoine Labeyrie showed that Fourier analysis (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 or closure phases 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 with better resolving power than the telescope would otherwise have. This aperture masking technique was pioneered by the Cavendish Astrophysics Group.

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 enables real-time monitoring of dynamical systems and video image analysis to understand biological processes.

See also

• Astronomical interferometer
• Holographic interferometry
• Electronic Speckle Pattern Interferometry
• Bispectral analysis
• Optical interferometry
• Aperture synthesis
• Aperture Masking Interferometry
• Diffraction-limited system
• Lucky Imaging
• Super-resolution

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. Speckle imaging can produce images with four times better resolution than these.

• WR 104
• WR 98a
• LKHa 101
• MWC 349A
• Betelgeuse