Image Restoration And Atmospheric Turbulence

Investigator(s):

The project is concerned with the restoration of atmospherically degraded telescopic images, both of astronomical objects and of earth-based objects, for surveillance purposes. As part of the image restoration, a new method of visualising atmospheric turbulence has been found, which is being developed into a useful tool for atmospheric research. A former Ph.D. student, Glen Thorpe, has been associated with much of the initial project development.

The apparent ``wobbling" distortion of a scene viewed through an open fire or across a hot road is a familiar phenomenon. The wobbling is caused by gradients in refractive index in the atmosphere resulting from temperature gradients in the turbulent mixing. The effects occur under most atmospheric conditions, but are otherwise only noticeable and of importance in telescopic imaging. This is a major reason why high mountains are chosen for astronomical observatories (to move above the worst of the atmospheric effects) and a reason for the existence of Hubble Space Telescope.

The cost of a space telescope is high, so image restoration algorithms and/or adaptive optics have become an important research area in astronomical imaging. Considerable progress has been achieved over the past two decades in improving results of earth-based observation. Telescopic surveillance of objects and scenes at ground level or anywhere in the atmosphere suffers from similar problems, and worse; in this case, image restoration (or adaptive optics) is the only means of improvement, since the problems cannot be eliminated simply by leaving the atmosphere behind.

We have been concentrating on the restoration of images covering a comparatively wide field of view. Sequences of short exposure images of a scene, such as the surface of the moon or a horizontally imaged scene on the earth, are captured with an interline-transfer CCD digital camera attached to a telescope. We have a small observatory on the roof of the building and three reflecting telescopes for different purposes. The image field of view, 100 arc secs to several hundred arc secs across, is wide compared to that in currentastronomical ``speckle" restoration techniques. The main effect we observe at this scale is a random, differential wobbling of points within each image. An exposure time of 5 to 10 ms ``freezes" the atmospheric wobble to provide a sequence of randomly warped images. Under these conditions, the point spread function (PSF) for each image, due to the atmosphere and telescope, approximates a position-dependent randomly-displaced delta function (if we temporarily ignore instantaneous speckle and instrument blurring).

Cause and effect are illustrated in Figure . Beams from three distant objects ``illuminate" or pass through different regions of atmospheric turbulence. Thus, wavefronts which are initially approximately planar are tipped and tilted differentially by the atmosphere, causing relative random shifts of the imagesof the objects. The ``corrugations" in the tilted wavefronts indicate higher-order distortion, leading to position-dependent speckle defocus effects. Astronomical restoration in the literature has been concerned with correcting speckle blur; but, unlike our problem, this has been over a much narrower field of view (e.g., 1 arc sec or less) where the instantaneous speckle PSF can be considered approximately position-independent.

We have developed a hierarchically-windowed phase-correlation technique to register each pixel in each image in a time sequence to a corresponding point in a prototype image, to sub-pixular accuracy. Although the problem is one of optical flow, we have not applied classical methods, partly because our temporal sampling is too coarse. The prototype is formed initially by simple averaging of the image sequence, which results in a motion-blurred, but geometrically correct image. The registration procedure creates x and y shift-maps corresponding to the distortion in each raw image. The shift-maps appear to have considerable spatial coherence. Two frames from a time sequence of x shift-map images, where white indicates left- and black indicates right-shift, derived in this way from a lunar observation (a 100 arc secs wide view of the crater Theophilus), are shown in Figure . Displaying the x or y shift sequence as a movie creates the impression of viewing the ``boiling" underside of a cumulus cloud, providing a striking visualisation of the effectsof turbulent mixing, including any translation by wind (some movies can be viewed at http://lucente.ee.adfa.edu.au/~widearea).

We intend to use this new visualisation technique to study atmospheric turbulence under different conditions. Information, such as the mean angular size of turbulent ``seeing-cells", average translation speed (which is related to the wind speed) is available. We are able to measure the translation by cross-correlating and averaging the result over successive pairs of x and y shift-maps in a sequence, as shown in Figure . The bright region at about 45 degrees from the centre indicates the highest correlation, which allows us to estimate the average translation per image (i.e., about one half of the radial distance at 45, in this case).

Meanwhile, the shift maps are used to inverse-warp each image to its true geometry. A summation of the corrected images provides a new prototype image (of the scene), in which motion blur has been reduced and signal-to-noise ratio improved, but which includes a small, residual blur due to higher-order corrugations in the wavefront (e.g., speckle-blur effects). The residual blur can be further partially restored by a global deconvolution, if the residual PSF is estimated, since it has been made position-independent by the registration and averaging. The process is repeated, using the newly derived prototype as a better reference for another round of registration, shift-map generation and motion blur correction. It is found, in practice, that two iterations are usually sufficient (see Figure ).

In addition to the astronomical context, we are currently exploring the technique at low elevation angles during both night and day, and a portable telescope, lent to us by DSTO, is to be used for this purpose. In this context,we image objects in the near horizontal direction - we have imaged aircraft buildings, etc., at or beyond Canberra airport, 3 to 6 km away. We are detecting a very different pattern of turbulence-induced distortion, particularly during the day. An example of a raw image and the motion-compensated result, including a further global restoration of residual blur, are shown in Figure .

The success of the project depends on being able to obtain high resolution shift-maps showing the registration of each pixel in each distorted image to a prototype. So far, we have used a hierarchical, two-dimensional phase-correlation registration method which is similar to methods used in stereo image-pair matching. Other approaches, including a method using wavelets, will be investigated. Successful registration requires fine-tuning, such as multiple peak search, with minimum mean absolute difference confirmation and interpolative region expansion for sub-pixular resolution. In fact, we have successfully applied our two-dimensional registration algorithm to stereo digital elevation model generation from aerial stereo photography, asa means of testing its versatility.

The visualisation and characterization of atmospheric turbulence (where there is mixing of cells of different refractive index) is of considerable interest to atmospheric scientists, earth-based astronomers, and also for long-range surveillance. In astronomy and surveillance, this technique could help to overcome some of the degrading effects of turbulence, while it could also provide a new means of testing possible sites for astronomical observatories.

 

please also visit Laboratory for Imaging through Turbulence & http://www.ee.adfa.edu.au/widearea/ for related research and images.

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