An iterative method of restoring degraded images was developed by treating images, point spread functions, and degraded images as probability-frequency functions and by applying Bayes’s theorem. The method functions effectively in the presence of noise and is adaptable to computer operation.

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Bayesian-Based Iterative Method of Image Restoration

Publisher Summary This chapter discusses the effects of atmospheric turbulence in optical astronomy, summarizes the present state of the theory, reviews the experimental checks that have been made, and discusses the implications in the domain of astronomical observations. Diffraction limited resolution has been obtained with large telescopes up to magnitude 13 by means of speckle interferometry. A Michelson interferometer is already working in the visible on a 20 m baseline up to magnitude 4, and many projects are nearing completion. However, such technological progress can be useful only if accurate quantitative measurements prove to be feasible through atmospheric turbulence. In addition, much work remains to be done before achieving a full understanding of atmospheric effects. The relationship between isoplanicity or speckle boiling and the structure of the atmosphere is still not clear.

V The Effects of Atmospheric Turbulence in Optical Astronomy

: The field of picture processing by computer is reviewed from a technique-oriented standpoint. Only the processing of given pictures (as opposed to computer-synthesized pictures) is considered. Specific areas covered include: (a) Pictures as information sources and their efficient encoding; (b) Approximation of pictures - sampling and quantization techniques; (c) Position-invariant operations on pictures and their implementation (digital, electro-optical, optical); applications to matched filtering (template matching), spatial frequency filtering and image restoration, measurement of image quality, and image enhancement ('smoothing' and 'sharpening'); (d) Picture properties (linear; local and 'textural'; random) useful for pictorial pattern recognition; (e) 'Figure extraction' from pictures; figure properties (topology, size, shape); (f) Picture description and 'picture languages.' (Author)

Picture processing by computer

We have developed an active optical imaging system capable of correcting optical wave-front errors in real time at frequencies in the kilohertz range. Wave-front errors due to atmospheric turbulence in the propagation path, as well as optical figure aberrations and wave-front errors due to mechanical and thermal changes may be compensated. The system used an ac shearing interferometer, a parallel analog data processor, and a monolithic piezoelectric active mirror arranged in a closed-loop configuration. This compensation system can be applied to apertures of any size; experimental results are shown for a system with 21 correction zones.

Real-time atmospheric compensation

The aim of collecting data is to gain meaningful information about a phenomenon of interest. Unfortunately, often the phenomenon is not a direct physical observable. Instead, e.g., the data at hand may be a linear superposition of the desired quantities. This linear, and simplest type of information mixing is endemic in the physical sciences, arising in fields as diverse as atmospheric physics and medial diagnostics (see listing in Section 5.1). The common problem confronting workers in these fields is how to “unmix” (or, restore, enhance, de-blur, de-convolve), the data.

Image enhancement and restoration

Turbulence-degraded images have been processed to obtain an improvement of their visual image quality. The initial objects were photographed through laboratory-generated turbulence. The resulting transparencies of the degraded images were digitized by a photoelectric scanner and processed on a digital computer. The processing consisted of applying corrections to the amplitude and phase coefficients of the two-dimensional Fourier series representing the degraded images. The correction factors were obtained from the optical transfer function of the turbulence measured at the time the images were photographed. The experiment was done for 5-msec and 1-min exposure times. The processed data were used to generate photographs. The processed images were found to have significantly more visual detail than the original degraded images; the 5-msec-exposure restorations were superior to the 1-min-exposure restorations.

Restoration of Turbulence-Degraded Images*

Techniques developed for the planetary exploration program are being applied by the Image Processing Laboratory of JPL to other astronomical images. Plates of the galactic cluster Stephans Quintet were scanned and digitized. Faint nebulosity was enhanced by removing foreground stars and subjecting the resulting image to a high pass filter. Exaggerated true color images were generated by color representation of the ratios of calibrated images taken in red and blue light. Partial compensation for atmospheric degradation was accomplished with a positionally dependent convolution kernel based upon a Wiener noise-additive model. The signal to noise of the kernel was allowed to vary as a function of the local standard deviation. Photographs of Saturn were digitized and processed in an effort to obtain more information about the D-ring region. Because of the low signal level, straightforward enhancement techniques were not sufficient to bring out possible structure in this region. By transformation to a polar coordinate image, summation techniques were able to increase the apparent signal to noise of radially symmetric brightness elements. Spectra from several planets were digitized in an effort to quantify possible spectral shift as a function of position in the image. Each spectrum scan line was cross-correlated with the central scan line. From the results of this cross-correlation, a most probable spectral line tilt angle was determined.

Benjamin L. McGlamery

Papers

Restoration of Turbulence-Degraded Images*

Computer simulation studies of restoration of turbulence-degraded images (A)