Short-exposure Images Research Articles

Probabilistic Diffraction Limited Imaging Through Turbulence

The possibility of considerably increasing the resolution of an extended image taken through a turbulent atmosphere by selecting random "lucky" diffraction limited exposures out of many normal-turbulence degraded-short exposures is experimentally explored. For an imaging aperture D, larger than the atmospheric spatial coherence length ro, the probability P of getting a diffraction limited short exposure image of a point source is found to be exp[-0.6(D/r0)2 ]. This result is in agreement with Fried's prediction. The angular isoplanatism is measured to be -X/ro. However, observed random wavefront tilts scramble the diffraction limited picture elements in an isoplanatic patch, thus complicating the probabilistic imaging method.

Speckle Interferometry with the BTA Telescope

AbstractThe description of a speckle camera used with the BTA 6-meter telescope is given. Observational data recorded on photographic film are processed with a Fourier optical spectrum analyzer. Results of binary star measurements are presented. Analysis of short exposure images of a point source obtained with telescopes of various sizes allows the estimation of atmospheric parameters which are necessary for correct application of speckle interferometry.

Measurement of the probability of getting a lucky short-exposure image through turbulence

The probability P of getting a lucky short-exposure image through the atmosphere has been measured. This measurement was made by photographing two point sources separated by a length Δ corresponding to the resolution limit of the imaging system with an aperture D. r0 was measured simultaneously. The distance between the imaging system and the point sources was 6000 m. Six observers independently determined whether the sources were resolved. By changing D, a plot of P versus D/r0 was obtained. It is shown that ln P ~ (D/r0)2, as predicted by Fried [ J. Opt. Soc. Am.68, 1651 ( 1978)].

Probability of getting a lucky short-exposure image through turbulence*

In short-exposure imaging through turbulence, there is some probability that the image will be nearly diffraction limited because the instantaneous wave-front distortion over the aperture was negligible. A number of years ago in a rather brief paper, Hufnagel (1966) argued heuristically that the probability of getting a good image would decrease exponentially with aperture area. This paper undertakes a rigorous quantitative analysis of the probability. We find that the probability of obtaining a good short-exposure image is Prob ≈ 5.6 exp[−0.1557 (D/r0)2] (for D/r0 ≥ 3.5), where D is the aperture diameter and r0 is the coherence length of the distorted wave front, as defined by Fried (1967). A good image is taken to be one for which the squared wave-front distortion over the aperture is 1 rad2 or less. The analysis is based on the decomposition of the distorted wave front over the aperture, in an orthonormal series with randomly independent coefficients. The orthonormal functions used are the eigenfunctions of a Karhunen-Loeve integral equation. The integral equation is solved using a separation of variables into radial and azimuthal dependence. The azimuthal dependence was solved analytically and the radial, numerically. The first 569 radial eigenfunctions and eigenvalues were obtained. The probability of obtaining a good short-exposure image corresponds to a hyperspace integral in which the spatial dimensions are the independent random coefficients in the orthonormal series expansion. It is equal to the probability that a randomly chosen point in the hyperspace will lie within a hypersphere of unit radius, the points in the hyperspace being randomly chosen in accordance with the product of independent Gaussian probability distribution—one distribution for each dimension. The variance of these distrbutions is directly proportional to the eigenvalues of the Karhunen-Loeve equation. This hyperspace integral (involving up to several hundred dimensions) has been evaluated using Monte Carlo techniques.

Measurements of atmospheric isoplanatism using speckle interferometry*

Measurements of isoplanatism for speckle interferometry and speckle imaging applications have been made at a 1.57 meter aperture telescope in Hawaii. The measurements were obtained from optically produced spatial power spectra of short-exposure images showing pairs of stars with different angular separations. The result of this process is a sequence of plots of correlation versus spatial frequency in the image for 0.25, 0.5, 1.9, and 4.7 arc sec separation binary stars. Substantial correlation is found to at least 0.6 of the diffraction limit cutoff for the 4.7 arc sec pair.

Speckle interferometry lens-atmosphere MTF measurements*

Measurements are presented of lens-atmosphere modulation transfer functions for short-exposure speckle imaging at the AMOS observatory in Maui, Hawaii. Star images were recorded with a video sensor system and processed digitally. Near-diffraction-limited modulation transfer functions were recorded and analyzed for a 122 cm aperture instrument during fair to poor seeing conditions. Mean values for r0, the aperture wave-front correlation scale, ranged between 4.1 and 6.4 cm. Total projected rms image wander ranged from 0.2 to 1.1 arc sec. The results are in substantial agreement with theoretical predictions and laboratory simulation results.

A quantitative treatment of solar ?seeing?, I

Measurements of temperature-fluctuation statistics in a locally homogeneous, isotropic turbulent atmosphere above level land are shown to enable the quality of telescopic images of celestial objects to be calculated. Data obtained with captive-balloon-borne apparatus are used, together with other existing data, to calculate the modulation transfer function and Strehl Definition for both long- and short-exposure images formed by typical solar telescopes operating under a variety of meteorological conditions. The size of telescope may thus be matched to the expected atmospheric conditions; the improvement in performance and utilization of the instrument, obtainable by raising it on a tower, may be calculated. An 11-cm aperture telescope, for example, is shown to be atmosphere-limited for long exposures in average daytime conditions; raising it from 2 to 30 m above the ground makes an almost threefold improvement in definition. If observations are confined to intervals of good ‘seeing’ the full resolution of such a telescope may be realized. The existence of such intervals is attributed to convective thermal structure in the atmosphere and observational statistics of periods of below-average temperature fluctuation are given for a range of general meteorological conditions.