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

In 1975, we reviewed the recent developments on wave propagation in turbulent media. In this paper, we update that paper to include recent results on adaptive optics, intensity scintillations, pulse propagation, atmospheric measurements at visible, IR, and millimeter wave frequencies, speckle interferometry, and other related topics.

Electromagnetic beam propagation in turbulent media: An update

Towards true imaging by wideband speckle interferometry

The relations between surface statistics and the near- and far-field scattered light statistics are surveyed, mainly using scalar diffraction theory. The methods which have been proposed and used are grouped and described according to whether they operate in the near-field or the far-field and whether they use monochromatic or polychromatic light. Several methods emerge as promising for practical application to non-contacting and non-destructive testing.

Optical estimation of statistics of surface roughness from light scattering measurements

A method to obtain an estimate of Fried’s seeing parameter r0 from time series of an arbitrarily shaped, resolved structure that exhibits degradation resulting from atmospheric turbulence is presented. The basic idea is to evaluate the ratio of the observed squared modulus of the average Fourier transform and the observed average power spectrum. The theory of the method is developed, and the influence of noise on the ratio is discussed. The method has been applied to five consecutive time series of observations of solar granulation under different seeing conditions. The power spectra, which are reconstructed with appropriate theoretical modulation transfer functions, converge.

Estimating Fried’s parameter from a time series of an arbitrary resolved object imaged through atmospheric turbulence

The effects of wavelength, spectral bandpass, and exposure time on the speckle lens-atmosphere modulation transfer function have been measured using bright stellar sources.

Speckle interferometry at finite spectral bandwidths and exposure times

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.

Speckle interferometry lens-atmosphere MTF measurements.

The statistics of laser-speckle patterns in a plane some distance from a coherently illuminated object are considered in more-general terms than previously. The results obtained show that the rms irradiance is equal to the mean. The irradiance spectrum consists of two terms of equal energy. Assuming that the angular size of the object is much less than the surface roughness diffraction angle, we find that the irradiance autocorrelation function separates into a product of object irradiance and surface-roughness terms. The spectrum separates into the sum of low- and high-frequency contributions. Previous calculations are shown to be special cases or consistent with the present analysis.

Second-order statistics of laser-speckle patterns*

The parameter characterizing nonisoplanatic effects in speckle interferometry can be measured by observing double stars. An experimental method is developed which permits estimation of this parameter in the presence of inherently large photon and detector noises as well as unequal double-star component brightnesses. Data are presented on five double stars ranging from 0.22 to 3.48 arc sec in separation. The results are compared to theory and the implications to both speckle interferometry and compensated imaging are discussed.

Speckle interferometry measurements of atmospheric nonisoplanicity using double stars

Quantitative measurements of the modulation transfer function for speckle interferometry in the absence and presence of severe defocus demonstrate that near-diffraction-limited resolution is possible in both cases.

Arthur M. Schneiderman

Papers

Speckle interferometry at finite spectral bandwidths and exposure times

Speckle interferometry lens-atmosphere MTF measurements.

Second-order statistics of laser-speckle patterns*

Speckle interferometry measurements of atmospheric nonisoplanicity using double stars

Speckle interferometry with severely aberrated telescopes