The refractive irregularities that are responsible for the atmospheric degradation of optical images arise from variations in temperature of the atmosphere. We present a non-mathematical, physically based description of these irregularities and how they contribute to the degradation of an image. Irregularities near the image contribute only through the distortion of the wave front, thereby distorting or spreading the image of a point source. More distant irregularities produce, in addition, scintillations or fluctuations in the intensity of the light. The random apodization resulting from scintillations further degrades the image.

This paper presents an elementary derivation of the basic phase statistics of an optical wave (both plane and spherical) propagating in a turbulent medium. The results are general in that they apply to an arbitrary passive spatially homogeneous turbulent medium. Explicit application of the analysis is directed to the atmosphere where we obtain the well known results of Tatarskii and others. The present approach provides an intuitive appreciation of the physical behavior of optical wave propagation through a medium which exhibits a spatially random index of refraction. As such, it is complementary to the rigorous mathematical derivations that appear in the literature.

The only condition for separation of the optical transfer function treated in the literature is the long-exposure (ensemble average) condition. Other conditions are considered here. One particular condition based upon the Taylor "frozen atmosphere" hypothesis may be widely applicable for intermediate exposure times. A computer simulation for testing separation in this case is proposed.

Isoplanatism is a somewhat exotic term used to indicate that the transfer function of an optical system is dependent on the field-angle, or to denote the region, called the isoplanatic patch, over which the transfer function is virtually independent of field-angle. For many years, the term has been used mostly as a sort of "charm" to "ward-off" the possibility that others might think we were unaware of mathematical subtleties we intended to ignore because they were physically inconsequential. However, isoplanatism assumes physical significance in imaging through turbulence. The need to take account of this has created some confusion since different types of imagery have different isoplanatic dependencies and so should be denoted by different terms. There are a variety of different effects each of which can be classi-fied as isoplanatism each distinct in its dependence on the propagation path. We have identified five distinct varieties of isoplanatism, which we call 1) predetection compensation isoplanatism, 2) post-detection short-exposure imagery compensation isoplanatism, 3) post-detection long-exposure compensa-tion isoplanatism, 4) angle-of-arrival isoplanatism, and 5) speckle interferometry isoplanatism. Formulas giverning each of these types of isoplanatism will be presented.

Measurements were made of the atmospheric temperature turbulence surrounding and above the ARPA Maui Optical Station (AMOS) using several advanced remote turbulence sensors. Simultaneously, optical propagation parameters were measured directly. A brief description of the various instruments and their measurement capabilities is given. Typical atmospheric turbulence data for the measurement period are presented. Comparisons between optical propagation parameters measured directly and those calculated from the measured turbulence are presented.

The wavefront distortions produced by atmospheric fluctuations are discussed in this paper. The problem at hand is: What is the best way to process the measurements of these distortions so that appropriate corrections for them can be made? If a set of N independent wavefront measurements are made, the measured wavefront can be established as some linear combination of these measurements. The measurements themselves need not be direct phase measurements but could be a set of wavefront slope measurements. Nevertheless, the problem is to find a procedure that gives a best estimate of the wave-front from the set of N measurements. With such a procedure, the system designer can make an estimate of the number of measurements required to achieve a certain desired level of performance as well as the dynamical system complexity required to process the data. What is considered here is an application and adaptation of the theory of optimal estimates to the problem of random wavefront estimation.

The experiment to be described is intended to obtain a measure of the limit on the phase coherent propagation of light along a vertical path from a point source. This experiment utilizes an argon laser to generate a pair of coherent point sources in an aircraft. These sources generate a fringe pattern on the ground. As the aircraft flies along a track over a set of ground detectors, a frequency modulated signal is generated in the photoelectric detectors, the frequency modulation being proportional to the phase shift difference along the two paths from the plane. A Fourier transform of the data produces a measure of the phase coherence function or the Atmospheric Transfer Function of the atmospheric path. A modification of the direct experiment uses polarized sources in the transmitter to permit reconstruction of the phase difference function along the paths. From this data, the statistical parameters of the phase structure and log-amplitude behaviour can be obtained.

We observe the turbulence-induced scintillation (twinkling) of a single star to measure, from the ground, the vertical profile of refractive-index turbulence in the atmosphere. A linear combination, with appropriate weights, of the strength of the scintillations observed with receivers of various spatial wavelengths allows us to synthesize a path weighting function centered at a specific height. The central height and height resolution of the measurement can be controlled by changing the relative coefficients and spatial wavelengths of the receiver outputs. Twenty-minute measurements, made with stars of second magnitude or brighter and with a 36-cm Schmidt-Cassegrain telescope, show that the atmospheric turbulence can be divided into four independent height regions with reasonable accuracy. The measurements of the different spatial wavelengths are made sequentially with the same telescope, and the statistical stationarity of the atmosphere during the 20-minute observation period is crucial to the accuracy of the deduced profile. Stationarity is roughly checked by continuously monitoring the whole-aperture scintillation of the star. The observed profiles agree with the strength and general shape of accepted models of the atmosphere and with profiles obtained from aircraft-mounted and previously used balloon-borne in-situ sensors.

A new turbulence sensor has been designed which uses the dispersion in the atmosphere to intersect two beams of narrow band light at different altitudes. The wavefront tilts of the two beams are correlated which gives a weighted average of the turbulence distribution in the atmosphere. By varying the separation of the two beams at ground level, the altitude at which they intersect is shifted from ground level to infinity. The correlation of tilt for several separations allows the distribution of turbulence to be deduced with fair speed and accuracy.

Shipboard measurements of small scale temperature and velocity fluctuations have been accomplished to determine optical wave propagation properties of the marine boundary layer. Measurements were recorded for ocean conditions in Monterey Bay and in the confines of the Pacific Missile Range. Turbulence parameters measured were the temperature structure function parameter, CT2, and rate of dissipation of turbulent kinetic energy, E. There is satisfactory agreement with overland predictions for the variation of these parameters with height.

This paper briefly reviews the current status of speckle interferometry including the recent extension proposed by Knox and Thompson and the limitations imposed by non-isoplanicity. The speckle interfero-gram is characterized in terms of its scale lengths and photon statistics. The various subsystems of the instrument are reviewed in detail in terms of their required performance. The overall S/N is defined and discussed in terms of both unresolved and extended objects.

Speckle imaging is a technique for recovering diffraction limited images from sequences of atmosphere-degraded, short exposure photographs obtained at a large telescope. The technique is derived from speckle interferometry and shares many of the characteristics of that process, including dependence of the output signal-to-noise on number of frames processed and relative insensitivity to fixed telescope aberrations and noise in the image record. Speckle interferometry has been demonstrated to yield telescope-diffraction-limited information, but only in the form of spatial power spectra. Speckle imaging averages a different quantity, the statistical autocorrelation of the image Fourier transform, which contains all the information in the averaged power spectra plus the transform phase information required to recover an image. Two-dimensional digital simulations of the process for extended continuous-tone objects are presented, and include the case where severe static telescope aberrations are present.

We have built and tested a 30 cm x 5 cm aperture telescope which uses six moveable mirrors to compensate for atmospherically induced phase distortion. A feedback system adjusts the mirrors in real time to maximize the intensity of light passing through a narrow slit in the image plane. We have achieved essentially diffraction-limited performance when imaging both laser and white-light objects through 250 meters of turbulent atmosphere. The system has yet to achieve its full potential, but has already operated successfully for objects as dim as 5th magnitude. It is presently installed on an equatorial mount at an observatory, and we hope by the time of the conference to present preliminary results with astronomical objects.

This paper describes the utilization of very thin, electrostatically deflected membranes as an active optic in an image compensation system. The key design considerations are given in terms of deflections, frequency response, and drive signals. The advantages of a membrane are given in terms of its transfer characteristics, low voltages, zero hysteresis and its ability to accommodate hundreds of actuators. Pertinent performance data is presented. This paper also discusses the manufacturing techniques that are used to generate membrane mirrors of different materials, thicknesses, and geometries. The manufacturing technique is relatively simple and inexpensive and leads to a rugged active optic that is ideal for use in an image compensation system, where the correction of many waves is required.

To obtain high resolution images from large aperture optical systems, it is well known that the optical path must be corrected before the image is recorded and the phase information essentially lost. This predetection compensation requires fast response, adaptive optical elements in order to correct for optical path errors introduced by a turbulent atmospheric path. Fundamental concepts and operation of a laboratory system for wide band real time atmospheric compensation is discussed. The RTAC system operates closed-loop and automatically locks-in to correct phase aberrations of a rapidly varying turbulent atmosphere.

A theory of optical Bragg diffraction is given and it is shown that an array of Bragg cells, each cell carrying two orthogonal sound waves, can be used to correct in real time section-by-section amplitude and phase and overall tilt errors of an optical wavefront distorted by atmospheric turbulence. Because of the tilt correction an object is auto-matically tracked and the image stabilized. A section-by-section tilt correction can be achieved if two cell arrays are used. The spectral bandwidth of an image corrected by Bragg cells is also considered.

Rays from a given point on a celestial object will traverse different paths through the atmosphere due to atmospheric dispersion. They will therefore suffer different phase distortions due to atmospheric turbulence. When the mean distortion is corrected by a compensated imaging system a residual error, which is a function of spectral bandwidth, will remain. This error grows as sec4/3 tanS/6, where c is the zenith angle, and will limit the region of the sky over which satisfactory compensation is possible.

Adaptive optics systems for ground-based imaging through the earth's atmosphere must generally measure and correct for path distortions within a time period ranging from 0.5 to 10 milliseconds. For most astronomical objects, this requires a wavefront error sensor of the highest sensitivity -- typically a system which employs hundreds of quantum-limited photodetectors devoted exclusively to this task. This paper will point out how the system problems for figure control of orbiting telescopes are quite different since the error sources have periods which typically range from hours to years. Thus error signal integration times can be thousands of times larger for the orbiting optics, and it is feasible and economically advantageous to use low sensitivity dither adaptive optics systems, employing single detectors at the image plane. We will compare three classes of dither systems for this application: 1) one-element-at-a-time step systems; 2) half-at-a-time step systems; and 3) parallel sinusoidal dither (multidither) systems. Several types of signal processing will be compared from a signal-to-noise viewpoint. Computer simulations will be employed to illustrate the system performance at marginal signal-to-noise ratios.

There may be pitfalls to watch out for when recording imagery from active phase compensation devices located in the exit pupil of the system. At least three of these pitfalls are identified and each is manifested as a degradation in the imagery. Both nearby and high altitude atmospheric disturbances contribute to the degradation. The first pitfall is identified as residual phase errors caused by measurement and hardware limitations. The second pitfall is identified as non-isoplanatism and it occurs because wave-fronts from different source points experience different high altitude disturbances. The third pitfall is identified as amplitude fluctuations in the exit pupil of the system and it is also caused by the high altitude atmospheric disturbances. The two pitfalls caused by the high altitude disturbances are reduced by applying additional phase compensation in a plane that is the image of the high altitude disturbances. But even this may not be sufficient to eliminate the need for post-processing of the imagery of extended sources.

Restoration of atmospherically degraded images is limited most fundamentally by the photon noise inherent in any detected image. After presenting a general model for photon-limited images, we derive the form of the linear, space invariant filter which restores the image with minimum mean-squared error. Measures of the restorable bandwidth and image quality are developed. The theory is applied to the case of images degraded by atmospheric turbulence, both with and without perfect tilt removal. The relationship between the number of detected photoevents and the restorability of the degraded images is quantified.

Conventional post detection image processing techniques have been applied to three simulations of photon noise limited images of the moon which might be obtained through atmospheric turbulence. This study demonstrates that homomorphic filtering, parametric Wiener filtering, and constrained least squares filtering can produce nearly diffraction-limited imagery if the atmosphere is "frozen" for 1/100 - 1/10 sec.

A new method for post-detection compensation of atmospheric distortions of images of faint scenes has been outlined and initially tested. A sequence of short exposure (0.01 to 0.1 sec) visible light images is processed in terms of the statistics of the Fourier transform amplitudes. A "master image" is derived that is iteratively compared with each image (in Fourier space) so as to align the set of images on the basis of features in the scene. Aperture synthesis can be used to decrease aperture redundancy since the alignment uses only Fourier amplitudes that are prominent in the joint set of master image and the raw image sequence. The master image has an effective point spread function (PSF) comparable to the best PSF in the sequence but the phases are strongly quieted by the statistics of large numbers if 30 or more images are spread over a time interval of 15 or more sec. Thus spatial frequencies in excess of 1 cycle per arcsec may yield reliable photometry after correction for contrast loss and telescope aberrations. The degree of enhancement may be optimized, based on a separation of signal and noise in the data so that noise may be estimated. At faint levels quantum noise is severe. Since that noise is correlated with signal, the noise spectrum is not white but falls with increasing spatial frequency.