The origin of enhanced fluctuations in light scattered by very rough surface-like systems is discussed. Both Fresnel and Fraunhofer region effects are considered and some connection is established between observed features of the intensity pattern and surface type. Statistical models for non-gaussian scattering are reviewed and their predictions compared with experimental data.

A tutorial review of the analysis of speckle propagation through the turbulent atmosphere is presented. It includes the effects of the turbulent atmosphere on a laser source as it propagates to the target and on the target induced speckle field as it propagates back to the receiver. Formulations for the first and second order statistics of the received intensity are developed and illustrated with numerical examples and experimental data.

With a sufficiently narrow source spectrum, and either fiber movement or source frequency shift, a changing speckle pattern exists at a multimode optical fiber output plane which results in signal power fluctuations known as "modal noise." For the case of a step-index optical fiber, we report the measurement and analysis of the speckle spatial frequency distribution as a function of fiber parameters, and the correlation of two speckle patterns as a function of source frequency difference. We show how knowledge of the frequency correlation function and the source spectrum can be used to determine the speckle contrast. Again for a step-index fiber, we report the analysis and measurement of the probability density function of the optical power received by a detector at the end of a fiber as a function of the speckle's contrast and including the possibility of spatial filtration of the speckle, as might occur at a misaligned connector.

In this paper, several techniques to reduce speckle noise (more generally signal independent multiplicative noise) in images are studied. The techniques include gray scale modification, frame averaging, low-pass filtering in the intensity and density domains, and application of the short space spectral subtraction image restoration technique in the density domain. Some discussions on the theoretical basis of the techniques studied are given and their performances are illustrated by way of examples.

Digital filtering techniques for speckle reduction are studied using several conventional filters and homomorphic filters. It is shown that homomorphic filtering has higher resolution than straightforward linear filtering. Among the several filters considered, the homomorphic Wiener filter is found to yield the best results. Examples and possible extensions of these results are discussed.

The combined effects of non-isoplanatic conditions and telescopic aberrations on speckle imaging are analyzed. The general form of the two-point source wave-structure function for upward viewing through the turbulent atmosphere is used as a basis for developing descrip-tions of the second-order statistics used in speckle imaging. An analysis of the information recoverable from astronomical speckle imagery shows that diffraction limited resolution can be obtained. Two important assumptions which are usually satisfied have been made: 1) the isoplanatic patch encompasses the average spread function; 2) the greatest contribution to the atmospheric distortion comes from turbulence at low altitudes. Under these conditions, the aberrations of the telescope do not affect the second-order statistics and the integral equation relating the object and measured second-order statistics is well conditioned.

Speckle interferometric techniques are used to study the solar granulation. Calibration of the effects of atmospheric turbulence is performed by using either the difference in behaviour between redundant and non redundant apertures in presence of atmospheric turbulence, or by analysing moon-limb blurring during a solar eclipse, or by using the changes in seeing conditions during speckle-interferometric measurements. These techniques require a theoreti-cal knowledge of the effects of atmospheric turbulence on the modulation transfer function (M.T.F.) of the image as it is impratical to use an unresolved star near the sun as a reference source during day time observations. The agreement between the experimental M.T.F. obtained with an unresolved star and the theoretical form deduced from Korff's log-normal assumptions is extended to day time conditions.

The last decade has seen impressive progress towards the goal of removing degrading effects of the earth's atmosphere on astronomical data. Much of this work requires data obtained on tine scales shorter than change times in the atmospheric transfer function, typically 10 msec. Speckle interferometry, relying on post processing of short exposure images, provides two orders of magnitude increase in angular resolution for studying object sizes and binary star orbits. Instruments for detecting and recording individual photon arrivals extend speckle interferometry to at least stellar magnitude +15. Recent work shows that actual images are extractable from speckle data. Alternatively, deformable optics systems detect and correct wavefront errors to produce nearly diffraction-limited images in real time. Amplitude, Michelson, and intensity interferometry show good promise for getting very high resolution results from systems with optical path differences tens of meters in scale. Speckle and other forms of interferometry are now being extended to the infrared spectral region.

The present status of the Steward Observatory speckle interferometer system and the associated reduction and image analysis programs are reviewed. Some recent results on solar system objects and quasars are reported.

Comparison between theoretical and observed speckle data at large telescopes allow a better accuracy in star diameters measurements by speckle interferometry techniques. Astrophisical results will be presented, based on observations from 3.6 meter ESO and CFH ( Canada-France-Hawaii) telescopes.

The recent evolution of the technique of stellar speckle interferometry is reviewed with emphasis on calibration of atmospheric effects in the visible range and in the infra-red.

Image reconstruction from astronomical speckle data using the Knox-Thompson algorithm has now been extensively demonstrated as feasible through analysis and computer simulations. Experimental verification of the technique and its implementation for astronomy places stringent constraints on the recording system and requires complex processing algorithms to handle the many experimental details. In this paper we describe a video recording system specifically designed for the requirements of speckle imaging. This system has been built and tested, yielding high quality image reconstructions from a a laboratory-atmospheric simulator for a wide range of input light levels and test objects.

Diffraction-limited images, of resolution many times finer than what is ordinarily obtainable through large earth-bound telescopes, can be obtained by first measuring the modulus of the Fourier transform of an object by the method of Labeyrie's stellar speckle interferometry, and then reconstructing the object by an iterative method. Before reconstruction is performed, it is first necessary to compensate for weighting functions and noise in order to arrive at a good estimate of the object's Fourier modulus. A simple al-ternative to Worden's method of compensation for the MTF of the speckle process is described. Experimental reconstruction results are shown for the binary star system SAO 94163.

The turbulent atmosphere of the earth limits the resolution of conventional astrophotography to about 1 arc second. Much higher resolution can be obtained by Labeyrie's speckle interferometry. Speckle interferometry yields the diffraction-limited autocorrelation of astronomical objects, for example a resolution of 0.03 arc seconds in the case of a 3.6m telescope. After reviewing very briefly the method of speckle interferometry we will report the following projects (1) the reconstruction of direct images from speckle interferograms by using the speckle holography technique, i.e. the application of speckle interferometry for objects near to a point source. (2) Application of speckle interferometry for very faint astronomical objects by measuring the single photon events in speckle interferograms. We want to observe faint objects since many of the most interesting objects are rather faint as, for example, galactic nuclei and Quasars. In the following article we will describe various applications of speckle inter-ferometry and of speckle holography. The speckle holography measurements yielded direct images with diffraction-limited resolution. Speckle interferometry was successfully applied up to 14th magnitude.

In connection with the parameters of the optical configuration used to produce speckles and under illumination of a gaussian beam over the diffuse object, this paper discusses the statistical properties of dynamic speckle produced in the diffraction and image fields by a moving diffuse object in a plane with constant velocity. Especially, the space-time correlation function of the dynamic speckle intensity is investigated in detail. Two typical speckle motions of translation and boiling are interpreted for various optical configurations in the diffraction and image fields. As one of the interesting applications of dynamic speckle to metrology, several methods for the velocity measurement of the diffuse object will be introduced.

A tutorial review of speckle is presented in three main parts: I. Observations of speckle, II. Diffraction theory of speckle, and III. Statistical theory of speckle. Many of the characteristics of speckle are seen to follow from rather simple physical arguments, now that the formal theory is well established. These main properties are summarized in a few simple formulas collected to facilitate approximate calculations.

The speckle pattern formed when laser light is scattered by a large number of small spherical particles or droplets is investigated. Double-exposure speckle photography is used to measure the decrease of correlation which occurs when the angle of incidence of light on the scattering particles is changed by an amount a. Empirical equations relating to this loss of correlation to dimensionless groups involving the concentration, mean diameter and depth of the collection of scattering particles are given, and an analytical model which describes the basic phenomenon is presented.

Noncoherent light speckle photography utilizes the idea that a mass of fluid carrying particles or a solid surface which is illuminated obliquely will exhibit a unique pattern of spots or speckles. These speckles are recorded for two states of the specimen using high-resolution photography and, for dynamic problems, strobe lighting. A map of displacement during the interval for the specimen is extracted from the photograph using optical data processing. Experiments on a solid calibration specimen demonstrate the quantitative capability of the method. Preliminary flow experiments have used water loaded with aluminum or other particles. Qualitatively meaningful fringe patterns have been obtained for laminar and turbulent flow in a channel.

Projection matrices are used to derive relationships for determination of displacements from multiple specklegrams. The parameters necessary for solution of these equations are obtained from specklegrams by means of a computer compatible video camera and a temporal analyzer system. The experimental results correlate well with the theory.