We present a method for designing non-absorbing optical diffusers that, when illuminated by a converging beam, produce a specified intensity distribution along the optical axis. To evaluate the performance of the diffusers in imaging systems we calculate the three-dimensional distribution of the mean intensity in the neighborhood of focus. We find that the diffusers can be used as depth-of-focus extenders. We also propose and implement a method of fabricating the designed diffusers on photoresist-coated plates and present some experimental results obtained with the fabricated diffusers.

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We present an annularly distributed phase-only mask that generates an axial irradiance distribution identical to the point spread function of the Dowski-Cathey lens [Appl. Opt. 34, 1859 (1995)]. This apodizer has an ambiguity function with a bow-tie effect, and consequently its axial modulation transfer function varies slowly with spherical aberration.

An analysis of the contrast in speckle patterns produced by slightly rough diffusers is carried out without making use of the central limit theorem. The results obtained explain an effect observed in previous experimental work . A comparison with the behaviour of the contrast predicted by a gaussian approximation is presented .

An analysis of the speckle contrast in the diffraction field of a weak random phase screen when the illuminated region contains a few correlation areas is carried out . Curved illuminating wavefronts, and the Fresnel and off-axis terms are considered . The limitations of the method are pointed out . Comparison with a gaussian approximation is made . Some previous studies are examined to obtain a more comprehensive view of the problem . Some of the reasons proposed for observed departures of the theory from experimental results are discussed . . IntroductionJakeman and Pusey [1] made early studies of the normalized standard deviation of the scattered intensity or speckle contrast when the area of illumination includes a small number of correlation areas of a random-phase screen . They were concerned with strong random-phase fluctuations, and the subject was pursued by Jakeman and McWhirter [2] . Fujii et al. [3] reported measurements of the speckle contrast for weak random phase fluctuations, some of which were for areas of illumination smaller than the correlation area of the phase fluctuations . These measurements were taken at the centre of the far diffraction field, and the study was followed by a similar one for the image plane [4] . Several computer simulations were also published [5] . Escamilla [6] carried out an analysis for very weak phase fluctuations which reproduced the form of the speckle contrast variation reported by Fujii et al . [3] . Ohtsubo and Asakura [7] extended the experimental studies to strong-phase fluctuations in the image plane, and Chandley and Escamilla [8] made a similar study of the diffraction field .Fujii [9] analysed both weak and moderately strong phase fluctuations, for detection at the centre of the far field and illumination from plane wavefronts at the waist of a gaussian beam and, in accordance with Escamilla [6], found that for very weak phase fluctuations the experimental curves in [3] were significantly higher than the theoretical ones . He also found agreement for standard deviations of the phase fluctuations of about 2ir/3, and reported beyond this weak region results opposite to those for very weak fluctuations : that the theoretical curves were significantly higher than the experimental ones given in [8] . A further theoretical and experimental investigation by Deka et al. [10] in the region of strong phase fluctuations indicated that this trend became more accentuated in this region . It is important to point out t Present address : Departamento de Fisica Aplicada, CICESE, Apdo . Postal 2732, Ensenada, B .C ., Mexico . Downloaded by [University of Regina] at 17:50 18 November 2014 1656 H . M. Escamilla that all the experimental results mentioned so far are for scattering measurements made on ground glass surfaces, and also that all the theoretical studies mentioned so far are based on the model of correlated gaussian phase fluctuations .Jakeman and McWhirter's study [11] of strong phase fluctuations in the Fresnel and Fraunhofer regions included a different evalua...

Approved for public release; distribution unlimited.OCT 2 1 1993 ABSTRACT (Maximum 200 words)The problem of light scattering in folded-path or double-passage configurations is studied theoretically.Assuming as the random medium a deep phase screen that introduces Gaussian-distributed phase fluctuations, we study the motion of the speckle as the source is moved.Some attention is also given to the phenomenon of backscattering enhancement.Our analysis is based on a novel expression for the complex amplitude that has a simple physical interpretation.For simplicity, only the one-dimensional case is considered, but an extension of the analysis to two-dimensional screens is not difficult.Using the factorization properties of the moments of a complex Gaussian process, we are able to derive analytical expressions for the mean intensity and the intensity correlation of the backscattered radiation.We find that, in most cases, the speckle field decorrelates rapidly as one moves the angle of incidence and shifts toward the direction of specular reflection with a rate of motion that is different from that of the angle of incidence.We also find conditions under which, when the angle of incidence is modified, the speckle pattern Droduced in the region of observation tracks the backscattering direction. The problem of light scattering in folded-path or double-passage configurations is studied theoretically. Assuming as the random medium a deep phase screen that introduces Gausz:an diztributed phase fluctuations, we study the motion of the speckle as the source is moved. Some attention is also given to the phenomenon of backscattering enhancement. Our analysis is based on a novel expression for the complex amplitude that has a simple physical interpretation. For simplicity, only the one-dimensional case is considered, but an extension of the analysis to two-dimensional screens is not difficult. Using the factorization properties of the moments of a complex Gaussian process, we are able to derive analytical expressions for the mean intensity and the intensity correlation of the backscattered radiation. We find that, in most cases, the speckle field decorrelates rapidly as one moves the angle of incidence and shifts toward the direction of specular reflection with a rate of motion that is different from that of the angle of incidence. We also find conditions under which, when the angle of incidence is modified, the speckle pattern produced in the region of observation tracks the backscattering direction.

We present high efficiency, low noise electrically-controlled Fresnel phase zone plates that were made by creating ring-shaped 180 degrees ferroelectric domains in a lithium niobate wafer. The primary focal lengths of these lenses ranged from 5 to 43 cm, and the light-gathering efficiency was over 37%, very close to the maximum theoretical value of 40.5%.