The first 12 papers in this issue comprise the second part of two special issues of Optical Engineering on speckle. The first 12 papers appeared in the preceding issue (May 1986, Vol. 25, No. 5). Topics addressed in the present issue include speckle statistics, speckle metrology, speckle in imaging and radar systems, speckle in astronomy, and speckle interferometry.
We discuss various high resolution speckle methods that can overcome image degradation caused by the atmosphere and telescope aberrations. All methods yield diffraction-limited resolution, for example 0.03" for a 3.6m telescope. We show speckle interferometric observations of asteroids, Pluto/ Charon, double stars, and the gravitational-lens triple quasar. True diffraction-limited images can be reconstructed by speckle interferometry if there is a point, source in the isoplanatic neighborhood of the object (holographic speckle interferometry). Speckle masking is a triple-correlation method that yields diffraction-limited images of general astronomical objects. A point source near the object is not required. We describe an application of speckle masking to the central object in the giant HII region NGC 3603. Speckle spectroscopy is a speckle method that yields diffraction-limited objective prism spectra. It is also possible to apply speckle masking to multiple-mirror interferometers or long-baseline interferometers on the ground or in space. True images of very high angular resolution can be obtained by these techniques. Computer simulations are shown for illustration.
Differential speckle interferometry has been applied to data obtained using the fully phased six-mirror aperture of the Multiple Mirror Telescope. Wavelength-dependent differences in the appearance of a stellar object are derived from simultaneous observations at two distinct wavebands. The supergiant star Alpha Orionis was observed this way to investigate its appearance in hydrogen-alpha emission. Data reduction consists of a frame-by-frame weighted deconvolution. An inherent Wiener-type filtering must be removed in order to preserve high spatial frequency information. Results for Alpha Orionis are compared to similar results for the unresolved source Gamma Orionis.
A cross-spectrum analysis technique that makes it possible to compute an unbiased estimate of the speckle pattern Wiener spectrum has been developed at the University of Nice. Using a one-dimensional interferometer, the technique has given results on several subjects such as the study of atmospheric modulation transfer function, including anisotropy due to the geometry of the telescope aperture, the space-time properties of speckles, the angular structure of Betelgeuse, and the convective motions of solar photo-spheric microstructures. The cross-spectrum analysis technique also has been applied to speckle spectroscopy and to differential speckle interferometry. A theoretical study of the two-wavelength cross spectrum has been formulated, and the first experimental results are shown; they are in good agreement with the theory. Expressions are given for the signal-to-noise ratio for the amplitude and the uncertainty in the phase of the cross spectrum of two speckle images in the presence of photon shot noise. They are applied to the very promising differential speckle interferometry technique, which has already permitted us to measure angular microdisplacements due to atmospheric dispersion into the submilliarcsecond range.
We have applied a variant of the shift-and-add algorithm originally developed by Lynds, Worden, and Harvey [Astrophys. J. 207, 174 (1976)] to astronomical speckle interferometric data. A set of impulses corresponding in locations and magnitudes to the local maxima in each specklegram is generated and used to obtain an average speckle by means of a Wiener-type filter deconvolution procedure. This technique yields diffraction-limited images that appear to be self-calibrating for seeing effects. Realistic point spread functions have been obtained for a number of telescopes at different wavelengths, and results are also presented for the resolved red supergiant Alpha Orionis. The limiting signal-to-noise ratio of the technique as indicated by the results presented here suggests a dynamic range of =6 stellar magnitudes, with no evidence of residual seeing effects. A matched filter technique is demonstrated for use in locating the speckles of complicated objects or for objects dominated by photon noise.
We present results of an investigation into the visualization and measurement of retinal blood flow distribution by means of single-exposure laser-speckle fundus photography. The technique relies on the speckle effect produced when laser light is scattered at a diffusing structure and on the fact that the speckle will be averaged out to some extent when the structure concerned is moving and/or decorrelating. We discuss two alternative techniques used to process the specklegrams obtained from the retina. The first technique uses an analog optical spatial filtering procedure to enhance the resulting variations in speckle contrast. Although first results have shown the basic usefulness of this technique, it suffers from fundamental disadvantages. In the second technique we digitize the specklegram and use digital image processing techniques to (1) convert contrast variations in the fundus photography into color variations and (2) obtain the blood flow of the vessels with a reasonably low statistical error.
Second-order statistics have been derived for the speckle in diagnostic ultrasound that arises from diffuse (incoherent) scattering in the presence of distributed and organized specular (coherent) scattering. They serve as the basis for a three-dimensional feature space in which tissue textures can be classified. The covariance matrix of the measurements in this space is a generalization of the speckle spot number or sampling concept that arises in the study of signal or lesion detectability.
Tissue signatures are obtained from the first- and second-order statistics of ultrasonic B-scan texture. Laboratory measurements and early clinical results show that the image may be segmented to discriminate between different normal tissues and to detect abnormal conditions based on a multidimensional feature space. These features describe the intrinsic backscatter properties of the tissues imaged and may be used as the basis of an automatic tissue characterization algorithm.
The work described in this report represents a successful demonstration of a hybrid approach to the analysis of structural deformation. Mathematical modeling was incorporated into the process of reducing data from a digital correlation analysis of experimentally obtained speckle data. These experimental data were collected by both directly imaging the speckled surface of the test subject onto a vidicon camera/digitizer system and transmitting this image to the camera via a flexible coherent fiber optic image bundle. Considerable savings of time and resources can be realized through applications of this hybrid approach in which the strengths of the theoretical and experimental procedures complement each other beautifully. The final hybrid results compare very favorably with values obtained by both a theoretical mathematical (finite-element) analysis and an independent experimental (high frequency moire) study, demonstrating the accuracy and reliability of this hybrid procedure. Finally, the successful use of flexible optical fiber elements for data access demonstrates the potential for application of speckle hybrid techniques to the study of remote or otherwise inaccessible regions of a prototype structure.
The statistical theory of speckle is presented in detail, including discussions of the transmission functions for a surface roughness type of diffuser and the associated characteristic function. The correlation function for the output amplitude is calculated for a variety of optical systems. These second-order moments are written for two states of position and temporal-frequency variables so that one can analyze both the spatial and the wavelength dependence of speckle. We parallel the usual cases that are treated in Fourier optics, summarizing the following configurations: space-variant, Fourier transform, far-zone, and imaging.
One-dimensional speckle images can be characterized by maps of their zeros in the complex Fourier plane. Superimposing the zero-maps for a sequence of speckle images isolates the zeros defining the object. Computer simulations suggest this imaging technique should be successful even when the level of the noise contaminating the speckle images is significant.
The synthetic aperture radar (SAR) aboard Seasat in 1978 demonstrated a unique sensitivity to oceanic and geologic features imaged over a 100 km swath with 25 m resolution. The ability of the remote sensor to resolve the fine details of large environmental systems resulted in the orbiting of a similar system, the Shuttle Imaging Radar (SIR-B), aboard the Space Shuttle Challenger during October 1984. Coherent speckle noise observed for these Doppler imaging-radar systems is caused by random correlations of the illuminating radar chirp with the surface reflectance downrange. Radar speckle is similar to optical speckle in that respect, but it is also influenced by along-track sampling statistics. The Rayleigh statistics of coherent scattering and the Poisson statistics of radar pulse detection are employed to model the speckle observed in spatially random data samples. Speckle degradation of a radar scene may obstruct interpretations of scene detail, but it can also be useful in determining the spatial response of the remote sensor and scene correlator. Randomly speckled scenes that are otherwise featureless provide a white-noise input to the Doppler imaging process. Several such scenes have been processed with fast Fourier transform methods to estimate the point spread function and its Fourier-domain equivalent, the wavenumber response function. These measure-ments of spatial resolution are used to compare the Seasat SAR and the Challenger SIR-B remote sensors. In addition, two ground-scene correlators are compared in terms of the point spread estimate of spatial resolution for common input data from the SIR-B sensor.
This paper deals with early and accurate breast cancer risk assessment for women. The use of texture analysis tools for the eventual development of an automatic system is proposed. In a first step, a standard procedure for obtaining x-ray mammograms is set up, the resulting radiographic images then being classified into four risk groups by a specialist. In a second step, specific and selected texture algorithms using both global and local statistical properties of the images are implemented. A number of x-ray mammograms have been studied. One of the resulting important observations is that it seems inappropriate to define a set of distinct classes of risk; rather, an increasing gravity degree correlated to a continuous evolution of the mammographic textures from the lowest to the highest degree of risk is to be preferred. Finally, a systematic comparison between the human classification and the numerical coefficients provided by the texture analysis is performed. The coefficients do not allow risk classification by themselves. A critical examination of these preliminary results leads us to a constructive discussion concerning the future developments of the proposed method.
Off-axis aspheric optical elements cannot be fabricated using classical techniques. Itek has developed computer-controlled optical surfacing (CCOS) for fabricating aspheric optics. The process slowly moves a polishing or grinding tool assembly (with rapid tool motion) over the workpiece surface. The use of CCOS with orbital tool motion has been put on a scientific basis. Theoretical and experimental removal profiles have been obtained and used. A tool selection process has been developed to provide efficient CCOS error correction. The movement of the tool assembly along a path following the workpiece surface height contours has produced better smoothing and figure error correction. Computer simulations have aided process optimization and predicted excellent results for the use of orbital CCOS polishing. A recent fabrication effort has demonstrated the ability of the process to fabricate an optical element with both a smooth surface and good figure.
A high speed 16 mm cineradiographic system originally developed at the University of Michigan Transportation Research Institute (UMTRI) for use in biomechanics research has been undergoing continuous upgrading in capability. In addition to changes in the structural aspect of the cineradiography, improvements have been made in the procedures used to obtain better image quality, as well as in the methods for interpretation of the digitized results. The current improvements in the system include (1) filtering of the x-ray source before penetration of the subject to increase image contrast and to protect the image tube; (2) hypersensitization of the film to increase its effective speed; (3) development of a neutral density radio-contrast medium for outlining anatomic structure without using the vascular system; and (4) development of procedures for obtaining analytic information about motion of nonrigid anatomic structures from digitized film. This system now consists of cameras that view a 50 mm (2 in.) diameter output of a P-11 phosphor of a high gain, four-stage magnetically focused image intensifier tube, gated on and off synchronously with the motion picture camera shutter. A lens optically couples the input photocathode of the image tube to an x-ray fluorescent (rare earth) screen image produced by a smoothed dc x-ray generator of a conventional type. The system is capable of looking at a large variety of anatomic structures under a wide range of dynamic loading conditions.
A feasibility study was performed to determine if infrared thermography could be used to detect perturbations in the arc welding process that result in defects. Data were gathered using an infrared camera with a resolution of 0.2°C, which was trained on the molten metal pool during welding. Several defects were then intentionally induced, and the resulting thermal images were preserved on film. These images revealed that different types of weld defects induce different characteristic changes in the thermal image by detectably altering the temperature field around the weld. These perturbations in the temperature field can be used to identify and locate defects such as arc misalignment, plate gap, puddle impurities, etc. Macrostructural examinations permitted investigations into the relationships between weld puddle penetration depth and the temperature field. Using computer-aided processing of these thermal images, we expect that the welding process can be controlled to a higher degree than is presently possible.
With this issue, I have completed my first year as Editor of Optical Engineering. It seems like only yesterday that I was writing my first editorial (for the July/August 1985 issue), and it is hard to believe that an entire year has since gone by. If you read that editorial, you may recall that I wrote about an event that had occurred on May 31, 1985, and had a real impact on me-I had been hit by a truck while riding my bicycle. Well, by the time you read this editorial, another event will have had an impact on me exactly one year later, on May 31, 1986-my marriage to Sandra Barnes. It seems that May 31st has become my day, and I can only wonder what will happen tore on May 31, 1987.