The second part of the joint special issue on optical and digital processing consists of thirteen papers. This second set of papers surveys recent optical and digital work in various specific data processing applications and techniques. The list of subjects addressed may not be comprehensive, but it is representative of the commonality of techniques and applications in the two powerful disciplines of optical and digital processing.

The current generation of transaxial tomography scanners uses digital processing to compute the distribution of the x-ray attenuation coefficient in a section of a body from projection data of that section. However, the operations required to reconstruct this distribution from the projection data also appertain to the domain of optical processing. Among the reconstruction algorithms that can be implemented optically are filtered and unfiltered back projection, one-dimensional convolution, circular harmonic transform, and Fourier synthesis. These approaches to transaxial tomography are functionally quite distinct, although mathematically equivalent. This paper presents a review of the research efforts in this area with special emphasis on the practical realization of these diverse formulations.

A research and development program was begun two years ago at the Los Alamos Scientific Laboratory (LASL) to study nonmedical applications of computed tomography. This program has several goals. The first goal was to develop the necessary reconstruction algorithms to accurately reconstruct cross sections of nonmedical industrial objects. The second goal was to be able to perform extensive tomographic simulations to determine the efficacy of tomographic reconstruction with a variety of hardware configurations. The final goal was to construct an inexpensive industrial prototype scanner with a high degree of design flexibility. This paper will describe the implementation of these program goals.

A coded aperture camera is similar to a pinhole camera in that no reflecting or refracting optics are used to form an image. However, it is different due to the fact that the single opening of the conventional pinhole camera has been replaced with a pattern of holes which may number in the hundreds or thousands. The resulting image is the superposition of many individual pinhole images and must be unscrambled to be meaningful. The advantage of the coded aperture is that many more photons are collected in a given period of time, and hence the resulting decoded image is of higher quality than if a conventional single pinhole camera were used. An additional advantage lies in the ability to obtain three-dimensional depth information from a single view. This paper presents an overview of past coded aperture imaging efforts which include the use of Fresnel zone plates, random arrays, and nonredundant pinhole arrays. The theory underlying their use is presented as well as a review of the digital and optical methods used in decoding. Recent important advances in the field, such as the use of uniformly redundant arrays, are presented. Typical results from some of the above-mentioned systems are shown and discussed.

Image interpreters often express the desire to extract a "maximum of information" from a given picture. We have devised a new norm of restoration that, in fact, realizes this aim. The image data are forced to contain a maximum of information about the object, through variation of the object estimate. This maximum information (MI) norm restores the ideal object which, had it existed, would have maximized the throughput of information from object to image planes. Or, the object estimate achieves the "channel capacity" of the image-forming medium. The following simple model for image formation is used. The imaging system is regarded as a transducer of photon position, from x in the object plane toy in the image plane. Then the conditional probability p(y1 x) is just s(y-x), the point spread function for the imagery, plus an unknown noise probability law n(y) independent of x (signal) for those transitions to y that are due to noise. The average information per photon transition x-y may then be calculated, using the correspondence of probability law p(x) with the object and p(y) with the image. When the image law p(y) is constrained to equal the data, the only set of unknowns remaining is the object, which may be varied to maximize the information. Restorations by this method are compared with corresponding ones by maximum entropy and show some advantage over the latter.

This paper discusses an iterative computer method that can be used to solve a number of problems in optics. This method can be applied to two types of problems: (1) synthesis of a Fourier transform pair having desirable properties in both domains, and (2) reconstruction of an object when only partial information is available in any one domain. Illustrating the first type of problem, the method is applied to spectrum shaping for computer-generated holograms to reduce quantization noise. A problem of the second type is the reconstruction of astronomical objects from stellar speckle interferometer data. The solution of the latter problem will allow a great increase in resolution over what is ordinarily obtainable through a large telescope limited by atmospheric turbulence. Experimental results are shown. Other applications are mentioned briefly.

Source encoding for digital image transmission is revisited with an energy distribution approach in the perceptual domain. Past investigations have utilized power spectral density in conjunction with the Frei eye model and full image Fourier transform coding. In this investigation, the cosine transform is utilized on a partitioned image. A cosine energy function is defined and weighted by the eye model. This results in a circular symmetric form of a bit map which simplifies source coding. This approach outperforms a standard bit allocation procedure allowing graceful degradation at 1, .75, and .5 bits/pixel. Analysis includes the perceptual mean square error and peak signal-to-noise ratio as metrics of performance. This procedure suggests a more rapid hardware implementation.

Machines that have been developed to determine the topography of a region from stereo-pair photographs are subject to correlation errors resulting in incorrect elevation calculations. In this paper, the determination of the location of the peak of the correlation function of two similar arrays of picture elements is modeled as a parameter estimation problem. The Cramer-Rao lower bound and various measures of contrast are considered as possible features in recognition schemes for predicting the magnitude of correlation errors. Preliminary simulation results are included.

During the past two decades, a number of methods have been proposed for performing bipolar spatial filtering operations with incoherent optical systems. These methods are conveniently categorized as to being based on geometrical optics or on diffraction optics. Some methods require a mechanical scanning of the input object, others are fully parallel in their operation. Still others are optically parallel, but employ an image plane scan to provide an electrical signal representation of the bipolar processed image. This paper reviews these methods and, to a limited extent, compares them.

Multiple views of a scene generally contain informa-tion that is implicit in the differences between the views. Such information can be of great interest when images are taken under different conditions or at different times, as it may provide insight into underlying physical or biological processes. Digital image change detection permits to detect and helps interpret such change information where the human observer otherwise fails. The method described here produces a "change image," which portrays image differences according to a simple convention. In the change image, previously invisible differences clearly stand out, often in meaningful patterns, and they can be further enhanced for easy visual interpretation. Examples are presented of this method applied successfully in widely different fields - remote sensing, radiology, nuclear medicine - illustrating the potential of digital image change detection, and also suggesting further avenues of research.

This paper reviews the area of coherent optical techniques for performing either one-dimensional or two-dimensional linear, space-variant operations. These techniques are becoming increasingly important due to the variety of possible applications for space-variant optical processors. Examples are presented to illustrate the major categories of processors.

The use of feedback for enhancing the capabilities of optical image processing systems as well as introducing new operational characteristics is the subject of much recent interest. This paper presents a review of the various processing schemes utilizing feedback developed in the past two years. Such schemes are categorized into optical analog and digital optical techniques. Analog processors with feedback can achieve greater effective dynamic range and a wider variety of transfer functions. Incorporation of gain into the feedback loop helps enhance these aspects, and further adds the possibility of constructing an optical operational amplifier. Nonlinear and space-variant response can also be obtained. Digital optical systems operate on binary rather than analog images. The use of feedback leads to the realization of image thresholding devices and optical flip-flop memories (both of which are vitally important to any digital system) using materials without natural hysteresis or sharp nonlinear characteristics. Existing schemes using dif-ferent materials and configurations will be reviewed.

A number of signal-processing devices have been developed that use the Bragg interaction between laser beams and surface acoustic waves in transparent delay lines. Convolvers and correlators having time-bandwidth products of up to 10,000 have been constructed and have been used to obtain signal-to-noise enhancement of signals buried in noise. A real-time, continuous Fourier transformer has been achieved. Initial results have been obtained in performing a discrete Fourier transform using an acoustooptic implementation of the triple-product convolver. A programmable memory correlator based on the acousto-photorefractive effect has been demonstrated using two distinct writing modes and writing-laser wavelengths.

Time integrating acousto-optic processors realize flexible, multipurpose complex signal processing architectures based on correlation algorithms. One- and two-dimensional techniques are presented including examples of spectral analysis and ambiguity function processing. Noncoherent optical processor implementation using interferometric detection with electronic reference is described and experimental results are given.

The paper concerns the measurement of the position of a target point in space by means of several angle-measuring optical instruments. Using statistical analysis it derives an error function which gives expected measurement error as a function of the number of instruments used, their qualities, and their locations. Properties of the error function are discussed, and it is shown how the model may be employed to find good solutions to instrument location problems. Finally, it is pointed out that the same approach may be applied to location problems involving instruments of arbitrary type which measure parameters different from those treated here.

An instrumentation system has been designed for the evaluation of thermal blooming compensation. The purpose is to investigate the maximization of 10.6 um CO2 laser radiation in the target plane through maximization of the return 3-5 um radiation from the laser-induced "hot spot" by using a pinhole sensor and a slow dither algorithm. The adaptive optical component to be used in the evaluation is a three-actuator modal deformable mirror supplied to the USAF by Perkin-Elmer Corporation. This paper deals primarily with the design of a thermal blooming cell that will be used for simulating atmospheric path lengths of several kilometers within a laboratory setup where the total path length is limited to a few meters. The theory required to perform the scaling is currently available in the literature. We present it in a format designed to aid the optical engineer, whose primary concern is the evaluation of an adaptive optical system for thermal blooming compensation. The interplay of the many parameters that may be varied is illustrated in graphical form to facilitate choices. As an example, we included our design for a one-meter cell to be incorporated in the slow dither experiment.

Device configurations of optical channel waveguide arrays coupled to integrated charge-coupled devices (CCDs) will be presented. Optical and electrical performance of these devices will be discussed. A channel waveguide array formed in a fan-out pattern is then introduced as a means of enhancing optical waveguide focal plane resolution in integrated optical devices utilizing optical waveguide lenses. High spatial resolution can thus be obtained without making detector spacings too small, thus avoiding detector problems with regard to fabrication, cross talk, linearity and charge transfer efficiency. To fabricate the fan-out channel waveguide array, a new differential heating and photo-resist lift-off process is discussed which allows high resolution patterns to be reproducibly formed in polyurethane. Propagation of light from a HeNe laser in these fan-out channel waveguide arrays has been demonstrated with only a small amount of scattering. Low scattering is consistent with the smooth channel waveguide surfaces apparent in scanning electron microscope pictures presented. Applications of optical channel waveguide arrays coupled to integrated CCDs to fiber multiplexing and transversal filtering will also be discussed.

This paper reports the results of the physical survey of more than twenty-five computerized tomographic scanners. Comparisons are made of noise, low contrast detectability, high contrast resolution, and radiation dose.

An unusual, highly modified, Baker reflector-corrector class telescope has been adapted for wide field survey photography in the near infrared. This optical system uses a full field corrector plate and a field flattening lens to provide a flat field subtending about 4 5 on the sky. The small aperture telescope (20 inch primary) has been modified for use in the Newtonian focus configuration while preserving the optical elements of the prime focus configuration. The telescope has been further modified to accept a very large format (146 mm diameter photocathode) image intensifier camera to serve as a detector. The camera output is recorded photographically on film rather than glass plates. This unique instrument system is used in a program of sky survey photography in the optical infrared (8000 to 9000 angstrom bandpass) supplemented by visual bandpass photography. The photographs obtained with this system are of value not only for the extreme redness of the band but also because of their high resolution and their freedom from hydrogen emission.

Optical image formation (and processing) is strongly affected by film grain noise. The noise effects depend on the spatial coherence of the illumination. In this paper we shall analyze these phenomena in the case of Kohler illumination. The effective transmittance of any photographic image is instrument dependent due to diffusion by the grain (Callier effect). Thus the question arises: what is the meaningful physical quantity in image formation? The Callier effect directly influences the contrast of weak modulations, which happens to be maximum in symmetric partially coherent illumination. Ultimately, the detection of weak modulations is not limited by the contrast but by the signal-to-noise ratio. Using reasonable statistical assumptions for the noise behavior, the optimal conditions for weak modula-tion detection will be discussed. This study is primarily devoted to imaging problems, but its results may be partly extended to double-slit microdensitometry. In that case, however, the illumination setup makes the complete study more difficult than in the Kohler illumination case.

One of the major problems in scene analysis is segmentation of a scene. In this paper a particular gray-level based segmentation technique is used to partition one particular scene. The same scene is then segmented into the material classes that comprise it by using the explicit information about the existing materials. A comparison of the two sets of results is made. A set of probabilities of detection based on various information about material boundaries is then derived. This set quantifies the limitations of gray-level based segmentation schemes in detecting the material boundaries, and can be used as a measure for comparing various segmentation techniques.

The techniques used for storing matched filters in image processing units of the optical matched filter image correlator (OMFIC) type determine to a large extent the capacity and discrimination of the complete system. Coherent and non-coherent addition of images for overlayed matched filter recording are investigated and reported upon. Results are related by performance in the areas of diffraction efficiency and signal-to-clutter measurements. Dichromated gelatins are used as matched filter recording media and the results compared with silver salt photographic materials. Finally, a formula is derived for matched filter capacity and the analysis extended to the case where the medium sets the resolution for matched filter recording.

A new type of silicon charge coupled device (CCD) imager which provides nine simultaneous video outputs representing a 3X3 pixel block that scans the imaging array has been used to emphasize edges and fine detail in various images. The device can also compensate for nonuniform scene illumination. Experimental results indicate that the device can be used to combine real-time analog image processing with subsequent digital processing to form a powerful image acquisition and processing system.

Profile analysis and piecewise correlation techniques for measuring internal machine part clearances by digital processing of industrial radiographs are described in this paper. These methods were developed at the Image and Pattern Analysis Laboratory of Pratt & Whitney Aircraft Group. Profile analysis requires mathematical modeling of the expected optical density of a radiograph as a function of machine part position. Part separations are estimated on the basis of individual image scan lines. A final part separation estimate is produced by fitting a polynominal to the individual estimates and correcting for imaging and processing degradations which are simulated using a mathematical model. Piecewise correlation involves an application of image registration where radiographs are correlated in a piecewise fashion to allow inference of the relative motion of machine parts in a time varying series of images. Each image is divided into segments which are dominated by a small number of features. Segments from one image are cross-correlated with subsequent images to identify machine part motion in image space. Correlation peak magnitude is used in assessing the confidence that a particular motion has occurred between images. The rigid feature motion of machine parts requires image registration by discon-tinuous parts. This method differs from the continuous deformations one encounters in perspective projective transformations characteristic of remote sensing applications.

We now describe a new sounding rocket payload that has been developed for x-ray spectroscopic studies of the solar corona. The instrument incorporates a grazing incidence Rowland mounted grating spectrograph and an extreme off-axis parabolic sector telescope to isolate regions of the sun of order 1 X10 arc seconds in size. The focal surface of the spectrograph is shared by photographic and photoelectric detection systems, with the latter serving as a part of the rocket pointing system control loop. Fabrication and alignment of the optical system are based on high precision machining and mechanical metrology techniques. The spectrograph covers the 10 to 50 angstrom interval and has a resolution of 16 milliangstroms in the current version. Modifications planned for future flights will improve the resolution to around 5 milliangstroms, permitting line widths to be measured.

A step-by-step procedure for designating the optical axis by superimposing a laser beam on it is presented. The procedure is a fast converging one, and alignment to within a fraction of a miliradian is a matter of a few minutes.

While most of us regard optical engineering as a small-scale laboratory activity, one of my friends at the Max Planck Institut in Munich, Dr. Gerhard Haerendel, and his colleagues from around the world are about to use a much larger laboratory. Project Fircwheel is an enterprise which uses the magneto sphere as its optics laboratory. To plasma clouds, one of lithium and one of barium vapor, will be generated' at various distances from the earth. The aim is to study the interaction of the injected dense and cool plasmas with their dilute and hot environment. To this end, more than twenty diagnostic instruments have been installed on the Firewheel satellite. The clouds will also be studied by optical means from Earth. The optically visible display will be the largest man-made display in history.

One of the most rapidly developing areas in laser velocimetry is concerned with measuring aerosol velocity using methods that do not directly depend on the coherence properties of the laser. These methods do not rely on an interferometric measurement of the Doppler shift in the scattered light frequency to determine particle velocity. Some other method such as time of flight between two or more beams, particle arrival rate through a single beam, or pulse shape analysis is used. In this column I want to discuss some relatively recent work in the development of these techniques.