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Particle measurements are of importance in the study of aerosols, combustion processes, and pharmaceuticals. In this report, first we briefly review a simple derivation of an inversion formula from basic principles. We describe a modification to the usual form based upon intensity superposition so that one has a form that is accurate at tiny scattering angles. Then, we present the results of a new study of the wavelength dependence of the optical transform of a particulate distribution. Starting with the idealized amplitude transmittance, p(x−x m ,y−y m )for a particle at spatial position (x m ,y m ) and taking the Fourier transform, one finds immediately the exponential term given by exp [−i2π(f x x m + fY m )] in which the transform frequencies are f x = ξν/(Fc) and f y = ην/(Fc). We show how this exponent contains the essence of the temporal frequency dependence of the speckle pattern for the particulate cloud. We calculate the second moment of the intensity in the optical transform. We prove theoretically that it is possible to measure the axial distribution of a particulate sample simply by gathering optical transform data by using illumination by a tunable laser. This novel technique is then demonstrated with (1) computer simulations and (2) masks with various axial distributions. Some concluding remarks will also be made about the use of neural network software in re mote sensing of particulate sizing and spatial distributions.

Automatic recognition of faces is now a reality. In our experiments we seek to establish bounds on the information content required as a function of the configuration of the machine. In general with the direct image, excellent recognition is obtained for information capacity below Harmon’s (1973) benchmark value of 500. Our main data base is gathered from twenty-five people consisting of three views (front, 30° turn, 60° turn) and ten separate exposures for each view. Typically, these are grouped into a learning set of five and a testing set of five. In the first series of experiments, an optical Fourier transform configuration is used which includes a ring-wedge photodetector interface together with neural network software. Good recognition is obtained, and we report on the training using front and side views. In the second series of experiments, frame-grabbed images are used, again with the neural network software. Tests are made of the information capacity required as a function of the image coding. Comparative error rates are presented for recognition in the following cases: with 256 grey levels or using global binarization or using an error-diffusion halftoning algorithm. Particularly good results are obtained from the error-diffusion form of the imagery.

Using halftone techniques and additive color mixture notions, we have implemented different ways to obtain colors matching CIE specifications from hard-copy color printing devices. We also report on our similar studies for matching colors to the Optical Society of America uniform color scales. The range of color reproduction is obtained by determining the tristimulus values of the color primaries. As long as the given color is within this color reproduction range, it can be reproduced by selecting the proper color primaries and the required amount of each primary. For colors outside the color reproduction range, we compare different ways to make the closest match. We performed experiments in which we used a thermal-wax-print color image printer that was calibrated by a precision spectrophotometer. We describe the error in matching colors quantitatively in units of "just-noticeable differences."

Using a pulsed, pump-probe experimental arrangement, we have investigated the speckle generated by a 100 μm path-length cell of smectic A liquid crystal of 4-cyano-4′- octylbiphenyl doped with 0.1% wt/wt dichroic dye. Upon irradiation, the guest-host system undergoes a phase transition from an initially transparent condition to a scattering state. From the statistical theory of speckle, we are seeking to establish the effective scales of turbulence in the liquid crystal, both transversely and longitudinally. A time-resolved analysis of the observed speckle during the relaxation of the system back to the ordered, homeotropic condition revealed the effective scale lengths of the liquid-crystaldye mixture in the irradiated region. Dynamic response as a function of molecular anchoring conditions was also investigated. The importance of this research to power-limiting applications will be discussed.

A theoretical study is presented comparing the performance of several correlation filters including the Fourier-based matched filter, the Hartley transform system, and the sine-filter-cosine configuration.1 In principle all these can be realized in systems using incoherent illumination, but the latter two possess the distinct advantage that the filter transmittance is a real number. Both a sine filter and a binarized sine filter are studied for the sine-cosine cascade correlator, and the latter is clearly shown to be superior. The evaluation is based on calculations of the ratio of peak output signal-to-noise as is customary. Additionally it is important to consider the ambient background signal in regions near the correlation peak and the spatial variation in this local background. We show that all four systems provide matched filter performance. However, the sine transform filter and its binary version are superior, since for these the mean value of the local background is zero. Computer simulations are provided, illustrating the two important applications of sorting pictorial scenes and words.

While diffraction pattern sampling has been widely used in the classification of patterns, its usage has been somewhat limited by the need to devise rather sophisticated algorithms. We describe sorting or classifying a variety of patterns using the ring-wedge photodetector and commercially available neural network software. With this combination, it is no longer necessary to write specialized software, and experiments which previously might have taken 4-6 months are now completed in 4 h or less. Three separate experiments are described quantitatively. First, thumbprints are sorted for eight individuals using six prints from each person. A learning set of four prints is shown to give excellent results and both ring and wedge data are used for the input neuron signals. Second, as an experiment in particulate analysis, colloidal suspensions of polyvinyltoluene spheres have been measured over a concentration of 256-1. Finally, automatic image quality assessment is described using a variety of input imagery. Widespread new uses are predicted for this hybrid system that combines the ring-wedge photodetector and the neural network.

Optical transforms of 2-D and 3-D objects taken in spatially incoherent broadband illumination are described. Two optical systems are compared: one is a lensless Fresnel-zone system and the other uses a Fourier achromat. Both are optoelectronic hybrids with a twin-imaging interferometer, a CCD array, and an output digital computer. Diffraction-limited performance is obtained and a variety of transforms including 2-D spatial sine, cosine, Fresnel, and Hartley are discussed. Also we describe a series of correlation experiments in which an optical transform and a computer-stored transform are multiplied and inverted. In this manner objects correlated include fingerprints on opaque cards, actual rough currency, and 3-D models. In a separate group of experiments image reconstructions were obtained. First, a computer method is used to invert the optical transform after bias removal and filtering, and the image reconstruction is displayed on a video terminal. This gives us an excellent means of measuring our overall space–bandwidth product. Second, image reconstruction using a cascade of two twin imaging interferometers is also described. Interesting optical processor applications for this two-stage system are briefly described.

A novel sine-filter-cosine correlator is described for coherent optical processing. The advantages of this system are that it uses filter masks that are real-valued and non-negative while still providing a maximum value of SNR in the output, i.e., matched filter performance. Additionally and quite importantly, this system also provides desirable control over the shape of the correlation signal. Theoretical justification is presented by calculations of the shape of the cross-correlation of two real-valued functions compared and contrasted with corresponding correlations of their even and odd parts separately.

In earlier work an optoelectronic hybrid consisting of a twin-imaging interferometer with crossed roof prisms, a Fourier transform achromat, a CCD array, and a digital computer was described. Spatial cosinusoidal optical transforms can be recorded for rough objects using bandlimited white light. We describe optical metrology and feature extraction using this system. If we consider an idealized amplitude transmittance t(x,y), the advantage in the white light system is that it measures the spatial transform of |t(x,y)|2. In cases where the phase portion contributes a signal that is of little or no interest, clearly the white light transform can be preferable, say, to a system that measures and transforms t(x,y). We describe two separate experiments. For optical metrology, we measure the film grain scattering from commercially available color negative film of various ISO ratings and at different densities. In a separate series of experiments we measured the optical transform pattern that results from printouts of various digital halftones, i.e., the analog of film grain scattering in the electronic printing industry. Finally, we conclude with a discussion of pattern recognition using this white light system combined with neural network software.