Morris Gm

Diffraction theory for an achromatic Fourier transformation

A three-lens achromatic Fourier transform system is analyzed in the context of paraxial Fresnel diffraction theory. From the analysis a general solution for the required wavelength dependence of the various lenses is found. A particular arrangement of the general system is then considered. Using first-order lens design principles, it is shown that each dispersive lens can be fabricated using a holographic zone lens and glass element cascade. The paraxial chromatic aberrations of the resulting system are calculated. It is found that this system design yields an achromatic transformation that is well corrected (paraxially) over the entire visible spectrum.

Scale, rotation, and shift invariant image recognition

A circular harmonic filter illuminated with white light illumination is used to achieve scale, rotation, and shift invariant image recognition. The circular harmonic expansion of an object is utilized to achieve rotation and shift invariant image recognition. Scale invariance is added using a broadband dispersion-compensation technique. When illuminated with broadband light, the frequency-plane filter simply selects the wavelength from the spectrum that produces the same size transform as that recorded in the filter. Laboratory experiments that demonstrate the operation of the technique are presented.

Design of a wide field diffractive landscape lens.

The third-order aberrations of a diffractive optical element with paraxial zone spacings are derived as a function of aperture stop position. It is shown that by placing the stop in the front focal plane, coma and astigmatism are identically zero, assuming an infinitely distant object. In addition, since the element is diffractive, the Petzval sum is also zero. Modulation transfer function comparisons with other lenses are given. The correction of spherical aberration using an aspheric plate located in the aperture stop and nonmonochromatic imaging performance are discussed. The distortion of the resulting system is shown to be the proper amount for use as a Fourier transform lens. An estimate for the space-bandwidth product of this Fourier transform system is given.

Design of diffractive singlets for monochromatic imaging.

The Seidel aberrations of a rotationally-symmetric diffractive lens with an arbitrary phase profile are presented. It is shown that by a proper choice of phase function and aperture stop position, third-order coma and astigmatism can be eliminated for any chosen conjugate ratio. Since a diffractive lens has an inherent zero value for the Petzval sum, the image plane is flat in both tangential and sagittal meridians. The substrate curvature of the lens may be chosen to introduce a prescribed amount of distortion to allow for use as a Fourier transform lens or a laser scan lens. Examples are given of lens performance in finite conjugate imaging and laser scanning, where the f - theta condition is satisfied.

Space and wavelength dependence of a dispersion-compensated matched filter

A technique to eliminate the lateral dispersion in the correlation signal from a holographic Vander Lugt filter is described. Both spatially coherent, and spatially noncoherent, object illumination are considered; and expressions for the color-corrected correlation intensity are written in each case. Experimental results of the correlation plane intensity are shown using laser and spatially noncoherent white-light illumination. The latter is seen to be useful to search automatically for object scale.

Image correlation at low light levels: a computer simulation

The effectiveness of photon-limited image correlation for recognition of realistic imagery is investigated. The correlation signal is obtained by cross correlating a low light-level input scene and a high light-level reference image. The dependence of the probability density function of the correlation signal on the average number of detected photoevents and on the number of gray levels in the images is illustrated. Monte Carlo simulations of image correlation using low light-level scenes are found to be in close agreement with the theoretical predictions.

Achromatic waveguide input/output coupler design

An investigation into methods for achromatizing the coupling angle characteristics of waveguide input/output couplers is described. The basic approach involves correcting the inherent angular dispersion of conventional waveguide couplers with a diffraction grating. Two configurations are analyzed in detail: a hybrid prism/grating coupler and a double grating coupler. Expressions are derived for values of the grating parameters that produce achromatic coupling. A method is also presented to predict the achromatic wavelength range and maximize it with the available degrees of freedom. For a coupling angle tolerance of 0.005 degrees , it is found that with double grating couplers achromatic wavelength ranges of the order of 10 nm can be obtained, and that with prism/grating couplers this range can be as large as 200 nm.

Generation of random arrays using clipped laser speckle.

A technique for generating 2-D arrays of random numbers using clipped laser speckle is presented. A 2-D detector array is exposed to a fully developed laser speckle pattern. When the output of the array is clipped, the elements with value above threshold are set to unity while the others are set to zero. The result is an array of randomly positioned elements of unit value. The spatial coordinates of the elements above threshold are taken as the random deviates. By controlling the clipping threshold for each element, one can dictate the probability that the clipped output from each element will be above threshold. Any distribution can be produced by varying the probability that the output from each element is above threshold. We present experiments performed on a 256 × 256-element detector array for which the elements were individually addressable. The integration time for each detector can be adjusted to obtain various distributions. Applications of random arrays include Monte Carlo calculations and coherent pattern recognition.

Optical random number generator based on photoevent locations

A 2-D position-sensitive photon-counting detector is used in an optical random number generator in which the locations of detected photoevents provide the random numbers. The spatial distribution of photoevent locations is dictated by imaging a control object onto the detector. An iterative calibration procedure is used to determine the brightness distribution of the control object. Two control objects were examined-film and a video monitor. With both control objects, the performance of the optical random number generator approached that of pseudorandom number generators.

Correlation measurements using clipped laser speckle

Clipped laser speckle is used to measure the correlation of time-varying laser speckle. As with standard intensity correlation, clipped speckle is correlated to determine the magnitude of the correlation coefficient. The simple nature of clipped speckle permits high-speed measurements of correlation and velocity. A closed form approximation to the clipped correlation function valid for arbitrary clipping thresholds is presented. The approximation is used to make correlation measurements on speckle from a rotating diffuser using a 2-D random access detector array.