Einstein-Podolsky-Rosen spatial entanglement in ordered and anderson photonic lattices.

We demonstrate quantum walks of a photon pair in a spatially extended Einstein-Podolsky-Rosen state coupled into an on-chip multiport photonic lattice. By varying the degree of entanglement we observe Anderson localization for pairs in a separable state and Anderson colocalization for pairs in an Einstein-Podolsky-Rosen entangled state. In the former case, each photon localizes independently, while in the latter neither photon localizes, but the pair colocalizes--revealing unexpected survival of the spatial correlations through strong disorder.

Fading time of retinally-stabilized images as a function of background luminance and target width.

Fading time of a retinally-stabilized difference-of-Gaussian (DOG) stimulus depends on the background luminance, contrast and spatial frequency content of the stimulus. A model of the visual system including a nonlinear multiplicative, non-local and fast process followed by a linear subtractive, local and slower process accounts for these effects. Analysis of the fading time data allows us to estimate the spatiotemporal characteristics of the proposed adaptation processes. The model is consistent with recent models of normal light adaptation from the probe-flash paradigm.

Adaptation with a stabilized retinal image: effect of luminance and contrast.

The addition of a uniform increment of luminance (L) to a faded retinally-stabilized target results in the subjective reappearance of the image with contrast opposite to that of the target. This phenomenon, called apparent phase reversal (APR), reveals a nonlinear gain mechanism in the adaptation process. The magnitude of the threshold increment to elicit APR (Lapr) is a measure of the state of stabilized adaptation. In the experiments reported here, Lapr was studied as a function of background luminance (Lo) and contrast (m) of the adapting stimulus. It was found that Lapr increases with increasing Lo, but does not depend on m. The data are analyzed within the context of a previously proposed model of stabilized image fading consisting of a multiplicative inverse gain followed by a subtractive process. It was found that the addition of a contrast processing stage was required to account for the relationship between Lapr and m.

Image design: generation of a prescribed image at the output of a band-limited system.

Image design involves determining the object distribution which produces a prescribed image at the output of a given imaging system. We solve the problem of generating two parallel lines at the output of an imaging system that is modeled by a linear band-limited system foliowed by a point nonlinearity of the hardlimiting type. It is shown that a solution always exists whatever the system's bandwidth. In principle, infinite two-line resolution is achievable. In practice, resolution much higher than the conventional resolution of the imaging system is possible.

Estimation of the location of an optical object with photodetectors limited by quantum noise.

We study the maximum likelihood estimation of the location of an incoherent object, the light from which is distorted by an optical system and detected by photoelectric detectors with quantum noise. The noise is treated as a set of uncorrelated Gaussian variables with variances proportional to the signal plus background at their corresponding detectors. By the simulation of the noise, a large number of cases are tested and curves for the probability distribution of the error distance are obtained.

Trade off between resolution and noise in restoration by superposition of images.

The inversion technique of Backus and Gilbert is applied to the problem of restoration of optical objects by superposition of images. The problem is formulated in the general case of space-variant systems. Curves for the trade off between resolution and noise in restoring objects degraded by simple diffraction and susceptible to uncorrelated noise are obtained. The technique is used to restore a test object whose image is sampled at the Nyquist rate and to which noise (simulated on a computer) is added. Restorations corresponding to several points on the trade-off curve are obtained.

Bilinear processing of 1-D signals by use of linear 2-D coherent optical processors.

The capabilities of optical computers are extended to perform the class of bilinear transformations (of nonzero spread) on 1-D signals. Use is made of the additional degree of freedom in 2-D linear processing. The technique is applied to the study of partially coherent optical systems and to systems in which coherent optical processing is followed by postdetection linear spatial filtering.

Wiener restoration of defocused partially coherent images.

Wiener filters are developed for the restoration of images that are distorted by diffraction and defocusing under conditions of partially coherent illumination. Performance of the restoration filter is assessed by the reduction of mean square error and the improvement of two-point resolution.

Performance of single photon decay spectrometers with pile-up correction.

The distortion and the statistical accuracy of single photon decay spectrometers with and without pile-up correction are determined. The effect of the statistical properties of the radiation is discussed.

Complex amplitude reflectance of the liquid crystal light valve.

The complex amplitude reflectance of the liquid crystal light valve (LCLV) is determined as a function of the writing intensity and applied voltage using an approximate model. The input and output polarizers are assumed to have arbitrary directions. The theoretical results based on this model match our experimental measurements. This theory allows us to optimize the operation of the LCLV as an intensity or phase-only spatial light modulator. When the polarizers are orthogonal and the input polarizer is at -34 degrees with the front liquid crystal director, the intensity reflectance reaches 100% (compared to 81% for the conventional configuration). Phase-only modulation is realizable by use of appropriate applied voltage bias and configuration of polarizers.

Moment invariants in the space and frequency domains.

Moment invariants of the Fourier transform of an image are introduced. It is found that a feature set composed of moment invariants from both the space domain and the Fourier domain gives better performance for a wide range of classification tasks than does the same number of moment invariants from either domain alone. Redundancy among moments of the two domains is examined by using the correlation coefficient between the feature kernels as a measure. Examples are used to compare the feature sets and to assess their performance in classification tasks. Moment invariants of the magnitude of the Fourier transform and, by inference, some popular features, such as the spectral ring-wedge detector, are found to fall far short in performance compared with those in which the phase of the Fourier transform is also utilized. Coherent optical systems to compute the dual-domain moment invariants are proposed.

Multiplication and refractoriness in the cat's retinal-ganglion-cell discharge at low light levels.

Measurements of the pulse-interval distribution and pulse-number distribution for cat retinal ganglion cells in darkness and light have been carried out by Barlow, Levick, and Yoon. The experimental results for an on-center brisk-sustained cell are in accord with a mathematical model incorporating four features: Poisson quantum fluctuations, additive dark noise, multiplication noise (random multiple neural spikes per absorbed quantum), and refractoriness. The data cannot be properly explained by a model lacking any one of these features. Parameters extracted from the model are in good agreement with physiological values.

Lateral and focal shifts of phase-conjugated beams in photorefractive materials.

It is predicted that when a dc electric field is present or when a probe beam contains temporal frequencies different from that of the pump waves a beam reflected from a photorefractive phase-conjugate mirror will experience lateral and focal shifts. These shifts are a consequence of angular dependence of the phase of the reflectivity and are similar to the Goos-Hänchen effect. The phenomenon becomes more pronounced near resonance.

Optical implementation of the Hopfield algorithm using correlations.

We propose a method for the implementation of the Hopfield algorithm using inner products of unipolar data. This approach is particularly useful for image recognition.

Reconstruction of a complex-valued object in coherent imaging through a random-phase screen.

We consider the reconstruction of a complex-valued object that is coherently illuminated and then viewed through a random-phase screen. The reconstruction involves a phase retrieval based on two intensity measurements. The first is a measurement of the long-exposure averaged intensity of a Fourier transform of the image; it yields full information on the magnitude of the object Fourier transform but noi nformation on its phase. The second measurement is made with the image field modulated by an exponential function. This modulation has the effect of shifting the Fourier-transform function along the imaginary axis of the complex plane of its argument, thus making its intensity dependent on the unknown object phase. This method is capable of reconstructing the object except for an inherent ambiguity corresponding to a simple displacement. The effects of the noise arising from averaging over finite, instead of infinite, exposure times and the quantum noise were assessed. A computer-simulated example of reconstru ting a two-dimensional object demonstrated that the reconstruction is robust. The reconstruction error increases with an increase of the variance of the random-phase function and with a decrease of its correlation length.

Optical location of centroids of nonoverlapping objects.

We present an optical technique for finding the centroids of nonoverlapping objects in a scene, thus locating the objects and preserving the underlying advantage of matched filtering approaches to pattern recognition. One is then free to extract any feature desired at these centroid locations rather than restricted to the matched filter test statistic. Furthermore, this allows general feature extraction avoiding prior scene segmentation into individual objects. The technique can also be used for tracking the motion of rigid or nonrigid objects. It consists of cross-correlating the input f(x,y) with a windowed version of the function x + iy and detecting the zeros of the magnitude of the resulting correlation. At these points the x and y first moments vanish. The window is selected based on the size and separation of the objects in a scene. Experimental verification as well as restrictions are also presented.

Image restoration under random time-varying blur.

We present a method for restoring a fixed scene, which is imaged through a random time-varying medium, from a number of observation frames contaminated by additive detection noise. The method is based on frame-pixel separability. First, frames are deblurred individually (ignoring additive noise). Then a pixel is treated individually by finding an estimate of its value based on its values in all deblurred frames. In some conditions the final estimate turns out to depend on only two statistics: the frame-averaged image and the frame-averaged spatial correlation function. The latter is the basis of speckle interferometry.

Reducing Berreman's 4 x 4 formulation of liquid-crystal-display optics to 2 x 2 Jones vector equations.

We use a perturbation expansion to obtain a generalized 2 x 2 Jones vector description that is equivalent to Berreman's description. We show that for typical liquid-crystal displays (LCD's) the bulk reflections are weak so that the first-order 2 x 2 Jones solution is generally sufficient and affords fast and reasonably accurate computations of the overall optical properties of LCD devices.

Signal-to-noise ratio improvement by stochastic resonance in a unidirectional photorefractive ring resonator.

All-optical signal-to-noise ratio improvements by stochastic resonance have been obtained by use of the intensity bistability of a unidirectional photorefractive ring resonator. A signal-to-noise ratio gain of 10.5 dB has been obtained with a near-unity signal-to-noise ratio input signal at 6 mHz.

Reconstruction of a vibrating object from its time-averaged image intensities by the use of exponential filtering.

We consider the reconstruction of a complex-valued object that vibrates in some out-of-plane modes. The reconstruction is based on the phase-retrieval method with the use of two intensity measurements: the two time-averaged image intensities of the object illuminated coherently, which are modulated in two Fourier-transform planes of the object by the use of two filters with exponentially decaying transmittances that complement each other. We discuss the necessary condition of the vibration for the reconstruction method. Computer-simulated examples of retrieving the phases of one-dimensional objects demonstrate that the reconstruction of a sinusoidal-vibrating and a Gaussian random-vibrating object can be treated by this method.