Abdul A. S. Awwal

Multicast traffic grooming in WDM optical mesh networks

We consider the grooming of multicast traffic in WDM optical mesh networks with sparse nodal light splitting capability. Given multicast routing trees for individual multicast sessions, the multicast traffic grooming problem is NP-hard. Moreover, constructing an optimal multicast routing tree in WDM optical mesh networks is also an NP-hard problem. We formulate the problem of multicast traffic grooming in WDM optical mesh networks as an integer linear program. We propose a heuristic algorithm for constructing multicast routing trees and a first-fit algorithm for traffic grooming, assuming wavelength conversion capability in the network nodes. By intelligently grooming several multicast sessions with fractional wavelength bandwidth requirements onto a single wavelength, we demonstrate that our algorithms achieve a significant reduction in the maximum number of wavelengths required in a link as well as in the total number of wavelength links needed.

Optical processing based on conditional higher-order trinary modified signed-digit symbolic substitution

Techniques for higher-order modified signed-digit trinary arithmetic by using optical symbolic substitution are presented. This method provides fast multibit computation by adopting a two-step symbolicsubstitution scheme. Since more information is represented in fewer digits, this technique leads to a compact design. A content-addressable memory-based and a joint transform correlator-based optical implemention for the proposed technique are also presented.

Modified signed-digit trinary arithmetic by using optical symbolic substitution

Carry-free addition and borrow-free subtraction of modified signed-digit trinary numbers with optical symbolic substitution are presented. The proposed two-step and three-step algorithms can be easily implemented by using phase-only holograms, optical content-addressable memories, a multichannel correlator, or a polarization-encoded optical shadow-casting system.

Diffraction-free beam generation using refracting systems

Abstract An optical refracting system has been designed to transform an input Gaussian laser beam into a diffraction-free Bessel beam. The optical systems characteristics are optimized for ease of fabrication.

What can we learn from the shape of a correlation peak for position estimation

Matched filtering is a robust technique to identify and locate objects in the presence of noise. Traditionally, the amplitude of the correlation peak is used for detection of a match. However, when distinguishing objects that are not significantly different or detecting objects under high noise imaging conditions, the normalized peak amplitude alone may not provide sufficient discrimination. In this paper, we demonstrate that measurements derived from the shape of the correlation peak offer not only higher levels of discrimination but also accurate position estimation. To our knowledge, this is the first time such features have been used in a real-time system, like the National Ignition Facility, where such techniques enable real-time, accurate position estimation and alignment under challenging imaging conditions. It is envisioned that systems utilizing matched filtering will greatly benefit from incorporating additional shape based information.

Artificial neural networks using complex numbers and phase encoded weights

The model of a simple perceptron using phase-encoded inputs and complex-valued weights is proposed. The aggregation function, activation function, and learning rule for the proposed neuron are derived and applied to Boolean logic functions and simple computer vision tasks. The complex-valued neuron (CVN) is shown to be superior to traditional perceptrons. An improvement of 135% over the theoretical maximum of 104 linearly separable problems (of three variables) solvable by conventional perceptrons is achieved without additional logic, neuron stages, or higher order terms such as those required in polynomial logic gates. The application of CVN in distortion invariant character recognition and image segmentation is demonstrated. Implementation details are discussed, and the CVN is shown to be very attractive for optical implementation since optical computations are naturally complex. The cost of the CVN is less in all cases than the traditional neuron when implemented optically. Therefore, all the benefits of the CVN can be obtained without additional cost. However, on those implementations dependent on standard serial computers, CVN will be more cost effective only in those applications where its increased power can offset the requirement for additional neurons.

Optical implementation of an efficient modified signed-digit trinary addition

Abstract Efficient parallel schemes for carry-propagation-free addition of modified signed-digit trinary numbers are presented. The necessary minterms for implementation using an optical programmable logic array area are derived. The proposed schemes require only a truth table of 25 entries compared with an earlier scheme of 625 entries. The proposed schemes are amenable to optical implementation. Experimental results using an optical programmable logic array are demonstrated. The experiments show the problems of noise and crosstalk. This suggests some dc bias is necessary to increase the signal-to-noise ratio of the optical circuit.

Detection and tracking of the backreflection of potassium dihydrogen phosphate images in the presence or absence of a phase mask

The potassium dihydrogen phosphate (KDP) crystals present in the final optics assembly at the National Ignition Facility (NIF) are used for conversion of an infrared laser light beam into an ultraviolet beam. The conversion is highest for a certain incident angle, the alignment of which is determined from the position of the backreflection beam, which exhibits a distinct characteristic shape. When a phase-plate device is introduced before the final assembly to increase the uniformity of the beam, the backreflection pattern changes drastically. The algorithm that is best for tracking the special-shaped beam is no longer suitable for tracking the phase-modified beam. We discuss our detection schemes for both situations. In particular, we demonstrate how the algorithm senses the modified beam by using a newly proposed criterion of correlation peak pedestal area and executes an alternate algorithm in real time without operator intervention. This new algorithm continuously tracks the beam pattern to guarantee reliable and repeatable sensing. Results from simulation and real-world implementation of the algorithm at the NIF facility are presented.

Optimal position estimation for the automatic alignment of a high-energy laser

The alignment of high-energy laser beams for potential fusion experiments demands high precision and accuracy by the underlying positioning algorithms whether it be for actuator control or for monitoring the beam line for potential anomalies. The feasibility of employing on-line optimal position estimators in the form of model-based processors to achieve the desired results is examined. We discuss the modeling, the development, the implementation, and the processing of model-based processors applied to both simulated and actual beamline data.

Characterization and operation of a liquid crystal adaptive optics phoropter

Adaptive optics (AO), a mature technology developed for astronomy to compensate for the effects of atmospheric turbulence, can also be used to correct the aberrations of the eye. The classic phoropter is used by ophthalmologists and optometrists to estimate and correct the lower-order aberrations of the eye, defocus and astigmatism, in order to derive a vision correction prescription for their patients. An adaptive optics phoropter measures and corrects the aberrations in the human eye using adaptive optics techniques, which are capable of dealing with both the standard low-order aberrations and higher-order aberrations, including coma and spherical aberration. High-order aberrations have been shown to degrade visual performance for clinical subjects in initial investigations. An adaptive optics phoropter has been designed and constructed based on a Shack-Hartmann sensor to measure the aberrations of the eye, and a liquid crystal spatial light modulator to compensate for them. This system should produce near diffraction-limited optical image quality at the retina, which will enable investigation of the psychophysical limits of human vision. This paper describes the characterization and operation of the AO phoropter with results from human subject testing.