Marion O. Hagler

Multiplex holography with chirp-modulated binary phase-coded reference-beam masks.

Certain binary codes developed for spread-spectrum communication applications can be used to construct families of pseudorandom diffuser masks suitable for multiplex holography. Binary codes are used so that fabrication of the diffuser masks can be relatively straightforward. A simple technique is described for chirp-modulating the binary diffuser masks to achieve the advantage of polyphase masks, i.e., improved correlation properties, without having to construct them. Numerical comparisons of the correlation properties of optimal binary codes with and without chirp-modulation are presented.

Electrode Erosion Phenomena in a High-Energy Pulsed Discharge

The erosion rates for hemispherical electrodes, 2.5 cm in diameter, made of graphite, copper-graphite, brass, two types of copper-tungsten, and three types of stainless steel, have been examined in a spark gap filled with air or nitrogen at one atmosphere. The electrodes were subjected to 50 000 unipolar pulses (25¿s, 4-25 kA, 5-30 kV, 0.1-0.6 C/shot) at repetition rates ranging from 0.5 to 5 pulses per second (pps). Severe surface conditioning occurred, resulting in the formation of several spectacular surface patterns (craters up to 0.6 cm in diameter and nipples and dendrites up to 0.2 cm in height). Surface damage was limited to approximately 80 ¿m in depth and was considerably less in nitrogen gas than in air. Anode erosion rates varied from a slight gain (a negative erosion rate), for several materials in nitrogen, to 5 ¿cm3/C for graphite in air. Cathode erosion rates of 0.4 ¿cm3/C for copper-tungsten in nitrogen to 25 ¿cm3/C for graphite in air were also measured.

Spreadsheet Solution of Partial Differential Equations

This paper points out that a spreadsheet program on a home or personal computer permits the solution of partial differential equations in two independent variables with considerably less effort than conventional programming languages. The computational molecule approach is identified as a natural approach for using spreadsheets to solve elliptic, parabolic, and hyperbolic partial differential equations in rectangular, skew, and curvilinear coordinate systems. The technique is relatively independent of the type of spreadsheet or host computer employed, although the spreadsheet must allow forward or circular references for iteration. Each of the examples in the paper was run on a home computer with 48K RAM.

Holographic representations of space-variant systems using phase-coded reference beams

A new holographic implementation of a sampling technique permits, in principle, a straightforward representation of 2-D space-variant optical systems. The set of sample transfer functions required for the representation is recorded on a single holographic plate by utilizing phase coded reference beams. Because this approach does not depend on volume effects in the recording medium in an essential way, the holograms can be produced digitally, as well as optically. Basic concepts and preliminary experimental investigations related to this approach are presented and discussed.

Space-variant processing of 1-D signals

Two general schemes for 1-D space-variant processing are proposed. The direct output display scheme gives the space-variant system output along a line in the processors output plane. The output spectrum display scheme directly computes the space-variant systems output spectrum. Both of these schemes utilize a 1-D input and a line spread function mask. Example applications and experimental results are also presented.

A sampling theorem for space-variant systems

A sampling theorem applicable to that class of linear systems characterized by sufficiently slowly varying line-spread functions is developed. For band-limited inputs such systems can be exactly characterized with knowledge of the sampled system line-spread function and the corresponding sampled input. The desired sampling rate is shown to be determined by both the system and the input. The corresponding output is shown to be band limited. A discrete matrix representation of the specific system class is also presented. Applications to digital processing and coherent space-variant system representation are suggested.

Integrated component web-based interactive learning systems for engineering

Dynamic web-based learning tools are indispensable in modern teaching, especially considering their capability for interaction on demand as a means of stimulating and engaging students. The experience on which the results reported here are based has grown out of progressive testing of different approaches for publishing technical sketches and mathematical notations from the field of electromagnetics on the web, starting in 1997 with simple static web pages of solved examples. The encouraging results from using and evaluating this educational material and the needs expressed by students for learning from more dynamic and interactive web learning materials that offer the possibility of changing parameters in online calculations motivated a search for new approaches to publishing interactive learning materials on the web. Integration of already developed components for building animations, presenting mathematical equations, and performing online computations with browser scripting led to development of a learning environment where animations are synchronized with corresponding derivations of equations and supported by dynamic, parametric-driven calculations and visualizations that can be integrated with sound and video. The system supports tests and examinations in which the answers are provided as mathematical notations. The use of Mathematical Markup Language (MathML) permits equations in the learning materials to be copied and pasted into most of the popular mathematical software tools for algebraic manipulation or numerical computation. Examples demonstrate how the system can be used with a course on electromagnetics, although the basic approach is applicable in other fields of engineering and natural science.

Optical measurement of high electric and magnetic fields

Electric fields are determined by interferometrically measuring the phase difference introduced between light polarized parallel and perpendicular to the electric field. The phase difference is introduced by nitrobenzene in the electric-field volume. Magnetic fields are determined by interferometrically measuring the phase difference introduced between left and right circularly polarized light by Faraday rotational glass placed in the magnetic field. The result of either measurement is a finite fringe interference pattern. The position displacement of the fringes is observed in time using a continuous laser and a streak camera to yield the time behavior of the field or in space using a pulsed laser and photographic film to yield the spatial behavior of the field.

Representations of space-variant optical systems using volume holograms.

A technique is described for recording representations of space-variant optical systems as volume holograms. The transfer-function holographic representations obtained are then placed in the Fourier plane of a coherent optical processor for playback. Due to the space-variant nature of the systems represented, the input plane of the system to be represented holographically is spatially sampled. As a result, the volume hologram medium actually contains a number of holograms that have been angle multiplexed to avoid interference problems. Limitations associated with the thickness of the recording medium are calculated for imaging systems, and experimental results are presented for one lens and two lens magnifiers.

Correlation properties of random phase diffusers for multiplex holography.

Random phase diffusers used to individually code the reference beams employed in multiplexing a set of holograms are best characterized by their autocorrelation and cross-correlation properties. In this paper multilevel (n-level) phase diffusers and ground-glass diffuser models based on a spatial random telegraph wave are employed to investigate the performance of such diffusers for both plane wave and spherical wave illumination. The advantage of using balanced phase diffusers is indicated, and it is shown that a binary phase diffuser can, in principle, perform as well as a multilevel (n > 2) diffuser, and even as well as ground glass if the spatial fineness of the diffusers is comparable. Two signal-to-noise ratio measures of the performance of the various diffuser systems in a multiplex holography application are evaluated and discussed.