Diffraction characteristics of general dielectric planar (slab) gratings and surface-relief (corrugated) gratings are reviewed. Applications to laser-beam deflection, guidance, modulation, coupling, filtering, wavefront reconstruction, and distributed feedback in the fields of acoustooptics, integrated optics, holography, and spectral analysis are discussed. An exact formulation of the grating diffraction problem without approximations (rigorous coupled-wave theory developed by the authors) is presented. The method of solution is in terms of state variables and this is presented in detail. Then, using a series of fundamental assumptions, this rigorous theory is shown to reduce to the various existing approximate theories in the appropriate limits. The effects of these fundamental assumptions in the approximate theories are quantified and discussed.

Analysis and applications of optical diffraction by gratings

The (auto)triple correlation l(3)(t 1 , t 2 ) is defined as the triple function integral, applied to the signal l(t) l(3)(t 1 , t 2 ) = ∫ l(t)l(t + t 1 )l(t + t 2 ) dt. The triple correlation l(3)(t 1 , t 2 ) is less popular than the standard (double) correlation l(2)(t 1 ) for several reasons: l(2)is sometimes easier to observe and to process, l(3)is small for many bipolar or complex signals, the mathematics associated with l(2)is better known. On the other hand, the triple correlation l(3)knows more about the signal l than does the ordinary autocorrelation l(2). Also l(3)is in some ways more sensitive, in other ways less sensitive to noise, to bias drifts, etc. Hence, there are situations, where it is quite favorable to evaluate one-dimensional signals or two-dimensional pictures by means of their triple correlations. We will review the underlying mathematical tools and report on our projects where triple correlations were employed for studying laser pulse shapes, sound quality, halftone print statistics, mobility of bacteria, and astronomical speckle interferometry. We will mention also how others have used the triple correlation for ocean waves, engine noises, intensity interferometry, and other optical signal processing tasks.

http://ieeexplore.ieee.org/iel5/5/31339/01457214.pdf

Triple correlations

The use of acousto-optic devices in real-time signal convolution and correlation has increased dramatically during the past decade because of improvements in device characteristics and implementation techniques. Depending on the application, processing can be implemented via spatial or temporal integration. Two-dimensional signal processing (including image processing) is possile, in spite of the inherent one-dimensional nature of the acousto-optic device as a spatial light modulator.

Acousto-optic signal processing: Convolution and correlation

The paper first reviews the historical development of acousto-optics and its applications. Following this, a heuristic explanation of acousto-optic effects is presented, with the emphasis on the plane wave model of interaction. Finally, there is a discussion of some basic configurations of relevance to signal processing.

Acousto-optics&#8212;A review of fundamentals

The recent development of titanium-indiffusion proton-exchange (TIPE) microlenses and lens arrays has made possible the construction of a variety of single- and multichannel integrated acoustooptic (AO) and acoustooptic-electrooptic (EO) circuits in LiNbO/sub 3/ channel-planar waveguides 0.1*1.0*2.0 cm/sup 3/ in size. These hybrid AO and AO-EO circuits can be fabricated through compatible and well-established technologies. The most recent realization of ion-milled microlenses and lens arrays together with the recent development of gigahertz AO Bragg modulators and EO Bragg modulator arrays have also paved the way for construction of similar but monolithic AO and AO-EO GaAs/GaAlAs waveguides of comparable size. Both types of integrated AO and AO-EO circuits suggest versatile applications in communications signal processing, and computing. Efficient and simultaneous excitation of the channel waveguide array using an ion-milled planar microlens array has facilitated the demonstration of some of these applications. >

Integrated acoustooptic circuits and applications

Over the past few years there has been an exponential increase in interest in analog processing technology. This is largely due to economics. The cost of digital processing at very high data rates is often prohibitive. In addition, many of the components required for optical processing have matured to the "off-the-shelf" stage. A significant portion of the effort in optical processing has shifted from components development to processing architecture. The time integration architecture offers the following advantages: a. It makes the most effective use of CCD arrays as sensors. b. It often produces a significant data rate reduction. (output rate is often orders cf magnitude below the input rate) c. It does not require a two dimensional electrooptic modulator to implement two dimensional operations. The following paper reviews past efforts in one dimensional time integrating processors and introduces the two dimensional time integrating correlator. This correlator can implement a variety of operations including ambiguity functions and large time bandwidth spectrum analysis (two dimensional).

Terry M. Turpin

Papers

Time Integrating Optical Processors