This PDF file contains the editorial “Editorial: Life After Provosting” for OE Vol. 33 Issue 07

This PDF file contains the editorial “Guest Editorial: Adaptive Wavelet Transforms” for OE Vol. 33 Issue 07

A scaling function is the solution to a dilation equation Φ(t) = Σc_kΦ(2t - k), in which the coefficients come from a low-pass filter. The coefficients in the wavelet W(t) = Σd_kΦ(2t - k) come from a high-pass filter. When these coefficients are matrices, Φ and W are vectors: there are two or more scaling functions and an equal number of wavelets. By dilation and translation of the wavelets, we have an orthogonal basis W_ijk = W_i(2^jt - k) for all functions of finite energy. These "multiwavelets" open new possibilities. They can be shorter, with more vanishing moments, than single wavelets. They can be symmetric, which is impossible for scalar wavelets (except for Haar's). We determine the conditions to impose on the matrix coefficients c_k in the design of multiwavelets, and we construct a new pair of piecewise linear orthogonal wavelets with two vanishing moments.

The notion of oversampled frames differs from the more well-known concept of oversampling in that no additional data information is required in the implementation of the oversampled frame algorithms and that redundancy can be separated in a combinatoric way into linearly independent subfamilies of complete systems. This combinatoric scheme is used to design real-time algorithms for wavelet and wavelet packet frame decompositions and reconstructions.

We prove several theorems and construct explicitly the bridge between the continuous and discrete adaptive wavelet transform (AWT). The computational efficiency of the AWT is a result of its compact support closely matching linearly the signal's time-frequency characteristics, and is also a result of a larger redundancy factor of the superposition-mother s(x) (super-mother), created adaptively by a linear superposition of other admissible mother wavelets. The super-mother always forms a complete basis, but is usually associated with a higher redundancy number than its constituent complete orthonormal (CON) bases. The robustness of super-mother suffers less noise contamination (since noise is everywhere, and a redundant sampling by bandpassings can suppress the noise and enhance the signal). Since the continuous super-mother has been created off-line by AWT (using least-mean-squares neural nets), we wish to accomplish fast AWT on line. Thus, we formulate AWT in discrete high-pass (H) and low-pass (L) filter bank coefficients via the quadrature mirror filter (QMF), a digital subband lossless coding. A linear combination of two special cases of the complete biorthogonal normalized (Cbi-ON) QMF [L(z),H(z),L⁺(z),H⁺(z)], called α-bank and β-bank, becomes a hybrid aα + bβ-bank (for any real positive constants a and b) that is still admissible, meaning Cbi-ON and lossless. Finally, the power of AWT is the implementation by means of wavelet chips and neurochips, in which each node is a daughter wavelet similar to a radial basis function using dyadic affine scaling.

We discuss smooth local trigonometric bases and their applications to signal compression. In image compression, these bases can reduce the blocking effect that occurs in the Joint Photographic Experts Group (JPEG). We present and compare two generalizations of the original construction of Malvar, Coifman, and Meyer: biorthogonal and equal parity bases. These have the advantage that constant and linear components, respectively, can be represented efficiently. We show how they reduce blocking effects and improve the SNR.

Wavelet decomposition of data has been used with success in a large class of signal and image processing tasks. The wavelet packets representation is a decomposition that includes as a special case the wavelet transform. In this scheme, wavelet packets are assembled as a representation of the signal. There exist a large number of possible wavelet combinations for each signal. An adaptation scheme based on the genetic optimization method is presented for determining an optimal representation for data compression. Experiment results using real data as well as autoregressive random processes are used to compare the performance of the adapted packets and the wavelet transform.

Neurons in the primary auditory cortex exhibit distinctive selectivities in responses to various acoustic features. Recent physiological studies suggest that there are three spatial dimensions along which the neural response patterns can be systematically organized: the tuning frequencies of the neurons are logarithmically mapped on the tonotopic axis, and the shapes of the tuning curves, in terms of symmetry and bandwidth, vary gradually along two other spatial dimensions. It is shown that these variations can be effectively modeled by a complex wavelet transform. With such a tie, one can employ well-established wavelet theories to analyzing and understanding how acoustic signals are processed in the auditory system, and thereby design novel engineering applications that are perceptually oriented.

Experience suggests the existence of a connection between the contrast of a gray-scale image and the gradient magnitude of intensity edges in the neighborhood where the contrast is measured. This observation motivates the development of edge-based contrast enhancement techniques. We present a simple and effective method for image contrast enhancement based on the multiscale edge representation of images. The contrast of an image can be enhanced simply by stretching or upscaling the multiscale gradient maxima of the image. This method offers flexibility to selectively enhance features of different sizes and ability to control noise magnification. We present some experimental results from enhancing medical images and discuss the advantages of this wavelet approach over other edge-based techniques.

Wavelet transforms are used to analyze electroencephalographic data recorded from individual subdural electrodes and 2-D electrode grids in direct contact with the brain. Surrogate data techniques are used to filter noise and resolve structure in the data. Spike and seizure detection from individual electrodes with wavelet transforms are compared with windowed Fourier transforms. Wavelet transforms are a powerful means to identify epileptiform activity such as spikes from such data and also ofter a method to localize the foci of epileptic seizures from electrode grids.

We describe the development of adapted waveform analysis (AWA) as a tool for fast processing of the various identification tasks involved in medical diagnostics and automatic target recognition. Such tasks consist of steps: representing the signal as a superposition of component functions, choosing to retain some of the components and discard the others, then reconstructing a new, approximate signal from what was kept. AWA provides tools for each of these steps, accelerating the decomposition and reconstruction computations, providing new functions for analysis and modeling, and extracting new features for recognition and classification. AWA extends Fourier analysis by providing new libraries of standard waveforms with properties akin to windowed sines and cosines, and it extends principal component analysis and eigen-function expansions by adapting the standard functions to individual operators. The cost of representing a function can be measured by how many components must be superposed to obtain a desired degree of approximation, and this cost can be minimized by a fast search through the library of representations. The analysis can be iterated to sift coherent signals from noise. We consider applications to signal and image compression, feature detection, and medical image denoising.

A transient signal detector based on M-band wavepackets, using an M-band, translation-invariant wavelet transform is presented. The detection statistic consists of the maximum energy value in the best basis, derived from the full M-band wavepacket decomposition. The full wavepacket decomposition uses the M-band translation-invariant wavelet transform (MTI), recently developed by Weiss. Use of the MTI provides two advantages over the use of traditional wavepacket methods. One advantage is that the MTI detector pertormance is independent of sample shifts of the input signal. The second advantage is that use of the MTI provides superior energy concentration; more energy is concentrated in fewer coefficients. This results in higher peak energy values. We present receiver operating characteristic curves generated by Monte-Carlo simulation, illustrating detector performance on exponentially damped sinusoids. Performance is compared to similar detectors based on the nominal wavepacket decomposition and the Mallat wavelet decomposition.

Computing the optimal expansion of a signal in a redundant dictionary of waveforms is an NP-hard problem. We introduce a greedy algorithm, called a matching pursuit, which computes a suboptimal expansion. The dictionary waveforms that best match a signal's structures are chosen iteratively. An orthogonalized version of the matching pursuit is also developed. Matching pursuits are general procedures for computing adaptive signal representations. With a dictionary of Gabor functions, a matching pursuit defines an adaptive time-frequency transform. Matching pursuits are chaotic maps whose attractors define a generic noise with respect to the dictionary. We derive an algorithm that isolates the coherent structures of a signal and describe an application to pattern extraction from noisy signals.

The utility and robustness of wavelet features is demonstrated through three practical case studies of detecting objects in multispectral electro-optical imagery, sidescan sonar imagery, and acoustic backscatter. Attention is given to choosing proper waveforms for particular applications. Using artificial neural networks (ANNs), evidence is fused from multiple-waveform types that detect local features. The wavelet waveforms and their dilation and shift parameters are adaptively computed with ANNs to maximize classification accuracy. Emphasis is placed on the acoustic backscatter case study, involving detecting a metallic man-made object from natural and synthetic specular clutter with reverberation noise. The synthetic clutter is shown to be a good model for the natural clutter, which appears promising for avoiding huge data collection efforts for natural clutter and for better delineating the classification boundary. The classifier computes the locations, sizes, and weights of Gaussian patches in time-scale space that contain the most discriminatory information. This new approach is shown to give higher classification rates than an ANN with commonly used power spectral features. The new approach also reduces the number of free parameters in the classifier based on all wavelet features, which leads to simpler implementation for applications and to potentially better generalization to test data.

Our objective is to demonstrate the applicability of adaptive wavelets for speech applications. In particular, we discuss two applications, namely, classification of unvoiced sounds and speaker identification. First, a method to classify unvoiced sounds using adaptive wavelets, which would help in developing a unified algorithm to classify phonemes (speech sounds), is described. Next, the applicability of adaptive wavelets to identify speakers using very short speech data (one pitch period) is exhibited. The described text-independent phoneme based speaker identification algorithm identifies a speaker by first modeling phonemes and then by clustering all the phonemes belonging to the same speaker into one class. For both applications, we use feed-forward neural network architecture. We demonstrate the performance of both unvoiced sounds classifier and speaker identification algorithms by using representative real speech examples.

We review the relation between the radar ambiguity function and the matched filter, and then introduce a geometric concept of the matched filter as a slice of the ambiguity function along a frequency-shift line. With the help of this geometric concept, the conventional matched filter can be generalized to a time-varying matched filter, which is equivalent to the optimum time-frequency correlator and can be implemented with wavelet transforms. The application of the optimum wavelet correlator to the inverse synthetic aperture radar is illustrated.

Several current attempts to use acoustic and electromagnetic wave propagation for modeling physical phenomena and the role that wavelet analysis is playing in these efforts are discussed. The first probem involves the recent application of wavelets to computational fluid dynamics. The second problem involves geophysical modeling of the ocean floor, using acoustic waves, and wavelets have recently been shown to play an important role here already. The third problem involves modeling of synthetic aperture radar (SAR) images in the context of automatic target recognition efforts. The fourth problem is global illumination in computer graphics, i.e., simulation of reflected and absorbed light for everyday environments. The role of wavelets is more embryonic in the last two areas, but there are some common principles in all of these modeling efforts, and the methodology of wavelets seems well suited to certain aspects of these problems.

We use large libraries of template waveforms with remarkable orthogonality properties to recast the relatively complex principal orthogonal decomposition (POD) into an optimization problem with a fast solution algorithm. Then it becomes practical to use POD to solve two related problems: recognizing or classifying images, and inverting a complicated map from a low-dimensional configuration space to a highdimensional measurement space. In the case where the number N of pixels or measurements is more than 1000 or so, the classical O(N³) POD algorithm becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(N² logN). A variation of POD can also be used to compute an approximate Jacobian for the complicated map.

A wavelet-based system for computing localized velocity fields associated with time-sequential imagery is described. The approach combines the mathematical rigor of the multiresolution wavelet analysis with well-known spatiotemporal frequency flow computation principles. The foundation of the approach consists of a unique, nonhomogeneous multiresolution wavelet filter bank designed to extract moving objects in a 3-D image sequence based on their location, size, and speed. The filter bank is generated by an unconventional 3-D subband coding scheme that generates 20 orientation-tuned filters at each spatial and temporal resolution. The frequency responses of the wavelet filter bank are combined using a least-squares method to assign a velocity vector to each spatial location in an image sequence. Several examples are provided to demonstrate the flow computation abilities of the wavelet vector motion sensor.

We discuss a novel multiscale approach to the detection of moving objects in a sequence of images. The approach is based in part on a multiframe generalization of an optical flow estimation algorithm previously developed by two of the authors. This algorithm provides an extremely efficient multiscale method for estimating optical flow in an image sequence and allows for the temporal accumulation of motion information. Moving objects in a sequence correspond to discontinuities in the true optical flow and, as a result, the residual image associated with the estimated optical flow can be used as a basis for detecting these objects. We propose an approach to detection based on morphological processing of the residual image, and illustrate its potential on real data.

We fuse the output from our real Gabor function macro detection filter with the outputs from a clutter Gabor filter and an imaginary Gabor filter. This fusion reduces false alarm clutter (P_FA), while retaining high probability of detection (P_D). Initial test results are given for a large set of 34 scenes with 189 targets in six different classes with full 360-deg distortions and contrast differences in the presence of clutter. We find P_D = 97.9% and P_FA = 0.038%. All three new Gabor transform outputs are achieved on a correlator with different filter functions.

We consider the detection of multiple classes of objects in clutter with 3-D object distortions and contrast differences present. We use a correlator because shift invariance is necessary to locate and recognize one object whose position is not known and to handle multiple objects in the same scene. The detection filter used is a linear combination of the real part of different Gabor filters, which we refer to as a macro Gabor filter (MGF). A new analysis of the parameters for the initial set of Gabor functions in the MGF is given, and a new neural network algorithm to refine these initial filter parameters and to determine the combination coefficients to produce the final MGF detection filter is detailed. Initial detection results are given. Use of this general neural network technique to design correlation filters for other applications seems very attractive.

The performance of a wavelet-based edge detector is characterized by a set of digital filters that implement the wavelet transform. We clarify the issue of whether an implementation filter for the wavelet transform can be centered at the origin while still maintaining the desired spatial domain localization. It is shown that this is possible only when the filter (or the wavelet) possesses an even-symmetry^* with respect to the origin. When the filter (or the wavelet) is antisymmetric with respect to the origin, however, the filter coefficients converge in the order of 1/n, producing a poor spatial domain localization. We show that the optimal axis of antisymmetry for the filter is located at the half-sample point to either side of the origin. We also present a scheme to adjust the degree of spatial filtering to balance between two conflicting factors of suppressing noise and preserving edges.

The wavelet transform is applied to signal processing of synthetic aperture radar and techniques for determining the range, cross-range, and rotation of the target as well as adaptive process for better resolution are studied. We also optically implement the wavelet transform in the laboratory for real-time processing of radar data, and describe methods for adaptive processing.

The wavelet-matched filter performs the continuous wavelet transform for edge feature enhancement and the correlation between two wavelet transforms for pattern recognition in a single step. The composite wavelet-matched filter is a combination of the wavelet-matched filters, that yields desired outputs for a given set of training mages. We present the definition, the iterative design algorithm, the quasi-orthogonality of the components, and the optical implementation of the composite wavelet-matched filter. The filter yields a sharp correlation peak at the origin without sidelobe. A comparison between the composite wavelet-matched filter with the conventional composite filter is also given.

A hybrid optical/electronic image processing system is proposed for the real-time implementation of a wavelet transform. Specifically, the difference-of-Gaussians (DOG) wavelet is synthesized in the hybrid system and used to process an input object. In the implementation, two laser beams with different temporal frequencies are first generated by an acousto-optic modulator. The two optical beams are then combined spatially and used to scan and process the object. The scattered light from the object is then picked up by a photodetector. The photodetector's electrical output signal, after appropriate electronic filtering, represents a scanned and processed version of the original object and can be sent to a monitor for real-time display or to a digital storage device for possible further processing. Because the proposed hybrid system is based on optical scanning, it is an incoherent system and hence has a much better signal-to-noise ratio (SNR) as compared with its coherent counterpart. Experimental results are presented and are shown to be in excellent agreement with computer simulations.

We have developed a technique for image analysis, representation, and decomposition. This technique was motivated by Mallat and Zhang's matching-pursuit algorithm. We have altered and simplified the mechanics of this algorithm to enable an extremely fast implementation via optical processing. Initial computer simulations show that our algorithm is capable of decomposing and representing a 2-D image as a linear combination of basis images with both high speed and high fidelity.

Both discrete wavelet transform (DWT) and inverse DWT are implemented using the lossless quadrature mirror filter (QMF) bank. The image passing through the finite impulse response QMF filtering becomes blurred and thus requires fewer number of pixels. Such a decimation amounts to the critical sampling that leads to the complexity O(N) for N data. The data compression comes from the permissible bits per pixel dynamic range compression of those filtered images having fewer details. The image reconstruction at a telereceiving station is accomplished by means of the inverse DWT. Thus, a complete biorthogonal basis of QMF is implemented by a fast wavelet transform chip designed with Verilog HDL and the image processing is demonstrated numerically. Adaptive DWT is sketched.

A new optical architecture is developed, based on fractional Fourier transforms, that compromises between shift-invariant (frequency) and position-dependent filtering. The analogy of this architecture to wavelet transforms and adaptive neural networks is also presented. The ambiguity and Wigner distribution functions are obtainable from special cases of the filter. The filter design corresponds to the training of the neural networks, and an adaptive learning algorithm is developed based on gradient-descent error minimization and error back propagation. The extension to multilayer architecture is straightforward.

A detailed analysis of the characteristics, regularities, and relationships of the centroiding errors of image spots caused by discrete and limited sampling, photon noise, and readout noise of the detector in a Hartmann-Shack wavefront sensor, wherein an image intensified charge-coupled device used as a photon detector is presented. The theoretical analysis and experimental results herein prove useful for optimum design and application of the sensor.

Although analyses general enough to account for both the temporal and spatial characteristics of the adaptive optical system exist, they are complex and require detailed information regarding the wavefront sensor, the deformable mirror, and the control algorithm. This investigation develops a frequency-domain analysis that predicts the performance of an adaptive optical system having an arbitrary temporal response. The analysis takes into account aperture piston and tilt removal and spatial bandwidth limitations due to the wavefront sensor's finite subaperture size and the deformable mirror's finite actuator spacing. The unique aspect of this model is the relative ease with which performance characteristics of different spatial and temporal system response functions can be investigated.

A model predicting temperature and damage fields in soft tissue exposed to CO₂ laser radiation has been devised and previously described. It failed, in its previous version, to explain the following experimental phenomenon: under low laser irradiances, a black substance defined as char is accumulated at the bottom of the crater. We modified the basic model in the attempt to provide an explanation to the phenomenon of char formation. The basic model solves the heat equation over a 2-D grid assuming cylindrical symmetry. The terms participating in the basic heat equation are as follows: laser radiation as a source, radiation emission from the sample, conduction between neighboring grid cells, and convection terms that may be responsible for char formation under low laser irradiance. A series of assumptions regarding these convection mechanisms and the characteristics of char, in particular its absorption coefficient, are made in this work and their implications are investigated.

Numerical modeling and experimental studies of the photoelectric characteristics of a linear two-channel bulk charge-coupled device (CCD) with surface (n-type) and bulk (p-type) channels in the wavelength range 0.4 to 1.1 μm were accomplished. A system of two nonlinear differential equations, which describes the process of the simultaneous photorelaxation of CCD channels taking into account a diffusion component of the photocurrents from the semiconductor substrate, was determined. With the help of numerical modeling for this system, it was established that the common photorelaxation time of the channels is mainly defined by the photorelaxation process of the bulk channel, and its typical value is approximately equal to 0.5 ms (when the power density of the irradiation is 10 μW/sm²). Photoelectric measurements were carried out by means of an optical probe with a diameter of 80 rim, which was focused on the CCD surface using a stand equipped with a monochromator, a "Helios-44" lens, a filament lamp, and a condenser. The electric regime was as follows: the clock frequency of the timing negative voltage impulses was 75 kHz, and the impulse amplitude was 20 V. In theoretical and experimental investigations, different spectral photosensitivities of the channels were obtained. The maxima of their values are about 0.75 μm for the bulk channel and 0.55 μm for the surface channel. A good quantitative agreement between the theoretical simulations and the experimental investigations is shown.

The potential of multiwave interference phenomena for display applications is discussed. It is aimed at the realization of polarizer and color-filter-free flat-panel displays on the basis of liquid crystal display technologies. It is shown that the system of even thick optical resonators can be tuned so that large-scale selectivity (superspectrum) over the visible spectrum is achieved. Parameters of superspectra can be controlled electrically with the aid of intracavity electro-optical materials. Polarization effects of multiwave interterence phenomena in cholesteric liquid crystals allow for new display principles-through effective redistribution of polarization states over the frequency spectrum. It is emphasized that this distribution is an important characteristic of wide-spectrum sources determining the state of radiation along with coherence matrix and correlation function.

The general expression of the optical path function and the focusing conditions of a variable line-spacing concave grating with a spherical surface are given. The spectral imaging of our flat-field grating spectrograph with a HITACHI flat-field grating was investigated and the typical experimental results of the two modes of the spectrograph (that is, the astigmatic mode and the stigmatic mode) are presented.

A holographic configuration for the measurement of slope variations of an arbitrarily shaped diffuse object is reported. The method's sensitivity can be varied continuously over a wide range.

One well-known method to solve ill-posed problems in image restoration is to use regularization techniques. A new scheme is proposed for digital image restoration based on a regularization method and on the biorthogonal wavelet transform. We show that, in cases where the blur filter can be considered as a low-pass filter of a biorthogonal multiresolution analysis, it is possible to obtain an efficient family of regularization operators from the convolution operator alone.

Standard diffractive estimates based on the system f/# were at odds with geometric predictions concerning beam footprint size at a relayed pupil image plane due to an object point at infinity. The reason for this was that the relay optic was well within the defractive depth of focus of an intermediate star image. This invalidated geometric predictions for the system f/# and the location and size of the system impulse response. Accurate predictions emerged when Fourier transforms of the highly apodized planar wavefront incident on the relay optic were calculated.

A new procedure is proposed for image compression as an improvement on vector quantization of subbands. Codewords with vertical and horizontal shape are used to vector-quantize the high-frequency subimages obtained from a multiresolution analysis scheme. The codeword shapes take into account the orientation and resolution of each subband detail to preserve edges at low bit rates. Their sizes are defined according to the correlation distances in each subband for the horizontal and vertical directions.

The characteristics of orientation conjugation in a system of rotating reflecting prisms are studied. A generalized coordinate system is introduced to describe the orientation and rotation of the system of reflecting prisms and images. A method is then presented for quantifying the second-order image rotations relating to multiple rotations of these reflecting prisms. The method is useful for the designer and manufacturer of optical systems to estimate and compensate the errors of image orientations and can be applied to the image stabilization system.

The importance of testing IR imagers and missile seekers with realistic IR scenes warrants a review of the current technologies used in dynamic infrared scene projection. These technologies include resistive arrays, deformable mirror arrays, mirror membrane devices, liquid crystal light valves, laser writers, laser diode arrays, and CRTs. Other methods include frustrated total internal reflection, thermoelectric devices, galvanic cells, Bly cells, and vanadium dioxide. A description of each technology is presented along with a discussion of their relative benefits and disadvantages. The current state of each methodology is also summarized. Finally, the methods are compared and contrasted in terms of their performance parameters.

A new technique is described that can be used to estimate basic parameters such as target size (projected area), surface temperature, and spectral emissivity based on the optical radiation measured by a multiband infrared radiometer. This is of great interest in science and industry where the ability to measure temperature and surface optical characteristics via noncontact methods is vital to the analysis and control of many processes. This new technique is designed to compensate for reflected radiation from other background sources not in the sensor field of view. The technique is based on applying a simple closed form expression for the optical signal measured by the sensor and expanding the unknown emissivity in a series of orthogonal functions. To obtain the parameters of interest nonlinear least-squares estimation techniques are employed. To test the overall procedure data were collected on targets specifically designed to span the range from gray to highly nongray. The optical radiation from these targets was measured in a ground-based space simulation chamber in the presence of known and controlled warm background sources. The targets were instrumented with thermocouples that measured the surface temperature throughout the experiment. Results of the data analysis show that, using a three- or four-band radiometer, it is possible to measure surface temperature to a high degree of accuracy, and that the technique is robust in the presence of noise. Other applications are also explored. These include the simultaneous estimation of the target size (projected area) for point targets at a known distance from the optical sensor, as well as a detailed estimate of the material spectral emissivity using data provided by a spectrometer.

An intracavity HeNe birefringent dual-frequency laser is investigated for applications. The substrate of such a laser cavity mirror is made of quartz crystal instead of ordinary optical glass. The surface that functions as the laser cavity mirror is coated with a high-reflecting thin film layer, while the surface joined to the discharge tube is coated with an antireflecting thin film layer. Thus, the laser is an intracavity laser and the quartz crystal located inside the cavity causes the longitudinal mode to split into two modes (frequencies). To obtain the appropriate design parameters for various frequency differences, a series of quartz crystal cavity mirrors with different cut angles is experimentally investigated. The relationship of mode splitting and the cut angle are observed. To estimate the splitting by one mirror for different cavity lengths, the following concepts are presented: relative mode (frequency) splitting (ration of mode splitting versus longitudinal mode spacing) and relative optical path difference (ration of optical path difference versus half-wavelength).

One method of improving the transverse spatial coherence of x-ray lasers (XRLs) is by adaptive spatial filtering of XRL apertures using geometric shaping in the form of bowtie or wedge XRLs. However, we must maintain the desired geometric shapes in exploding foil or slab configurations during the lasing period. As a first step toward understanding lasing in such geometries, we study the behavior of simple stripe XRLs. Past experience with stripe XRLs deposited on thick plastic substrates resulted in significantly weaker laser intensities as compared to line-focused slab XRLs. Possible reasons for this intensity reduction of stripe XRLs could include mixing at the laser boundary, and changes in plasma, kinetics, and hydrodynamic properties that affect laser gains and propagation. We present experimental and theoretical characterizations of germanium line-focused slab and stripe XRLs. Key experimental parameters we are studying include images of emission profiles of the laser blowoff, angular divergences, XRL output intensities, and ionization balances as we vary XRL designs. We compare the experimental results with 2-D laser deposition and hydrodynamics simulations using LASNEX, and study the changes in ionization balances and level populations from postprocessing LASNEX results.

Fine lines of α-Fe₂O₃ have been formed on quartz substrates by laser beam direct writing on metalorganic spin-coated films. A modulated krypton ion writing laser beam and a He-Ne probing laser beam were colinearly focused onto the films with a spot size about 10 to 50 m in diameter. A series of characterizations have been conducted on the written lines by employing different techniques ranging from thermogravimetric analysis (TGA), Fourier transform infrared (FTIR) spectroscopy, scanning electron spectroscopy (SEM), and x-ray diffraction (XRD) to transmission electron microscopy (TEM). In this way, a better understanding has been achieved regarding the metalorganic decomposition mechanism, structure, and morphology of the laser written lines. From the time-resolved transmittance change induced by the krypton ion laser pulse irradiation, transient behavior of laser decomposition process of metalorganic materials has also been studied.

A method is presented to compute signal characteristics in a dual-beam laser Doppler velocimeter of any configuration and, as a first application, the influence of the optical configuration on signal visibility is also investigated. A simplified model of signal generation is also introduced by which the behavior of signal properties can be physically explained. This model shows that signal visibility is due to a coupling effect between the spatial period of the scattered interference pattern and the angle subtended by the detection aperture. Closed analytical expressions are derived for this period for the scattering components of reflection and refraction without internal reflections. A similar study concerning the evolution of signal phase shift is now in progress.

Laser beam profiling can be accomplished by several techniques, which have different degrees of accuracy. For the description of near-Gaussian beams using the M² parameter, the scanning slit method is a convenient and accurate profiling technique. The profiling of a tightly focused Q-switched laser beam is described. It is possible to correct very simply for the finite slit size, and it is not necessary for the slit width to be much less than the waist radius. This correction can also be applied in the CCD camera measurement technique, in which some correction can be made for the nonzero pixel size.

A particular video spot detector is applied to video records of a sea surface. The detector provides an irradiance time series from an arbitrarily chosen pixel in the video frame. Because the technique picks out only one pixel, it allows for a real-time sampling of a long time series at a high sampling rate (50 Hz) without the need for a large storage capacity. Another advantage is the (statistical) homogenous (space-independent) light conditions within each pixel. The technique is analyzed theoretically by a pure sky light reflection model, i.e., irradiance distributions from beneath the surface are neglected. A remarkably linear correspondence is found between detected irradiance and the horizontal wave slope component parallel with the line-of-sight incidence plane when an overcast sky is assumed (cardioidal radiance model). The pure reflection model requires, however, small look angles with the horizontal that introduce a strong nonlinear geometrical (projection) effect. The great impact that this effect has on, for example, the statistical distribution of the detected irradiance values, is studied assuming a Gaussian ocean wave surface. The theoretical findings are verified by experimental evidence taken from the North Sea. This indicates that the effect of geometric projection is a strong one that should be considered properly by optical analysis of the sea surface.

A particular video spot detector provides an irradiance time series from an arbitrarily chosen pixel in the video frame. The detector is applied to video records of the ocean surface, and the correspondence between the 1 -D irradiance frequency spectrum and the corresponding ocean surface elevation spectrum is studied. A major experimental result is that the frequency peak in the irradiance spectrum for a typical wind-driven sea is significantly enhanced compared to the surface slope spectrum. Video experiments from the oil rig Gullfaks A in the North Sea show an excellent agreement between the enhanced peak frequency in the irradiance spectrum and the peak frequency in the surface elevation spectrum measured by a microwave remote ocean surveillance wave radar. The enhancement of the peak in the irradiance spectrum is explained by a strong nonlinear geometrical projection effect. This is due to the rather small look angle with the horizontal, which is chosen so as to neglect irradiance contributions from beneath the sea surface. Based on a simple stochastic model that takes the geometric effect into account, irradiance spectra are simulated and are in good agreement with the experimental spectra.

A four-aspherical mirror system with unit magnification is investigated for use in deep ultraviolet (DUV) optical lithography. It is derived from the solution of all zero third-order aberrations for the four-spherical mirror system with unit magnification. We have first examined the holosymmetric four-spherical mirror system in which all third-order aberrations are zero and all orders of coma and distortion are also zero. However, the system does not have any optical design freedom left for the correction of higher order aberrations, so a new solution of nonholosymmetric system is derived. In this system aspherizations on the spherical surfaces are carried out to reduce the residual aberrations. The aspherization is optimized to give near diffraction-limited performance for DUV wavelengths of 0.193 μm (ArF excimer laser line). The final system we have obtained consists of all aspherized mirrors with a numerical aperture of 0.35. This reflective system is compact in size and expected to be useful in optical lithographic applications.

This PDF file contains the editorial “Book Rvw: Lasers and Optical Fibers in Medicine," by Abraham Katzir for OE Vol. 33 Issue 07