This PDF file contains the editorial “The Postal Service—An Amazing Record” for OE Vol. 35 Issue 04

An optically efficient interferometric acousto-optic architecture for the tunable generation and control of low-frequency signals is proposed using two radio frequency (rf) or microwave band Bragg cells in an in-line configuration. Critical beam deflection optics, such as a dove prism, ensure that the interfering beams are collinear and stationary, thus providing the high heterodyning efficiency required at the fixed optical detector. Tunable 1- to 15-MHz ultrasonic band signal generation is demonstrated with rf Bragg cells, showing high (107 dB/Hz) carrier-tonoise ratios. This free-space interferometric acousto-optic system with two collinear output beams with a relative color shift is required for making a compact, lightweight, and powerful optical platform for baseband/ low-frequency optical signal processing and control functions, such as required in advanced phased-array systems used in sonar, medical, and industrial applications.

By using the detective quantum efficiency (DQE), which represents the transfer efficiencies of the signal and noise, we expressed the Wiener spectrum of the quantum mottle. Using the new equation of the quantum mottle and the equation of the structure mottle proposed in 1992, we modified our method for separating the screen mottle, and proposed a new method for obtaining the DQE. Using the new method, we experimentally obtained the tube voltage dependence of the DQE, and the density and tube voltage dependence of the Wiener spectra of the quantum mottle. To explain the tube voltage dependence of the DQEs at a spatial frequency of 0 mm-1, we theoretically obtained the tube voltage dependence of the first and second moments of x-ray photon spectra absorbed by the screen. We found that the tube voltage dependence of the DQEs was caused by the fact that the output signal from the screen varied only slightly with tube voltage, while the output noise increased. Using the tube voltage dependence of the DQEs and the number of x-ray photons incident on the screens, we explain the dependence of the Wiener spectral values of the quantum mottle.

This paper reviews the state of the art of some new photoncounting detectors. We measured the performance of various commercial silicon, germanium, and InGaAs/InP single-photon avalanche diodes (SPADs) in the 0.8- to 1.55-µm wavelength range. Optimized silicon devices reach 70% quantum efficiency at 800 nm and can work up to 1.1 µm. However, germanium and InGaAs SPADs are sensitive up to 1.4 and 1.6 mm, respectively, with a few percent quantum efficiency. In all samples we measured noise equivalent powers less than 10-15 W/Hz1/2. Compared with vacuum tubes, SPADs have different advantages such as reliability, roughness, low voltage and simple electronic requirements. Furthermore, it is easy to arrange them in the form of arrays, which are required in astronomy and luminescence measurements. Moreover we investigated the performance of a SPAD germanium quad sensor. By using proper driving electronics we avoided optical cross-talk between pixels and we present here the preliminary results of our experiments.

The Fraunhofer diffraction is compared with a numerical simulation based on the Lorenz-Mie theory to improve the performance of a laser diffraction instrument. This instrument, based on the analysis of diffraction fringes at the focal plane of a lens, is especially suitable for individual wire diameter measurements. We show that the error due to Fraunhofer approximation increases with an increase of the reflectivity and a decrease of the object diameter. Comparison with Lorenz-Mie theory enables us to correct these errors. For a given object, the laser diffraction instrument reproduces diameter measurements with a very small dispersion.

A noninterferometric technique is presented for determining the phase modulating characteristics of spatial light modulators. Examining the far-field diffraction pattern intensity distribution for specific input functions enables the phase modulation to be calculated. Results are compared with usual interferometric techniques for a liquid crystal based modulator.

Recent advances in interferometric fiber optic gyroscope (IFOG) technology have enabled these devices to equal, and in some respects exceed, the performance of the floated, spinning wheel rate integrating gyroscope. However, their ability to perform in a space radiation environment has been a significant concern. Test results are presented addressing the effects of space radiation on the performance of a high precision pointing grade IFOG. Proton induced degradation of the optical components of an IFOG is evaluated based on testing performed at the Harvard Cyclotron Laboratory (HCL). Rationale is provided for using the HCL proton accelerator as a reasonable simulation of the space environment. An analysis is presented that prioritizes the component-level dose tests based on expected radiation sensitivities. The evaluation addresses both total dose (to about 12 krad) and dose rate effects. Testing was performed at the component level as well as the system level with an expanded version of a closed-loop operational IFOG. Primary concerns include permanent attenuation and spectral transmission (wavelength) sensitivity to total dose, and angle random walk and bias stability degradation as a function of dose rate. Component-level results are presented for a superfluorescent light source, an integrated optics chip (IOC), a coupler and polarization maintaining fiber coils. Closed-loop transient noise results are evaluated based on dose rate testing of the IOC, coupler, and fiber coil.

Direct recording of Fresnel holograms on a charge-coupled device and their numerical reconstruction is possible if the maximum spatial frequency of the holographic microstructure is adapted to the spatial resolution of the detector array. The maximum spatial frequency is determined by the angle between the interfering waves. For standard CCDs with spatial resolutions of ~100 lines/mm, the angle between reference and object wave is limited to a few degrees. This limits the size of the objects to be recorded or requires a great distance between object and CCD target. A method is described in which the primary object angle is optically reduced so that objects with larger dimensions can be recorded. The principle is demonstrated for the example of deformation analysis. Two Fresnel holograms, which represent the undeformed and the deformed states of the object, are generated on a CCD target, stored electronically, and the wave fields are reconstructed numerically. The interference phase can be calculated directly from the digital holograms, without generating an interference pattern. As an application of this method, we present the transient deformation field of a plate that is loaded by an impact.

Fabrication of the bidirectional optical backplane bus, employing arrays of multiplexed polymer-based waveguide holograms on a waveguiding plate, is reviewed. An analysis of its functionality is presented for the first time. After an objective function for the system is established, the fan-out intensity fluctuations among all the different channels are minimized by solving a set of nonlinear equations numerically. To further ensure the validity of our calculation, a different objective function is considered and the same optimized result is obtained. Particularly, we optimized the fan-out distribution for the case in which nine boards on one side of the optical bus are presented. It was found that a globally optimized diffraction efficiency distribution exists and the minimum fan-out intensity after optimization is about 1.5% of the incident power, which means a minimum laser diode power for this bidirectional optical bus has to be above 7.0 mW for a system speed of 1.2 Gbit/s and a bit error rate of 10-15. Finally, the surface normal fanout beams come out of both directions of the backplane. Therefore, the best hardware implementation scheme integrates the processor/memory boards on both sides of the backplane bus. As a result, the optimal member of processor/memory boards is 16, i.e., 9 ± (922), rather than 9.

In this discrete cosine transform (DCT) based image coding, the DCT kernel matrix is decomposed into a product of two matrices. The first matrix is called the discrete cosine preprocessing transform (DCPT), whose kernels are ±1 or ±1/2. The second matrix is the postprocessing stage treated as a correction stage that converts the DCPT to the DCT. On applying the DCPT to image coding, image blocks are processed by the DCPT, then a decision is made to determine whether the processed image blocks are inactive or active in the DCPT domain. If the processed image blocks are inactive, then the compactness of the processed image blocks is the same as that of the image blocks processed by the DCT. However, if the processed image blocks are active, a correction process is required; this is achieved by multiplying the processed image block by the postprocessing stage. As a result, this adaptive image coding achieves the same performance as the DCT image coding, and both the overall computation and the round-off error are reduced, because both the DCPT and the postprocessing stage can be implemented by distributed arithmetic or fast computation algorithms.

A novel optodigital pattern recognition method that has shift, rotation, and scale invariant properties is proposed for recognizing 2-D images having straight lines. The proposed method is composed of three stages. In the first stage, the line features of the image are extracted. The second stage imposes shift, rotation, and scale invariant properties on the extracted features through the proposed operations. In the last stage, an artificial feed forward neural network is trained with the extracted features. To evaluate the proposed algorithm, nine different edgeenhanced images are utilized as the experimental patterns. The successful recognition results through the optodigital experiment are presented.

In this paper we present a new thinning algorithm based on distance transformation. Because the choice of a distance measure will influence the result of skeletonization, we introduce an approach to Euclidean distance transformation that achieves a better accuracy than D4 , D8 , or octagonal distance transformation. We have developed a fast method to compute the Euclidean distance transformation. Using this technique, we can extract a reliable skeleton efficiently to represent a binary pattern. Our method works well on real images and compares favorably with other methods.

An amplitude-coupled minimum-average correlation energy algorithm is implemented and tested for a rotation invariance feature. The algorithm is tested on synthetic aperture radar images for probability of correct classification.

Iterative algorithms are currently the most effective approaches to solving a number of difficult signal reconstruction and recovery problems, and all of these algorithms suffer from stagnation and computational complexity. We propose a new multiresolution iterative approach that employs the concept of a multiresolution pyramid. This method attempts to solve the problem of image reconstruction from the measurement of the image’s Fourier modulus by decomposing the problem onto different resolution grids, which enables the iterative algorithm to avoid stagnation by providing a better initial guess and enabling a higher likelihood of arriving at a global minimum while dramatically reducing the computational cost. Results on both synthetic and real-world images are shown; a performance comparison with the direct iterative algorithm demonstrates the effectiveness of our approach in terms of convergence, robustness and computational efficiency.

Adaptive optics systems have been used to compensate for the degrading effects of atmospheric turbulence in images collected with large astronomical telescopes. Postdetection processing techniques are also employed to further improve adaptive optics compensated images. Typically, many short-exposure images are collected, recentered to compensate for tilt, and then averaged to overcome randomness in the images and improve signal-to-noise ratio (SNR). Experience shows that some short-exposure images in a data set are better than others. The frame selection postdetection processing technique uses an image quality metric to discard low-quality frames and improve image spectrum SNR. We address key issues pertaining to frame selection performance limits. Noise trade-offs are used to investigate minimum object brightness for successful application of the frame selection technique. Limits imposed by noise effects result in a minimum object brightness of apparent visual magnitude +8 for point sources and +4 for a +2-m length representative extended object imaged with a 1-m-diam telescope with no central obscuration. Effective average point spread functions for the point source and the representative extended object after frame selection processing under equivalent seeing conditions are almost identical. Thus, deconvolution could be applied to these images obtained via frame selection.

Images of atmospheric airglow emissions are often characterized by known or assumed power spectral density functions that have an asymptotic negative power law slope dependency. Various filter synthesis methods are routinely employed to generate synthetic scenes from random arrays by passing stochastic data through filters that provide a desired correlation structure and power spectral dependency. A 2-D array, or vertical sheet, of nonstationary synthetic structure is produced by means of a nonlinear ‘‘stretched space’’ transformation. Since computations that apply multidimensional transforms to large data arrays consume enormous computer resources and run times, an alternative autoregressive method is employed to reduce the heavy computational burden. Future editions of the Phillips Laboratory Strategic High Altitude Atmospheric Radiance Code (SHARC) will feature an ability to compute structured radiance. The method explored provides a process for rapidly generating large arrays of 2-D nonstationary structure.

The modification of an iterative algorithm of image reconstruction from only the phase of its Fourier transform is described. This task is important for images distorted by the Gaussian transfer function. The results of reconstructing images of the Moon and Saturn are shown.

We describe the functional topography of human brain activity due to motor stimulation by using near-infrared spectroscopy. Finger motion by each hand was used as the motor stimulation, and activity in the left fronto-central region of the brain was measured. A greater change in oxyhemoglobin concentration due to brain activity during the stimulation was obtained for the right hand than for the left hand. Localization of the activity was obtained by topographically mapping the measured changes for ten positions within the region.

A simple method for measuring the outer diameter of an optical fiber is presented. The method is based on observing the interference of light reflected in the fiber–air interfaces of a fiber side illuminated by a laser beam at oblique incidence. This technique is easy to implement and could be used for real-time monitoring of fiber diameter during fiber drawing.

A differentiating interferometer is proposed for measuring time varying signals. The system comprising a modified fiber ring resonator was implemented to measure electrical current. The ring interferometer consists of a length of fiber between one of the input and output ports of a directional coupler. This length of fiber forms a delay line resulting in a constant delay time. The other coupler output port is connected to the sensing element and a reflector. By virtue of the time delay the system detects the derivative of the unknown perturbation signal at the common input/output port of the interferometer. This configuration ensures a zero path length imbalance. Electrical current measurements are achieved by means of a current transformer terminated with a resistive load, which drives a piezoelectric phase modulator. The interferometer can be optically biased by a polarization controller to measure differential phase linearly over the range -?/2 to ?/2 rad. An integration function yields the unknown electrical current. By employing a directional coupler in the system another reflective interferometer arm can be formed for multiplexed operation. The introduction of frequency domain demultiplexing allows interrogation of the sensors in each of these arms. Different phase generated carriers are applied to each arm with two additional piezoelectric phase modulators. Synchronous and quadrature phase detection yield the two current signals. Results of current measurements between 9 A and 300 A on two 50 Hz phases are discussed for the optically biased and phase generated carrier configurations.

An all-fiber Fabry-Perot interferometer using coherence demultiplexing and rugate mirror reflectors grown with electron cyclotron resonance, plasma-enhanced chemical vapor deposition (ECR–PECVD) on the fiber ends is proposed. The interferometer consists of a laser diode source, two optical fiber cavities, three rugate mirrors, an optical phase modulator, and a quadrature phase detection system. Coherence demultiplexing allowed the use of fiber cavities of several meters in length with a partially coherent illuminating light source. Truly inhomogeneous refractive index mirrors were designed, taking into account dispersion and losses of SiOxNy at the required wavelength of 1.3 µm. The reflectance/transmittance ratios during growth were adjustable from 0.05/0.95 to 0.95/0.05 and mirrors used in the experimental interferometer had nominal reflectances of 40, 68, and 40%, respectively. Design and fabrication procedures permitted implementation of window functions and matching layers for flexible control over transmittance and reflectance characteristics. The long-cavity Fabry-Perot sensor was demonstrated for use as a strain gauge. Good agreement was shown with the results obtained by a conventional strain gauge.

We present an analysis of the interference of light scattered from different planes in a simple interferometer, to establish a method that will allow the final output fringe contrast to be enhanced through spatial noise removal. The approach developed involves modifying the spatial coherence of the illuminating wave. By controlling the correlation length of this wave, a time-averaged interferogram along with another for which a ? phase shift has been introduced into the reference arm is shown to provide the information necessary to retrieve the fringe pattern with relatively little noise remaining. The approach suggested allows the controlling parameters to be easily varied optically in order to suppress different spatial noise types and scales. The greatest benefits of this method are in cases where large-scale and slowly varying surfaces or index profiles are to be accurately measured. Simulations are presented and the effectiveness of the proposed coherence degradation procedure is evaluated.

A novel light source using a laser diode is proposed for optical heterodyne interferometry. The light from this source has a twofrequency beam with mutually orthogonal polarization directions. The light source consists of a laser diode and some optical elements. A Mach–Zehnder interferometer using polarizing beam splitters and a right-angle prism creates orthogonal linearly polarized two-frequency light. The laser diode is easily available to give frequency modulation by current injection. A two-frequency beam is created by giving the time difference due to different optical paths in the Mach–Zehnder interferometer. The frequency difference between two beams remains constant regardless of frequency modulation of the laser diode. Moreover, in order to compensate for the power fluctuation by injection current modulation and to keep the total power constant, another incoherent laser diode is added. This light source is suitable for practical applications and requires a smaller and less expensive unit than such conventional light sources as a Zeeman laser or an acousto-optic modulator. This source is applied to a differential interferometer to demonstrate utility for three-dimensional surface profilometry.

Two-wavelength surface contouring systems using either electronic speckle pattern interferometry (ESPI) or an electronic holography procedure by modulating directly the current of a laser diode are reported. Two states of the test object corresponding to each wavelength of the laser can be recorded in both fields of a single video frame. This is achieved by synchronizing the interline-transfer CCD (charge-coupled device) camera in a noninterlaced mode to the current modulation of the diode. Environmental disturbances at low frequencies such as air turbulence, slow object drift and stress in the object have no influence on the measurements. The test object does not need to be on a vibration isolated table. Quantitative experimental results are presented.

A technique for measuring in-plane displacement under impact loading using digital speckle pattern interferometry (DSPI) is presented. To capture the speckle field produced by a ruby laser, an instantaneous digital image capturing system is proposed. Thus the dynamic speckle images can be recorded and stored in a digital frame store and the quality of speckle fringe patterns is improved using digital subtraction. As an example, the displacement field of a semi-infinite model under impact loading is measured. The results show agreement with those of the finite element method.

The amplification characteristics of a dye laser amplifier with a gain length of 20 mm pumped by a high-average-power copper vapor laser system are studied. The characteristics of the dye laser amplifier are analyzed by rate equations in which excited-state absorption (ESA) and amplified spontaneous emission (ASE) are taken into consideration. In the experiment, the energy extraction efficiency of about 48% is obtained for the amplifier. The calculation shows that the main factors of the energy loss in the amplifier are ASE and ESA and the former is dominant at the low-input-power region and the latter at the high-input-power region. The output power decreases around 10% by the ESA near the peak wavelength of rhodamine 6G dye.

The authors design and demonstrate a high-reflector broadband Bragg mirror for a fiber laser system. A T-matrix formalism was used to design a broadband intracore mirror consisting of a series of Bragg gratings. Ultraviolet light from a KrF excimer laser was used in an interferometric setup to inscribe these Bragg gratings in a photosensitive fiber. This resulted in a broadband Bragg mirror covering a wavelength range of approximately 3.5 nm. An all-Bragg grating, erbium-doped fiber laser cavity is demonstrated using this Bragg mirror as the high reflector and a single narrowband Bragg grating centered at 1550 nm as the output coupler. Tunability of the fiber laser was achieved over the range of the high reflector using strain-induced changes on the output coupler.

Frequency tuning based on pressure control is demonstrated on an etalon-narrowed Littrow-type single-mode dye laser oscillator pumped by a copper vapor laser. The oscillator is installed in a pressure vessel and the frequency is scanned by controlling the refractive index of the air inside the vessel. To scan the dye laser frequency continuously without mode hopping, the cavity length is also controlled in addition to the pressure change. The frequency stability of the oscillator in a pressure vessel is within 100 MHz/1.5 hr and the oscillator can be scanned with a frequency range of 29 GHz at a scan rate of around 2.5 GHz/min.

A probability theory of laser safety at sea is presented. A method is developed to calculate the probability that the human eye in the neighborhood of a laser operation at sea will be damaged by the laser beam. It takes into account the laser power, pulse rate, the sea state, specular reflectance, foam reflectance, angle of incidence, position of the eye with respect to the laser spot on the sea, the typical stare time of the eye, the maximum permissible exposure to a given type of laser beam, etc. The known sea reflectance formulas are used to develop the theory with the help of the Poisson distribution. Contour maps showing the probability of eye damage near a laser spot on the sea under typical conditions are presented.

The development of a differential absorption lidar (DIAL) system in the mid-IR region for the detection and monitoring of light hydrocarbons is presented. Two lithium niobate optical parametric oscillators provided the signal and reference wavelengths. With the aid of a retroreflector, the system detected 0.63 ppm of propane and 0.05 ppm of methane in the atmosphere at a greater than 1 mile range in the controlled release tests. Subsequently, the system mapped a petroleum deposit in eastern New Mexico.

The Maxwell Garnett approach has been used to estimate the effective properties of a nonlinear, bianisotropic particulate composite. This composite is formed by randomly dispersing electrically small, linear bianisotropic inclusions in a nonlinear, homogeneous, isotropic dielectric-magnetic medium. The dielectric susceptibility of the host medium is assumed to depend on the electric field. Various types of nonlinear bianisotropic composites can thus be tailored by materials scientists for optical purposes.

We demonstrate the use of optical gating techniques for determining the size and location of defects in advanced ceramic materials. The subsurface region in a bearing-grade silicon nitride ceramic material is probed using an optical gate based on broadband Raman scattering. Experimental results indicate that the size and distribution of small subsurface defects can be determined.

A new technique for measuring ophthalmologic surfaces such as aspheric contact lenses and the human cornea is proposed in this paper. The method is based on the principle of moire´ deflectometry. In moire´ deflectometry, two fringe patterns (deflectograms) are generated, each providing a piece of information about the measured wavefront. Compared with interferometric techniques, interpretation of the fringe patterns obtained is more difficult. Therefore synthetic deflectograms for surfaces with known parameters are generated. Computer simulation of deflectograms in the case of aberrations introduced by an aspherical object is also performed. Experimental results for various curved surfaces, including contact lenses and the human cornea, are demonstrated.

Based on the two-step modified signed-digit (MSD) algorithm, we present a one-step algorithm for the parallel addition and subtraction of two MSD numbers. This algorithm is reached by classifying the three neighboring digit pairs into 10 groups and then making a decision on the groups. It has only a look-up truth table, and can be further formulated by eight computation rules. A joint spatial encoding technique is developed to represent both the input data and the computation rules. Furthermore, an optical correlation architecture is suggested to implement the MSD adder in parallel. An experimental demonstration is also given.

A simple parallel optical computing technique using recoded quaternary signed-digit arithmetic is presented in this paper. An efficient shared content-addressable memory-based optical implementation that employs a fixed number of minterms for any operand length is developed. This technique requires the minimum number of minterms compared with similar previously reported techniques.

Optical designs for the Rosetta narrow-angle camera (NAC) and its UV spectrograph are presented. The NAC requires a 600 mm focal length system of focal ratio f/7 imaging a square field of width 2.3 deg onto a square detector array 2048 pixels wide. A cartographic method has been used to search for flat-field, three-mirror anastigmats (TMA) with the required geometrical constraints and at least one spherical surface; the use of spherical surfaces reduces fabrication cost and complexity and facilitates alignment. Two such systems are described, one with a spherical secondary, the other with a spherical tertiary. A deterministic alignment method is outlined where alignment defects are calculated from measurements of image position and Zernike wavefront coefficients. For the spectrograph, an all-reflecting, Thevenin-type concentric spectrograph has been designed. This design offers excellent image quality both spectrally and spatially along a long slit and it is compact and easily accommodated.

A modest aspheric deformation of a hemisphere refines a two-reflection whispering gallery to aplanatic image conditions.

Collimation of a laser beam is tested by exploiting its temporal coherence. This technique does not require additional optics.

An instrument is designed to measure the intensity distribution of light scattered from optical surfaces. It uses two photodiodes, one to collect specularly reflected light and the other to record scattered light. This configuration enables us to measure both the reflected and scattered light intensities within a dynamic range over seven decades without introducing neutral density filters. The signal-to-noise ratio of the instrument is also improved in comparison with the single photodetector configuration. The instrument is capable of measuring scattering as close as 0.05 deg to the specularly reflected beam.

Several coronagraphs with mirror objectives are planned or have been constructed for terrestrial and space-based observatories. To justify the nontraditional choice of an internally occulted, reflective design for the inner coronal channel of the large-angle spectrometric coronagraph (LASCO) instrument constructed for the Solar Heliospheric Observatory satellite, we measured the near-specular (0.09 to 1.25 deg) scatter of two superpolished, spherical coronagraph mirrors with a unique geometry scatterometer. The visible stray light emanating from defectfree portions of the best mirror was measured to be 3.5 X 10-7B/B? (coronal brightness relative to the mean solar brightness) at 2R? (heliocentric distance in solar radii) and 2 X 10-7B/B? at 3R? . These levels are well below typical sky brightnesses of ~10-5 B/B? present at mountaintop observatories with clear skies. This stray light level would allow spectroscopic differencing observations of visible coronal emission lines (~4 X 10-8 B/B? at 2R? for coronal green line features) well into the inner corona from a space-based platform. An aspheric mirror with better performance than this stray light has been installed in the LASCO flight instrument. We describe the scatterometer apparatus, detail the experimental results, and present a comparison between predicted coronagraph stray light levels and nominal coronal signal levels.

In this paper we study the relationship between the intensity speckle correlation of light scattered by ground glass and the diffraction index variation of liquids in which the diffusers are immersed. The results allow us to develop a simple method for measuring surface roughness.

First, the theory of diffraction field speckle displacement is extended to include speckle patterns arising from a cylindrical object subject to general deformation. Second, the usefulness of the derived relations are demonstrated by measuring the axial strain component on a Teflon cylinder and torque (shear strain) on a twisted steel cylinder. We performed real-time measurement of these quantities using the setup adopted for the laser speckle strain gauge. With this equipment, we obtained resolutions of 37.5 µ strain in the axial strain measurement and of 1.8 N m in the torque measurement. Both experiments agreed within 4% with simultaneous results obtained from an electrical strain gauge and with the known applied torque.

We present an analysis using conventional heat-transfer theory of a common type of synchrotron-radiation-beam-line mirror with rectangular cooling channels. The analysis leads to a simple analytic expression for the slope error, which enables the distortion performance to be estimated in practical situations. It also provides an understanding of the effect of the various parameters on the goodness of the cooling process and an insight into the underlying physics. The analysis is applied to determining the design steps needed to achieve low slope errors and/or high-heat-removal rates with this type of mirror. The slope-error performance of various materials in a specific design are compared and the best performance is obtained from (in order) invar, silicon, and silicon carbide.

Two-dimensional discrete wavelet transforms (DWTs) have become a very powerful tool in computer vision. When implementing DWT in hardware, finite precision arithmetic introduces quantization errors. The hardware designer must look for the optimum register length which, while ensuring the minimum accuracy criteria, would also lead to a high-speed implementation with a small chip area. We obtain expressions to characterize the mean and the variance of the quantization errors produced in the calculation of DWT components. The theoretical results have been compared with the experimental ones obtained from algorithm simulation on the Lena test image. Since the maxima representation proposed by Mallat and Zhong is defined from both the amplitude and position of the discrete maxima, the effects of quantization in the maxima amplitude and maxima position are analyzed. Besides the quantization error, another potential source of error is the hardware implementation of the arithmetic operations that appears in the algorithm. We have analyzed the effect of replacing the square root using one of the Filip’s approximations.

The collapsing process of the shaped charge is studied by 300 kV pulsed x-ray photographs and pictures of the involved case swelling process and the wave shaper are acquired. Image processing technology is developed to analyze the experimental pictures, to study the collapsing process of the shaped charge, and to judge the boundary of the shaped charge. The boundary curve equations are derived.

There are many researchers who propose calculating a signal centroid using the pixels nearest to the signal peak. Thus, for a two-dimensional rectangular grid they use only nine pixels centered around the signal peak,1–3 and for a one-dimensional signal they use only three pixels.4 This truncation simplifies and speeds up the centroid calculation without affecting the centroid accuracy if the signal is limited to this small local region. In addition, when the signal is corrupted by noise, there is an optimum window size that balances the effects of systematic error and the error due to the random noise.

This PDF file contains the editorial “The Ray and Wave Theory of Lenses” for OE Vol. 35 Issue 04