This PDF file contains the editorial “Editorial” for OE Vol. 40 Issue 07

We propose a new design for introducing a tunable chirp on a uniform fiber Bragg grating by a controllable temperature gradient. The device consists of an unchirped Bragg grating in a bare fiber that is mounted in a plastic sleeve whose surface is coiled with a length of wire heater. The desired temperature distribution produces a chirp on the grating and at a rate that can be adjusted by varying the current. We demonstrate an electrically tunable chirped fiber Bragg grating that enables a tuning range of an average chirp rate up to 0.93 nm/cm with an electrical power of 3.3 W. We also demonstrate a tunable chirped fiber Bragg grating in which dispersion is adjustable from -1632 to -667 ps/nm with an electrical power of less than 0.5 W.

We demonstrate a hybrid dense-wavelength- division-multiplexing (DWDM) system for CATV and 256- QAM transport, using a four-wavelength system as an example. Excellent performances of carrier-to-noise ratio (CNR) >50 dB, composite second order (CSO) >70 dB, and composite triple beat (CTB) >65 dB are obtained for the full channel band. Low bit error rate (BER) < 10-9 is achieved for the eight 256-QAM digital channels after a 100-km large effective area fiber (LEAF) transport.

Experimental results on multimode interference (MMI) coupler performance, when the access waveguides are not single mode, are shown. The 3-dB MMI couplers based on restricted interference are fabricated in InP/ InGaAsP buried waveguides. Unbalanced measurements for different excitation conditions are shown. A drastically unbalanced decline of 30% is reported for an alignment deviation of 6 ?m. Less critical effects are measured when misalignment is controlled below 2 ?m. A beam propagation method and modal analysis are used to validate experimental results.

Optics has been behind various enabling technologies to cope with the ever-increasing bandwidth demands at internet backbone level. Dense-wavelength-division-multiplexing (DWDM) allows concurrent transmissions of many channels of wide bandwidth data through a single fiber. The success of erbium-doped fiber amplifiers (EDFA) pushes the data regeneration distance longer and longer. The emerging massively parallel optical switches are revolutionizing all-optical communication networks. We are witnessing an era of renaissance of optics due to the communication infrastructure upgrade frenzy. High speed optics, once so prohibitively expensive that only long-haul communications was feasible, is being applied to ever-shorter distances, penetrating from metro-area to access and intra-computer interconnect networks. Bulk free-space optics is being miniaturized and integrated to serve critical missions to keep the pace of bandwidth booms. At the same time, the pace of developing wider bandwidth and more cost-effective solutions to sustain the explosive growth of bandwidth presents huge challenges and opportunities for optical scientists and engineers.

We review and contrast key technologies developed to address the optical components market for telecom and datacom applications. We first look at different material systems, compare their properties, and describe the functions achieved to date in each of them. The material systems reviewed include glass fiber, silica on silicon, silicon on insulator, silicon oxynitride, sol-gels, polymers, thin film dielectrics, lithium niobate, indium phosphide, gallium arsenide, magneto-optic materials, and birefringent crystals. We then look at the most commonly used classes of technology and present their pros and cons as well as the functions achieved to date in each. The technologies reviewed include passive, actuation, and active technologies. The passive technologies described include fused fibers, dispersion-compensating fiber, beam steering (e.g., AWG), Bragg gratings, diffraction gratings, holographic elements, thin film filters, photonic crystals, microrings, and birefringent elements. The actuation technologies include thermo-optics, electro-optics, acousto-optics, magneto-optics, liquid crystals, total internal reflection technologies (e.g., bubble technology), and mechanical actuation (e.g., moving fibers and MEMS). We finally describe active technologies including heterostructures, quantum wells, rare earth doping, and semiconductor optical amplifiers. We also investigate the use of different material systems and technologies to achieve building block functions including lasers, amplifiers, detectors, modulators, polarization controllers, couplers, filters, switches, attenuators, nonreciprocal elements (Faraday rotators or nonreciprocal phase shifters) for isolators and circulators, wavelength converters, and dispersion compensators.

An overview is given of recent experiments employing 850 or 980 nm emission wavelength vertical-cavity surface-emitting laser diodes (VCSELs) for high-throughput very short reach optical data transmission. For future high-speed building backbones, we demonstrate the first transport of 40 Gbit/s data rates over 300 m of a new generation multimode fiber by means of a four-channel coarse wavelength-division multiplexing system. As an attractive route to overcoming high-speed electrical signaling problems on printed circuit boards, we show 10 Gbit/s per channel data transmission for densely spaced integrated polymer waveguides. Error-free VCSEL operation at 2.5 Gbit/s with a temperature range from -20 to +100°C indicates compatibility with most industrial requirements. Finally, we demonstrate 850-nm bottom-emitting VCSEL arrays for direct flip-chip bonding, which might prove useful for twodimensional future silicon chip-to-chip interconnect solutions.

A vertical cavity multiple quantum well (MQW) modulator, which offers high contrast ratio, low insertion loss, low power consumption, low jitter and chirp, and easy two-dimensional integration with silicon electronics, is one of the essential components for dense optical interconnects. The devices we have investigated consist of quantum wells in a Fabry-Perot cavity configured as p-i-n diode. The absorptive characteristics of the MQW region can be modified through field-induced absorption change known as quantum-confined Stark effect (QCSE), which translate to the modulation in the device reflectivity. Modulators can also perform the dual function of a high-efficiency photodetector at the receiver end by using a different electronic control circuit. This has the advantage of doubling the optical I/O of a photonic layer and reducing power losses. In this paper, the high-speed performance of modulators and photodetectors will be presented. We use 26 pairs of 75-Å GaAs/AlGaAs quantum wells. The modulators have a high contrast ratio of 11 dB, small driving voltage of 3.5 V, and f3dB bandwidth greater than 18 GHz. If the device is used as a high-speed photodetector, it has a quantum efficiency of 95% and f3dB bandwidth greater than 10 GHz. Results of devices of different sizes, with different bias voltages and termination resistors, are presented.

We report one top-illumination and one bottom-illumination SiGe/Si multiple quantum-well (MQW) resonant-cavity-enhanced (RCE) photodetector fabricated on a separation-by-implanted-oxygen (SIMOX) wafer operating near 1300 nm. The buried oxygen layer in SIMOX is used as a mirror to form a vertical cavity with the silicon dioxide/silicon Bragg reflector deposited on the top surface. A peak responsivity with a reverse bias of 5 V is measured 10.2 mA/W at 1285 nm, a full width at half maximum of 25 nm for the top-illumination RCE photodetector, 19 mA/W at 1305 nm, and a full width at half maximum of 14 nm for the bottom-illumination one. The external quantum efficiency of the bottom- illumination RCE photodetector is up to 2.9% at 1305 nm, with a reverse bias of 25 V. The responsivity of the bottom-illumination RCE photodetector is improved by two-fold compared with that of the top-illumination one.

Power conversion efficiency of various erbium-doped fibers is characterized at a wavelength of 1585 nm and at a pump wavelength of 1480 nm by using a two stage amplifier and a C-band amplified spontaneous emission filter. There is good agreement between experiment and simulation. Trade-off exists between erbium doping concentration and pair-induced quenching. High Al doping and optimization of numerical apertures can help improve the efficiency, and the erbium doping region has a significant impact on the performance of low cutoff erbium-doped fibers.

A narrowband optical amplifier ("amplet") is proposed and demonstrated that can be constructed into an amplifier-based subsystem to perform dispersion compensation and dynamic power management in a wide DWDM bandwidth. The amplet is designed to inherently provide two important networking features: narrowband accessibility and bandwidth scalability. The narrowband accessibility allows for the realization of inline dispersion compensation and dynamic gain management; and the bandwidth scalability provides an economic solution to meet capacity demand. As a demonstration, a modular bandwidth management subsystem is developed using this amplet technology to simultaneously provide dispersion compensation, dynamic power management, and amplification. The experimental results show that wide band dynamic gain control is achieved using this new bandwidth management architecture. We demonstrate system power penalties less than 1 dB using this subsystem in a long-haul system testbed with accumulated dispersion varying from -600 to -1600ps/nm.

We first review the working principle of grating-based wavelength division (de)multiplexers [WD(D)M] for optical networks. We also address issues regarding optical design of grating-based WD(D)Ms for commercial uses. Next, several grating-based WD(D)M structures are analyzed. Based on these designs and analyses, we develop several versions of highly reliable WD(D)Ms, from coarse to dense, with low insertion loss and low cost. Last, we present the experimental data for these WD(D)Ms.

We introduce a new integrated solid optics component, an X-cube, which can perform various lossless beamsplitting and filtering functions among four input beams. The X-cube can also be used for various coarse wavelength-division multiplexing-based communication and interconnection applications, such as star coupling, wavelength routing, and add/drop multiplexing. our demonstrated fiber-interfaced X-cube optomechanical packaging shows an insertion loss of 2.1 dB, a uniformity ratio of 1.036, with a uniformity variance of 0.279.

Beam steering devices without moving parts are highly desirable for their potential application in emerging optical technologies such as holographic optical storage systems, all optical networks, and optical switches. We demonstrate a thin-film waveguide beam deflector device that consists of an electro-optic prism array within a polymer waveguide. An electrode structure defines the prism array within the planar waveguide. The deflection efficiency of 28 mrad/kV and the maximum deflection angle of ±8.4 mrad at ±300 V are obtained for this demonstration device. Further optimization of electrode-field poling and processing is likely to improve these results by at least an order of magnitude.

A theory of electrically controllable long-period gratings built in a liquid-crystal fiber has been presented by means of an anisotropic waveguide analysis and the coupled-mode theory with the discretization method. Effective propagation and coupling constants have been found for a circular cross-sectional fiber with a nematic liquid-crystal core, the optic axis of which is in the direction of the fiber axis. The results show that when uniaxial perturbations of the liquid-crystal director exist in the core, the mode couplings can occur between modes with different azimuth variations as well as between modes with the same. Among them, the cross couplings between the fundamental core mode HEco11 and the transverse-magnetic cladding modes TMclmare most strong compared even to the self-coupling of the fundamental core mode, and thus the spectral shift with the growth of the director modulation becomes negligible. Using the derived theoretical results, we discuss numerical examples of long-period liquid-crystal fiber gratings with respect to the modulation depth of the director and the polarization states of the fundamental core mode.

We report the concept for a device to simplify the receiver in fiber-optic radio frequency (RF) transmission systems. We present a photonic RF mixer based on metal-semiconductor-metal (MSM) photodetectors, by a brief theoretical analysis of the principle and performance of the device. The experimental result shows good agreement with the calculation. Our experiment demonstrated mixer conversion efficiency of -12 dB, and we conclude that -10 dB is achievable in optimum operational conditions.

The design of some communication systems requires the implementation of time delays within the system. These time delays can be accomplished with a variety of optics technologies, which could be readily fabricated and integrated into the communication system without significant impacts on the system design. We describe three different potential applications of optics designs, which could be implemented to accomplish the time delay requirements associated with communication systems. One application would be in Ku/Ka band phased array antennas, where the optics application provides the time delay to the various transmit/receive units in the phased array to accomplish beam forming and switching. Another application would be in an aircraft interference cancellation system. Yet another application would be in a satellite communication test system, where the propagation time to the satellite (for synchronous satellites a nominal 36,000 km) needs to be simulated for ground testing with the earth terminals. Optical modules could be used for some applications, and optics technologies have the potential to be used for a wide range of applications in communication systems.

A simple nondestructive method of measuring groove depth in lamellar gratings is presented. The method is based on processing scatterometry data for a wavelength much smaller than the grating pitch using formulas derived by means of scalar diffraction theory. The method has structural and optical limitations that are specified. The intensities of the 0th and ±1st orders reflected from silicon grating samples irradiated by a He-Ne laser, as functions of the incident angle, are measured and processed to determine the groove depths. The diffraction efficiencies calculated using the thus determined groove depths by means of rigorous diffraction theory agree with the experimental data. For the examples studied in this paper the uncertainty in the determined groove depths is as small as 10 nm.

Selective laser-tissue interaction is a promising method for noninvasive treatment of deep tumors. Using a laser beam with a wavelength in the near-infrared region and an intratumoral injection of a laserabsorbing dye, the laser energy can destroy targeted tumor cells while sparing normal surrounding tissue. Introducing an immunoadjuvant can achieve possible systemic antitumor immune response, hence augmenting the selective laser-tissue interaction. Administration of the dye and the immunoadjuvant, and the time window for optimal laser application, are crucial in determining the outcome of the treatment. To determine the dynamic distribution of intratumor-injected laser-absorbing dye and immunoadjuvant, a digital x-ray imaging technique was employed. Indocyanine green as the laser-absorbing dye and glycated chitosan as the immunoadjuvant were injected into the center of a rat tumor, and the transmitted x-ray signals through tumor tissue and surrounding normal tissue, before and after the injection, were acquired and analyzed. The transmitted signals through tissue were reduced due to the injection of either dye or immunoadjuvant solution. The diffusion of aqueous solutions in tissue was a function of time and of the properties of the solutes. The indocyanine green solution, due to its low molecular weight, diffused through the tumor almost immediately after injection, then gradually dispersed into the surrounding tissue. The glycated chitosan, on the other hand, due to its high molecular weight and high viscosity, dispersed slowly and took about 20 to 25 min to reach maximum accumulation at the edge of the tumor. Our results showed that the digital x-ray images could be used to guide the precise positioning of the injecting needle, and to determine the distributions of the dye and immunoadjuvant in the tumor and in the surrounding normal tissue. Apparently, the dynamic observation of dye and immunoadjuvant administration and their diffusion process could be used to optimize the parameters for laser treatment of deep tumors.

We report a high-density wavelength division demultiplexer (Demux) capable of demultiplexing a 32-channel 100-GHz-spaced wavelength, with a working wavelength range of operation from 1541.37 to 1565.47 nm. The design, packaging, and performance of the Demux using the 22nd diffraction order of an echelle grating is described. The typical insertion loss of the device is -3.0±0.2 dB, the cross talk between adjacent channels for all 32 channels is about -30 dB, and the average 1-dB optical passband is 0.256 nm. We found the experimental measurement result of the 1-dB passband to be in good agreement with the theoretical 1-dB passband as calculated. The device has singlemode fiber in and multimode fiber out, and thus can bridge the telecommunication backbone and local area networks.

We describe a simple, fast, and accurate technique for the angular alignment of a polarization-maintaining monomode optical fiber. The method uses simple mechanical supports and is based on the detection of the ellipticity of the light polarization at the fiber output, with the help of a simple rotating polarizer, a photodetector, and an oscilloscope.

We describe a simple, fast, and accurate technique for the angular alignment of a polarization-maintaining monomode optical fiber. The method uses simple mechanical supports and is based on the detection of the ellipticity of the light polarization at the fiber output, with the help of a simple rotating polarizer, a photodetector, and an oscilloscope.

Sandwich holography is proposed for simultaneous temperature mapping and heat transfer coefficient measurement. The latter task requires the knowledge of the temperature gradient. The remarkable feature of the proposed method is that the temperature gradient is obtained avoiding numerical differentiation, which adds errors to the measured data, as well as phase extraction and phase unwrapping procedures. Theory and experimental results are given.

Several standard series of photographs (Zweigle KG-741, ASTM D3512, EMPA, and JIS L 1076) widely used for pilling evaluation in fabric testing laboratories are analyzed. Common information is extracted from two standard series, the Zweigle and the American Society for Testing and Materials (ASTM) standards, by applying an objective and automatic method of image analysis previously developed for pilling evaluation. The information obtained reveals that both standards approach the same underlying logarithmic function between the total area of pilling and the degree of pilling. Another important feature, the density of pilling, is also extracted and discussed.

We describe a new class of computationally efficient algorithms designed to solve incomplete-data problems frequently encountered in image processing and computer vision. The basis of this framework is the marriage of the expectation-maximization (EM) procedure with two powerful methodologies. In particular, we have incorporated optimal multiscale estimators into the EM procedure to compute estimates and error statistics efficiently. In addition, mean-field theory (MFT) from statistical mechanics is incorporated into the EM procedure to help solve the computational problems that arise from our use of Markov random-field (MRF) modeling of the hidden data in the EM formulation. We have applied this algorithmic framework and shown that it is effective in solving a wide variety of image-processing and computer-vision problems. We demonstrate the application of our algorithmic framework to solve the problem of simultaneous anomaly detection, segmentation, and object profile estimation for noisy and speckled laser radar range images.

The use of the Karhunen-Loève transform (KLT) for region- based segmentation of aerial images by color and textural attributes is presented. Our aerial images are shown to be homogeneous color images within the Karhunen-Loève color representation space, which means they can be represented more easily and the region-based segmentation algorithms can be optimized. For texture analysis, the KLT is the basis of the local linear transform (LLT) and allows structural information about textures to be represented in an optimal and condensed manner. The LLT provides a system of textural analysis in the form of an adapted filter bank. We end the paper by presenting a method for merging texture and color segmentations.

A new destriping technique based on wavelet analysis and its application to satellite imagery is presented. The method was tested on a heavily striped Landsat MSS image using Daubechies wavelets of different orders. Qualitative and quantitative analyses were carried out to evaluate the performance for each wavelet, both by visual inspection and by measuring the signal-to-noise ratio of the denoised images. The outcome demonstrates the viability of the wavelet transform as a destriping tool by significantly reducing striping noise. Furthermore, the method proved to defeat some of the problems commonly found with traditional destriping techniques, such as the Gibbs phenomenon, border effects, edge blurring, and the preservation of radiometric level. In addition to its relatively easy implementation, the method is inexpensive in computer time and storage space, as well as suitable for application to problems other than the field of remote sensing.

The modification of thin Teflon AF® films by He+ ion irradiation was investigated. As an integrated optical measurement technique, leaky-mode spectroscopy has been applied, and an increase of ?n = 8 x 10-3 for the real part of the refractive index has been found in the irradiated surface region of the film. The irradiated films can be regarded as a bilayer system consisting of a layer with low refractive index and a layer with high refractive index. The latter can be used as an optical waveguide with a substrate of unmodified Teflon AF. In addition, a decrease of the initial film thickness, an increase in UV absorption, and no significant increase in absorption of near-infrared light were found.

A multiplexed laser interferometer is presented that allows for the simultaneous detection of acoustic waves from a number of points on the surface of a specimen. Phase gratings are used to create an array of laser beams that are directed to the specimen. The beams are collected using a lens system, combined with a single reference beam in a photorefractive crystal, and imaged on separate photodetector elements. Detection of surface acoustic waves scattered from a defect in an aluminum specimen is demonstrated using a nine-element receiver. Focusing of the array interferometer, by applying appropriate phase shifts between the detected signals, is also shown. The wide bandwidth and noncontact nature of this receiver make it well suited for phased array detection and ultrasonic imaging applications.

The phase at different pixels along the direction of dispersion, also known as the chromaticity axis, is determined in spectrally resolved white light interferometry (SRWLI). Phase shifting interferometry has been used for this purpose. Previously, the phase shifted intensity values required for phase calculation were obtained from phase shifts due to wavelength variation (spatial phase shifting). This required the intensity values from different pixels be used in the calculations, resulting in errors due to variation in pixel sensitivity. We propose to use multiple intensity values, required for phase calculation obtained from the same pixel, and investigate the use of a polarization phase shifter and the conventional PZT phase shifter for this purpose. The polarization phase shifter aims at introducing nearly the same phase shift (achromatic phase shift) at all the pixels receiving light of different wavelengths. In the PZT phase shifter, the phase shift varies considerably at different pixels, but analysis shows that good measurements can still be made with it.

An autofocusing system used for a laser burst-cutting-area (BCA) marking system for a DlVX production line has been developed. The principle of focus error detection is based on a method that takes advantage of the focusing properties of simple optical elements. A differential detection method is used to achieve high resolution, and a position servo is designed to accomplish the autofocusing. Some design considerations, system modeling, simulation, and experiments are described. Experimental results are presented to show the feasibility of this system.

We report the use of an open photoacoustic cell configuration for the evaluation of thermal effusivity of liquid crystals. Initially, the method is calibrated using water and glycerol as transparent liquid samples, and the role of thermal conductivity of these liquids on the photoacoustic signal amplitude is discussed. To demonstrate the application of the present method for the evaluation of thermal effusivity of liquid crystals, we have used certain multicomponent nematic liquid crystal mixtures, namely BL001, BL002, BL032, and BL035. Each of these liquid crystal mixtures contains four to nine components and are primarily based on the cyanobiphenyl structure. The measured values of thermal effusivity of BL001 and BL002 were found to be almost the same, but differ from those of BL032 and BL035, which implies a difference in composition of the latter two from the former two mixtures.

We describe progress in the development of a multiple quantum well modulating retroreflector, including a description of recent demonstrations of an infrared data link between a small rotary-wing unmanned airborne vehicle and a ground-based laser interrogator using the device designed and fabricated at the Naval Research Laboratory (NRL). Modulating retroreflector systems couple an optical retroreflector, such as a corner cube, and an electro-optic shutter to allow two-way optical communications using a laser, telescope, and pointer-tracker on only one platform. The NRL modulating retroreflector uses a semiconductor-based multiple quantum well shutter capable of modulation rates greater than 10 Mbps, depending on link characteristics. The technology enables the use of near-infrared frequencies, which is well known to provide covert communications immune to frequency allocation problems. This specific device has the added advantage of being compact, lightweight, covert, and requires very low paper. Up to an order of magnitude in onboard power can be saved using a small array of these devices instead of the radio frequency equivalent. In the described demonstration, a Mbps optical link to an unmanned aerial vehicle in flight at a range of 100 to 200 feet is shown. Near real-time compressed video was also demonstrated at the Mbps level and is described.

We have developed a simulation model to investigate the demultiplexing of all-optical-time-division-multiplexed data, employing an optical time-division demultiplexer. Particular attention is paid to the cross-talk performance when selected parameters of the system are varied. The system used to demultiplex the data is the asymmetric semiconductor laser amplifier loop mirror (ASLALOM), which is capable of selecting high-speed optical pulses within a data train. The authors use a model of the ASLALOM that includes a time and space analysis of a traveling-wave semiconductor laser amplifier. Our investigation shows that this system produces cross talk that is dependent on the data rate, control pulse energy, and control pulse rate.

We present a probabilistic method for fusion of images produced by multiple sensors. The approach is based on an image formation model in which the sensor images are noisy, locally linear functions of an underlying true scene (latent variable). A Bayesian framework then provides for maximum-likelihood or maximum a posteriori estimates of the true scene from the sensor images. Least-squares estimates of the parameters of the image formation model involve (local) second-order image statistics, and are related to local principal-component analysis. We demonstrate the efficacy of the method on images from visible-band and infrared sensors.

Linear integer unconcerned phase-map fringe projection pro- filometry has been used to measure the 3-D shape of objects with discontinuous height steps. The projection is carried out with the conventional crossed-optical-axes geometry. Linear integer unconcerned phase maps are obtained by changing the projecting angle of the grating. A lookup-table algorithm is applied to phase unwrapping. An automated analysis of the fringe patterns is carried out by the Fourier transform method. Experimental results are presented that demonstrate the validity of the principle.

A frequency-sweeping technique is proposed to measure the shape of objects with discontinuous height steps and/or spatially separated surfaces, which have been impossible to measure with conventional shadow moirè topography. By controlling the rotation angle of the grating, spatiotemporal moirè patterns are produced with different contour intervals. The Fourier-transform technique has been applied to analyze these patterns and obtain the temporal carrier frequency, to which the height distribution of the object is related. Experimental results show the validity of this method.

International standards such as ITU-T H.263 (H.261) and ISO MPEG use a hybrid coding scheme based on the discrete cosine transform (DCT). Although the DCT is an established technique for encoding interframe differences, it is not an optimal transform for low-correlation interframe differences, since its energy compaction performance largely depends on the correlation of the data. In this paper an effective technique for encoding interframe difference is proposed and verified on an MPEG2 software encoder. The technique decomposes the interframe difference into two sources in order to exploit their improved statistical properties. The two-source interframe difference is encoded with a combined transform, which consists of the DCT and the Hadamard transform (HT). Two-source decomposition increases the correlation of the decomposed prediction error, and the DCT-HT scheme is shown to efficiently encode the decomposed interframe difference with increased performance. Analytic and experimental comparison shows that the proposed DCT-HT scheme gives significant objective and subjective gains over the conventional DCT-based video encoding method.

The authors propose an image authentication scheme, which is able to detect malicious tampering while tolerating some incidental distortions. By modeling the magnitude changes caused by incidental distortion and malicious tampering as Gaussian distributions with small and large variances, respectively, they propose to embed a watermark by using a mean-quantization technique in the wavelet domain. The proposed scheme is superior to the conventional quantization-based approaches in credibility of authentication. Statistical analysis is conducted to show that the probabilities of watermark errors caused by malicious tampering and incidental distortion will be, respectively, maximized and minimized when the new scheme is applied. Experimental results demonstrate that the credibility of the method is superior to that of the conventional quantization-based methods under malicious attack followed by an incidental modification, such as JPEG compression, sharpening or blurring.

In previous work,1 we introduced the idea of using moment patterns (MPs) in the radon space (RS) for recognition and classification of multidimensional (m-D) objects from their projections. In 2-D, for example, an MP of order k in the RS is the set of moments (of order k) associated with the (1-D) projections of an image. The 1-D MPs can be rendered invariant to geometric transformations of the object within the RS.

The realization of high quality refractive microlenses is well known and has been reported several times in the past.1 Various fabrication techniques have been used to obtain accurate surface-relief refractive microlenses. Well known are direct writing techniques and graytone lithography.

In a Michelson interferometer, an incident beam of light ~typically at infrared wavelengths! is split into two beams that travel different distances in the device. Because of the difference in path length (x), there is a phase difference between the two beams.