Abstract: We present a new method for the extraction of quantitative phase data from microscopic phase samples by use of partially coherent illumination and an ordinary transmission microscope. The technique produces quantitative images of the phase profile of the sample without phase unwrapping. The technique is able to recover phase even in the presence of amplitude modulation, making it significantly more powerful than existing methods of phase microscopy. We demonstrate the technique by providing quantitatively correct phase images of well-characterized test samples and show that the results obtained for more-complex samples correlate with structures observed with Nomarski differential interference contrast techniques.

Abstract: Frequency conversion in nonlinear optical crystals1,2 is an effective means of generating coherent light at frequencies where lasers perform poorly or are unavailable. For efficient conversion, it is necessary to compensate for optical dispersion, which results in different phase velocities for light of different frequencies. In anisotropic birefringent crystals such as LiNbO3 or KH2PO4 (‘KDP’), phase matching can be achieved between electromagnetic waves having different polarizations. But this is not possible for optically isotropic materials, and as a result, cubic materials such as GaAs (which otherwise have attractive nonlinear optical properties) have been little exploited for frequency conversion applications. Quasi-phase-matching schemes1,3, which have achieved considerable success in LiNbO3 (ref. 4), provide a route to circumventing this problem5,6, but the difficulty of producing the required pattern of nonlinear properties in isotropic materials, particularly semiconductors, has limited the practical utility of such approaches. Here we demonstrate a different route to phase matching — based on a concept proposed by Van der Ziel 22 years ago7 — which exploits the artificial birefringence of multilayer composites of GaAs and oxidised AlAs. As GaAs is the material of choice for semiconductor lasers, such optical sources could be integrated in the core of frequency converters based on these composite structures.

Abstract: It is shown that when branch points are present in the phase of a turbulence-distorted optical field, the ability of an adaptive optics system that utilizes a least mean square error type of wave-front reconstructor to sense all of the turbulence-induced phase perturbations is limited. There is a portion of the turbulence-induced phase perturbation, which portion we refer to as the hidden phase, that such a least mean square error type of wave-front reconstructor will, in effect, ignore. It is shown that the presence of branch points indicates that the measured phase-difference vector field cannot be considered to be simply the gradient of some scalar potential—the phase function—but is in part also the curl of a vector potential function. A solution is developed for this vector potential, and from this a simple closed-form solution for the hidden phase is developed. Sample numerical results are presented showing the nature of the hidden phase. Suggestions are provided for a branch-point-tolerant wave-front reconstructor based on use of the closed-form solution for the hidden phase.

Abstract: The phase gradient approach is used to construct averages and differences of interferograms without phase unwrapping. Our objectives for change detection are to increase fringe clarity and decrease errors due to tropospheric and ionospheric delay by averaging many interferograms. The standard approach requires phase unwrapping, scaling the phase according to the ratio of the perpendicular baseline, and finally forming the average or difference; however, unique phase unwrapping is usually not possible. Since the phase gradient due to topography is proportional to the perpendicular baseline, phase unwrapping is unnecessary prior to averaging or differencing. Phase unwrapping may be needed to interpret the results, but it is delayed until all of the largest topographic signals are removed. We demonstrate the method by averaging and differencing six interferograms having a suite of perpendicular baselines ranging from 18 to 406 m. Cross-spectral analysis of the difference between two Tandem interferograms provides estimates of spatial resolution, which are used to design prestack filters. A wide range of perpendicular baselines provides the best topographic recovery in terms of accuracy and coverage. Outside of mountainous areas the topography has a relative accuracy of better than 2 m. Residual interferograms (single interferogram minus stack) have tilts across the unwrapped phase that are typically 50 mm in both range and azimuth, reflecting both orbit error and atmospheric delay. Smaller-scale waves with amplitudes of 15 mm are interpreted as atmospheric lee waves. A few Global Positioning System (GPS) control points within a frame could increase the precision to -20 mm for a single interferogram; further improvements may be achieved by stacking residual interferograms.

Abstract: We implement an optical encryption system based on double-random phase encoding of the data at the input and the Fourier planes. In our method we decrypt the image by generating a conjugate of the encrypted image through phase conjugation in a photorefractive crystal. The use of phase conjugation results in near-diffraction-limited imaging. Also, the key that is used during encryption can also be used for decrypting the data, thereby alleviating the need for using a conjugate of the key. The effect of a finite space–bandwidth product of the random phase mask on the encryption system’s performance is discussed. A theoretical analysis is given of the sensitivity of the system to misalignment errors of a Fourier plane random phase mask.

Abstract: The performance of a scanning force microscope (SFM) operated in the dynamic mode at high oscillation amplitudes is determined by the response of the system to a given set of interaction forces between the probing tip and the sample surface. To clarify the details of the cantilever/tip dynamics two different aspects were investigated in experiment and computer simulation. First, the interaction forces dominating the oscillatory motion of the probe were varied by applying an additional electrostatic force field. It is shown that such variations in the attractive part of the interaction potential can cause a switching between two different oscillation states and thereby significantly contribute to the contrast obtained from phase imaging. Secondly, the interaction forces were kept constant but the system response itself was varied by modifying the effective quality factor of the oscillating cantilever with an active feedback circuit. This provides a means to influence the transition from the attractive to the partly repulsive interaction regime, i.e. the onset of the intermittent contact or tapping mode. Operating an SFM in the dynamic mode at high amplitudes (> 10 nm) offers the possibility of minimizing the contact time of the probing tip with the sample surface and thereby reduce lateral or friction forces involved in the scanning process. It also allows the collection of additional data related to different sample properties by recording the phase shift between the force driving the cantilever and its oscillation. In the last few years these features of operating the SFM in the dynamic mode [1, 2] were shown to be very useful to characterize several different kinds of sample surfaces, e.g. thin organic films, polymers, biological samples or even liquid droplets [3]. Although this has led to a steady increase in the number of possible applications, there are still several details of the interaction process between the tip and the sample that need further clarification. The overall goal must be to relate the experimentally accessible data, such as the amplitude and ∗ Corresponding author phase signal, more or less directly to specific sample properties, such as topography, elasticity and viscoelasticity. Because highly nonlinear interaction forces are involved when the oscillating tip is in close proximity to a solid surface, the analysis of the dynamic system becomes quite complex. Therefore supplementary computer simulations based on proper mathematical models are useful to investigate the details of the interaction process. Basically, the equation of motion describing the dynamic properties of the probing tip has to be solved in such a way that the influence of different parameters characterizing the probe as well as the sample surface can be examined. There have been several reports recently on different approaches to this problem, providing analytical [4] as well as numerical [5–11] solutions. Most of them are based on the point-mass model, but there are also approaches which describe the complete flexural motion of the cantilever beam supporting the probing tip, as this becomes more relevant when the system is driven well above its resonance frequency [12]. Thus by simulating the dynamic system one can gain useful information on the complex interaction process of the oscillating tip and the sample surface. 1 Experimental and simulation methods The simulation results presented here are all based on the point-mass model with the interaction forces being derived from MYD/BHW calculations [11, 13, 14] and applying the Verlet algorithm [15] to solve the equation of motion numerically. All experiments were performed with a NanoScope III MultiMode stage (Digital Instruments) equipped with an additional lock-in amplifier (EG&G Instruments, Princeton Applied Research, Model 5302) to measure the phase lag between the driving force and the cantilever response quantitatively. Rectangular cantilevers made of doped silicon (Nanosensors) with a nominal length of L = 125 μm were used. By analogy with measurements of quasistatic forcedistance curves in contact mode, the amplitude and phase shift as a function of the z-position were quantitatively investigated in the dynamic mode by means of simulation and

Abstract: A dual-reflector microwave antenna comprises the combination of a paraboloidal main reflector having an axis; a waveguide and dual-mode feed horn extending along the axis of the main reflector, a subreflector for reflecting radiation from the feed horn onto the main reflector in the transmitting mode, and a shield extending from the outer edge of the main reflector and generally parallel to the axis of the main reflector, the inside surface of the shield being lined with absorptive material for absorbing undesired radiation. The subreflector is shaped to produce an aperture power distribution that is substantially confined to the region of the main reflector outside the shadow of the subreflector. The support for the subreflector is preferably a hollow dielectric cone having a resonant thickness to cause energy passing through said cone to be in phase with energy reflected off of said cone so as to achieve phase cancellation.

Abstract: A digital communication system (20) communicates using a polar amplitude phase shift keyed (P-APSK) phase point constellation (70, 70', 70"). Pragmatic encoding is accommodated using the constellation (70, 70', 70") to simultaneously communicate both encoded and uncoded information bits (69, 51). The constellation (70, 70', 70") has an even number of phase point rings (74) and equal numbers of phase points (72) in ring pairs (75, 76, 77). Encoded information bits (69) specify secondary modulation and uncoded information bits (51) specify primary modulation. The constellation (70, 70', 70") is configured so secondary sub-constellations (78) include four phase points (72) arranged so that two of the four phase points (72) exhibit two phase angles at one magnitude and the other two of the four phase points (72) exhibit phase angles that are at another magnitude. The difference between the phase angles at different magnitudes within a secondary sub-constellation (78) is constant.

Abstract: A digital transmit beamformer system with multiple beam transmit capability has a plurality of multi-channel transmitters, each channel with a source of sampled, complex-valued initial waveform information representative of the ultimate desired waveform to be applied to one or more corresponding transducer elements for each beam. Each multi-channel transmitter applies beamformation delays and apodization to each channel's respective initial waveform information digitally, digitally modulates the information by a carrier frequency, and interpolates the information to the DAC sample rate for conversion to an analog signal and application to the associated transducer element(s). The beamformer transmitters can be programmed per channel and per beam with carrier frequency, delay, apodization and calibration values. For pulsed wave operation, pulse waveform parameters can be specified to the beamformer transmitters on a per firing basis, without degrading the scan frame rate to non-useful diagnostic levels. Waveform parameters can be specified to the transmitters by an external central control system which is responsible for higher level flexibility, such as scan formats, focusing depths and fields of view. The transmit pulse delay specified per-channel to each transmitter is applied in at least two components: a focusing time delay component and a focusing phase component. The carrier frequency can be specified for each transmit beam, to any desired frequency within a substantially continuous predefined range of frequencies, and a beam-interleaved signal processing path permits operation in any of several predefined processing modes, which define different parameter sets in a trade-off among (1) the number of beams produced; (2) per-beam initial waveform sample interval; and (3) transmit frequency.

Abstract: A heterodyne optical measurement system for studying the phase shift of surface plasmon resonance (SPR) is presented. The system utilizes a frequency-stabilized Zeeman laser as a detection light source and is suitable for real-time phase measurement in SPR-sensing applications. The phase shift in an angular dispersion SPR excitation setup was measured ranging from +180 degrees to -120 degrees around the SPR excitation region. The experimental results fit well with the theoretical analysis. Compared with the reflection coefficient variation that is widely investigated in SPR studies, phase shift is estimated to provide a higher sensitivity to sensor systems and more information about the resonance phenomenon.

Abstract: We compute the tunneling probability from the symmetric phase to the true vacuum, in the first order electroweak phase transition of the MSSM, and the corresponding Higgs profiles along the bubble wall. We use the resummed two-loop temperature-dependent effective potential, and pay particular attention to the light stop scenario, where the phase transition can be sufficiently strongly first order not to wipe off any previously generated baryon asymmetry. We compute the bubble parameters which are relevant for the baryogenesis mechanism: the wall thickness and $\Delta\beta$. The two-loop corrections provide important enhancement effects, with respect to the one-loop results, in the amount of baryon asymmetry.

Abstract: Two-wavelength interferometry that is based on a Fourier-transform method has been investigated. A phase profile at a synthetic wavelength has been measured from a two-wavelength interferogram with two spatial carrier frequencies. A phase error caused by the difference between modulation intensities at two wavelengths has been theoretically and numerically analyzed. A phase map without the error can be obtained from a power-spectrum adjustment in the two-wavelength interferogram.

Abstract: A phase controlled dimming system having an active filter (30) for receiving the AC line voltage waveform, and for recovering the AC fundamental waveform therefrom is disclosed. The recovered AC fundamental waveform is supplied to a zero crossing detector (28) that provides zero crossing indications of the AC fundamental waveform. The recovered AC fundamental is substantially free of noise or distortion, and of frequency components greater than at least second order harmonics, that may be present on the AC line voltage waveform, and that might otherwise result in faulty or incorrect zero crossing detection. An output of the zero crossing detector is supplied to a microprocessor (26) that controls the gating of a controllably conductive device (22) interposed between the controlled load (14) and the AC source (12) based on the zero crossing information. The filter may take an analog or digital (software) form.

Abstract: For exact (i.e., non-paraxial) waves ψ representing freely propagating Gaussian beams in two and three dimensions, the patterns of phase singularities, that is zeros of ψ, are studied in detail. The zeros (points in two dimensions, and rings in three) are phase dislocations (optical vortices). The waves depend on a single parameter L, representing the radius of the waist of the beam. As L increases, pairs of dislocations interact and depart from the focal plane. Each such interaction comprises three events where the phase topology of ψ changes; each event is a reaction between the dislocations and associated phase saddles, conserving two topological quantum numbers. The same behaviour was predicted and observed by Karman et al. for beams truncated by apertures. The geometrical sensitivity of the wave to L is astonishing: changes in phase topology can occur when the waist expands by a few thousandths of a wavelength. The integral representing ψ is evaluated asymptotically, leading to a global expl...

Abstract: The current state of the acoustic wave phase conjugation (PC) problem is reviewed. The generation of phase conjugate ultrasonic waves is discussed with emphasis on the parametric method using electromagnetic pumping in solids. The giant-amplification supercritical parametric PC mode is considered in detail. Ultrasonic PC with a gain in excess of 80 dB is demonstrated for a soft magnetic ceramics-based amplifier. The high quality of supercritical parametric PC sound is confirmed by acoustic-optical visualization. Acoustic PC effects, such as anomalous sound reflection at the PC mirror and the autofocusing and self-targeting of phase conjugate sound beams incident on a scatterer in a liquid, are shown. Recent experimental results demonstrating the potential of PC for applications are presented.

Abstract: Waveform synthesizers represent an input waveform as a sequence of numerical codes in a number base, each numerical code comprising a plurality of digits ordered by place significance. A plurality of bilateral amplifiers is provided, a respective one of which is associated with a respective one of the digits. The bilateral amplifiers consume current from the DC power supply and return current to the DC power supply based on the value of the associated digit, to thereby generate an output voltage level that is proportional to the value of the associated digit. The output voltage levels of the plurality of bilateral amplifiers are serially coupled to the load, with a weighting that is based upon the place significance of the associated digit. Waveform synthesizers that are so constructed are capable of theoretical efficiencies of 100% for any signal waveform. These waveform synthesizers may be used efficiently to amplify to a transmit power level or radio signal that varies in amplitude as well as phase. These waveform synthesizers may also be used as a DC-to-AC converter having a sinusoidal output waveform.

Abstract: The phase of a single-mode field can be measured in a single-shot measurement by interfering the field with an effectively classical local oscillator of known phase. The standard technique is to have the local oscillator detuned from the system (heterodyne detection) so that it is sometimes in phase and sometimes in quadrature with the system over the course of the measurement. This enables both quadratures of the system to be measured, from which the phase can be estimated. One of us [H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] has shown recently that it is possible to make a much better estimate of the phase by using an adaptive technique in which a resonant local oscillator has its phase adjusted by a feedback loop during the single-shot measurement. In a previous work [H. M. Wiseman and R. B. Killip, Phys. Rev. A 56, 944 (1997)] we presented a semiclassical analysis of a particular adaptive scheme, which yielded asymptotic results for the phase variance of strong fields. In this paper we present an exact quantum mechanical treatment. This is necessary for calculating the phase variance for fields with small photon numbers, and also for considering figures of merit other than the phase variance. Our results show that an adaptive scheme is always superior to heterodyne detection as far as the variance is concerned. However, the tails of the probability distribution are surprisingly high for this adaptive measurement, so that it does not always result in a smaller probability of error in phase-based optical communication.

Abstract: A vibratory rotation sensor includes a heimspherical resonator, a ring forcer electrode and a plurality of discrete forcer and pick-off electrodes. A vibratory or flexural standing wave pattern is established in the resonator and signals from the pick-off electrodes are combined to produce first (E c ) and second (E s ) signals that represent two independent components of the vibration pattern. A reference phase generator generates timing signal that are used to demodulate E c and E s to obtain in-phase and quadrature components thereof. The quadrature components are transformed in a computer to generate nodal and antinodal quadrature signals. The nodal quadrature signal is used as the error signal in a quadrature control loop that keeps both components of the vibration pattern in phase. The antinodal quadrature signal is used as the error signal in a phase-locked loop that keeps the phase of the reference phase generator locked to the phase of the vibration.

Abstract: The properties of the ambiguity function and the uncertainty relation of Fourier transforms assert fundamental limitations on the ability of any single radar waveform of constrained time-bandwidth product to distinguish two or more targets closely spaced in both time-delay (range) and Doppler-shift (radial velocity). These same mechanisms place fundamental limits on the ability radar imaging systems to distinguish separate scatterers in delay and Doppler. In this paper, the problem of using multiple waveform sets to make enhanced discrimination delay-Doppler measurements is considered. While small coded waveform sets for enhanced discrimination delay-only measurement are known (e.g., the Golay sequences), these waveforms do not have good Doppler discrimination properties. The problem of designing multiple waveform sets for enhanced discrimination delay-Doppler measurement is investigated, and the composite ambiguity function (CAF) is introduced as a tool to measure the delay-Doppler discrimination characteristics of these waveform sets. The problem of designing optimal coded waveform sets under a time-bandwidth product constraint is considered, and explicit optimal phase, frequency, and joint phase-frequency coded waveform sets having constant amplitude are presented. Algorithms for the construction of such waveform sets of arbitrary size and practical implementation issues are also presented.

Abstract: A stream of complex numbers is converted into polar form, including an amplitude-representative part and a phase-representative part. The amplitude-representative part of each of the converted complex numbers is represented as a plurality of digits of decreasing numerical significance. The phase-representative part of each of the converted complex numbers is phase-modulated at the radio carrier frequency to produce a phase-modulated drive signal. The phase-modulated drive signal is amplified in a plurality of power amplifiers. A respective one of the power amplifiers provides a maximum output power level at a respective amplifier output that is related to a respective one of the decreasing numerical significance. The output amplitude of a respective one of the plurality of power amplifiers is controlled by applying a respective one of the plurality of digits of decreasing numerical significance to a respective one of the plurality of power amplifiers. The amplifier outputs of the plurality of power amplifiers are combined to form the modulated radio power signal.

Abstract: A novel and simple method to measure the amplitude and the phase of optical pulses is presented. The technique basically involves modulating the optical pulse train in a particular manner and then directly examining the resultant optical spectrum. This experimental measurement technique, which is extremely accurate and sensitive and can be implemented with an all-fiber setup, permits direct measurement of the phase of the optical signal in the frequency domain. Experimental results demonstrate the use of this measurement technique for characterizing optical pulses at 10 GHz from a gain-switched laser diode.

Abstract: A new method of obtaining Bragg reflection phases in an x-ray diffraction experiment is presented. It combines the phase-sensitive principles of multiple-beam diffraction and x-ray standing waves, and allows direct phase measurements of many multiple reflections simultaneously using a Bragg-inclined oscillating-crystal geometry. A modified-two-beam intensity function is devised to extract the phase information in a way similar to the standing wave analyses. [S0031-9007(98)05790-1]

Abstract: A fractional synthesis approach and arrangement are presented which achieve fine frequency resolution with low phase noise while at the same time retaining a high phase comparison frequency/fast frequency changing speed. An output signal having a desired output frequency is generated by a voltage controlled oscillator (VCO). An output divider divides the output frequency by an output divisor N to produce an output pulse train. The output divisor N may be equal to an output integer N or the output integer plus one N+1, for example, and may change during the generation of a single output frequency. For different desired output frequencies, the value of the output integer N may be varied. A reference divider divides a reference frequency by a reference divisor M to produce a reference pulse train. The reference divisor M may be equal to a reference integer M or the reference integer plus one M+1, for example, and may change during the generation of a single output frequency. A fractional controller may vary the value of the divisor M between successive pulses from the reference divider to produce a mean output pulse frequency having a non-integral relationship to the reference frequency. A phase error detector compares the pulse trains and generates a phase error signal. This signal, which may be filtered or otherwise processed, controls the VCO to produce the output signal at the desired output frequency.

Abstract: A phase interpolated frequency synthesizer with on chip tuning includes a voltage controlled oscillator, a fractional-N divider, phase compensation and on chip tuning circuits, a phase detector, and a loop filter. The phase compensation and on chip tuning circuits compensate for the phase lag from the fractional-N divider. The phase compensation circuit can include a series of voltage controlled delay elements with the tuning circuit providing a control voltage.

Abstract: A technique has been developed and tested for achieving phase conjugation in the microwave and millimeter-wave regime. The effective nonlinearity required for this phase-conjugation process is provided by electronic mixing elements feeding an array of antennas. Using these balanced mixing circuits in conjunction with a one-dimensional array antenna, we have demonstrated two-dimensional free-space phase conjugation at 10.24 GHz. A critical factor of this technique is the delivery of a 2/spl omega/ pump signal to each array element with the same phase. Two types of interconnects, electrical and a more versatile optical technique, have been implemented to distribute the pump signal in our demonstrations. In both systems, two-dimensional free-space phase conjugation was observed and verified by directly measuring the electric-field amplitude and phase distribution under various conditions. The electric-field wave-fronts exhibited retro-directivity and the auto-correction characteristics of phase conjugation. Furthermore, these experiments have shown amplified conjugate-wave power up to ten times of that of the incoming wave. This amplifying ability demonstrates the potential of such arrays to be used in novel communications applications.

Abstract: While holographic interferometry gives a good picture of the stress distribution over a complex structure, its use in stress-analysis has been limited by the fact that quantitative information on the deformation of the surface is directly available only at points on the fringe maxima or minima, and interpolation between these points is slow and not very accurate. An improved phase-measurement system for real-time holographic interferometry is described. This uses a diode array television camera to view the interference pattern, and digital electronics to calculate and store the phase difference at a 100 × 100 grid of points. This permits measurements of the phase with an accuracy estimated at ±2°.

Abstract: Delay variations are typically accounted for by increasing cycle time margins. Adaptive synchronization eliminates this on inter-modular interfaces in very large, high performance chips. The chip is divided into multiple smaller synchronous modules. Multi-synchronous hierarchical clocking provides the same frequency to all modules, but does not maintain any particular phase. Adaptive synchronizers adapt to the time-varying inter-modular clock and data phases, and out-perform conventional synchronizers.