Phase Ambiguity Problem Research Articles

Deformation measurement using dual-frequency projection grating phase-shift profilometry

ABSTRACT 2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phase- shifting profilometry (PSP) can be used to solve such an issue. In the measurement, two proper- chosen frequency gratings are utilized to synthesize an equivalent wavelength grating which ensures the computed phase in a principal phase range. Thus, the error caused by the phase unwrapping process with the conventional phase reconstruct algorithm can be eliminated. Finally, experimental result of a specimen with large plastic deformation is given to prove that the proposed method is effective to handle the phase discontinuity.

Continuous wavelet transform for micro-component profile measurement using vertical scanning interferometry

White-light interferometric techniques have been widely used in three-dimensional (3D) profiling. This paper presents a new method based on vertical scanning interferometry (VSI) for the 3D profile measurement of a micro-component that contains sharp steps. The use of a white-light source in the system overcomes the phase ambiguity problem often encountered in monochromatic interferometry and also reduces speckle noises. A new algorithm based on the continuous wavelet transform (CWT) is used to retrieve the phase of an interferogram. The algorithm accurately determines local fringe peak and improves the vertical resolution of the measurement. The proposed method is highly resistant to noise and is able to achieve high accuracy. A micro-component (lamellar grating) fabricated by sacrificial etching technique is used as a test specimen to verify the proposed method. The measurement uncertainty of the experimental results is discussed.

A novel semi-blind time-frequency domain tracking algorithm suitable for MPSK-OFDM

This paper presents a semi-blind tracking algorithm used for Multiple Phase Shift Keying based Orthogonal Frequency Division Multiplexing (MPSK-OFDM) system. By using special preambles to assist the decision of a feedback loop and to solve the problem of phase ambiguity, the tracking performance of the algorithm has been improved greatly. Only a few preambles are needed in the algorithm since the preambles are not used to estimate the frequency offset but used to provide the variation information of the phase due to the presence of frequency offset. Simulations verify that the algorithm has low SNR bound for tracking as well as high tracking accuracy and the tracking range is expanded to 30% of one subcarrier spacing.

Angle differential‐QAM scheme for resolving phase ambiguity in continuous transmission system

AbstractAn angle differential quadrature amplitude modulation (ADQAM) scheme is proposed to solve phase ambiguity problem in non‐data‐aided continuous transmission system with square QAM constellation. Starting from the 16‐ADQAM case, we derive differential encoding and decoding schemes in terms of two differential angles and use a solar system analogy for explanation. The 16‐ADQAM system incurs only about 0.5‐dB performance degradation compared with the coherent 16‐QAM system under AWGN channel. Generalization of flat fading channel and higher‐level ADQAM is straightforward. Copyright © 2007 John Wiley & Sons, Ltd.

Vibration measurement by temporal Fourier analyses of a digital hologram sequence

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.

Wavelength-scanning Talbot effect and its application for arbitrary three-dimensional step-height measurement

We demonstrate the phenomenon of Talbot self-image plane shift by tuning the wavelength of the broadband light source. A superluminescent diode (SLD) is used as a broad-band light source and an acousto-optic tunable filter (AOTF) as wavelength-scanning device. A periodic grating is illuminated by the wavelength tuned light of SLD using AOTF and Talbot self-image plane is shifted continuously in the longitudinal direction without mechanically moving the grating. The wavelength-scanning Talbot effect is then implemented for the measurement of arbitrary step-height of discontinuous objects with extended range. The main advantages of the proposed system are non-mechanical scanning, high stability because of it’s common-path geometry and compactness. Since the measurement of the phase is not required the system is free from phase ambiguity problem and therefore, the range of measurement is large as compare to interferometric techniques.

Retrospective analysis of haplotype-based case-control studies under a flexible model for gene-environment association

Genetic epidemiologic studies often involve investigation of the association of a disease with a genomic region in terms of the underlying haplotypes, that is the combination of alleles at multiple loci along homologous chromosomes. In this article, we consider the problem of estimating haplotype-environment interactions from case-control studies when some of the environmental exposures themselves may be influenced by genetic susceptibility. We specify the distribution of the diplotypes (haplotype pair) given environmental exposures for the underlying population based on a novel semiparametric model that allows haplotypes to be potentially related with environmental exposures, while allowing the marginal distribution of the diplotypes to maintain certain population genetics constraints such as Hardy-Weinberg equilibrium. The marginal distribution of the environmental exposures is allowed to remain completely nonparametric. We develop a semiparametric estimating equation methodology and related asymptotic theory for estimation of the disease odds ratios associated with the haplotypes, environmental exposures, and their interactions, parameters that characterize haplotype-environment associations and the marginal haplotype frequencies. The problem of phase ambiguity of genotype data is handled using a suitable expectation-maximization algorithm. We study the finite-sample performance of the proposed methodology using simulated data. An application of the methodology is illustrated using a case-control study of colorectal adenoma, designed to investigate how the smoking-related risk of colorectal adenoma can be modified by "NAT2," a smoking-metabolism gene that may potentially influence susceptibility to smoking itself.

Radio interferometer for geosynchronous-satellite direction finding

A radio interferometer capable of azimuth-elevation direction finding for geosynchronous satellites has been developed. The interferometer has two small-diameter antennas and four movable planar mirrors. The movable mirrors reflect the microwaves from the satellite and guide them to the fixed receiving antennas. Two of the movable mirrors are mounted on a rotary arm, so that the baseline of the interferometer can rotate in the horizontal plane. This configuration enables the interferometer to eliminate phase-ambiguity problems and cable-phase errors, resulting in a direction finding accuracy of better than 0.01 deg in the Ku band.

Supervised Phase Correction of Blind Space–Time DS-CDMA Channel Estimates

Blind channel-estimation algorithms return phase-ambiguous estimates. From a receiver design point of view, the phase-ambiguity problem can be by-passed by differential modulation and detection at the expense of a well-known performance loss, in comparison with direct modulation and coherent detection schemes. An alternative approach is followed in this paper. A theoretical minimum mean-square error phase-estimation criterion leads to a supervised phase-recovery procedure that directly corrects the phase of arbitrary linear filter receivers through a simple closed-form projection operation. Conveniently, any known blind channel-estimation algorithm can be used to provide the initial phase-ambiguous estimate. The presentation is given in the context of adaptive space-time receiver designs for binary phase-shift keying direct-sequence code-division-multiple-access antenna array systems. Numerical and simulation studies support the theoretical developments and show that effective phase correction and multiple-access interference suppression can be achieved with about 2% pilot signaling

Two-wavelength Talbot effect and its application for three-dimensional step-height measurement

The phenomenon of Talbot self-image shift by changing the wavelength of the illuminating light is described and demonstrated experimentally. A periodic grating is illuminated by light with wavelengths lambda1 and lambda2 generated by two lasers, and the Talbot self-images are recorded along the longitudinal direction at individual wavelengths. The Talbot self-image shift due to the change in the wavelength of light is implemented for the measurement of the three-dimensional step height of a large discontinuous object without any phase ambiguity problem. Fourier-transform fringe analysis was used to determine the maximum contrast of the high-visibility bands for the measurement of the step height of the object. The main advantages of the proposed system are nonmechanical scanning, high stability because of its common path geometry, compactness, and a wide range of measurement as compared to interferometric three- dimensional profilers.

Wavelet analysis of digital shearing speckle patterns with a temporal carrier

Shearography is an optical technique allows direct measurement of deflection derivatives. This paper presents a novel temporal phase analysis technique based on wavelet transform when shearography is applied to measure a continuously deforming object. A series of shearing speckle patterns is captured by a high-speed camera during the deformation. To avoid the phase ambiguity problem, a temporal carrier is generated by a piezoelectrical transducer (PZT) stage in one beam of the modified Michelson interferometer. The intensity variation of each pixel on recorded images is then analyzed along time axis by a robust mathematical tool – complex Morlet wavelet transform. After the temporal carrier is removed, the absolute phase change representing the first-order derivative of the continuous deformation is obtained without the need of temporal or spatial phase unwrapping process. The results obtained by wavelet transform are compared with those from temporal Fourier transform.

Trellis-Based Iterative Adaptive Blind Sequence Estimation for Uncoded/Coded Systems with Differential Precoding

We propose iterative, adaptive trellis-based blind sequence estimators, which can be interpreted as reduced-complexity receivers derived from the joint ML data/channel estimation problem. The number of states in the trellis is considered as a design parameter, providing a trade-off between performance and complexity. For symmetrical signal constellations, differential encoding or generalizations thereof are necessary to combat the phase ambiguity. At the receiver, the structure of the super-trellis (representing differential encoding and intersymbol interference) is explicitly exploited rather than doing differential decoding just for resolving the problem of phase ambiguity. In uncoded systems, it is shown that the data sequence can only be determined up to an unknown shift index. This shift ambiguity can be resolved by taking an outer channel encoder into account. The average magnitude of the soft outputs from the corresponding channel decoder is exploited to identify the shift index. For frequency-hopping systems over fading channels, a double serially concatenated scheme is proposed, where the inner code is applied to combat the shift ambiguity and the outer code provides time diversity in conjunction with an interburst interleaver.

Joint Phase/Amplitude Estimation and Symbol Detection for Wireless ICI Self-Cancellation Coded OFDM Systems

OFDM has been applied in the current wireless local-area networks and digital video broadcasting systems since it has the advantage over the conventional single-carrier modulation schemes when the frequency-selective fadings are present. Nevertheless, intercarrier-interference (ICI) due to Doppler frequency drift, phase offset, local oscillator frequency drift, and multipath fading will be a severe problem in OFDM systems. Previous ICI self-cancellation coding schemes can greatly reduce the ICI, but they are very sensitive to the phase ambiguity, which is due to the composite effect of the phase offset, the multipath fading and the local frequency drift. In this paper, the phase ambiguity and amplitude ambiguity problems in ICI self-cancellation coded OFDM receivers will be formulated and discussed. Then, a novel receiver which combines the current ICI self-cancellation coding techniques with a new expectation-maximization-based joint phase/amplitude estimation and symbol detection scheme is proposed. The outstanding performance of this proposed scheme is shown and compared with other existing methods at different noise levels through OFDM simulations.

Totally blind APP channel estimation for mobile OFDM systems

A new two-dimensional blind channel estimation scheme for coherent detection of orthogonal frequency-division multiplexing (OFDM) signals in a mobile environment is presented. The channel estimation is based on the a posteriori probability (APP) calculation algorithm. The time-variant channel transfer function is completely recovered without phase ambiguity with no need for any pilot or reference symbols, thus maximizing the spectral efficiency of the underlying OFDM system. The phase ambiguity problem is solved by using a 4-QAM (quadrature amplitude modulation) scheme with asymmetrical arrangement. The results clearly indicate that totally blind channel estimation is possible for virtually any realistic time-variant mobile channel.

Differential wavelength-scanning heterodyne interferometer for measuring large step height.

An interferometer based on the differential heterodyne configuration and wavelength-scanning interferometry for measuring large step heights is presented. The proposed interferometer is less sensitive to environmental disturbances than other interferometers and can accurately measure interference phases. A tunable diode laser is utilized to illuminate the interferometer and thus solve the phase ambiguity problem. Counting the interference fringes as the wavelength is scanned through a known change in wavelength directly determines the step height. Three gauge blocks of different lengths, 5, 10, and 50 mm, are individually wrung on a steel plate to simulate large step heights. Comparing the results measured by the proposed interferometer with those by the gauge block interferometer reveals that the accuracy is approximately 100 nm.

Resolution of the phase-ambiguity problem in the centrosymmetric P [1] space group by Monte Carlo methods.

Simulated-annealing methods have been used to resolve the phase-ambiguity problem in the centrosymmetric P¿bar¿1¿ space group. First, an energy function based on the Sayre equation is introduced and a formal comparison with classical spin systems is drawn. The energy landscape is studied in detail and the validity of several energy criteria thoroughly tested. Classical Monte Carlo methods proved to be successful using a multistart optimization of the Sayre score, along with the additional monitoring of other energetic criteria. These involved the Terwilliger map quality index in reciprocal space in the absence of envelope information, and an envelope score if the shape of the molecule is known. The inherent phase-ambiguity problem of the P¿bar¿1¿ space group was therefore technically solved by Monte Carlo methods. The method should also work to resolve phase ambiguity in the SIR method of protein crystallography.

General formalism for phase combination and phase refinement: a statistical thermodynamics approach in reciprocal space

The mean-field optimization methodology has been used to recast in a single formalism the problem of phase optimization using an arbitrary energy function in the presence of an experimentally determined phase probability distribution function. It results naturally in the generalization of the notions of figure of merit and centroid phase where the weight of the energy refinement is controlled by an effective temperature in a self-consistent manner. In the limit of high temperature, the formalism reduces of course to the Blow & Crick [Acta Cryst. (1959), 12, 794-802] classical treatment. If a model is available, Sim's [Acta Cryst. (1960), 13, 511-512] weighting scheme for a combined map appears as the first step of a refinement to be conducted until self-consistency is achieved. Assuming that MIR phases exist and that they agree reasonably well with the phases of the model, a first-order expansion gives an estimate of the changes of weights and phases to be performed for the Fourier synthesis. This provides for a new way of doing phase combination that might prove useful in challenging cases of model refinement, e.g. in large macromolecular complexes. Thermodynamic considerations have been used to discuss the best determination of weights in phase refinement; they also suggest that a variational expression of maximum likelihood is best suited as a target for refinement because it is the free energy of the system. The formalism readily allows use of solvent flattening, density averaging and the atomicity criterion to refine phases, and automatically assigns a figure of merit to each reflection. Numerical tests of the method are presented in an attempt to resolve the phase-ambiguity problem of protein crystallography in the centrosymmetric P¿1¿ space group using an energy derived from the Sayre equation.

Hyperacuity in time: a CNN model of a time-coding pathway of sound localization

This paper discusses a new multilayer one-dimensional (1-D) cellular neural network model of the time-coding pathway of sound localization. The key feature of the model is lateral inhibition, which is supposed to play a crucial role in sound localization. The possible role of this inhibition is examined on the basis of our model and several conclusions are drawn concerning the expected nature of inhibition. It is also shown that by use of inhibition, a group of neurons may be much more sensitive to interaural time difference than one individual neuron. Thus, our model of the first stage of the sound localization system solves a hyperacuity in time problem. The second part of the paper introduces a CNN model of that part of the sound localization system which is characterized by a massive convergence of different frequency channels to resolve the so-called phase ambiguity problem. We show that with inhibition good results can be achieved here too. Quantitative studies show the robustness of the model.

Combination of BCM and TCM with 90°, 180°, and 270° phase rotational invariance

Two systematic schemes to combine block-coded modulation (BCM) and trellis-coded modulation (TCM) are proposed. In the first scheme, the signal points which are used in TCM should be partitioned by the proper BCM systems constructed by a multilevel construction method. The asymptotic coding gain will be 6.02-3.01/n dB, where n is the length of the BCM systems. Since the average transmission power can be reduced by using a denser signal lattice, the main idea of the second scheme is to construct the TCM system based on the signal points of a denser lattice formed by a proper BCM system. Hence, we can get a higher coding gain which is a combination of both the distance gain of TCM and the density gain of BCM. Theoretically, the net coding gain of this proposed scheme can reach 5.27 dB in the case of an 8-D constellation and 7.15 dB in the case of a 16-D constellation. For practical implementation, the phase ambiguity problems for both schemes are considered and solved by a differential encoder/decoder.

Performance of open loop digital frequency estimation techniques for burst‐mode transmission

AbstractThis paper presents the variance analysis, and performance comparison, of the least‐squares frequency estimator (LSFE), and a specific version of the nonlinear frequency estimator (NIX). The results are obtained for the case where the received signal contains both phase and frequency errors (ΔΘ and Δf respectively). It is shown that under rather restrictive conditions, the LSFE is a low signal‐to‐noise ratio approximation to the ML estimate of Δ f Also considered are the effects on the moments of this estimate, if any of these conditions are violated. The latter part of the paper deals with the various versions of the NFE. The problem of phase ambiguity associated with these nonlinear estimators is investigated, and a resolution technique is proposed.