Phase Detection Algorithm Research Articles

Design of asynchronous phase detection algorithms optimized for wide frequency response

In many fringe pattern processing applications the local phase has to be obtained from a sinusoidal irradiance signal with unknown local frequency. This process is called asynchronous phase demodulation. Existing algorithms for asynchronous phase detection, or asynchronous algorithms, have been designed to yield no algebraic error in the recovered value of the phase for any signal frequency. However, each asynchronous algorithm has a characteristic frequency response curve. Existing asynchronous algorithms present a range of frequencies with low response, reaching zero for particular values of the signal frequency. For real noisy signals, low response implies a low signal-to-noise ratio in the recovered phase and therefore unreliable results. We present a new Fourier-based methodology for designing asynchronous algorithms with any user-defined frequency response curve and known limit of algebraic error. We show how asynchronous algorithms designed with this method can have better properties for real conditions of noise and signal frequency variation.

Spatial phase stepping wavelength meter

A new way of evaluating the ratio between a reference wavelength radiation and an unknown wavelength radiation in a two-beam interferometer is proposed here. The advantage of two-beam interferometry is the sinusoidal fringe signal for which precise phase detection algorithms exist. Modern algorithms can cope with different sources of errors, and correct them. We recall the principle of the Michelson-type lambdameter using temporal interference and we introduce the Young-type lambdameter using spatial interference. The Young-type lambdameter is based on the acquisition of the interference pattern from two point sources (e.g. two ends of monomode fibres projected onto a CCD camera). The measurement of an unknown wavelength can be achieved by comparing with a reference wavelength. Accurate interference phase maps can be calculated using spatial phase shifting. In this way, each small group of contiguous pixels acts as a single interferometer, and the whole set of pixels corresponds to many hundreds or thousands of interferometric measurement system units. The analysis of uncertainties shows that resolutions better than 10−7 can be achieved. An advantage of the fibre wavelength metre described here is the measurement velocity that takes only a few seconds.

Multi-gigabit-rate clock and data recovery based on blind oversampling

This article addresses issues with designing a blind oversampling clock and data recovery unit (CDR) that meets jitter tolerance specifications. Asymptotic limits on jitter tolerance are derived assuming ideal phase detection based on a priori statistics of the received signal, proving that the coarse timing resolution of blind oversampling CDR relies on a phase detection algorithm that makes good estimates of the signal's statistics with a finite number of discrete samples and at reasonable hardware costs. The statistical simulation methodology outlined here enables quick verification of the bit error rate and comparisons between the jitter tolerances of various blind oversampling CDR architectures.

Effect of Mechanical Vibrations on Coriolis Mass Flow Meters

An analytical study of the response of a simple Coriolis meter subjected to external mechanical vibrations and corresponding finite element studies of three commercially available meters are presented. These show that vibrations produce additional components in the meter sensor signals but that these components are only at the frequency of the vibrations. The results show that errors reported in vibration experiments, using any frequency except the meter drive frequency, are due to failure of the determination of the phase difference between the sensor signals. The results also show that external vibrations at the meter drive frequency produce a meter error regardless of the phase detection algorithm.

Experimental comparison of a liquid-crystal point-diffraction interferometer (LCPDI) and a commercial phase-shifting interferometer and methods to improve LCPDI accuracy.

We compare the phase measurements of a fused-silica witness sample made with a liquid-crystal point-diffraction interferometer (LCPDI) with measurements made with a Zygo Mark IV xp phase-shifting interferometer and find close agreement. Two phase-shift-error sources in the LCPDI that contribute to measurement discrepancies are frame-to-frame intensity changes caused by the dichroism of the dye and alignment distortions of the host liquid crystal. An empirical model of the phase-shift error caused by the host alignment distortions is presented and used to investigate the performance of two different phase-detection algorithms. It is suggested that by proper choice of LCPDI fabrication parameters and phase-acquisition methods, the device's accuracy can be significantly improved.

Computerised acoustical respiratory phase detection without airflow measurement.

A simple, non-invasive acoustical method is developed to detect respiratory phases in relationship to swallows without the direct measurement of airflow. In 21 healthy subjects (4-51 years) breath sounds are recorded at the trachea and at five different recording locations at the chest wall, with simultaneous recording of airflow by a pneumotachograph. The chest signal with the greatest inspiratory-expiratory power difference ('best location') is either in the mid-clavicular line in the second interspace on the left or third interspace on the right. Using the 'best location' on the chest wall and the tracheal signal, a phase detection algorithm is developed and achieves 100% accuracy in the estimation of respiratory phases without using the measured airflow signal. Thus, acoustically monitoring breaths and swallows holds promise as a non-invasive and reliable assessment tool in the study of swallowing dysfunction.

Some properties of a window function on signal sampling algorithms

The properties of the phase detection algorithms found in the literature are determined by the Fourier transform of the sampling reference functions. Most algorithms take just one signal period. As shown before in the literature, we can take two periods and multiply it by a periodic function, called the window function, to improve the algorithm properties. Here, we will explore how this window function can be chosen to obtain the best possible algorithm.

Graphical vector description of sampling weights in phase-detecting algorithms

A theory of phase-detecting algorithms based on Fourier theory was described by Freischlad and Koliopoulos (1990). We present an application of this theory to a discrete sampling. It is shown that Greivenkamp (1984) results for a least-squares fitting of the sampling points can be obtained from this Fourier theory. We also present a new graphical vector description of the conditions required by the sampling weights in synchronous phase detection algorithms. Some applications of this graphical representation are presented.

Design of phase-detection algorithms insensitive to bias modulation

For digital phase detection, the characteristic polynomial method permits algorithms that are insensitive to the harmonic content of the signal and insensitive to miscalibration to be designed easily. It is shown here that this method can also be used to design algorithms that are insensitive to a possible bias modulation of the intensity.

Phase resetting associated with changes of burst shape

Based on our stochastic approach to phase resetting of an ensemble of oscillators, in this article we investigate two stimulation mechanisms which exhibit qualitatively different dynamical behaviour as compared with the stimulation mechanism analysed in a previous study. Both the ‘old’ as well as one of the ‘new’ stimulation mechanisms give rise to a characteristic desynchronization behaviour: A stimulus of a given (non-vanishing) intensity administered at a critical initial ensemble phase for a critical duration Tcrit annihilates the ensemble's synchronized oscillation. When the stimulation duration exceeds Tcrit a transition from type 1 resetting to type 0 resetting occurs. The second ‘new’ stimulation mechanism does not cause a desynchronization which is connected with a phase singularity. Correspondingly this mechanism only leads to type 1 resetting. In contrast to the stimulation mechanism analysed in a previous study, both ‘new’ stimulation mechanisms cause burst splitting. According to our results, in this case peak or onset detection algorithms are not able to reveal a correct estimate of the ensemble phase. Thus, whenever stimulation induced burst splitting occurs, phase-resetting curves determined by means of peak or onset detection may be nothing but artifacts. Therefore it is necessary to understand burst splitting in order to develop reliable phase detection algorithms, which are e.g. based on detecting bursts' centers of mass. Our results are important for experimentalists: Burst splitting is, for instance, well-known from tremor resetting experiments. Thus, it often turned out to be at least rather difficult to derive reliable phase-resetting curves from experimental data.

Automatic profilometry of 3-D diffuse objects by spatial phase detection

A method automatically processing a projected grating to profile a 3-D diffuse object is proposed. A deformed grating pattern projected on the object is regarded as a phase modulated pattern with a constant spatial carrier frequency. To retrieve phase modulation, acquired data in a microcomputer are sinusoidally fitted using a phase detection algorithm similar to that used in communication techniques. High sensitivity measurements of height distribution can be done using simple optical geometry. Random and systematic errors inherent in the method are discussed in detail.