Phase Difference Error Research Articles

Probability density of the differential phase difference in applications to passive wireless surface acoustic wave sensing

The probability density function (pdf) is discussed of the differential phase difference (DPD) in the radio frequency (RF) pulse-burst perturbed by Gaussian noise at the coherent receiver. Statistical properties of the DPD are of importance for error estimation in coherent systems such as remote passive wireless surface acoustic wave (SAW) sensing with multiple differential phase measurement. The rigorous probability density of the DPD is derived and its particular functions, all having no closed forms, are given for different signal-to-noise ratios (SNRs) in the RF pulses. Employing the von Mises/Tikhonov distribution, an efficient approximation is proposed via the modified Bessel functions of the first kind and zeroth order. Engineering features and small errors of the approximation are demonstrated. Applications are given for the phase difference drift rate and error probability for the drift rate to exceed a threshold.

A Technique for Rephasing$\,+\,$2R Regeneration of 40-Gb/s NRZ-DPSK Data

A novel technique for rephasing, reshaping, and reamplifying (Rp + 2R) of nonreturn-to-zero differential phase- shift keying (NRZ-DPSK) data is demonstrated. The regenerator operation and performance are evaluated using numerical simulations. The system can regenerate 40-Gb/s NRZ-DPSK data degraded with both random amplitude and phase noise (linear or nonlinear). Regenerated NRZ-DPSK has the same original data pattern and wavelength. The DPSK quality-factor and optical signal-to-noise ratio (OSNR) improves significantly, and the output differential phase error is very small. The bit-error ratio (BER) shows improvement of the received data OSNR ranging from 9.5 dB at 10-4 BER up to 10.5 dB at 10-9 BER.

Atmospheric Artifact Compensation in Ground-Based DInSAR Applications

In this letter, a coherence-based technique for atmospheric artifact removal in ground-based (GB) zero-baseline synthetic aperture radar (SAR) acquisitions is proposed. For this purpose, polarimetric measurements acquired using the GB-SAR sensor developed at the Universitat Politecnica de Catalunya are employed. The heterogeneous environment of Collserola Park in the outskirts of Barcelona, Spain, was selected as the test area. Data sets were acquired at X-band during one week in June 2005. The effects of the atmosphere variations between successive zero-baseline SAR polarimetric acquisitions are treated here in detail. The need to compensate for the resulting phase-difference errors when retrieving interferometric information is put forward. A compensation technique is then proposed and evaluated using the control points placed inside the observed scene.

Frequency and Phase Difference Control Using Fractional-$N$ PLL Synthesizers by Composition of Control Data

This paper proposes novel frequency and phase difference control of output signals in multiple fractional- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> PLL (F-PLL) synthesizers sharing a reference signal. In the proposed F-PLL synthesizers, frequency control and phase difference control can be performed independently through cyclic shift and composition of control data of frequency dividers. The proposed synthesizers are demonstrated in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> -band, realizing highly accurate output frequency and phase difference control. The measured phase difference error from a designed value is plusmn2deg or less.

Analysis of frequency mixing error on heterodyne interferometric ellipsometry

A heterodyne interferometric ellipsometer, with no moving parts and a transverse Zeeman laser, is demonstrated. The modified Mach–Zehnder interferometer characterized as a separate frequency and common-path configuration is designed and theoretically analyzed. The experimental data show a fluctuation mainly resulting from the frequency mixing error which is caused by the imperfection of polarizing beam splitters (PBS), the elliptical polarization and non-orthogonality of light beams. The producing mechanism of the frequency mixing error and its influence on measurement are analyzed with the Jones matrix method; the calculation indicates that it results in an error up to several nanometres in the thickness measurement of thin films. The non-orthogonality has no contribution to the phase difference error when it is relatively small; the elliptical polarization and the imperfection of PBS have a major effect on the error.

Coherent combining of the output of two semiconductor lasers using optical phase-lock loops

We have experimentally demonstrated current-injection optical phase-lock loops (OPLLs) based on commercial single-section semiconductor distributed-feedback (DFB) lasers. Using two parallel OPLLs, we have obtained 87% efficient coherent power combining of the two DFB lasers. The rms differential phase error between the two lasers is about 30 degrees .

Coherent power combination of two Master-oscillator-power-amplifier (MOPA) semiconductor lasers using optical phase lock loops

Using heterodyne Optical Phase-Locked Loops (OPLLs), two 1W high power 1550 nm master-oscillator-power-amplifier (MOPA) semiconductor lasers operating as current controlled oscillators are phase-locked to a 1 mW reference laser. The signals of the two MOPAs are then coherently combined and their mutual coherence is studied. In each OPLL, the acquisition range is increased to +/-1.1GHz with the help of an aided- acquisition circuit. Control of the phase of a single slave MOPA is demonstrated using a RF phase shifter. The differential phase error between two MOPAs locked to the common reference laser is typically 22 degrees.

Measurement of Stokes Parameters by Quarter-Wave Plate and Polarizer

Formulations of the theory of automated photoelasticity are expressed simply by use of the Stokes parameters. In the automated photoelasticity, the measurement of the total relative phase retardation must often be performed over a wide wavelength range. The Stokes parameters (S0, S1, S2 and S3) need to be measured over a wide wavelength range. The Stokes parameters of monochromatic light can be measured by the adjustable azimuth settings of a retarder and analyzer (ARA) method. When undertaking the measurement of the Stokes parameters of light of an arbitrary wavelength over a wide wavelength range, the measurement of S3 by the conventional ARA method is dependent on the phase difference error ρ i of a quarter-wave plate mismatch as well as Stokes parameter S2. The measurement of S3 by a judicious choice of azimuth settings of a quarter-wave plate and a polarizer (JCAQP) as in the method proposed can be obtained by considering ρ I . The JCAQP method is clarified by employing the Poincaré sphere. It is shown that application of the JCAQP method yields the principal axis and the relative phase retardation of the birefringent plate free from the ρ i of the quarter-wave plate for incident elliptically polarized light of an arbitrary wavelength.

Phase-and-amplitude regeneration of differential phase-shift keyed signals using a phase-sensitive amplifier

DPSK phase-and-amplitude regeneration with a NOLM-based phase-sensitive amplifier is demonstrated experimentally. For a highly degraded input signal, maximum differential phase errors were reduced from 82 degrees to 41 degrees , while the SNR was improved by more than 5-dB. Differential phase Q-factor improvement was better than 6-dB. The PSA was operated free of excess noise due to stimulated Brillouin scattering by using a binary phase modulated pulse train as the pump. The impact of pump fluctuations on regeneration performance is clarified. The regenerated signal was characterized by measurement of the constellation diagram by linear optical sampling, giving the first directly measured evidence of DPSK phase regeneration.

Analysis of the phase noise in saturated SOAs for DPSK applications

A theoretical model is used to analyze the impact of phase noise on the performance of semiconductor optical amplifiers (SOAs) in the saturation regime for differential phase-shift keying (DPSK) applications. It is found that the variance of the differential phase error scales as T/sup 2///spl tau//sub c//sup 2/ for /spl tau//sub c//spl Gt/T, where T is the bit period and /spl tau//sub c/ is the carrier lifetime of the SOA. This suggests that the adverse effect of saturation-induced phase noise can be significantly reduced by increasing the bit rate or the carrier lifetime.

Rice statistical propagation channel sounding: coherence bandwidth measurement by microwave interferometric sensor

Numerical and wireless communications systems are led by the coherent frequency bandwidth (BC) of the propagation channel where the wireless link is considered. An original method is presented to achieve the BC of a channel having a Rice's statistic law (one or more paths are without reflection between transmitter and receiver) which is based on the mitigation, by using a microwave interferometric sensor and a narrowband multitone transmitter, of the phase difference error due to multipaths.

A New Fuzzy Bandwidth Carrier Recovery System in GPS for Robust Phase Tracking

Fast carrier recovery loops are essential in high-dynamic global positioning system receivers. A new digital phase-locked loop (DPLL) system incorporating a fuzzy bandwidth controller (FBC) is presented in this letter. The FBC provides a time-varying bandwidth and adjusts the loop filter coefficients to improve DPLL tracking capability. When the phase error or phase difference error becomes large in the presence of significant accelerations, the loop bandwidth increases adaptively and performs rapid locking. Simulation results show that our receiver does achieve a superior performance over conventional tracking loops in terms of shorter settling time and wider frequency ramp range, while preventing the occurrence of cycle slipping.

Bit Error Rate Performance of an Optical IM-DD Transmission System with Wavelength Converter

An analytical approach is presented to evaluate the bit error rate (BER) performance results of an optical IM-DD system with wavelength conversion based on cross-phase modulation in two semiconductor optical amplifiers (SOAs) arranged in the two arms of a Mach-Zehnder interferometer (MZI) followed by a Fabry-Perot filter. It is found that the signal-to-noise ratio (SNR) at the output of the converter critically depends on the differential phase of the converter signal between the two arms of the MZI and attains a maximum value corresponding to an optimum value of the differential phase. There is an optimum value of BER corresponding to the maximum SNR. At values of SNR other than maximum, the system suffers a penalty in signal power at a given HER and is found to increase with increase in the phase error and significantly high in the presence of phase noise due to the transmitting and converter wave laser sources. It is noticed that the penalty is 1.4 dB for normalized laser linewidth ΔνTh = 0.0 and becomes almost 8 dB for AvT =.005 and is exceedingly high at increased value of ΔνT when the differential phase error at the output of the MZI is 0.75 π.

Precise 90° quadrature current-controlled oscillator tunable between 50–130 MHz

A VLSI continuous time sinusoidal OTA-C quadrature oscillator fabricated in a standard double-poly 0.8 µm CMOS process is presented. The oscillator is tunable in the frequency range from 50–130 MHz. The two phases produced by the oscillator show an extremely low phase difference error (less than 2° over the whole frequency range). A novel current mode amplitude control scheme is developed that allows for very small amplitudes. Experimental results are provided.

Interferometric hartmann wave-front sensing for active optics at the 6.5-m conversion of the multiple mirror telescope.

A little-used interferometric modification to the classical Hartmann optical test is being used for active optics corrections at the 6.5-m Multiple Mirror Telescope (MMT) Observatory. The technique produces compact interference spots whose positions depend on discrete wave-front phase-difference errors. A diffraction model illustrates the formation of interference spots. The limitations on wave-front sampling that are due to atmospheric seeing are estimated. Two data reduction matrix strategies are given. A single correction of collimation and primary mirror figure produces a nearly diffraction-limited telescope image. Wave-front polynomial coefficients ranging from several nanometers to several micrometers in amplitude are reliably detected.

Geodesy using the Swedish permanent GPS network: Effects of signal scattering on estimates of relative site positions

This paper presents results from a study of elevation‐angle‐dependent systematic effects on estimates of relative site positions within the Swedish permanent Global Positioning System (GPS) network. Two months of data from 16 sites have been analyzed with three different elevation cutoff angles, namely, 10°, 15°, and 20°. We present offsets between these solutions and demonstrate that estimates of the vertical component of several baselines strongly depend on the minimum elevation angle (elevation cutoff angle) of the data analyzed. Offsets of 22.3 ± 1.6 mm in the vertical component are evident when the elevation cutoff angle is changed from 10° to 20°. We investigate these offsets and conclude that a significant part is due to differential phase errors caused by scattering from structures associated with the mounting of the antenna to the pillar and with the pillar itself. The horizontal components of baseline are less affected. We found, however, that the offsets in the horizontal components increase with baseline length. For the longest baselines (∼1500 km) offsets of more than 5 mm are evident in the north component when the elevation cutoff angle is changed from 10° to 20°. These offsets are most likely due to differential phase errors caused by nonuniform antenna phase patterns; an effect that presumably increases with baseline length and which also might increase because of scattering from the pillars and the antenna mounts. We identify the scattering structure and reduce associated errors in the vertical component of baseline to a significant degree on one of the sites by using microwave‐absorbing material. The results presented are of importance for those analyzing data from existing networks and for those who intend to establish permanent GPS geodetic networks.

Stokes parameters measurement of light over a wide wavelength range by judicious choice of azimuthal settings of quarter-wave plate and linear polarizer

The Stokes parameters ( S p, S 1, S 2, S 3) of light are measured at an arbitrary wavelength over a wide wavelength range. The Stokes parameters S 1 and S 2 are easily obtained. But the Stokes parameter S 3 at the arbitrary wavelength is affected by the phase difference error Δϱ 1 of the quarter-wave plate mismatch and the Stokes parameters S 1 or S 2. Therefore, in this paper, S 3 is obtained from both the intensity measurements by the circular polarizer rotating the quarter-wave plate by 0° and 90°. Then, S 3 is obtained by considering only Δϱ 1, but is not affected by S 1 and S 2. Also, though Δϱ 1 is not accounted for, S 3 is measured more accurately.

Influence of the Measurement Volume on the Phase Error in Phase Doppler Anemometry. Part 1: Reflective mode operation

AbstractIn phase Doppler anemometry (PDA), phase difference errors are caused by the Gaussian intensity distribution of the laser beam and the curvature of the phase fronts outside of the beam waist. This results in erroneous particle sizes. Based on a physical analysis by geometrical optics [1], this phase difference error is evaluated for reflected mode operation (Part I) and for refracted mode operation (Part II). By varying the particle trajectories statistically, the error in determining the particle size and the mass flow can be simulated. By the method described the error in the measured phase difference can easily be estimated.

A comprehensive expression for P–P measurements in planar standing waves

The latest draft standards from IEC and ASTM concerning P–P intensity probe qualification tests specify a standing wave test that addresses concerns for channel phase difference errors under reactive conditions. Two such errors are recognized, channel phase bias and back vent influences. The following analysis determines an expression for probe response, including both errors, when the probe is employed within a planar standing wave. This will lead to a better understanding of the test circumstances and may lead to generally applicable correction terms.

Design of IIR digital filters with given magnitude specifications using allpass networks

AbstractThis paper proposes a direct design method in the z‐domain for the IIR digital filter with a parallel structure composed of allpass networks with complex and real coefficients, with the specifications for the bandedge frequencies of the passband and stopband as well as the magnitude in the passband (or stopband).First, a filter composed of two allpass networks with conjugate complex coefficients is considered. Also, the phase difference characteristic between the two networks is considered. By specifying the phase difference error, the determination of the filter coefficients is reduced to the eigenvalue problem of the matrix using Remez' algorithm. The filter coefficients are determined from the eigenvector corresponding to the maximum eigenvalue. Then iterative calculation is executed to realize the equiripple characteristic, and the optimal solution is derived.Next, the relation between the phase difference errors and the magnitude errors is discussed and it is shown that the filter can be designed by the proposed method by specifying the absolute value of the magnitude error. The usefulness of the proposed method is shown by design examples. The filter based on two allpass networks with real coefficients is also considered, and it is shown that the filter can be designed by the same procedure by formulating the procedure for the sum and the difference of the filter coefficients.