Accuracy Of Phase Extraction Research Articles

Phase tracking using a Kalman filter based on probability density distribution in frequency-scanning interferometry

Frequency-scanning interferometry (FSI) utilizing external cavity diode lasers (ECDL) stands out as a potent technique for absolute distance measurement. Nevertheless, the inherent scanning nonlinearity of ECDL and phase noise pose a challenge, as it can compromise the accuracy of phase extraction from interference signals, thereby reducing the measurement accuracy of FSI. In this study, we propose a composite algorithm aimed at mitigating non-orthogonal errors by integrating the least-squares and Heydemann correction technique. Furthermore, we employ Kalman filtering for precise phase tracking. We introduce a parameter selection strategy based on the statistical distribution of instantaneous frequency to achieve the fusion estimation of phase observation values and theoretical models, which starts a new perspective for the application of multi-dimensional data fusion in FSI measurement. Through simulation and experimental validation, the efficacy of this approach is confirmed. The experimental results show promising outcomes: with an average phase error of 0.12%, a standard deviation of less than 1.7 µm in absolute distance measurement, and an average positioning accuracy error of 0.29 µm.

Adjustable accuracy of phase steps in a double-aperture common-path interferometer by rotating and displacing grating at Fourier plane

Detuning errors limit the accuracy of phase extraction in phase-shifting interferometry (PSI). To improve this accuracy, the systems to control the phase shifter dispositive must be highly accurate, involving high technology, exhaustive calibration, high cost, and constant maintenance. This manuscript presents a method for improving the accuracy of the phase step generated at the Fourier plane by rotating and displacing the grating in a double-aperture common-path interferometer. It is demonstrated that both the detuning errors and the phase extraction uncertainty decrease with the grating rotation angle. The experimental implementation is very simple, as it does not require any sophisticated mechanical system to improve the accuracy, no exhaustive calibration, and no additional mechanical and optical dispositive. With the present approach, the PSI method could be achieved very simply and with high accuracy by using a low-accuracy actuator. The theoretical model and experimental results are presented to demonstrate the present proposal.

Sub-regional phase error compensation based ona probability distribution function and gammaprecoding.

In this paper, a phase error compensation method based on a probability distribution function (PDF) is proposed to improve the accuracy of phase extraction, which is helpful for three-dimensional (3D) reconstruction. First, the relationship between the gamma and the gray values is established to segment the projection regions. Then a new method based on a PDF is designed to represent the variation degree of phase error, which fits the precoded gamma value in the minimum range of the phase error. After that, the error compensation method is applied to the self-built system and packaged independently from the 3D reconstruction system to unwrap phases with high precision. The experimental results show that the proposed method can reduce the standard deviation of the phaseerror by 46.9% compared without phase error compensation, and decrease the standard deviation of thephase error by 30% compared with the whole precoding. Generally, our method can effectively avoid overcompensation or under-compensation caused by single global gamma precoding correction, and better reduce the phase error and improve the 3D reconstruction accuracy in the fringe projection system.

Temporal-spatial binary encoding method based on dynamic threshold optimization for 3D shape measurement.

The binary encoding method has been widely used for three-dimensional (3D) shape measurement due to the high-speed projection characteristics of its digital mirror device (DMD)-based projector. However, traditional binary encoding methods require a larger defocus to achieve a good sinusoidality, leading to a reduction in the measurement depth of field and signal-to-noise ratio (SNR) of captured images, which can adversely affect the accuracy of phase extraction, particularly high-frequency fringes for 3D reconstruction. This paper proposes a spatial-temporal binary encoding method based on dynamic threshold optimization for 3D shape measurement. The proposed method decomposes an 8-bit sinusoidal fringe pattern into multiple(K) binary patterns, which can be outlined into two steps: determining the dynamic threshold and then performing temporal-spatial error diffusion encoding. By using an integral imaging strategy, approximate sinusoidal patterns can be obtained under nearly focused projection, which can then be subjected to absolute phase unwrapping and 3D reconstruction. The experiments show that compared to the three comparative algorithms under the same experimental conditions, this proposed method improves the reconstruction error of measuring a plane and an object by at least 13.66% and 12.57% when K=2. The dynamic experimental result on the palm confirms that the proposed method can reliably reconstruct the 3D shape of the moving object.

Step Surface Profile Measurement Based on Fringe Projection Phase-Shifting Using Selective Sampling

Fringe projection is a non-contact optical method that is widely used in the optical precision measurement of complex stepped surfaces. However, the accuracy of the fringe phase extraction employed has a direct impact on the measurement precision of the surface shape. Where phase-shifting measurement is used, the classical equal step phase extraction algorithm can only be used to measure simple and smooth surfaces, and leads to measurement errors on complex stepped surfaces, which affects the accuracy of the phase extraction. In addition, the iterative process lasts for a long time, resulting in a low efficiency. This paper proposes a step-by-step phase-shifting extraction algorithm based on selective sampling to measure the contour of the stepped surface. Firstly, the fringe pattern is sampled at equal intervals to reduce the iterative calculation time. Finally, the accurate measurement phase is calculated by the alternating iteration method. The phase extraction accuracy and iteration times are compared in experimental measurements between classical iterative algorithms such as four-step phase-shifting algorithms and the variable phase shift phase interpolation algorithm based on selective sampling. It is shown that the variable frequency phase-shifting extraction algorithm based on selective sampling has a shorter operation time, smaller error, and higher accuracy than the traditional iterative algorithm in fringe projection measuring complex stepped surfaces.

Accurate Measurement for the Subsequent Perturbation in the Coherent Φ-OTDR System with Small Laser-Frequency-Drift

In the coherent Φ-OTDR system with small laser-frequency-drift less than 50 kHz, the phase change in the quiet region without external perturbation is theoretically deduced to be linear with the fiber length while its waveform in the direction of pulse sequence is highly similar with the external perturbation acting on the fiber before the quiet region. Moreover, the phase information of one position contains the perturbation information of all foregoing positions. Consequently, a simple and accurate solution of differential operation for acquiring the phase information of subsequent perturbation which is behind the initial perturbation occurring on the fiber is proposed. The fitted phase change trace between the foregoing and the subsequent perturbation is extended to the region behind the subsequent perturbation. Then, behind the subsequent perturbation, the extended phase change trace is subtracted by the fitted phase change trace containing two perturbations. Moreover, in order to afford the fitting data with less noise as much as possible, the phase changes at positions where the value of modulus of coherent Φ-OTDR is lower than the set threshold value is firstly eliminated. To verify these methods, an experiment with two PZT vibrations in this paper is described. For the subsequent PZT vibration, the sinusoidal phase signal with a frequency of 50 Hz is perfectly retrieved when the threshold is set to be 10 mV. And the discussion about threshold value shows that it is satisfactory for the accuracy of phase extraction of the subsequent perturbation if the threshold is set as or above the noise level in the form of modulus in the experiment.

Pre‐filter phase‐locked loop: principles and effects with inter‐harmonic perturbation

The phase-locked loop (PLL) is an available synchronisation technique that can extract the fundamental frequency and phase of the grid. Benefited from the filter properties, pre-filter PLL is widely applied in voltage source inverters (VSIs) to enhance the accuracy of phase extraction. With the consideration of inter-harmonic perturbation, the principles between pre-filter PLL and VSI performance as well as the effects of pre-filter PLL on VSI are investigated in this study. Based on the conventional PLL, the small signal of pre-filter PLL is proposed. To fully represent the pre-filter PLL effects, the simplified VSI model is established and the current performance of VSI could be presented by the pre-filter PLL. From the angles of current total harmonic distortion, the effects of pre-filter PLL under inter-harmonic perturbation are clarified. The effects of pre-filter PLL on VSI are validated under the inter-harmonic perturbation based on the experiment platform. The results indicate that the current performance of VSI could be improved with the decreased bandwidth of both pre-filter and PLL, which shows a valuable application reference for the optimised design of VSI.

Fast and high precision spatial carrier frequency phase shifting algorithm based on the second order difference

A spatial carrier phase shifting algorithm based on the second-order difference (SCFPS-SD) is proposed. By numerically calculating the first and second order difference of one spatial carrier frequency interferogram (SCFI) and then using a normalization algorithm, the high accuracy of phase extraction will be obtained rapidly. Based on the original differential extraction phase (SCFPS based on derivative method, SCFPS-DM) method, the proposed SCFPS-SD algorithm does not need to calculate the carrier frequency in advance and the achieved result is not affected by the accuracy of the extraction carrier frequency algorithm. Compared with current SCFPS algorithm, the proposed algorithm reveals obvious advantage in calculation speed and precision even if the sample height, carrier frequency and noise level are greatly changed. Both advantages and effectiveness of the proposed SCFPS-SD algorithm can be demonstrated by simulation and experiment.

A novel dual-wavelength iterative method for generalized dual-wavelength phase-shifting interferometry with second-order harmonics

To address dual-wavelength interferograms with arbitrary phase shifts and second-order harmonics, a novel dual-wavelength iterative method (DWIM) based on the least-squares algorithm is proposed. In generalized dual-wavelength phase-shifting interferometry, to compensate for the phase-shift errors consisting of systematic and random phase-shift error, the wrapped phases of single-wavelength with high accuracy can be simultaneously obtained from generalized dual-wavelength interferograms without second-order harmonics. In addition, this method is also employed to deal with randomly phase-shifted dual-wavelength interferograms with the second-order harmonics, and then the effects of the fringe number in interferogram and the number of interferograms used on the accuracy of phase extraction are investigated by numerical simulations. Based on theoretical analysis and simulation results of DWIM, we present the basic relationship between the number of wavelengths, the second-order harmonics and the requirement of the minimum number of interferograms. Finally, the effectiveness of this method is proved by the simulation results of the spherical cap, and its applicability is verified with the results of the micro-sphere, the HeLa cell and the red blood cell, respectively.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0×10 −4 corresponding to 1 °C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10 −8 rad.