Phase Error Compensation Method Research Articles

LUT-based phase error compensation method for large-step phase-shifting algorithm in DLP4500-based FPP system

As a low-cost professional digital light projection device, the DLP4500 have been widely applied in fringe projection profilometry (FPP), for both laboratory and practical application. However, our recent experiments revealed a new hardware-induced projection instability when the projection pattern data exceeds its buffer capacity (48 bits). This phenomenon undermines the measurement accuracy advantage of the phase-shifting (PS) algorithms with large number of shifting steps, and eventually leads unwanted and complicated error to 3D reconstruction. In this paper, we experimentally investigate the new hardware-induced phase error and proposed a LUT-based phase error compensation method. In this method, a standard plate with a precision manufactured plate is used as the standard reference for the phase error evaluation, where an ideal plane fitting and the projector pixel reprojection process are introduced to generate the ideal reference phase. Comprehensive experiments are conduct to verify the stability of the proposed method in LUT creation. Comprehensive experiments are conduct, and the results show that (i) the method works creates LUTs stably at different plate positions, (ii) the plate with regular manufacturing accuracy (not exceeding 0.01 mm) can meet the application requirements of the proposed method. Both quantitative and qualitative experimental results successfully verify the effectiveness of proposed method in LUT creation and phase error reduction.

A Rapid Circuit Phase Error Identification and Compensation Method for MEMS QMG Achieving 99.7% Reduction in ZRO Drift

A Rapid Circuit Phase Error Identification and Compensation Method for MEMS QMG Achieving 99.7% Reduction in ZRO Drift

An In-Run Automatic Demodulation Phase Error Compensation Method for MEMS Gyroscope in Full Temperature Range.

The demodulation phase error will cause the quadrature error to be coupled to the rate output, resulting in performance deterioration of the MEMS gyroscope. To solve this problem, an in-run automatic demodulation phase error compensation method is proposed in this paper. This method applies square wave angular rate input to the gyroscope and automatically identifies the value of the demodulation phase error through the designed automatic identification algorithm. To realize in-run automatic compensation, the demodulation phase error corresponding to the temperature point is measured every 10 °C in the full-temperature environment (-40~60 °C). The relationship between temperature and demodulation phase error is fitted by a third-order polynomial. The temperature is obtained by the temperature sensor and encapsulated in the ceramic packages of the MEMS gyroscope, and the in-run automatic compensation is realized based on the fitting curve. The temperature hysteresis effect on the zero-rate output (ZRO) of the gyroscope is eliminated after compensation. The bias instability (BI) of the three gyroscopes at room temperature (25 °C) is reduced by four to eight times to 0.1°/h, while that at full-temperature environment (-40~60 °C) is reduced by three to four times to 0.1°/h after in-run compensation.

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.

Saturation-Induced Phase Error Compensation Method Using Complementary Phase.

Intensity saturation can induce phase error and, thus, measurement error in fringe projection profilometry. To reduce saturation-induced phase errors, a compensation method is developed. The mathematical model of saturation-induced phase errors is analyzed for N-step phase-shifting profilometry, and the phase error is approximately N-folder of the frequency of the projected fringe. Additional N-step phase-shifting fringe patterns with initial phase-shift π/N are projected for generating a complementary phase map. The final phase map is obtained by averaging the original phase map extracted from the original fringe patterns and the complementary phase map, and then the phase error can be canceled out. Both simulations and experiments demonstrated that the proposed method can substantially reduce the saturation-induced phase error and realize accurate measurements for a highly dynamic range of scenarios.

Robust dynamic spectroscopic imaging ellipsometer based on a monolithic polarizing Linnik interferometer.

We describe a robust dynamic spectroscopic imaging ellipsometer (DSIE) based on a monolithic Linnik-type polarizing interferometer. The Linnik-type monolithic scheme combined with an additional compensation channel solves the long-term stability problem of previous single-channel DSIE. The importance of a global mapping phase error compensation method is also addressed for accurate 3-D cubic spectroscopic ellipsometric mapping in large-scale applications. To evaluate the effectiveness of the proposed compensation method for enhancing system robustness and reliability, a whole thin film wafer mapping is conducted in a general environment where various external disturbances affect the system.

A phase error compensation method for three-dimensional shape measurement using improved iteration algorithm

The binary defocusing has been extensively studied in the three-dimensional measurement. But if the projector is slightly defocused, the binary fringes after defocusing still contain high-order harmonics compared with the ideal sinusoidal fringes, so the phase error caused by the nonlinear response is not negligible. In this paper, two models are proposed to calculate and compensate phase error, which include a double-precision iterative compensation model (DPICM) and a dual-domain iterative compensation model (DDICM). These two models obtain accurate phase errors by fusing the phases at different precision and domains. DPICM is composed of the double precision method and the improved iterative algorithm, and DDICM consists of the dual-domain method and the improved iterative algorithm. This improved iterative algorithm is used to compensate phase error, which can improve phase accuracy. DPICM and DDICM reduce the RMS error by 25.5% and 13.5% respectively.

Phase error model and compensation method for reflectivity and distance discontinuities in fringe projection profilometry.

Phase shifting fringe projection profilometry is a widely used optical 3D surface measurement method due to its high resolution, high speed, and full-field inspection. However, the measurement accuracy decreases in regions with a reflectivity or distance discontinuity. To this end, first, a general continuous quasi-one-dimensional phase error model is proposed for discontinuity representation. Second, the discontinuities are further divided into degenerate and nondegenerate discontinuities to improve the computational speed. Third, a phase error compensation algorithm is proposed with a parameter estimation method to improve the measurement accuracy. Simulations and experiments demonstrate that the proposed methods are effective.

Active projection nonlinear γ correction method for fringe projection profilometry.

In fringe projection profilometry (FPP), the luminance nonlinearity generated by the superimposed γ effect of the projector and camera can lead to distortion of the intensity of the sinusoidal phase-shift fringe, resulting in a reduction of measurement precision and resolution. Traditional phase error compensation and γ-correction methods need to focus on the projector's optimal performance. However, commercial projectors often have huge apertures and are, therefore, unable to project a perfectly focused sinusoidal fringe image. This paper proposes an easy-to-implement active projection error correction method with high precision that is insensitive to projector defocus. After calibrating the projector to establish the nonlinear γ-response model of the optical measurement system, inverse γ compensation is performed. By generating and projecting a set of precorrected sinusoidal fringes, the camera can capture the high-quality sinusoidal fringe image and decrease the phase measurement error caused by the nonlinear γ effect of the FPP system. Computer simulations and experiments verify the effectiveness and feasibility of the proposed method for estimating and correcting the nonlinear γ distortion of the FPP system. The experimental results show that using the proposed active projection method to compensate for the error of the three-step phase-shift algorithm can achieve a high-precision measurement, and the influence of the system's nonlinear γ effect on the measurement accuracy is significantly suppressed.

Moving target imaging of a dual-channel ISAL with binary phase shift keying signals and large squint angles.

A dual-channel inverse synthetic aperture ladar imaging experimental system based on wide-pulse binary phase coded signals and its moving target imaging are introduced. The analysis, simulation, and experimental data processing results of binary phase coded signal Doppler compensation and pulse compression are included. The method of motion phase error estimation based on interferometric processing and the imaging method with small computation in the case of large squint angles are proposed, and the simulation results are presented. The effectiveness of the imaging method is verified by experimental data processing. Doppler frequency curves are estimated based on time-frequency analysis of echo signals, and the coarse compensation of motion phase error is realized. According to the interferometric phase and coherence coefficient of dual-channel echo signals' time-frequency analysis, the coherence of the dual-channel echo signals is checked, and along-track interferometry can be applied to the precise compensation. The stable interferometric phase and increased coherence coefficient of actual dual-channel data imaging results indicate the effectiveness of the motion phase error compensation method proposed. Considering characteristics of inverse synthetic aperture ladar (ISAL) imaging, after dividing echo signals into multiple sub-apertures, range-Doppler algorithm and sub-aperture stitching are adopted, the stitched image is corrected geometrically through Stolt transformation, and the computation is reduced.

Efficient ArcSAR Focusing in the Wavenumber Domain

Arc synthetic aperture radar (ArcSAR) is a ground-based remote imaging technology with the ability to cover wide fields of view. However, because its azimuth is formed by scanning angle rotation, the focusing of ArcSAR images is different from classical SAR focusing. Since the existing imaging methods cannot give a good balance between computational efficiency and accuracy, the wavenumber domain algorithm (WMA) could become an interesting alternative. Due to the fact that in ArcSAR imaging, the slant range measurement depends on a sine term of the scanning angle, no dedicated WMA-based approach for ArcSAR imaging has been formulated yet. The main challenge in this context is that the solution of the stationary phase point cannot be resolved explicitly via Fourier transform (FT). This article proposes a new wavenumber domain imaging method, which exploits the sine law in the process of solving the stationary phase point during FT along the direction of the received echo using the triangular relationship formed by the target, the radar, and the rotation center of radar and then obtains the exact phase error expression in range and angular wavenumber domain without any approximation of the slant range or scanning angle. Using this formulation, we develop the corresponding phase error compensation method and complete image focusing. Through point target simulation and experiments on real ArcSAR data, the effectiveness of this method is verified in terms of imaging accuracy and computational efficiency.

Gamma Precorrection and Phase Error Compensation Methods Based on Three-Frequency with Three-Phase Shift

Digital fringe projection measurement technology has been widely used in computer vision and optical three-dimensional (3D) measurement. Considering the phase error caused by the gamma distortion and nonlinear error, the active gamma precorrection and phase error compensation methods based on the three-frequency with three-phase shifts are designed to reversely solve the initial phase and accurately compensate phase error. On the one hand, the gamma coefficient of the measurement system depends on precoding two groups of fringe sequences with different gamma coefficients to calculate the corresponded proportional coefficient of harmonic component. On the other hand, the phase error compensation method is designed to compensate the phase error and improve the accuracy and speed of phase calculation after gamma correction. Experiments show that the proposed precalibration gamma coefficient method can effectively reduce the sinusoidal error in nearly 80 percent which only needs fewer fringe patterns. Compared with the traditional three-frequency with four-phase shift method, the proposed method not only has higher phase accuracy and better noise resistance but also has good robustness and flexibility, which is not limited to the gamma distortion model.

Phase error compensation based on Tree-Net using deep learning

The nonlinear effect in phase shifting profilometry (PSP) is an essential source of phase error in 3D measurement. In this paper, we propose a universal phase error compensation method with a three-to-three deep learning framework (Tree-Net). Perfectly meeting the phase error compensation requirements, Tree-Net can construct six-step phase-shifting patterns from three-step. As a result, this compact network of fringe-to-fringe transformation has excellent performance when coping with different PSP systems after only one training. Experimental results demonstrate that the phase error can be reduced by about 90% in three-step PSP, which verified the effectiveness, universality, and robustness of the proposed method.

Modified three-wavelength phase unwrapping algorithm for dynamic three-dimensional shape measurement

Digital fringe projection (DFP) method has been widely used in three-dimensional (3D) shape measurement. Lots of studies have been conducted to enhance the measurement accuracy and speed by modulating the patterns. However, it is still hard to acquire enough number of 3D results to ensure the continuity of dynamic 3D shape measurement when phase shifting profilometry and temporal phase unwrapping algorithm is adopted. Besides, object motion can introduce phase error and thus measurement error for phase shifting profilometry. To this end, a dynamic 3D reconstruction framework based on modified three-wavelength phase unwrapping algorithm and phase error compensation method is proposed to solve this problem. By redefining the order of fringe patterns projected by the digital light processing (DLP) projector, the number of required patterns for 3D reconstruction can be reduced and the speed of dynamic 3D shape measurement can be improved. And using phase error compensation method based on Hilbert transform, the accuracy of 3D reconstruction can also be improved. Experiments were carried out to demonstrated the effectiveness of the proposed framework. And the modified algorithm successfully improved the speed of dynamic 3D shape measurement by 1∕3.

Antenna Phase Error Compensation for Terahertz Coded-Aperture Imaging

Coded-aperture antenna plays an important role in terahertz coded-aperture imaging radar system. However, the performance of a system is inevitably affected by the phase errors introduced by the coded-aperture antenna elements. In this paper, we propose a phase error compensation method by deducing a formula to compute all element phase errors accurately. According to the formula, the phase errors can be calibrated by using a calibrator and can be used to compensate the imaging model of the system. Numerical simulations demonstrate that the proposed method can effectively improve the imaging quality when the elemental phase error exceeds 10 ∘ .

A flexible phase error compensation method based on probability distribution functions in phase measuring profilometry

We demonstrate a fast and easy phase-error compensation technique based on statistical analysis of the wrapped phase distributions. The probability distribution functions (PDF) of the wrapped phase will become abnormal when there are nonlinear effects in a phase measuring profilometry. With the known iterative phase compensation algorithm, the most appropriate coefficients will be obtained by smoothing the PDF. The proposed method doesn’t need more fringe images than the choosing three or four step fringe images as well as reference images. It can lead to a fast and easy phase-error compensation. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.

ISAR Imaging and Cross-Range Scaling for Maneuvering Targets by Using the NCS-NLS Algorithm

The azimuth resolution of an inverse synthetic aperture radar (ISAR) image is determined by the angular diversity of the target. In order to improve the azimuth resolution of an ISAR image, it is necessary to view the target at more different aspect angles, which is commonly achieved by extending the coherent processing interval (CPI). However, as the CPI lengthens, the effective rotation of a target can no longer be approximated to be uniform and the rotational acceleration should be taken into consideration. The non-uniform rotation can bring about the 2-D space-variant phase error, which degrades the focusing quality of an ISAR image seriously. In this paper, a novel ISAR imaging and a cross-range scaling algorithm for a maneuvering target with a non-uniform rotation are proposed. In the proposed algorithm, the spatially variant phase error is compensated for by the joint phase error compensation method based on nonlinear chirp scaling (NCS) principle. The estimation of the effective rotational information required in the NCS-based joint phase error compensation method and the cross-range scaling is transformed into a nonlinear least-squares (NLS) problem. The NLS problem is solved by Gauss–Newton method and FFTs with high efficiency. The results acquired from the processing of both the simulation and real data validate the effectiveness of the proposed algorithm.

Multiple-gamma-value based phase error compensation method for phase measuring profilometry.

Three-dimensional measurement based on fringe projection has been widely used. However, the gamma nonlinearity and system nonlinearities usually result in significant phase error. Furthermore, there are various gamma values due to the non-uniform brightness distribution of the projector and nonlinear factors of the system, which makes the problem more complicated. To solve this problem, a sub-area compensation method based on multiple gamma values is proposed. In the beginning, a uniform image is projected on a standard whiteboard with a smooth surface. The obtained image is partitioned by using histogram statistics. Then, different phase error models are established for different regions. Finally, the phase error is compensated according to the regions. By applying this method, the accuracy of the phase algorithm is greatly improved. The method is simple and convenient compared with the existing methods.

A channel phase error compensation method for multi-channel synthetic aperture ladar

With the development of earth remote sensing technology, it is required to obtain high resolution and wide swath simultaneously. Synthetic Aperture Ladar(SAL) can achieve high-resolution images, but swath of images is limited. The multi-channel SAL combined with digital beamforming(DBF) technology provides a good solution to solve the problem. However, phase error between channels will degrade the quality of DBF. SAL is sensitive to phase error because of short wavelength of laser, which is at least three orders of magnitude shorter than that of synthetic aperture radar (SAR). Therefore, the conventional compensation methods can not satisfy the requirement of high compensation accuracy. In this paper, a compensation method based on antenna pattern and Doppler correlation coefficient is proposed, constructing a cost function. By minimizing the combined cost function, the phase error between channels is estimated with a good accuracy better than 1°. And simulation results validate the effectiveness of the proposed method.

Exponential fringe projection for alleviating phase error caused by gamma distortion based on principal component analysis

Fringe projection profilometry is commonly used for three-dimensional (3-D) shape measurement. The gamma effect caused by nonlinear intensity response of projector-camera system makes ideal sinusoidal waveforms nonsinusoidal, leading to phase and 3-D shape errors. The existing phase-error compensation methods or gamma correction methods are complicated and time-consuming. An exponential fringe projection method is proposed based on principal component analysis to alleviate phase error without requiring any complicated prior and post data. The experimental results demonstrate that the proposed method decreases the phase error effectively with high quality in the measured surfaces and needs low computational cost by comparing with the existing state-of-the-art methods.