Absolute Phase Error Research Articles

Deep learning-based frequency-multiplexing composite-fringe projection profilometry technique for one-shot 3D shape measurement

The pursuit of precise and efficient 3D shape measurement has long been a focal point within the fringe projection profilometry (FPP) domain. However, achieving precise 3D reconstruction for isolated objects from a single fringe image remains a challenging task in the field. In this paper, a deep learning-based frequency-multiplexing (FM) composite-fringe projection profilometry (DFCP) is proposed, where an end-to-end absolute phase retrieval network (APR-Net) is trained to directly recover the absolute phase map from a FM composite fringe pattern. The obtained absolute phase map exhibits exceptional precision and is devoid of spectrum crosstalk or leakage disturbance typically encountered in traditional FM techniques. APR-Net is intricately crafted, incorporating a nested strategy along with the concept of centralized information interaction. A diverse dataset encompassing various scenarios and free from spectrum aliasing is assembled to guide the training process. A seven-map loss calculation scheme is employed to guide the training process, of which the efficacy is proved through ablation experiments. In the first qualitative experiment, DFCP demonstrates comparable phase accuracy to ground truths with 47 fewer projected images, outperforming other three methods with mean absolute phase errors of 0.0052 rad, 0.1761 rad, 0.0169 rad, and 0.0139 rad. The second qualitative experiment and the quantitative evaluation respectively prove DFCP’s capability in high dynamic range 3D measurement and in precise 3D measurement, with sphere diameter errors of 0.0780 mm and 0.0726 mm, and a spherical centroid distance error of 0.0555 mm.

Method of unwrapped phase error correction in phase-measuring profilometry based on adaptive local window

Phase measurement profilometry (PMP) is widely used to reconstruct three-dimensional (3D) shape of objects. However, errors are introduced during standard phase unwrapping process, which considerably brings down measurement accuracy and lowers method reliability. This paper proposes a novel method to identify the errors, and subsequently correct these errors through erecting adaptive local windows. Under proposal, two robust algorithms are developed to correct these errors in initial rudimentary correction as well as in subsequent refined error removal. The adaptive local window is designed as such that the fringe order corresponding to each period of the wrapping phase is independent of each other. Therefore, it avoids the error transmission in the correction process. Experiments are carried out on absolute phase error correction and 3D point cloud reconstruction. Experimental results verified the developed method in terms of reducing the stratification of 3D point cloud and improving the quality of 3D measurement.

A 3D shape measurement method for high-reflective surface based on dual-view multi-intensity projection

Phase shifting profilometry has been commonly used in three-dimensional shape measurement with the advantages of high-precision and non-contact. However, it is still challenging to measure high-reflective surface because image saturation will lead to absolute phase errors and reconstruction errors. In this paper, a dual-view multi-intensity projection method was proposed. Compared with the single-view method, the proposed method can reconstruct more points at each projection intensity especially for pixels around the specular angle and reduce the number of projections to reduce the time consumption. First, we established the dual-view structured light system consisting of two monocular systems that share the same projector. Subsequently, a dual-view saturated pixel judging method was proposed that enables the reconstruction results under two views to be combined without duplicate points. The multi-intensity projection method was adopted by reducing the input projection intensity step by step and reconstructing the remaining pixels around the specular angle. Finally, the reconstruction result can be obtained by stitching point clouds at each projection intensity. Experiments verified that the proposed method could improve the integrity of reconstructed point clouds and measurement efficiency.

Pixel-Wise Phase Unwrapping With Adaptive Reference Phase Estimation for 3-D Shape Measurement

Phase unwrapping plays an important role in phase-based three-dimensional (3D) shape measurement. This paper proposes an effective pixel-wise phase unwrapping method without requiring additional fringe patterns. Firstly, compared with the geometric constraint-based (GCB) method which needs calibrate the fringe projection system and create a reference phase at the closest plane <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> within the measurement volume, the proposed method can adaptively and directly estimate the reference phase from the wrapped phase without system calibration and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> estimation. Secondly, based on the finding that the slope angle of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> plane ignored by the GCB method has significant impact on the measurement range, thus the phase gradients that highly correlates with the optimal slope angle are involved into reference phase estimation. The wrapped phase can be pixel-by-pixel unwrapped by comparing with the reference phase. Both simulations and experiments have been conducted to demonstrate the efficiency of the proposed method. Compared with traditional two-frequency method and phase-coding method, the proposed method can improve the measuring speed by 2 times. Experiment results show that the proposed method can effectively remove the phase unwrapping errors and achieve the mean absolute phase error of 0.0137 rad, which has obvious advantages relative to traditional methods.

A 3D shape measurement method for high-reflective surface based on accurate adaptive fringe projection

Fringe projection profilometry (FPP) is a popular three-dimensional (3D) shape measurement technique with advantages of high-precision and non-contact. However, measuring high-reflective surface is still a challenging task for conventional FPP because image saturation leads to absolute phase errors and reconstruction errors. In this paper, a new adaptive fringe projection (AFP) method is proposed. Compared with existing AFP methods, we simplify the experimental process and get more accurate coordinate mapping. First, we built the projection intensity model for each projector pixel rather than camera pixel. Then, a uniform gray pattern was projected and two images were captured under high and low exposures respectively to calculate the quantitative low projection intensity. In coordinate mapping, sub-pixel coordinates were mapped from camera image onto projector image. They were filtered with absolute phase to deal with resolution difference between camera and projector and get accurate coordinate correspondence. Finally, adaptive fringe patterns were generated. Besides, we proposed a novel quantitative criterion to evaluate the effectiveness of AFP methods called point cloud integrality (PCI), which is calculated based on the number of 3D points of high-reflective areas. The experiments demonstrate that the proposed method increases both the measurement accuracy and PCI compared with conventional FPP and some existing AFP methods.

Extended bilinear transform and multirate technique based approach for analog-to-digital transform

ABSTRACT In this paper, a new transformation polynomial for -to- plane is presented. This third-order transformation is derived by optimising the coefficients of the logarithmic series followed by utilising the multirate technique to extend its bandwidth. In terms of magnitude and phase response, the proposed transform correlates well with the ideal and shows mean absolute magnitude error and mean absolute phase error as dB and dB, respectively. The proposed transform is compared with the existing operators to demonstrate its performance. In addition, an example is also conferred, which establishes the viability of the transform in terms of the overall frequency response, when applied for analog-to-digital transformation.

Phase error correction method based on the Gaussian filtering algorithm and intensity variance

To overcome the invalid phase and phase jump phenomenon generated during the phase unwrapping, a phase error correction method based on the Gaussian filtering algorithm and intensity variance is proposed in this paper. First, a threshold of fringe intensity variance is set to identify and clear the phase in the invalid region. Then, the Gaussian filtering algorithm is employed to correct the phase order at the fringe junction, and then the absolute phase is corrected. Finally, the phase correction experiments of different geometric objects are carried out to verify the feasibility and accuracy of the proposed method. The method proposed in this paper can be extended to the correction of absolute phase error obtained by any coding method.

Esquemas de corrimiento de fase: estudio comparativo

La interferometría por corrimiento de fase es una técnica bien establecida para mediciones de fase, la cual requiere de una serie de patrones de franjas corridos en fase. En este trabajo, se analizan dos algoritmos de corrimiento de fase, los cuales se han usado para la recuperación de fase cuando se considera que los corrimientos de fase tienen error de calibración. El primer esquema analizado fue el algoritmo iterativo avanzado (AIA) y el segundo método es un esquema basado en el método de Levenberg-Marquardt (LM). Con el objetivo de mostrar su rendimiento, los evaluamos usando datos sintéticos y tomando en cuenta la exactitud, el orden de convergencia, así como el error por desentonamiento en los pasos. Los resultados muestran que ambos métodos reducen el error linealmente respecto al número de patrones de franjas; sin embargo, el esquema AIA tiene un desempeño significativamente mejor tanto en precisión como en tiempo de procesamiento. Este estudio arroja luz sobre las ventajas y desventajas de uso de las soluciones lineal y no lineal para la demodulación de patrones de franjas.

Uncertainty evaluation on the absolute phase error of digitizers

In many engineering applications the phase angle of a signal is a key parameter. Especially when measuring small angles, the measurement accuracy is of a vital importance. Often, the absolute phase error of a digitizer, which is defined as the phase displacement between the digitized output and the input analog waveform and which represents a systematic measurement error, is neglected. Therefore, in this paper, a new measurement technique for the evaluation of this absolute phase error is discussed, along with a deep theoretical analysis on the uncertainty sources and how to handle them. The measurement technique is validated through a high accuracy experimental setup. Experimental tests demonstrate that even high accuracy digitizers can show non-linear behavior in the absolute phase errors.

Uncertainty Evaluation on the Absolute Phase Error of Digitizers

Uncertainty Evaluation on the Absolute Phase Error of Digitizers

Phase-shifting coding method for absolute phase retrieval

Absolute phase retrieval has been widely studied, as it is not much influenced by the discontinuity and occlusion of objects in phase-measuring profilometry. In the practical measurement, however, fringe order determination is by no means easy when the grayscale of deformed patterns is degraded because of uneven reflectivity or the large curvature of measured objects. We introduce a phase-shifting coding (PSC) method to overcome that problem. In the PSC method, fringe order is encoded by the phase-shifting amounts of additional fringe patterns, and the decoding algorithm to retrieve absolute phase is designed on the basis of phase difference and neighborhood consistency. The special statistical filtering and self-correcting filtering methods are utilized to eliminate absolute phase errors. Experiment results demonstrate that the proposed PSC method is effective and has strong robustness in grayscale degradation regions.

An F-Band $n$ -Probe Standing Wave Detector for Complex Reflection Coefficient Measurements in 40-nm CMOS

This article presents an F-band-integrated standing wave detector for complex reflection measurements. The complex reflection coefficient is derived from a standing wave, measured by 312 power detectors coupled from underneath a transmission line (TL), taking the loss of the TL into account. For the proposed method of reflection coefficient derivation, the tradeoff between TL length and number of probes is shown through simulation. The standing wave detector is fabricated in the 40-nm CMOS process, and the measurements show complex reflection coefficient for input powers down to −20 dBm at 120 GHz while only consuming $112~{\mu }\text{W}$ of dc power. In measurements, the complex reflection detection is shown for multiple impedances achieving an absolute phase error of 8.3° with a sigma of 1.5° and a magnitude error of 0.33 dB with a sigma of 0.21 dB, compared to a VNA reference measurement.

Measurement of the Absolute Phase Error of Digitizers

This paper proposes a method for the measurement of digitizer absolute phase errors, defined as the phase displacement between the digitized output and the input analog waveform. The measurement procedure is based on the use of a phase reference signal (PRS), which is theoretically synchronous with the input analog waveform and that triggers the digitizer sampling clock. From the characterization of the waveform generator phase response and the measurement of the time delay of the digitizer sampling clock with respect to the PRS, an accurate evaluation of the digitizer absolute phase error is obtained. The method has been applied to a high-performance digitizer, measuring the absolute phase errors of two different channels. The expanded uncertainty of the method has been quantified as a few microradians at 50 Hz and 150 $\mu $ rad at 20 kHz.

A Method for the Measurement of Digitizers' Absolute Phase Error

A Method for the Measurement of Digitizers' Absolute Phase Error

A Method for the Measurement of Digitizers’ Absolute Phase Error

A lot of engineering applications, from telecommunications to power systems, require accurate measurement of phase angles. Some of them, like synchrophasor measurement and calibration of instrument transformers with digital output, in order to reach high phase measurement accuracy, require the knowledge of phase error of digitizers. Therefore, in this paper a method for the measurement of digitizers’ absolute phase errors is proposed. It adopts a sinewave and two square waves, that are the digitizer sample clock and a phase reference signal. Combining the measurements of the relative phase differences between the adopted signals it is possible to accurately evaluate the absolute phase error of a digitizer.

Optimal fractional delay-IIR filter design using cuckoo search algorithm

This paper applied a novel global meta-heuristic optimization algorithm, cuckoo search algorithm (CSA) to determine optimal coefficients of a fractional delay-infinite impulse response (FD-IIR) filter and trying to meet the ideal frequency response characteristics. Since fractional delay-IIR filter design is a multi-modal optimization problem, it cannot be computed efficiently using conventional gradient based optimization techniques. A weighted least square (WLS) based fitness function is used to improve the performance to a great extent. FD-IIR filters of different orders have been designed using the CSA. The simulation results of the proposed CSA based approach have been compared to those of well accepted evolutionary algorithms like Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The performance of the CSA based FD-IIR filter is superior to those obtained by GA and PSO. The simulation and statistical results affirm that the proposed approach using CSA outperforms GA and PSO, not only in the convergence rate but also in optimal performance of the designed FD-IIR filter (i.e., smaller magnitude error, smaller phase error, higher percentage improvement in magnitude and phase error, fast convergence rate). The absolute magnitude and phase error obtained for the designed 5th order FD-IIR filter are as low as 0.0037 and 0.0046, respectively. The percentage improvement in magnitude error for CSA based 5th order FD-IIR design with respect to GA and PSO are 80.93% and 74.83% respectively, and phase error are 76.04% and 71.25%, respectively.

SU-F-303-08: Four-Dimensional MRI Method Based On Internal Respiratory Surrogate Derived by Dimensionality Reduction

Purpose: To investigate the feasibility of constructing 4D MRI using non-navigator, image-based internal respiratory surrogate derived by dimensionality reduction (DR). Methods: DR is a mathematical process that derives a series of scalar indices from the corresponding image frames. We proposed a novel image acquisition scheme (A) designed for the DR- derived internal surrogates (Wachinger, 2012) to better match the temporal pattern of previously established surrogates such as diaphragm position. The idea is to acquire a pair of slices alternatingly so the phase of a slice can be more accurately determined with additional information from the other slice. This scheme was compared with the sequential acquisition scheme (B), the navigator-based approach (C), and a previously proposed method using body area as internal respiratory surrogate (Cai, 2011) (D). Correlation between internal surrogates from all schemes and the diaphragm position was studied using a publicly available 4D MRI dataset (von Siebenthal, 2007). Results: DR did not require any manual preprocessing. It took only a few minutes to process the entire 4D MRI data of 100 respiratory cycles with a common desktop computer. The respiratory surrogate signals were highly correlated with diaphragm positions. Correlation coefficients were 0.996, 0.993, 0.997, and 0.982 and mean absolute phase errors were 1.5%, 2.0%, 1.3%, and 3.3% for A, B, C and D, respectively. With the navigator-based approach C, the sampling rate of the regions of interest was reduced by half. Among those without the need for navigators, the novel acquisition scheme A reflected diaphragm positions better than the sequential scheme B and body area scheme D. Conclusion: The proposed image-based 4D MRI method with a novel acquisition scheme and the DR-derived internal respiratory surrogate compared favorably to the navigator-based approach and has twice the sampling rate. Although tested on sagittal slices, it is potentially applicable to any slice orientation.

Design of Digital Differentiators Using Interior Search Algorithm

Abstract This paper presents a novel metaheuristic algorithm called Interior Search Algorithm (ISA), which is applied for digital differentiator design problem. ISA is based on the principles of aesthetic techniques commonly used in interior design and decoration. ISA has a very quick convergence rate and only one control parameter. The approach presented here has alleviated from the problems of premature convergence, stagnation and revisiting of the same solution over and over again, which is common in other optimization techniques. Statistical and simulation results have been compared with already existing differentiator design methods such as segment rule, genetic algorithm (GA), simulated annealing (SA), pole zero method (PZ) and particle swarm optimization (PSO). The results affirm that the proposed method outperforms its counterparts in terms of absolute magnitude error and phase error.

Low-power broadband quadrature signal generator based on phase-tunable dividers

This paper presents the design and experimental results of a low-power 300---960 MHz I/Q signal generator for low-IF receivers. The circuit is based on phase-tunable dividers and uses delay-locked loops, which provide phase accuracy for the quadrature signals as well as low-sensitivity of the phase error against temperature and power supply variations. Thanks to the adopted technique, the phase error can be further reduced by trimming the reference voltage of the delay-locked loops through a calibration digital word, which can be stored in a non-volatile memory during manufacturing. The I/Q generator exhibits an absolute phase error before calibration that is lower than 1.5°. The I/Q phase drift due to temperature variations from ?40 to 85 °C and power supply variations from 1.1 to 1.3 V is 0.3° and 0.2°, respectively. By dividing the overall frequency range into four 165-MHz wide sub-bands and using only four 5-bit calibration words, the I/Q phase variation with respect to frequency, temperature, and power supply is lower than 1° in the 300---960 MHz operating band. The I/Q generator is implemented in a 90-nm CMOS technology and exhibits a current consumption as low as 0.5 mA.

Miniaturized 40–60 GHz On-Chip Balun With Capacitive Loading Compensation

A millimeter-wave balun by using the broadside-coupled transmission lines and capacitive loading compensation is proposed and investigated. The balun is designed and verified by using a commercial SiGe BiCMOS technology. The measured results show that in the frequency range of 40-60 GHz, the amplitude mismatching and absolute phase error are less than 0.2 dB and 2.7°, respectively. The compact size of the balun is only 200 μm × 180 μm including grounding shield.