Absolute Phase Values Research Articles

Efficient and accurate projector calibration method based on phase-shifting method with sinusoidal structured light

ObjectiveProjector calibration is one of the most basic and important steps in structured light three-dimensional measurement. However, such as complicated calibration process and low accuracy are still the inevitable problems in the calibration process. In this paper, a projector calibration method based on phase-shifting method with sinusoidal structured light is proposed to improve the accuracy of the calibration and simplify the operation of the calibration. MethodsFirstly, projecting a set of sinusoidal fringes onto a black-and-white circular calibration board, and collecting the images synchronously by a CCD camera; Secondly, establishing the correspondence between camera pixels and projector pixels by using the consistency of phase information which means that the absolute phase value of an arbitrary point on the calibration board is equal to the absolute phase value of this point in the camera image and virtual projector image; And then a set of virtual DMD images on the projector can be obtained by using the principle above; Finally, using this set of virtual DMD images, the parameters of the projector can be calibrated with camera calibration method based on circular calibration board. ResultsThe experimental results show that the maximum reprojection error of the projector calibrated by this method is 0.0419 pixels, and the average reprojection error is 0.0343 pixels. The equipment involved in the calibration process is simple and the experimental operation is easy. The experimental results indicated that this method has high calibration accuracy and efficiency.

Fast fringe projection profilometry using 3 + 1 phase retrieval strategy and fringe order correction.

Fringe projection profilometry (FPP) has attracted wide attention in optical 3D measurement field for its high resolution, high accuracy, and simple system construction. However, the inherent requirements of FPP's measurement speed and accuracy are contradictory. We adopt a 3+1 phase retrieval strategy combining phase shift and the Hilbert transform algorithm to achieve high-speed, high-precision simultaneous measurements with only four binary fringe patterns. Furthermore, when using temporal phase unwrapping, fringe order errors (FOEs) are inevitable. Although these FOEs do not affect neighboring pixels, they are brought into the final point cloud coordinates by the absolute phase value. We propose a fringe order correction method to eliminate FOEs. The feasibility and effectiveness of this method are verified by the experimental results.

Single-frequency and accurate phase unwrapping method using deep learning

Phase unwrapping is an important part of fringe projection profilometry(FPP), which greatly affects the efficiency and accuracy of reconstruction. Phase unwrapping methods with deep learning achieve single-frequency phase unwrapping without additional cameras. However, existing methods have low accuracy in the real complex scene, and can not process data whose resolution is greater than the resolution of training data. This paper introduces a neural convolutional network named as VRNet which achieves accurate and single-frequency phase unwrapping without extra cameras. VRNet with encoder-decoder structure gets multi-scale feature maps through feeding the wrapped phase map into the encoder, then fuses the feature maps recursively by using the proposed feature fusion module to accomplish precise prediction. In order to further improve the accuracy of phase unwrapping, this paper presents a phase correction method based on the distribution characteristics of the absolute phase. The method divides the cross-section of the absolute phase map into several curves and identifies a misclassified pixel by comparing its absolute phase value with the value of neighboring curves. In contrast to existing methods, the method is row-independent and does not require segmentation of image. Moreover, this paper accomplishes the prediction of high-resolution data through the phase stitching strategy and fine-tuning the phase correction method. Extensive experiments show that the proposed method is able to achieve high-accuracy and single-frequency phase unwrapping in real scenes which consist of at least one complex object, and is also effective for wrapped phase maps with a resolution larger than the training data.

An Absolute Wavenumber Calibration Method based on Characteristic Spectral Line and Constrained Fitting Phase

Spectral-domain Optical Coherence Tomography (SD-OCT) systems generally have nonlinear sampling problems in wavenumber domain. In order to realize the precise positioning of the discrete interfaces and the high-quality reconstruction of OCT images under conventional fast Fourier transform, it is necessary to solve the precise calibration problem of the absolute wavenumber of the discrete sampling points in the spectrometer. In this paper, an absolute wavenumber calibration method based on the absolute phase of the characteristic spectral line and the constraint polynomial fitting phase under precise optical path difference was proposed. In the sample arm of the SD-OCT system, metal gauges with precise thickness difference are used to obtain the absolute phase value of the characteristic spectral line, and the phase wrapping times corresponding to the characteristic spectral line are further accurately solved. Thus, this method overcomes the 2π ambiguity of spectral phase in conventional interferometric phase methods. At the same time, combined with the polynomial fitting phase of the high signal-to-ratio region under window constraint, the accurate calibration of the absolute wavenumber of each sampling point is realized. Finally, comprehensive comparisons between the proposed method and the traditional resampling method in terms of discrete interface positioning, axial resolution and image reconstruction quality verifies the significant advantages of this method.

An absolute wavenumber calibration method based on characteristic spectral line and constrained fitting phase

Spectral-domain optical coherence tomography (SD-OCT) systems generally have nonlinear sampling problems in wavenumber domain. In order to realize the precise positioning of the discrete interfaces and the high-quality reconstruction of OCT images under conventional fast Fourier transform, it is necessary to solve the precise calibration problem of the absolute wavenumber of the discrete sampling points in the spectrometer. In this work, an absolute wavenumber calibration method is proposed based on the absolute phase of the characteristic spectral line and the constraint polynomial fitting phase under precise optical path difference. In the sample arm of the SD-OCT system, the metal gauges with precise thickness difference are used to obtain the absolute phase value of the characteristic spectral line, and the phase wrapping times corresponding to the characteristic spectral line are further accurately solved. Thus, this method overcomes the 2π ambiguity of spectral phase in conventional interferometric phase methods. At the same time, combined with the polynomial fitting phase of the high signal-to-noise ratio region under window constraint, the accurate calibration of the absolute wavenumber of each sampling point is realized. Finally, comprehensive comparison between the proposed method and the traditional resampling method in terms of discrete interface positioning, axial resolution and image reconstruction quality verifies the significant advantages of this method.

Calibration of stereo cameras with a marked-crossed fringe pattern

Stereo cameras have been widely used for three-dimensional (3D) imaging, and their performances are highly depended on the calibration accuracy. This paper presents a marked-crossed fringe pattern for the calibration of stereo cameras. Some coded markers are also encoded into the crossed fringe pattern, and the feature points are encoded into the carried phase. Two wrapped phase maps are recovered by using the Fourier transform, and the markers are extracted and decoded for absolute phase unwrapping. Referring to the absolute phase values, the one-to-one mapping between the world points and the image points can be established to calibrate the stereo cameras. Compared with the traditional method, the proposed method adopts global coding, which can flexibly select any part of the feature points for calibration and obtain high-precision camera parameters. Simulations and experiments show the effectiveness of the method.

Absolute phase retrieval for a single-shot fringe projection profilometry based on deep learning

A deep learning-based method is proposed to recover the absolute phase value from a single fringe pattern. We propose a deep neural network architecture that includes two subnetworks used for wrapping phase calculation and phase unwrapping, respectively. The training set is generated with the absolute phase obtained by the combination of phase shifting and gray coding. In addition, a reference plane is adopted to provide periodic range information for phase unwrapping. Then according to the output of the well-trained network, a high-quality absolute phase is obtained through only a single fringe pattern of the measured object. Experiments on the test set verify that high accuracy for complex texture objects is acquired using the proposed method, which indicates its potential in high-speed measurement.

Increases in Load Carriage Magnitude and Forced Marching Change Lower-Extremity Coordination in Physically Active, Recruit-Aged Women

The objective was to examine the interactive effects of load magnitude and locomotion pattern on lower-extremity joint angles and intralimb coordination in recruit-aged women. Twelve women walked, ran, and forced marched at body weight and with loads of +25%, and +45% of body weight on an instrumented treadmill with infrared cameras. Joint angles were assessed in the sagittal plane. Intralimb coordination of the thigh-shank and shank-foot couple was assessed with continuous relative phase. Mean absolute relative phase (entire stride) and deviation phase (stance phase) were calculated from continuous relative phase. At heel strike, forced marching exhibited greater (P < .001) hip flexion, knee extension, and ankle plantar flexion compared with running. At mid-stance, knee flexion (P = .007) and ankle dorsiflexion (P = .04) increased with increased load magnitude for all locomotion patterns. Forced marching (P = .009) demonstrated a "stiff-legged" locomotion pattern compared with running, evidenced by the more in-phase mean absolute relative phase values. Running (P = .03) and walking (P = .003) had greater deviation phase than forced marching. Deviation phase increased for running (P = .03) and walking (P < .001) with increased load magnitude but not for forced marching. With loads of >25% of body weight, forced marching may increase risk of injury due to inhibited energy attenuation up the kinetic chain and lack of variability to disperse force across different supportive structures.

High-resolution Three-dimensional Surface Imaging Microscope Based on Digital Fringe Projection Technique

Abstract The three-dimensional (3-D) micro-scale surface imaging system based on the digital fringe projection technique for the assessments of microfiber and metric screw is presented in this paper. The proposed system comprises a digital light processing (DLP) projector, a set of optical lenses, a microscope, and a charge coupled device (CCD). The digital seven-step fringe patterns from the DLP projector pass through a set of optical lenses before being focused on the target surface. A set of optical lenses is designed for adjustment and size coupling of fringe patterns. A high-resolution CCD camera is employed to picture these distorted fringe patterns. The wrapped phase map is calculated by seven-step phase-shifting calculation from these distorted fringe patterns. The unwrapping calculation with quality guided path is introduced to compute the absolute phase values. The dimensional calibration methods are used to acquire the transformation between real 3-D shape and the absolute phase value. The capability of complex surface measurement for our system is demonstrated by using ISO standard screw M1.6. The experimental results for microfiber with 3 μm diameter indicate that the spatial and vertical resolutions can reach about 3 μm in our system. The proposed system provides a fast digital imaging system to examine the surface features with high-resolution for automatic optical inspection industry.

Investigation of Phase Pattern Modulation for Digital Fringe Projection Profilometry

Abstract The fringe projection profilometry with sinusoidal patterns based on phase-shifting algorithms is commonly distorted by the nonlinear intensity response of commercial projector. In order to solve this issue, sinusoidal width modulation is presented to generate binary sinusoidal patterns for defocusing the projection. However, the residual errors in the phase maps are usually notable for highly accurate three-dimensional shape measurements. In this paper, we propose the fringe patterns of the sinusoidal, square, and triangular periodic waveforms with seven-step phase-shifting algorithm to further improve the accuracy of three-dimensional profile reconstruction. The absolute phase values are calculated by using quality guided path unwrapping. We learn that by properly selecting fringe patterns according to the target shape, the undesired harmonics of the measured surface have negligible effect on the phase values. The experiments are presented to verify the imaging performances of three fringe patterns for different testing targets. The triangular fringe patterns are suitable for the shape measurements of complex targets with curved surfaces. The results provide a great possibility for high-accuracy shape measurement technique with wider measuring depth range.

Machine‐Learning Designs of Anisotropic Digital Coding Metasurfaces

AbstractDigital coding representations of meta‐atoms make it possible to realize intelligent designs of metasurfaces by means of machine learning algorithms. Here, a machine‐learning method to design anisotropic digital coding metasurfaces is proposed, and meta‐atoms may require any absolute phase values at different positions and under different polarizations. A deep‐learning neural network to predict the vast and complex system is proposed, in which only 70 000 training coding patterns are used to train the network. Another 10 000 randomly chosen coding patterns are employed to validate the neural network, showing an accuracy of 90.05% of phase responses with 2° error in the 360° phase. Using the learned network, the correct coding pattern among 18 billion of billions of choices for the required phase can be readily found in a second, finishing automatic design of anisotropic meta‐atoms. Three functional 1‐bit anisotropic coding metasurfaces are intelligently achieved by the learned network. It is convenient to realize dual‐beam scattering with left‐handed circular polarization (LHCP) for one beam while right‐handed circular polarization (RHCP) for the others, dual‐beam scattering with circular polarization for one beam while linear polarization (LP) for the others, and triple‐beam scattering with LHCP and RHCP for two beams while LP for the third one.

Phase-matching method based on optimization function for three-dimensional fringe projection

An optimization function-based phase-matching method is proposed for the three-dimensional (3-D) fringe projection method. As an essential procedure in 3-D fringe projection metrology, the phase-matching processing has a significant influence on the measurement accuracy. The traditional phase-matching method obtains the corresponding points in different images by comparing the phase-values directly, so its matching precision is easily affected by the phase-measurement error. The proposed method determines the corresponding points automatically and accurately by minimizing the cost function represented by the absolute phase values. The cost function consists of two parts: one for calculating the squared difference of the absolute phase to ensure matching precision, and the other is selected to guarantee optimization convergence. A series of experiments enable us to analyze the precision and effectiveness in practical application.

Reference image based phase unwrapping framework for a structured light system.

A novel real-time full-field phase unwrapping framework is proposed for the one-projector and one-camera structured light system. In this framework, only four patterns (including three fringe patterns and a binary speckle pattern) are required to measure the absolute 3D shape of the targets. We use the structured light system to capture four images of a nearly planar target (e.g. wall), of which the speckle image is taken as the reference image, and the corresponding absolute phase map is computed and stored, before measuring. So each pixel in the reference image can be mapped to an absolute phase value. In this way, if we can create the correspondences between the current and the reference speckle images in the process of measurement by using a matching algorithm, we can directly map the absolute values for the pixels of the current image. The mapped absolute phases can be used to determine the period of the relative phases. The experimental results verified the effectiveness and efficiency of the proposed framework. On a consumer-grade GPU (Nvidia GTX1060), our method can run at 187 fps.

An iterative PS-InSAR method for the analysis of large spatio-temporal baseline data stacks for land subsidence estimation

South-west of Tehran, the capital city of Iran, is subjected to a high deformation rate due to excessive groundwater extractions. Persistent Scatterrer SAR Interferometry (PS-InSAR) technique is used to monitor Tehran’s deformation. Three time series data including two Sentinel-1A (S-1A) spanning from 2014 to 2017, and an ENVISAT-ASAR data stack spanning from 2004 to 2010, are analyzed. The PS-InSAR technique does not perform well on ENVISAT-ASAR due to poor selection of PS points induced by large perpendicular baselines and strong temporal decorrelation of the dataset. In this paper, a novel Iterative PSI method (IPSI) is proposed to increase the PS points which are lost in PS-InSAR technique because of the unsuccessful derivation of the absolute phase value due to an integer ambiguity. The method selects PS points based on simultaneous analysis of their amplitude and phase. Results demonstrate that the density of PSs has been increased by about 4.5 times. Line of Sight (LOS) velocities obtained from both S-1A and ENVISAT-ASAR data analysis are highly compatible with each other, indicating the reliability of the both applied methods. The maximum cumulative displacements are estimated as 39.6 cm and 88.4 cm for Sentinel-1A and ENVISAT-ASAR datasets respectively. Moreover, the subsidence area has grown in the period between the data acquisition time. The methods are successfully validated by subsidence rates obtained from precise leveling and GPS observations.

Prediction of memory formation based on absolute electroencephalographic phases in rhinal cortex and hippocampus outperforms prediction based on stimulus-related phase shifts.

Absolute (i.e. measured) rhinal and hippocampal phase values are predictive for memory formation. It has been an open question, whether the capability of mediotemporal structures to react to stimulus presentation with phase shifts may be similarly indicative of successful memory formation. We analysed data from 27 epilepsy patients implanted with depth electrodes in the hippocampus and entorhinal cortex, who performed a continuous word recognition task. Electroencephalographic phase information related to the first presentation of repeatedly presented words was used for prediction of subsequent remembering vs. forgetting applying a support vector machine. The capability to predict successful memory formation based on stimulus-related phase shifts was compared to that based on absolute phase values. Average hippocampal phase shifts were larger and rhinal phase shifts were more accumulated for later remembered compared to forgotten trials. Nevertheless, prediction based on absolute phase values clearly outperformed phase shifts and there was no significant increase in prediction accuracies when combining both measures. Our findings indicate that absolute rhinal and hippocampal phases and not stimulus-related phase shifts are most relevant for successful memory formation. Absolute phases possibly affect memory formation via influencing neural membrane potentials and thereby controlling the timing of neural firing.

Comb-referenced frequency-sweeping interferometry for precisely measuring large stepped structures.

A precise 3D surface measurement method for large stepped structures without height ambiguity is proposed based on optical-frequency-comb-referenced frequency-sweeping interferometry and Fourier-transformed fractional phase retrieval. Unlike other interferometry that depends on the absolute phase value for several certain wavelengths, this method obtains results from the phase change during frequency sweeping and thus remains free from the confined non-ambiguity range. By reference to an optical frequency comb, the relative uncertainty from the tunable laser frequency was reduced by three orders of magnitude, and the sweeping frequency range can be precisely determined. Besides, the fractional phase can be rapidly retrieved in only one step using a Fourier transform method, with advantages of high accuracy and immunity to light intensity fluctuation and mechanical vibration noise. Samples of step heights from 1μm to 1mm were measured, and the standard uncertainty was 45nm. This permits applications such as quality assurance in microelectronics production and micro-electro-mechanical system (MEMS) manufacture.

Absolute phase unwrapping for dual-camera system without embedding statistical features

This paper proposes an absolute phase unwrapping method for three-dimensional measurement that uses two cameras and one projector. On the left camera image, each pixel has one wrapped phase value, which corresponds to multiple projector candidates with different absolute phase values. We use the geometric relationship of the system to map projector candidates into the right camera candidates. By applying a series of candidate rejection criteria, a unique correspondence pair between two camera images can be determined. Then, the absolute phase is obtained by tracing the correspondence point back to the projector space. Experimental results demonstrate that the proposed absolute phase unwrapping algorithm can successfully work on both complex geometry and multiple isolated objects measurement.

Fringe order correction for the absolute phase recovered by two selected spatial frequency fringe projections in fringe projection profilometry.

The performance of the two selected spatial frequency phase unwrapping methods is limited by a phase error bound beyond which errors will occur in the fringe order leading to a significant error in the recovered absolute phase map. In this paper, we propose a method to detect and correct the wrong fringe orders. Two constraints are introduced during the fringe order determination of two selected spatial frequency phase unwrapping methods. A strategy to detect and correct the wrong fringe orders is also described. Compared with the existing methods, we do not need to estimate the threshold associated with absolute phase values to determine the fringe order error, thus making it more reliable and avoiding the procedure of search in detecting and correcting successive fringe order errors. The effectiveness of the proposed method is validated by the experimental results.

Prediction of successful memory encoding based on single-trial rhinal and hippocampal phase information

Mediotemporal EEG characteristics are closely related to long-term memory formation. It has been reported that rhinal and hippocampal EEG measures reflecting the stability of phases across trials are better suited to distinguish subsequently remembered from forgotten trials than event-related potentials or amplitude-based measures. Theoretical models suggest that the phase of EEG oscillations reflects neural excitability and influences cellular plasticity. However, while previous studies have shown that the stability of phase values across trials is indeed a relevant predictor of subsequent memory performance, the effect of absolute single-trial phase values has been little explored. Here, we reanalyzed intracranial EEG recordings from the mediotemporal lobe of 27 epilepsy patients performing a continuous word recognition paradigm. Two-class classification using a support vector machine was performed to predict subsequently remembered vs. forgotten trials based on individually selected frequencies and time points. We demonstrate that it is possible to successfully predict single-trial memory formation in the majority of patients (23 out of 27) based on only three single-trial phase values given by a rhinal phase, a hippocampal phase, and a rhinal-hippocampal phase difference. Overall classification accuracy across all subjects was 69.2% choosing frequencies from the range between 0.5 and 50Hz and time points from the interval between −0.5s and 2s. For 19 patients, above chance prediction of subsequent memory was possible even when choosing only time points from the prestimulus interval (overall accuracy: 65.2%). Furthermore, prediction accuracies based on single-trial phase surpassed those based on single-trial power. Our results confirm the functional relevance of mediotemporal EEG phase for long-term memory operations and suggest that phase information may be utilized for memory enhancement applications based on deep brain stimulation.

Pixel-to-pixel correspondence alignment method of a 2CCD camera by using absolute phase map

An alignment method of a 2CCD camera to build pixel-to-pixel correspondence between the infrared (IR) CCD sensor and the visible CCD sensor by using the absolute phase data is presented. Vertical and horizontal sinusoidal fringe patterns are generated by software and displayed on a liquid crystal display screen. The displayed fringe patterns are captured simultaneously by the IR sensor and the visible sensor of the 2CCD camera. The absolute phase values of each pixel at IR and visible channels are calculated from the captured fringe pattern images by using Fourier transform and the optimum three-fringe number selection method. The accurate pixel corresponding relationship between the two sensors can be determined along the vertical and the horizontal directions by comparing the obtained absolute phase data in IR and visible channels. Experimental results show the high accuracy, effectiveness, and validity of the proposed 2CCD alignment method. By using the continuous absolute phase information, this method can determine the pixel-to-pixel correspondence with high resolution.