Phase noise filtering and phase unwrapping method based on unscented Kalman filter

This paper presents a new phase unwrapping algorithm based on the unscented Kalman filter（UKF） for synthetic aperture radar（SAR） interferometry.This method is the result of combining an UKF with path-following strategy and an omni-directional local phase slope estimator.This technique performs simultaneously noise filtering and phase unwrapping along the high-quality region to the low-quality region,which is also able to avoid going directly through the noisy regions.In addition,phase slope is estimated directly from the sample frequency spectrum of the complex interferogram,by which the underestimation of phase slope is overcome.Simulation and real data processing results validate the effectiveness of the proposed method,and show a significant improvement with respect to the extended Kalman filtering（EKF） algorithm and some conventional phase unwrapping algorithms in some situations.

DEFORMATION MEASUREMENT USING DUAL-FREQUENCY PROJECTION GRATING PHASE-SHIFT PROFILOMETRY

2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phaseshifting profilometry （PSP） can be used to solve such an issue. In the measurement, two properchosen frequency gratings are utilized to synthesize an equivalent wavelength grating which ensures the computed phase in a principal phase range. Thus, the error caused by the phase unwrapping process with the conventional phase reconstruct algorithm can be eliminated. Finally, experimental result of a specimen with large plastic deformation is given to prove that the proposed method is effective to handle the phase discontinuity.

Enhanced multi-baseline unscented Kalman filtering phase unwrapping algorithm

This paper presents an enhanced multi-baseline phase unwrapping algorithm by combining an unscented Kalman filter with an enhanced joint phase gradient estimator based on the amended matrix pencil model, and an optimal path-following strategy based on phase quality estimate function. The enhanced joint phase gradient estimator can accurately and effectively extract the phase gradient information of wrapped pixels from noisy interferograms, which greatly increases the performances of the proposed method. The optimal path-following strategy ensures that the proposed algorithm simultaneously performs noise suppression and phase unwrapping along the pixels with high-reliance to the pixels with low-reliance. Accordingly, the proposed algorithm can be predicted to obtain better results, with respect to some other algorithms, as will be demonstrated by the results obtained from synthetic data.

InSAR Kalman Filter Phase Unwrapping Algorithm Based on SRTM DEM

PU （phase unwrapping） is the key step and important problem in DEM （digital elevation model） extraction and the measurement of surface deformation of InSAR （Interferometric synthetic aperture radar）. The CKFPUA （conventional Kalman filter phase unwrapping algorithm） can obtain reliable results in the flat terrain areas, but it caused error transmission not making the accurate inversion of surface deformation information in the steep terrain. Considering this situation, so it needs to introduce topographic information for guiding phase unwrapping. Here the 90 m resolution DEM data have been used and it is obtained by SRTM （shuttle radar topography mission） measured jointly by NASA （National Aeronautics and Space Administration） and NIMA （National Imaging Mapping Agency） of U.S. Department of Defense. This paper presents a SD-KFPUA （Kalman filter phase unwrapping algorithm） based on SRTM DEM. With SRTM DEM directing InSAR image to implement phase unwrapping, the speed and accuracy are improved. By analyzing with the conventional Kalman filter phase unwrapping algorithms, it is shown that the proposed method can achieve good results in particular to improve unwrapping accuracy in the low coherence region.

Investigation on Three Types of Residues in Phase-unwrapping

In phase unwrapping, how to control the residues and cut lines is critical to unwrap ill-state wrapped phase map successfully. Some new concepts in phase unwrapping field are proposed. Firstly, the residues in three types, i.e., singular residues, normal residues and virtual residues, are classified, which leads to some rational unwrapping paths. Secondly, some differences between cut-line and curved line are analyzed. And finally, experiment is carried out to compare our new enhanced Goldstein algorithm with the original Goldstein algorithm.

Deep learning spatial phase unwrapping:a comparative review

Phase unwrapping is an indispensable step for many optical imaging and metrology techniques.The rapid development of deep learning has brought ideas to phase unwrapping.In the past four years,various phase dataset generation methods and deep-learning-involved spatial phase unwrapping methods have emerged quickly.However,these methods were proposed and analyzed individually,using different strategies,neural networks,and datasets,and applied to different scenarios.It is thus necessary to do a detailed comparison of these deep-learning-involved methods and the traditional methods in the same context.We first divide the phase dataset generation methods into random matrix enlargement,Gauss matrix superposition,and Zernike polynomials superposition,and then divide the deep-learning-involved phase unwrapping methods into deep-learning-performed regression,deep-learning-performed wrap count,and deep-learningassisted denoising.For the phase dataset generation methods,the richness of the datasets and the generalization capabilities of the trained networks are compared in detail.In addition,the deep-learning-involved methods are analyzed and compared with the traditional methods in ideal,noisy,discontinuous,and aliasing cases.Finally,we give suggestions on the best methods for different situations and propose the potential development direction for the dataset generation method,neural network structure,generalization ability enhancement,and neural network training strategy for the deep-learning-involved spatial phase unwrapping methods.

Deep-learning-enabled dual-frequency composite fringe projection profilometry for single-shot absolute 3D shape measurement

Single-shot high-speed 3D imaging is important for reconstructions of dynamic objects.For fringe projection profilometry(FPP),however,it is still challenging to recover accurate 3D shapes of isolated objects by a single fringe image.In this paper,we demonstrate that the deep neural networks can be trained to directly recover the absolute phase from a unique fringe image that involves spatially multiplexed fringe patterns of different frequencies.The extracted phase is free from spectrum-aliasing problem which is hard to avoid for traditional spatial-multiplexing methods.Experiments on both static and dynamic scenes show that the proposed approach is robust to object motion and can obtain high-quality 3D reconstructions of isolated objects within a single fringe image.

A new method of weight choice in InSAR least squares unwrapping

The de-coherence phenomena such as Low-SNR radar signal, shadows and layover caused by topography, etc. , causing phase data discontinuity, makes the result of unwrapping phase inaccuracy or even completely wrong. Based on the analysis of influencing factors to weight choice, this thesis develops a new method to choose the weights based on the measure of the confidence in the frequency domain. Experiments show that it could overcome the defect of sub-estimate to the slope of least squares method very well, which has a better rationale, stability and performance.

A new method of weighted choice in InSAR Least Squares unwrapping

The decorelation phenomena such as Low-SNR radar signal, shadows and layover caused by topography etc, causes phase data discontinuous and makes the result of unwrapping phase inaccurate or completely wrong. Based on the analysis of influencing factors to the weight selection, this paper develops a new method to choose the weights based on the measurement of confidence in frequency domain. Results show that it is more precise and robust than other methods, and can make up for the defect of sub-estimate to the slope of least squares method.

Segmentation-aided phase unwrapping for 3D reconstruction with airborne array-InSAR images

Unmanned aerial vehicle(UAV)array InSAR is a new type of single-flight 3D SAR imaging system with the advantages of high coherence and resolution.However,due to the low altitude of the platform,the elevation ambiguity of the system is smaller than the maximal terrain elevation.Since the spatial phase unwrapping is conducted based on the assumption of phase continuity,the inappropriate ambiguity will cause significant unwrapping errors.In this work,a 3D phase unwrapping algorithm assisted by image segmentation is proposed to address this issue.The Markov random field(MRF)is utilized for image segmentation.The optimal spatial phase unwrapping network is achieved based on the segmentation results.The asymptotic 3D phase unwrapping is adopted to get the refined 3D reconstruction.Results based on the real airborne array-InSAR data show that the proposed method effectively improves the elevation ambiguity.

Measurement of a discontinuous object based on a dual-frequency grating

The dual-frequency grating measurement theory is proposed in order to carry out the measurement of a discontinuous object. Firstly, the reason why frequency spectra are produced by low frequency gratings and high frequency gratings in the field of frequency is analysed, and the relationship between the wrapped-phase and the unwrapping-phase is discussed. Secondly, a method to combine the advantages of the two kinds of gratings is proposed： one stripe is produced in the mutation part of the object measured by a suitable low frequency grating designed by MATLAB, then the phase produced by the low frequency grating need not be unfolded. The integer series of stripes is produced by a high frequency grating designed by MATLAB based on the frequency ratio of the two kinds of gratings and the high frequency wrapped-phase, and the high frequency unwrapping-phase is then obtained. In order to verify the correctness of the theoretical analysis, a steep discontinuous object of 600×600 pixels and 10.00 mm in height is simulated and a discontinuous object of ladder shape which is 32.00 mm in height is used in experiment. Both the simulation and the experiment can restore the discontinuous object height accurately by using the dual-frequency grating measurement theory.

An Efficient Topography Adaptive Filter for Insar Processing

An efficient implementation of the topography adaptive filter based on local frequency estimation is proposed, where chirp z transform is applied to enhance the accuracy of the frequency estimation. As a by product of this adaptive filter, the linear approximated phase model of the interferogram is employed to improve the coherence estimation. The impacts of the adaptive filter on global and local phase unwrapping algorithms are discussed. Finally, aiming at the negative effect that the adaptive filter can bring to local phase unwrapping algorithms, a fusion scheme that takes advantage of least square and several local phase unwrapping algorithms is presented.

A Novel 360°3D Profilometry

A new method of 360° turning 3D shape measurement in which light sectioning and phase shifting techniques are both used is presented in this paper.A sine light field is applied in the projected light stripe,meanwhile phase shifting technique is used to calculate phase of the light slit.Thereafter wrapped phase distribution of the slit is formed and the unwrapping process will be made by means of the height information based on the light sectioning method.Therefore phase measuring results with better precision can be obtained.At last the target 3D shape data can be produced according to geometric relationships between phases and the object heights.The principles of this method are discussed in detail and experimental results are shown in this paper.

A review of the dual-wavelength technique for phase imaging and 3D topography

Optically transmissive and reflective objects may have varying surface profiles,which translate to arbitrary phase profiles for light either transmitted through or reflected from the object.For high-throughput applications,resolving arbitrary phases and absolute heights is a key problem.To extend the ability of measuring absolute phase jumps in existing 3D imaging techniques,the dual-wavelength concept,proposed in late 1800s,has been developed in the last few decades.By adopting an extra wavelength in measurements,a synthetic wavelength,usually larger than each of the single wavelengths,can be simulated to extract large phases or height variations from micron-level to tens of centimeters scale.We review a brief history of the developments in the dualwavelength technique and present the methodology of this technique for using the phase difference and/or the phase sum.Various applications of the dual-wavelength technique are discussed,including height feature extraction from micron scale to centimeter scale in holography and interferometry,single-shot dual-wavelength digital holography for high-speed imaging,nanometer height resolution with fringe subdivision method,and applications in other novel phase imaging techniques and optical modalities.The noise sources for dualwavelength techniques for phase imaging and 3D topography are discussed,and potential ways to reduce or remove the noise are mentioned.

Integrated phase unwrapping algorithm for the measurement of 3D shapes by Fourier transform profilometry

An integrated and reliable phase unwrapping algorithm is proposed based on residues and blocking-lines detection, closed contour extraction and quality map ordering for the measurement of 3D shapes by Fourier-transform profilometry (FTP). The proposed algorithm first detects the residues on the wrapped phase image, applies wavelet analysis to generate the blocking-lines that can just connect the residues of opposite polarity, then carries out the morphology operation to extract the closed contour of the shape, and finally uses the modulation intensity information and the Laplacian of Gaussian operation of the wrapped phase image as the quality map. The unwrapping process is completed from a region of high reliability to that of low reliability and the blocking-lines can prevent the phase error propagation effectively. Furthermore, by using the extracted closed contour to exclude the invalid areas from the phase unwrapping process, the algorithm becomes more efficient. The experiment shows the effec-tiveness of the new algorithm.

Phase unwrapping based on deep learning in light field fringe projection 3D measurement

Phase unwrapping is one of the key roles in fringe projection three-dimensional(3D)measurement technology.We propose a new method to achieve phase unwrapping in camera array light filed fringe projection 3D measurement based on deep learning.A multi-stream convolutional neural network(CNN)is proposed to learn the mapping relationship between camera array light filed wrapped phases and fringe orders of the expected central view,and is used to predict the fringe order to achieve the phase unwrapping.Experiments are performed on the light field fringe projection data generated by the simulated camera array fringe projection measurement system in Blender and by the experimental 3×3 camera array light field fringe projection system.The performance of the proposed network with light field wrapped phases using multiple directions as network input data is studied,and the advantages of phase unwrapping based on deep learning in light filed fringe projection are demonstrated.

Enhancement for φ-OTDR Performance by Using Narrow Linewidth Light Source and Signal Processing

In order to enhance the signal-to-noise-ratio of a distributed acoustic sensing system based on phase-sensitive optical time-domain reflectometry （φ-OTDR）, we have proposed a combination of segmented unwrapping algorithm, averaging estimation of phase difference, and infinite impulse response （IIR） filtering method. The enhancement of signal quality is numerically demonstrated. Moreover, we have studied the influence resulted from the light source noise on the φ-OTDR performance. The result has shown that when the linewidth of light source used in the φ-OTDR system is narrower, the performance of the system is better. In a word, such a φ-OTDR system could obtain higher quality demodulated signals when the narrower linewidth light source is chosen and the method of averaging estimation phase difference is used.

Reconstruction of Fabry–Perot cavity interferometer nanometer micro-displacement based on Hilbert transform

A novel reconstruction method of nanometer micro-displacement of Fabry-Perot(F-P)interference is proposed in this study.Hilbert transforms are performed for F-P interference fringes,and the obtained signal performs tangent operation with the original signal.Finally,the validity of the proposed algorithm and the structure are verified by simulation and several experimental measurements for vibration.Results from the experiments show that the maximum relative error is 4.9%.

Monitoring nonlinear and fast deformation caused byunderground mining exploitation using multi-temporal Sentinel-1 radar interferometry and corner reflectors: application,validation and processing obstacles

In this study,Differential Interferometric Synthetic Aperture Radar Interferometry(DInSAR)of artificial Corner Reflectors(CRs)were validated in the area of fast and nonlinear deformation gradient caused by active coal longwall exploitation.Three Sentinel-1 datasets were processed using conventional DInSAR,Persistent Scatterer Interferometry(PSI),and Small BAseline Subset methods implemented in ENVI SARscape™.For evaluation,leveling and Global Navigation Satellite System(GNSS)measurements were used.Considering the challenge of snow cover,the removal of all winter images was not a successful strategy due to the long temporal baseline and strong movement,which cause phase unwrapping problems and underestimate the real deformation.The results indicate that only conventional DInSAR and SBAS with low network redundancy allow us to capture maximal deformation gradient and the root mean square error calculated between the CRs and the ground truth is on the level of 2–3 cm for the vertical and easting deformation component,respectively.For the small deformation gradient represented by the permanent GNSS station(4 cm/year),all SBAS techniques appeared to be more accurate than DInSAR,which corresponds to higher redundancy and better removal of the atmospheric signal.In contrast,DInSAR results allowed to capture information about two subsidence basins,which was not possible with SBAS and PSI approaches.

An Improved Algorithm for Blind Carrier Frequency Estimation with Burst MPSK Transmissions

This paper presents an improved non-data-aided algo- rithm for carrier frequency estimation for burst M-ary PSK signals when modulation order M and training symbols are unknown. Unlike data-aided estimation, a phase clustering algorithm is used first to estimate M and modulated information is removed by a vari- able interval linear phase unwrapping. Then, a high-order correlation algorithm with proper correction is present, which reduces the probability of phase ambiguity and promotes anti-noise capability of the estimation. Simulations are given to analyze the unbiased esti- mation range, and the asymptotic performance and symbol number are needed to compare with the former algorithms. The new algo- rithm has a large estimation range close to the theoretical maximum value for non-data-aided estimation and has a better performance than earlier non-data-aided techniques for large frequency offset, low signal-to-noise ratio, and limited symbol numbers.