Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill

Digital filtering of ghost signal in phase measuring deflectometry

We introduce a method of geometric screen modification to remove ghost reflections commonly observed in deflectometry optical testing. The proposed method modifies the optical layout and illumination source area to bypass the generation of reflected rays from the undesired surface. The layout flexibility of deflectometry allows us to design specific system layouts that avoid the generation of interrupting secondary rays. The proposed method is supported by optical raytrace simulations, and experimental results are demonstrated with convex and concave lens case studies. Finally, the limitations of the digital masking method are discussed.

A Deep Learning-based Method to Extract Lumen and Media-Adventitia in Intravascular Ultrasound Images

Intravascular ultrasound (IVUS) imaging allows direct visualization of the coronary vessel wall and is suitable for assessing atherosclerosis and the degree of stenosis. Accurate segmentation and lumen and median-adventitia (MA) measurements from IVUS are essential for such a successful clinical evaluation. However, current automated segmentation by commercial software relies on manual corrections, which is time-consuming and user-dependent. We aim to develop a deep learning-based method using an encoder-decoder deep architecture to automatically and accurately extract both lumen and MA border. Inspired by the dual-path design of the state-of-the-art model IVUS-Net, our method named IVUS-U-Net++ achieved an extension of the U-Net++ model. More specifically, a feature pyramid network was added to the U-Net++ model, enabling the utilization of feature maps at different scales. Following the segmentation, the Pearson correlation and Bland-Altman analyses were performed to evaluate the correlations of 12 clinical parameters measured from our segmentation results and the ground truth. A dataset with 1746 IVUS images from 18 patients was used for training and testing. Our segmentation model at the patient level achieved a Jaccard measure (JM) of 0.9080 ± 0.0321 and a Hausdorff distance (HD) of 0.1484 ± 0.1584 mm for the lumen border; it achieved a JM of 0.9199 ± 0.0370 and an HD of 0.1781 ± 0.1906 mm for the MA border. The 12 clinical parameters measured from our segmentation results agreed well with those from the ground truth (all p-values are smaller than .01). Our proposed method shows great promise for its clinical use in IVUS segmentation.

Deep learning phase-unwrapping method based on adaptive noise evaluation

To address the problem of phase unwrapping for interferograms, a deep learning (DL) phase-unwrapping method based on adaptive noise evaluation is proposed to retrieve the unwrapped phase from the wrapped phase. First, this method uses a UNet3+ as the skeleton and combines with a residual neural network to build a network model suitable for unwrapping wrapped fringe patterns. Second, an adaptive noise level evaluation system for interferograms is designed to estimate the noise level of the interferograms by integrating phase quality maps and phase residues of the interferograms. Then, multiple training datasets with different noise levels are used to train the DL network to achieve the trained networks suitable for unwrapping interferograms with different noise levels. Finally, the interferograms are unwrapped by the trained networks with the same noise levels as the interferograms to be unwrapped. The results with simulated and experimental interferograms demonstrate that the proposed networks can obtain the popular unwrapped phase from the wrapped phase with different noise levels and show good robustness in the experiments of phase unwrapping for different types of fringe patterns.

Robust particle-Kalman filtering phase unwrapping algorithm for wrapped fringe patterns

This paper presents a robust phase unwrapping algorithm based on a particle-Kalman filter for wrapped fringe patterns by combining a particle filter and an extended Kalman filter, which formulates the phase unwrapping problem of wrapped fringe patterns as an optimal state estimation problem under the frame of the particle-Kalman filter. First, a state space equation for state variables is extended to the second order of Taylor series, and a local phase gradient estimator based on a modified matrix pencil model is used to obtain the first-order and second-order phase gradient information required by the extended state space equation, which is conducive to enhancing the phase unwrapping accuracy of the proposed procedure. Second, the initial estimate of unwrapped phase is obtained through applying an efficient phase unwrapping program based on a particle filter to unwrap noisy wrapped pixels. Finally, the initial estimate of unwrapped phase obtained by the particle filter is taken as the predicted estimate of state variables and further processed by the extended Kalman filter to obtain the final estimate of unwrapped phase. In addition, an efficient quality-guided strategy that has been demonstrated well is used to guarantee that the particle-Kalman filter efficiently and accurately unwraps wrapped pixels along a suitable path. Results obtained with synthetic data and experimental data demonstrate the effectiveness of the proposed method and show that this new approach can obtain more acceptable solutions from noisy wrapped fringe patterns, with respect to some of the most commonly used methods.

Center-environment feature models for materials image segmentation based on machine learning

Materials properties depend not only on their compositions but also their microstructures under various processing conditions. So far, the analyses of complex microstructure images rely mostly on human experience, lack of automatic quantitative characterization methods. Machine learning provides an emerging vital tool to identify various complex materials phases in an intelligent manner. In this work, we propose a “center-environment segmentation” (CES) feature model for image segmentation based on machine learning method with environment features and the annotation input of domain knowledge. The CES model introduces the information of neighbourhood as the features of a given pixel, reflecting the relationships between the studied pixel and its surrounding environment. Then, an iterative integrated machine learning method is adopted to train and correct the image segmentation model. The CES model was successfully applied to segment seven different material images with complex texture ranging from steels to woods. The overall performance of the CES method in determining boundary contours is better than many conventional methods in the case study of the segmentation of steel image. This work shows that the iterative introduction of domain knowledge and environment features improve the accuracy of machine learning based image segmentation for various complex materials microstructures.

Phase unwrapping algorithm based on a rank information filter

A robust phase unwrapping algorithm based on a rank information filter is proposed to retrieve the unambiguous unwrapped phase from noisy wrapped phase images. First, a recursive phase unwrapping program, based on a rank information filter, is proposed to transform the problem of phase unwrapping for wrapped phase into the problem of the state estimation for state variables under the framework of a rank information filter, where a local phase gradient estimator based on the amended matrix pencil model (AMPM) is used to obtain phase gradient information required by the recursive phase unwrapping program. Second, an efficient path-following strategy based on heap-sort is used to guide the phase unwrapping path, which ensures that the recursive phase unwrapping program based on a rank information filter unwraps wrapped phase images along the path from high-quality pixels to low-quality pixels. Finally, the results obtained from synthetic data and experimental measured data demonstrate the effectiveness of the proposed method and show this method can obtain robust solutions from noisy wrapped phase images.

Robust phase unwrapping algorithm for noisy and segmented phase measurements

This paper proposes a robust phase unwrapping algorithm (RPUA) for phase unwrapping in the presence of noise and segmented phase. The RPUA method presents a new model of phase derivatives combined with error-correction iterations to achieve an anti-noise effect. Moreover, it bridges the phase islands in the spatial domain using numerical carrier frequency and fringe extrapolation thus eliminating height faults to enable solving segmented phase unwrapping. Numerical simulation and comparison with three conventional methods were performed, proving the high robustness and efficiency of the RPUA. Further, three experiments demonstrated that the RPUA can obtain the unwrapped phase under different noise accurately and possesses the capability to process segmented phases, indicating reliable practicality.

An Improved Cloud Detection Method for GF-4 Imagery

Clouds are significant barriers to the application of optical remote sensing images. Accurate cloud detection can help to remove contaminated pixels and improve image quality. Many cloud detection methods have been developed. However, traditional methods either rely heavily on thermal infrared bands or clear-sky images. When traditional cloud detection methods are used with Gaofen 4 (GF-4) imagery, it is very difficult to separate objects with similar spectra, such as ice, snow, and bright sand, from clouds. In this paper, we propose a new method, named Real-Time-Difference (RTD), to detect clouds using a pair of images obtained by the GF-4 satellite. The RTD method has four main steps: (1) data preprocessing, including transforming digital value (DN) to Top of Atmosphere (TOA) reflectance, and orthographic and geometric correction; (2) the computation of a series of cloud indexes for a single image to highlight clouds; (3) the calculation of the difference between a pair of real-time images in order to obtain moved clouds; and (4) confirming the clouds and background by analyzing their physical and dynamic features. The RTD method was validated in three sites located in the Hainan, Liaoning, and Xinjiang areas of China. The results were compared with those of a popular classifier, Support Vector Machine (SVM). The results showed that RTD outperformed SVM; for the Hainan, Liaoning, and Xinjiang areas, respectively, the overall accuracy of RTD reached 95.9%, 94.1%, and 93.9%, and its Kappa coefficient reached 0.92, 0.88, and 0.88. In the future, we expect RTD to be developed into an important means for the rapid detection of clouds that can be used on images from geostationary orbit satellites.

Atrial fibrillation source area probability mapping using electrogram patterns of multipole catheters

BACKGROUND

Catheter ablation therapy involving isolation of pulmonary veins (PVs) from the left atrium is performed to terminate atrial fibrillation (AF). Unfortunately, standalone PV isolation procedure has shown to be a suboptimal success with AF continuation or recurrence. One reason, especially in patients with persistent or high-burden paroxysmal AF, is known to be due to the formation of repeating-pattern AF sources with a meandering core inside the atria. However, there is a need for accurate mapping and localization of these sources during catheter ablation.

METHODS

A novel AF source area probability (ASAP) mapping algorithm was developed and evaluated in 2D and 3D atrial simulated tissues with various arrhythmia scenarios and a retrospective study with three cases of clinical human AF. The ASAP mapping analyzes the electrograms collected from a multipole diagnostic catheter that is commonly used during catheter ablation procedure to intelligently sample the atria and delineate the trajectory path of a meandering repeating-pattern AF source. ASAP starts by placing the diagnostic catheter at an arbitrary location in the atria. It analyzes the recorded bipolar electrograms to build an ASAP map over the atrium anatomy and suggests an optimal location for the subsequent catheter location. ASAP then determines from the constructed ASAP map if an AF source has been delineated. If so, the catheter navigation is stopped and the algorithm provides the area of the AF source. Otherwise, the catheter is navigated to the suggested location, and the process is continued until an AF-source area is delineated.

RESULTS

ASAP delineated the AF source in over 95% of the simulated human AF cases within less than eight catheter placements regardless of the initial catheter placement. The success of ASAP in the clinical AF was confirmed by the ablation outcomes and the electrogram patterns at the delineated area.

CONCLUSION

Our analysis indicates the potential of the ASAP mapping to provide accurate information about the area of the meandering repeating-pattern AF sources as AF ablation targets for effective AF termination. Our algorithm could improve the success of AF catheter ablation therapy by locating and subsequently targeting patient-specific and repeating-pattern AF sources inside the atria.

SpikeSegNet-a deep learning approach utilizing encoder-decoder network with hourglass for spike segmentation and counting in wheat plant from visual imaging

BACKGROUND

High throughput non-destructive phenotyping is emerging as a significant approach for phenotyping germplasm and breeding populations for the identification of superior donors, elite lines, and QTLs. Detection and counting of spikes, the grain bearing organs of wheat, is critical for phenomics of a large set of germplasm and breeding lines in controlled and field conditions. It is also required for precision agriculture where the application of nitrogen, water, and other inputs at this critical stage is necessary. Further, counting of spikes is an important measure to determine yield. Digital image analysis and machine learning techniques play an essential role in non-destructive plant phenotyping analysis.

RESULTS

In this study, an approach based on computer vision, particularly object detection, to recognize and count the number of spikes of the wheat plant from the digital images is proposed. For spike identification, a novel deep-learning network, SpikeSegNet, has been developed by combining two proposed feature networks: Local Patch extraction Network (LPNet) and Global Mask refinement Network (GMRNet). In LPNet, the contextual and spatial features are learned at the local patch level. The output of LPNet is a segmented mask image, which is further refined at the global level using GMRNet. Visual (RGB) images of 200 wheat plants were captured using LemnaTec imaging system installed at Nanaji Deshmukh Plant Phenomics Centre, ICAR-IARI, New Delhi. The precision, accuracy, and robustness (F₁ score) of the proposed approach for spike segmentation are found to be 99.93%, 99.91%, and 99.91%, respectively. For counting the number of spikes, "analyse particles"-function of imageJ was applied on the output image of the proposed SpikeSegNet model. For spike counting, the average precision, accuracy, and robustness are 99%, 95%, and 97%, respectively. SpikeSegNet approach is tested for robustness with illuminated image dataset, and no significant difference is observed in the segmentation performance.

CONCLUSION

In this study, a new approach called as SpikeSegNet has been proposed based on combined digital image analysis and deep learning techniques. A dedicated deep learning approach has been developed to identify and count spikes in the wheat plants. The performance of the approach demonstrates that SpikeSegNet is an effective and robust approach for spike detection and counting. As detection and counting of wheat spikes are closely related to the crop yield, and the proposed approach is also non-destructive, it is a significant step forward in the area of non-destructive and high-throughput phenotyping of wheat.

Multi-anchor spatial phase unwrapping for fringe projection profilometry

Phase unwrapping is a necessary step in fringe-projection profilometry that produces accurate depth maps. However, the original wrapped phase is often corrupted by errors, and thus conventional spatial unwrapping suffers from error propagation, such as scanline-based unwrapping, and high complexity, such as quality-guided methods. In this paper, we propose a fast and robust spatial unwrapping method called multi-anchor scanline unwrapping (MASU). Different from previous work, when unwrapping each pixel, MASU refers to multiple anchors in the scanline, where each anchor has a threshold adapting to its location. In such a manner, a set of fringe order candidates are predicted by the anchors according to phase smoothness assumption, and the one with the highest number of votes is chosen. After that, with the obtained fringe order, the absolute phase and depth are computed. Simulation and experiments have shown that even corrupted by severe phase errors, the proposed MASU can still produce robust unwrapped results. In addition, MASU is thousands of times faster than quality-guided unwrapping with comparative or even superior depth accuracy.

Efficient phase unwrapping algorithm based on cubature information particle filter applied to unwrap noisy continuous phase maps

This paper presents a new phase unwrapping algorithm for wrapped phase fringes through combining a cubature information particle filter with an efficient local phase gradient estimator and an efficient quality-guided strategy based on heap-sort. The cubature information particle filter that not only is independent from noise statistics but also is not constrained by the nonlinearity of the model constructed is applied to retrieve unambiguous phase from modulus 2π wrapped fringe patterns through constructing a recursive cubature information particle filtering phase unwrapping procedure to perform simultaneously phase unwrapping and noise filtering for the first time to our knowledge, which can be expected to obtain more robust solutions from wrapped phase fringes. Phase gradient estimate is one of the key steps in almost all phase unwrapping algorithms and is directly related to the precision and the efficiency of phase unwrapping procedure. Accordingly, an efficient local phase gradient estimator that is more efficient than ones published previously is deduced to obtain phase gradient information required by the proposed algorithm, which can drastically decrease time consumption of unwrapping procedure and drastically improve the efficiency of the algorithm. The efficient quality-guided strategy based on heap-sort guarantees that the proposed algorithm efficiently unwraps wrapped pixels along the path from the high-reliance regions to the low-reliance regions of wrapped phase images. In addition, the accelerated version of the proposed algorithm is further developed through combing with reversible modulo wavelet operators to solve phase unwrapping problem of wrapped phase images in wavelet transform domain, which can reduce the amount of wrapped pixels that need to be unwrapped, and can further decrease time consumption of unwrapping procedure performing on wrapped phase images. This algorithm and its accelerated version under the frame of wavelet transform are demonstrated with various types of wrapped phase images, showing acceptable solutions.

Reference-plane-based fast pixel-by-pixel absolute phase retrieval for height measurement

Absolute phase retrieval is essential for height measurement in digital fringe projection. However, projections of additional structured patterns that are normally required for phase unwrapping increase the measurement complexity. In this paper, we propose two reference-plane-based pixel-by-pixel absolute phase retrieval techniques with as few projections as possible, suitable for different object depth ranges. The wrapped phase on the object is absolutely unwrapped by referring just to the absolute phase map on the reference plane. Single-frequency absolute phase retrieval with one-reference-plane-based calibration is first proposed for objects within a height limit that equals a calibrated system constant. To extend the measurement depth range, dual-frequency absolute phase retrieval with two parallel reference planes is further proposed. The additional low frequency is used to choose the unwrapping reference from the two reference plane phases for unwrapping the high-frequency phase. Moreover, the proposed techniques are capable of high-frequency absolute phase unwrapping for objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the efficiency of the proposed two techniques.

Unscented information filtering phase unwrapping algorithm for interferometric fringe patterns

This paper proposes a new phase unwrapping (PU) algorithm based on an unscented information filter for interferometric fringes. The proposed algorithm is the result of combining an unscented information filter with a Levenberg-Marquardt method, a robust phase gradient estimator called the amended matrix pencil model, and an efficient quality-guided strategy based on heapsort. The unscented information filter, a new type of filter that has recently been well applied to traditional nonlinear object tracking fields, is introduced to estimate the unambiguous unwrapped phase of wrapped phase images for the first time, to the best of our knowledge. First, a recursive PU procedure based on an unscented information filter is established to perform PU and noise filtering at the same time by combining the unscented information filter and the amended matrix pencil model, where the amended matrix pencil model is applied to acquire phase gradient information needed for the recursive PU procedure. Second, the above recursive PU procedure is further optimized to improve the accuracy of the phase estimate by inserting the Levenberg-Marquardt method. This is also the first time that the Levenberg-Marquardt method is combined with the unscented information filter for the unwrapping of interferometric fringes, to the best of our knowledge. Finally, the efficient quality-guided strategy based on heapsort is used to efficiently route the path of the unwrapping procedure and to guide the proposed method to efficiently unwrap wrapped pixels along the path from the high-reliance region to the low-reliance region of the wrapped fringes. Results obtained with synthetic data and real data show more acceptable solutions with the proposed method, compared to some of the most used algorithms.

Hybrid profilometry using a single monochromatic multi-frequency pattern

In this paper, we propose a novel profilometry scheme to acquire high quality depth, where only a single shot of a monochromatic pattern is utilized. We design a band-wise pattern consisting of fringe bands spatially modulated with coprime periods. After that, with the designed pattern, depth is obtained in a hybrid manner, where both phase-based profilometry and active stereo are incorporated. To be specific, pixels in smooth regions obtain their depth values through phases analysis. Especially, based on depth smooth property, we propose a novel phase unwrapping algorithm, which avoids the problem of error propagation and yields accurate unwrapping phases. On the other hand, for boundary regions, spatial stereo, which is more robust to depth discontinuities, is utilized to modify incorrect depth values. Both theoretical verification and experimental results demonstrate that the proposed scheme can generate high quality depth maps, even for complex scenes and isolated objects.

High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3D surface-shape measurement

A new fringe projection method for surface-shape measurement was developed using four high-frequency phase-shifted background modulation fringe patterns. The pattern frequency is determined using a new fringe-wavelength geometry-constraint model that allows only two corresponding-point candidates in the measurement volume. The correct corresponding point is selected with high reliability using a binary pattern computed from intensity background encoded in the fringe patterns. Equations of geometry-constraint parameters permit parameter calculation prior to measurement, thus reducing measurement computational cost. Experiments demonstrated the ability of the method to perform 3D shape measurement for a surface with geometric discontinuity, and for spatially isolated objects.

Weighted least-squares phase unwrapping algorithm based on a non-interfering image of an object

Conventional quality maps for weighted least-squares phase unwrapping are not appropriate in regions of abnormal fringes. In this paper, the use of a non-interfering image of an object for a reliability map is proposed for robust phase unwrapping. First, the conventional weighted least-squares algorithm is applied, and the unreliable region is detected. Then, the unreliable region is unwrapped iteratively using the non-interfering image of the object. Finally, both phase maps are combined and smoothed by a continuity operation. Experimental results show that the proposed algorithm is appropriate for unwrapping phase maps of abnormal fringes.

Multi-subzone algorithm for absolute phase retrieval in digital fringe projection profilometry

Codewords are important in encoded absolute phase retrieval techniques such as two-frequency, gray-code, and phase-coding. Each sinusoidal fringe is marked by a unique codeword so that an absolute fringe order can be determined by decoding the codeword. However, due to the limited number of unique codewords, sinusoidal fringe patterns do not contain high-frequency fringes without the use of additional patterns. A multi-subzone coding and decoding algorithm is thus proposed to overcome this limitation. Three multi-subzone coding methods based on two-frequency, gray-code, and phase-coding techniques are presented. The coding creates multiple subzones of unique codewords and the decoding enables it to use non-unique codewords to identify absolute fringe order. Specifically, the range of fringe order is estimated by the use of a wrapped phase map and the absolute fringe order is identified by a codeword. Experimental studies demonstrate the advantages of the proposed algorithm over existing coding methods. The proposed algorithm is suitable to measure objects with large step-height surface discontinuities.

Instantaneous phase shifting deflectometry

An instantaneous phase shifting deflectometry measurement method is presented and implemented by measuring a time varying deformable mirror with an iPhone ^® 6. The instantaneous method is based on multiplexing phase shifted fringe patterns with color, and decomposing them in x and y using Fourier techniques. Along with experimental data showing the capabilities of the instantaneous deflectometry system, a quantitative comparison with the Fourier transform profilometry method, which is a distinct phase measuring method from the phase shifting approach, is presented. Sources of error, nonlinear color-multiplexing induced error correction, and hardware limitations are discussed.

Iterated unscented Kalman filter for phase unwrapping of interferometric fringes

A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.

Robust method to improve the quality of shearographic phase maps obtained in harsh environments

This paper presents a new approach to improve the quality of shearographic phase maps acquired in a harsh environment. During in-field nondestructive inspections, the presence of higher disturbances, mainly vibrations, can introduce unknown phase deviations in the sequence of shearographic images. This paper presents a different approach that combines the N-dimensional Lissajous algorithm [Int. J. Optomechatron.8, 340 (2014)1559-961210.1080/15599612.2014.942933] and the concept of phase of differences [Proc. SPIE6345, 634510 (2006)PSISDG0277-786X10.1117/12.693149] to improve the quality of phase maps. The concept is compared with two other methods. Results, advantages, and difficulties of each method are also presented and discussed by using real fringe maps.

Efficient and robust phase unwrapping algorithm based on unscented Kalman filter, the strategy of quantizing paths-guided map, and pixel classification strategy

This paper presents an efficient and robust phase unwrapping algorithm which combines an unscented Kalman filter (UKF) with a strategy of quantizing a paths-guided map and a pixel classification strategy based on phase quality information. The advantages of the proposed method depend on the following contributions: (1) the strategy of quantizing the paths-guided map can accelerate the process of searching unwrapping paths and greatly reducing time consumption on the unwrapping procedure; (2) the pixel classification strategy proposed by this paper can reduce the error propagation effect by decreasing the amounts of pixels with equal quantized paths-guided value in the process of unwrapping; and (3) the unscented Kalman filter enables simultaneous filtering and unwrapping without the information loss caused by linearization of a nonlinear model. In addition, a new paths-guided map derived from a phase quality map is inserted into the strategy of quantizing the paths-guided map to provide a more robust path of unwrapping, and then ensures better unwrapping results. Results obtained from synthetic data and real data show that the proposed method can efficiently obtain better solutions with respect to some of the most used algorithms.

An optimization approach for mapping and measuring the divergence and correspondence between paths

Many domains of empirical research produce or analyze spatial paths as a measure of behavior. Previously, approaches for measuring the similarity or deviation between two paths have either required timing information or have used ad hoc or manual coding schemes. In this paper, we describe an optimization approach for robustly measuring the area-based deviation between two paths we call ALCAMP (Algorithm for finding the Least-Cost Areal Mapping between Paths). ALCAMP measures the deviation between two paths and produces a mapping between corresponding points on the two paths. The method is robust to a number of aspects in real path data, such as crossovers, self-intersections, differences in path segmentation, and partial or incomplete paths. Unlike similar algorithms that produce distance metrics between trajectories (i.e., paths that include timing information), this algorithm uses only the order of observed path segments to determine the mapping. We describe the algorithm and show its results on a number of sample problems and data sets, and demonstrate its effectiveness for assessing human memory for paths. We also describe available software code written in the R statistical computing language that implements the algorithm to enable data analysis.

Swarm-based algorithm for phase unwrapping

A novel algorithm for phase unwrapping based on swarm intelligence is proposed. The algorithm was designed based on three main goals: maximum coverage of reliable information, focused effort for better efficiency, and reliable unwrapping. Experiments were performed, and a new agent was designed to follow a simple set of five rules in order to collectively achieve these goals. These rules consist of random walking for unwrapping and searching, ambiguity evaluation by comparing unwrapped regions, and a replication behavior responsible for the good distribution of agents throughout the image. The results were comparable with the results from established methods. The swarm-based algorithm was able to suppress ambiguities better than the flood-fill algorithm without relying on lengthy processing times. In addition, future developments such as parallel processing and better-quality evaluation present great potential for the proposed method.

Mid-infrared digital holography and holographic interferometry with a tunable quantum cascade laser

Mid-infrared digital holography based on CO2 lasers has proven to be a powerful coherent imaging technique due to reduced sensitivity to mechanical vibrations, increased field of view, high optical power, and possible vision through scattering media, e.g., smoke. Here we demonstrate a similar and more compact holographic system based on an external cavity quantum cascade laser emitting at 8 μm. Such a setup, which includes a highly sensitive microbolometric camera, allows the acquisition of speckle holograms of scattering objects, which can be processed in real time. In addition, by exploiting the broad laser tunability, we can acquire holograms at different wavelengths, from which we extract phase images not subjected to phase wrapping, at synthetic wavelengths ranging from hundreds of micrometers to several millimeters.

Spatial quasi-phase-shifting technique for single-frame dynamic fringe analysis

Phase demodulation from carrier-frequency fringe patterns is the core of many optic measurements. We propose spatial quasi-phase-shifting technique by expressing the fringe signal in the frequency-modulated form, which requires only one frame fringe pattern for instantaneous and dynamic measurements. In an area smaller than a fringe period, there substantially exists an approximately constant phase shift between spatially adjacent sample points. The technique is capable of demodulating the phase with such intra-frame phase shifts, which makes the instantaneous and dynamic measurement possible. The technique implements demodulation within three spatially adjacent neighbors, achieving spatial localization as good as a several-point level. Both numerical simulation and experiment are presented to verify its performance.

A carrier removal method in phase measuring deflectometry based on the analytical carrier phase description

In phase measuring deflectometry (PMD), a camera observes a sinusoidal fringe pattern via the surface of a specular object under test. Any slope variations of the surface lead to distortions of the observed pattern. Without height-angle ambiguity, carrier removal process is adopted to evaluate the variation of surface slope from phase distribution when a quasi-plane is measured. However, in the usual measurement system, the carrier phase will be nonlinear due to the restrictions of system geometries. In this paper, based on the analytical carrier phase description in PMD, a carrier removal method is proposed to remove the nonlinear carrier phase. Both the theoretical analysis and the experiment results are presented. By comparison with reference-subtraction method and series-expansion method, this proposed method can achieve carrier removal process with only the measurement of one single object, as well as high accuracy and time-saving.

Applicability analysis of wavelet-transform profilometry

The applicability of the wavelet-transform profilometry is examined in detail. The wavelet-ridge-based phase demodulation is an integral operation of the fringe signal in the spatial domain. The accuracy of the phase demodulation is related to the local linearity of the phase modulated by the object surface. We present a more robust applicability condition which is based on the evaluation of the local linearity. Since high carrier frequency leads to the phase demodulation integral in a narrow interval and the narrow interval results in the high local linearity of modulated phase, we propose to increase the carrier fringe frequency to improve the applicability of the wavelet-transform profilometry and the measurement accuracy. The numerical simulations and the experiment are presented.

Radial phase variation computing: a tool to improve flaw detection in optical diagnosis by shearographic images

Shearography is an optical and nondestructive technique that has been largely used for damage detection in layered composite materials where delaminations and debondings are found to be among the most common flaws. Shearography detects derivative of the displacements. It is a relative measurement in which two images are recorded for different loading conditions of the sample. The applied loading induces some deformations into the sample, generating a displacement field on its surface. Thermal, acoustical, or mechanical loading are typical excitations applied in a static or dynamic way. The absolute difference between two phase maps recorded at two different loading instances produces an interference fringe pattern, which is directly correlated to the displacements produced on the material surface. In some cases, depending on the loading level and mainly on the sample geometry, interference patterns will contain fringes resulting from geometry changes. This will mask those fringes correlated to flaws introduced into the material, resulting in an image misinterpretation. This phenomenon takes place mainly when the sample has curved geometries, as in, for example, pipe or vessel surfaces. This paper presents an algorithm that uses a mathematical process to improve the visualization of flaws in shearographic images. The mathematical process is based on the calculation of the phase variation, and it is used to search for local deformations contained in the image. This algorithm highlights defect regions and eliminates fringes caused by geometry changes, providing an easier interpretation for complex shearographic images. This paper also shows the principle and the algorithm used for the process. Results, advantages, and difficulties of the method are presented and discussed by using simulated fringe maps as well as real ones.

Quantitative phase maps denoising of long holographic sequences by using SPADEDH algorithm

We propose a denoising method for digital holography mod 2π wrapped phase map by using an adaptation of the SPArsity DEnoising of Digital Holograms (SPADEDH) algorithm. SPADEDH is a l(1) minimization algorithm able to suppress the noise components on digital holograms without any prior knowledge or estimation about the statistics of noise. We test our algorithm with either general numerical simulated wrapped phase, quantifying the performance with different efficiency parameters and comparing it with two popular denoising strategies, i.e., median and Gaussian filters, and specific experimental tests, by focusing our attention on long-sequence wrapped quantitative phase maps (QPMs) of in vitro cells, which aim to have uncorrupted QPMs. In addition, we prove that the proposed algorithm can be used as a helper for the typical local phase unwrapping algorithms.

Fast algorithm for reliability-guided phase unwrapping in digital holographic microscopy

A fast reliability-guided phase unwrapping algorithm, using an optimized quality map and combining it with look-up table operation, is proposed for digital holographic microscopy. First, by detecting the residues in the wrapped phase map, an intensity threshold is calculated in the normalized intensity image and the measured region is distinguished into the reliable region and the doubtful region. An optimized quality map is derived by the method in which the intensity values in the reliable region are set to 1 and those in the doubtful region remain unchanged. Then the flood fill algorithm by look-up table is implemented with the optimized quality map to retrieve true phase map. The experimental results demonstrate that not only does the proposed algorithm perform well, but also the speed is significantly faster than that of the conventional flood fill algorithm using insert sorting.

Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies

Quality-guided phase unwrapping is a widely used technique with different quality definitions and guiding strategies reported. It is thus necessary to do a detailed comparison of these approaches to choose the optimal quality map and guiding strategy. For quality maps, in the presence of noise, transform-based methods are found to be the best choice. However in the presence of discontinuities, phase unwrapping is itself unresolved and hence quality-guided phase unwrapping is not sufficient. For guiding strategies, classical, two-section, and stack-chain guiding strategies are chosen for comparison. If accuracy is the foremost criterion then the classical guiding strategy with a data structure of indexed interwoven linked list is best. If speed is of essence then the stack-chain guiding strategy is the one to use.

Quality-guided phase unwrapping algorithm based on reliability evaluation

For optical interferometry, a new quality-guided phase unwrapping algorithm based on the reliability evaluation of each pixel of the wrapped phase is proposed. First, the parameters used as quality measures in the past quality-guided algorithms are classified into the reliability measure and the quality measure, and the intensity of the object image belongs to the reliability measure. Then, by computing and applying a threshold to the intensity of the object image, the valid region (i.e., the interference region) is distinguished into the reliable region and the doubtful region. The wrapped phase in the reliable region is subsequently unwrapped by the way of multipaths integration, and different paths are guided by separate quality measures. Finally, starting from the reliable region, the doubtful region is unwrapped by the way that each path takes in the reliable region. Experimental results have shown that the proposed algorithm not only performs well, but also computes efficiently.

Analysis and identification of phase error in phase measuring profilometry

Both the analysis of phase errors which occur at the abrupt discontinuities in phase measuring profilometry (PMP) and the identification method are presented in this paper. The sampling effect of CCD will cause a dilution of accuracy in PMP, especially at abrupt discontinuities on the object surface. The existing methods cannot efficiently identify the abrupt discontinuities. We analyze the relationship between the phase, the height and the equivalent wavelength. By viewing the phase as the argument of a vector we find out that CCD sampling introduces errors into the measurement and the phase is nonlinear to the equivalent wavelength at the abrupt discontinuities. Therefore temporal phase unwrapping (TPU) is introduced into the measurement to identify the abrupt discontinuities. Computer simulations and practical experiment validate the feasibility of this method.

Sensor fusion of phase measuring profilometry and stereo vision for three-dimensional inspection of electronic components assembled on printed circuit boards

Automatic optical inspection (AOI) for printed circuit board (PCB) assembly plays a very important role in modern electronics manufacturing industries. Well-developed inspection machines in each assembly process are required to ensure the manufacturing quality of the electronics products. However, generally almost all AOI machines are based on 2D image-analysis technology. In this paper, a 3D-measurement-method-based AOI system is proposed consisting of a phase shifting profilometer and a stereo vision system for assembled electronic components on a PCB after component mounting and the reflow process. In this system information from two visual systems is fused to extend the shape measurement range limited by 2pi phase ambiguity of the phase shifting profilometer, and finally to maintain fine measurement resolution and high accuracy of the phase shifting profilometer with the measurement range extended by the stereo vision. The main purpose is to overcome the low inspection reliability problem of 2D-based inspection machines by using 3D information of components. The 3D shape measurement results on PCB-mounted electronic components are shown and compared with results from contact and noncontact 3D measuring machines. Based on a series of experiments, the usefulness of the proposed sensor system and its fusion technique are discussed and analyzed in detail.

Refractive index and dispersion variation in precision optical glass molding by computed tomography

Glass compression molding is an alternative manufacturing method for efficient, high-quality, low-cost optical component manufacturing. However, in compression molding, refractive index variation is inadvertently introduced to glass, which can influence optical performance of molded glass lenses, especially for lenses used in high precision applications. In order to study refractive index variation and dispersion in molded glass lenses after cooling, a group of BK7 cylindrical glass lenses were thermally treated with various heating and cooling conditions. The molded glass lenses were measured by use of an optical setup based on a Mach-Zehnder interferometer with red, green, and blue lasers separately. Using the wavefront information extracted from fringe patterns, refractive index and dispersion variation in molded glass lenses were reconstructed using a filtered backprojection algorithm. Furthermore, refractive index and dispersion variation at different cooling rates and different soaking temperatures were investigated.

Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes

Accurate measurement of large step heights using multiple-wavelength holographic interferometry is realized using laser diodes. Due to the high-resolution wavelength tunability of such lasers, a pair of holograms with a wavelength difference of less than 0.01 nm is recorded and used to extract a phase difference having a large synthetic wavelength. Phase differences with synthetic wavelengths ranging from 2.5 to 73 mm are extracted by using pairs of holograms with wavelength differences between 0.3 and 0.01 nm. By combining the phase differences, measurements with a step height of 18 mm and an rms error of 0.04 mm could be achieved. The requirements for performing the phase unwrapping are discussed. Precise knowledge of the recording wavelengths is required to correctly perform this unwrapping.

Reliability-guided phase unwrapping in wavelet-transform profilometry

The phase unwrapping algorithm plays a very important role in many noncontact optical profilometries based on triangular measurement theory. Here we focus on discussing how to diminish the phase error caused by incorrect unwrapping path in wavelet transform profilometry. We employ the amplitude value map of wavelet transform coefficients at the wavelet-ridge position to identify the reliability of the phase data and the path of phase unwrapping. This means that the wrapped phase located at the pixel with the highest amplitude value will be selected as the starting point of the phase unwrapping, and that pixels with higher amplitude value will be unwrapped earlier. So the path of phase unwrapping is always in the direction of the pixel with highest amplitude value to the one with lowest amplitude value. Making full use of the amplitude information of wavelet coefficients at the wavelet-ridge position keeps the phase unwrapping error limited to local minimum areas even in the worst case. Computer simulations and experiments verify our theory.

Regional identification, partition, and integral phase unwrapping method for processing moiré interferometry images

We present a new method of regional identification, partition, and integral (RIPI) phase unwrapping for processing images, especially those with low quality, obtained from moiré interferometry experiments. By introducing the principle of preorder traversal of a general tree in data structures and then by applying the idea of a regional integral, the proposed method makes regional partition and phase evaluation much easier and more accurate, and it also overcomes the common faults that can occur when conventional approaches, such as line defects, are used. Examples are given to demonstrate the advantage and applicability of the proposed RIPI method when processing experimental images. It is shown that the proposed method works well for global phase distribution, and, at the same time, local mutational information is preserved and limited to its vicinity without affecting other parts.

Fast three-step phase-shifting algorithm

We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three-step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a lookup table. Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time three-dimensional shape measurement system, we were able to achieve a measurement speed of 40 frames per second at a resolution of 532 x 500 pixels, all with an ordinary personal computer.

Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry

Sinusoidal structured illumination is used widely in three-dimensional (3-D) sensing and machine vision. Phase algorithms, for example, in phase-measuring profilometry, are inherently free of errors only with perfect sinusoidal fringe projection. But it is difficult to produce a perfect sinusoidal grating. We propose a new concept, area modulation, to improve the sinusoidality of structured illumination. A binary-coded picture is made up of many micrometer units. An aperture is open in every micrometer unit, and its area is determined by the value of the sinusoidal function. When such a grating is projected onto an object surface, the image of the grating becomes sinusoidal because of the convolution function of an optical system. We have designed and manufactured an area modulation grating for sinusoidal structure illumination using a large-scale integration technique. The area modulation grating has been used in the high-precision phase-measuring profilometry system, and the phase errors caused by the area modulation grating are reduced to 0.1%. The grating guaranteed the entire measuring accuracy to a 1% equivalent wavelength. The experimental results proved that area modulation grating would be of significant help in improving the phase-measurement accuracy of the 3-D sensing system.

Phase-unwrapping algorithm based on frequency analysis for measurement of a complex object by the phase-measuring-profilometry method

A new phase-unwrapping algorithm based on fringe frequency analysis is presented that will achieve greater automation and precision in measuring complex objects by phase-measuring profilometry (PMP). The new algorithm, which combines digital weighted filtering in the frequency domain and modulation ordering in the spatial domain, can recognize corrupt pixels automatically and produce a better phase-unwrapping path. By frequency weighted filtering, the analysis of fringe frequency is converted into the analysis of fringe modulation. Then, based on a strong correlation between local spatial frequency and the reliability of phase data, ordering of the filtered modulation produces an optimized unwrapping path. Simulation and experiments verify the new algorithm.