Fringe Order Research Articles

Generalized phase unwrapping method that avoids jump errors for fringe projection profilometry.

Jump errors easily occur on the discontinuity of the wrapped phase because of the misalignment between wrapped phase and fringe order in fringe projection profilometry (FPP). In this paper, a phase unwrapping method that avoids jump errors is proposed for FPP. By building two other staggered wrapped phases from the original wrapped phase and dividing each period of fringe order into three parts, the proposed generalized tripartite phase unwrapping (Tri-PU) method can be used to avoid rather than compensatorily correct jump errors. It is suitable for the phase unwrapping method assisted by fringe order with a basic wrapped phase and fringe order, no matter which method is used to recover them. The experimental results demonstrate the effectiveness and generality of the proposed method, which is simple to implement and superior to measure complex objects with sharp edges.

A novel spatial phase-unwrapping method based on single-pixel binarized line pattern for real-time 3D measurement

A new spatial phase-unwrapping algorithm based on single-pixel binarized (SPB) line pattern is proposed. The conventional spatial phase-unwrapping method produces easily the accumulation and propagation of errors for the wrapped phase in the regions with isolated 2π jumps generated by shadow and sharp changing surfaces. In this paper, the SPB deformed line pattern extracted by the proposed small window retrieval method can determine accurately the corresponding fringe order; then the wrapped phase is unwrapped point-to-point, in which the small window is adaptive for each light line. The measuring accuracy of the proposed method is close to the quality-guided method with high precision, but it performs simultaneously at higher robustness to measure a multi-object image. Only one additional SPB line pattern is projected and the phase-unwrapping process does not involve a time-consuming point-by-point sorting, so the proposed method can be applied to the real-time 3D measurement. The experimental results verify the feasibility and effectiveness of the proposed method.

Using facial landmarks to assist the stereo matching in fringe projection based 3D face profilometry

A three-dimensional (3D) face profilometry based on facial landmarks and a multi-view system is proposed. Theoretically, at least three fringe patterns are required in phase-shifting profilometry, but the stereo relative phase pair obtained by a spatial unwrapping algorithm cannot be used for stereo matching directly because the starting points of phase unwrapping are not on the same fringe period order, so it will result in incorrect disparity. We proposed an innovative method that utilizes facial landmarks as prior knowledge to adjust the relative phase pair to the same phase reference for accurate stereo matching through a phase adjustment algorithm to determine the accurate fringe order difference. The three-step phase-shifting patterns are projected in a looping sequence, and each three-adjacent fringe stereo pair is treated as a group to obtain one frame of a 3D face, which means that the 3D face output of our proposed method can achieve the same frame rate as the camera. The accuracy evaluation and dynamic 3D facial expressions reconstruction verify the success of the proposed method.

Real-time motion-induced error compensation for 4-step phase-shifting profilometry.

Phase-shifting profilometry has been widely used in high-accuracy three-dimensional (3D) shape measurement. However, for dynamic scenarios, the object motion will lead to extra phase shift and then motion-induced error. Convenient and efficient motion-induced error compensation is still challenging. Therefore, we proposed a real-time motion-induced error compensation method for 4-step phase-shifting profilometry. The four phase-shifting images are divided into two groups to calculate two corresponding wrapped phases, one from the first three fringes and the other from the last three fringes. As the motion-induced error doubles the frequency of the projected fringes, the average phase can effectively compensate the motion-induced error because there is a π/2 phase shift between the adjacent frames. Furthermore, we designed a time sequence by recycling the projection fringes in a proper order, and the efficiency of 3D reconstruction could be effectively improved. This method performs pixel-wise error compensation, based on which we realized 50 fps real-time 3D measurement by GPU acceleration. Experimental results demonstrate that the proposed method can effectively reduce the motion-induced error.

Binary defocusing technique based on complementary decoding with unconstrained dual projectors

Binary defocusing technique can effectively break the limitation of hardware speed, which has been widely used in the real-time three-dimensional (3D) reconstruction. In addition, fusion technique can reduce captured images count for a 3D scene, which helps to improve real-time performance. Unfortunately, it is difficult for binary defocusing technique and fusion technique working simultaneously. To this end, our research established a novel system framework consisting of dual projectors and a camera, where the position and posture of the dual projectors are not strictly required. And, the dual projectors can adjust defocusing level independently. Based on this, this paper proposed a complementary decoding method with unconstrained dual projectors. The core idea is that low-resolution information is employed for high-resolution phase unwrapping. For this purpose, we developed the low-resolution depth extraction strategy based on periodic space-time coding patterns and the method from the low-resolution order to high-resolution order of fringe. Finally, experimental results demonstrated the performance of our proposed method, and the proposed method only requires three images for a 3D scene, as well as has strong robustness, expansibility, and implementation.

High-speed and accurate 3D shape measurement using DIC-assisted phase matching and triple-scanning

Structured-light (SL) three-dimensional (3D) shape measurements technique has been extensively studied and applied in various fields, but the real-time capability of SL system is limited by the number of projected SL patterns. This paper presents a digital image correlation (DIC) assisted phase matching and triple-scanning method for high-speed and accurate 3D shape measurements based on the combined projection of three-step phase-shifting patterns and one speckle pattern. Benefiting from the triple-view geometric constraints and DIC technique, stereo correspondence and absolute fringe order of each valid pixel in the left wrapped phase map can be explored without requiring spatial phase unwrapping process or any priori information, the initial disparity map and absolute phase map can be generated. Subsequently, an efficient disparity refinement scheme based on connectivity area segmentation and neighbor disparity check is applied to the initial disparity map and absolute phase map to compensate the pixels with wrong disparities. Several efficient strategies are developed in the pipeline of data processing to speed up the algorithm. To improve the measurement accuracy, stereo SL model is proposed to make adequate use of triple-view information to calculate 3D coordinates using the disparity map and absolute phase map, and the measurement error has been reduced by 33% compared with the conventional methods. The experimental results demonstrate that the proposed method can perform high-speed and accurate 3D shape measurements for arbitrary surfaces and dynamic scenes.

Phase Demodulation Method for Fringe Projection Measurement Based on Improved Variable-Frequency Coded Patterns.

The phase-to-height imaging model, as a three-dimensional (3D) measurement technology, has been commonly applied in fringe projection to assist surface profile measurement, where the efficient and accurate calculation of phase plays a critical role in precise imaging. To deal with multiple extra coded patterns and 2 jump error caused to the existing absolute phase demodulation methods, a novel method of phase demodulation is proposed based on dual variable-frequency (VF) coded patterns. In this paper, the frequency of coded fringe is defined as the number of coded fringes within a single sinusoidal fringe period. First, the effective wrapped phase (EWP) as calculated using the four-step phase shifting method was split into the wrapped phase region with complete period and the wrapped phase region without complete period. Second, the fringe orders in wrapped phase region with complete period were decoded according to the frequency of the VF coded fringes and the continuous characteristic of the fringe order. Notably, the sampling frequency of fast Fourier transform (FFT) was determined by the length of the decoding interval and can be adjusted automatically with the variation in height of the object. Third, the fringe orders in wrapped phase region without complete period were decoded depending on the consistency of fringe orders in the connected region of wrapped phase. Last, phase demodulation was performed. The experimental results were obtained to confirm the effectiveness of the proposed method in the phase demodulation of both discontinuous objects and highly abrupt objects.

Influence of Cement Thickness on the Polymerization Shrinkage Stress of Adhesively Cemented Composite Inlays: Photoelastic and Finite Element Analysis

The objective of this study was to analyze the effect of cement thickness on the strain and stresses resulting from the polymerization of resin cement using photoelasticity and Finite Element Analysis (FEA). For this study, twenty upper first premolars with inlay cavity preparation were constructed from photoelastic resin and restored with composite resin inlay. The samples were divided into two groups (n = 10) according to the film thickness of resin cement material. For Group 1, the film thickness was 100 μm; for Group 2, the film thickness was 400 μm. After polymerization of the cement, photoelastic analysis and finite element analysis (FEA) were performed. In the photoelastic analysis, Group 2 showed higher strain with the presence of second-order fringe even after 24 h. In Group 1, the formation of first order fringes was not observed, even after 24 h. In the FEA analysis, the greatest cusp deflection and tensile stress occurred in Group 2 (0.00026 mm and 0.305 MPa, respectively) due to the polymerization shrinkage in the lingual cusp compared to Group 1 (0.000107 mm and 0.210 MPa, respectively). It can be concluded that the thickness of the resin cement influences the cusp deflection, with the greater thickness of the cement layer, the greater stresses and deformations in the tooth structure occur.

Spatial-temporal phase unwrapping algorithm for fringe projection profilometry

In this paper, a generalized spatial-temporal phase unwrapping algorithm (STPUA) is proposed for extracting the absolute phase of the isolated objects with intricate surfaces. This proposed algorithm can eliminate thoroughly the order jumps of various temporal phase unwrapping algorithms (TPUAs), while inheriting the high measuring accuracy of quality-guided phase unwrapping algorithms (QGPUAs). Differing from the traditional phase unwrapping algorithms, wrapped phase is first divided into several regional wrapped phases, which can be extracted successively according to its areas and unwrapped individually by QGPUAs. Meanwhile, a series of reliable points from the fringe order map obtained from the code deformed patterns are selected to map the corresponding regional unwrapped phases into an absolute phase. The radii of selecting reliable points can provide the high measuring robustness compared with the classical point-to-point TPUAs for the complex surfaces and the motion blur, while keeping the same number of patterns. Therefore, the proposed STPUA combining SPUAs and TPUAs also can be employed in real-time three-dimensional (3D) reconstruction. Theoretical analysis and experimental results are performed to verify the effectiveness and capability of the proposed algorithm.

Three-dimensional shape measurement based on spatial-temporal binary-coding method

Binary coding methods have been widely used for three-dimensional (3D) shape measurement. However, traditional binary coding methods always require a sequence of binary patterns to encode the fringe order. This paper presents a spatial-temporal binary coding (STBC) method for 3D shape measurement with three binary patterns, including a spatial pattern and two temporal patterns. Specifically, the spatial pattern is used to encode a 4-bit spatial code, and the temporal patterns are used to encode the 2-bit temporal code. By combining the spatial code and the temporal code, 6-bit code words can be obtained that distinguish fringe periods of sinusoidal phase-shifting patterns. A robust dual-region labeling decoding scheme is also developed to extract the 6-bit code word for fringe order determination, and then absolute-phase unwrapping can be carried out. Experiments have been conducted, and their results confirm that the STBC method can reliably reconstruct the 3D shapes of measured objects with only three binary patterns.

Mechanical analysis of square shaped PMMA using reflection photoelasticity

This research involves an application of reflection photoelasticity used to analyze stressed samples. The poly(methyl methacrylate) (PMMA) had a rectangular shape 2.5 × 2.5 × 0.6 cm and was compressed by hydraulic press system. The observation of a stressed sample using reflection photoelasticity showed isochromatic and isoclinic fringe patterns. We adjusted the polariscope to determine the photoelastic parameters, namely fringe order, angle principal stress and strain value, which were used to calculate the stress-strain based on calibration, shear difference method and stress-strain optic law. It was found that maximum normal stress (y-direction) and strain values were at contact area and decreased to the edge and center along horizontal and vertical direction of sample. Shear stress depended on multiple of fringe order and sin2θ. It was zero along center of vertical and horizontal direction of sample.

Shading-based absolute phase unwrapping.

Absolute phase unwrapping in the phase-shifting profilometry (PSP) is significant for dynamic 3-D measurements over a large depth range. Among traditional phase unwrapping methods, spatial phase unwrapping can only retrieve a relative phase map, and temporal phase unwrapping requires auxiliary projection sequences. We propose a shading-based absolute phase unwrapping (SAPU) framework for in situ 3-D measurements without additional projection patterns. First, the wrapped phase map is calculated from three captured images. Then, the continuous relative phase map is obtained using the phase histogram check (PHC), from which the absolute phase map candidates are derived with different fringe orders. Finally, the correct absolute phase map candidate can be determined without additional patterns or spatial references by applying the shading matching check (SMC). The experimental results demonstrate the validity of the proposed method.

High order phase contrast and source divergence in low energy electron microscopy

We present experimental observations of high order phase contrast in aberration corrected low energy electron microscopy (AC-LEEM). Phase contrast produced by atomic steps on a Ag (111) surface exhibits prominent high order interference fringes, which have not been reported before. These phase contrast features depend upon defocus and incident electron energy, similar to the prominent first order fringes observed previously and in agreement with Fourier optics (FO) model predictions. The comparison of experimental results and FO model simulations demonstrates that fringe amplitudes are strongly affected at large defocus by the source divergence. This effect is exploited to quantitatively determine the divergence, 0.055 ± 0.005 mrad, of the field emission source in AC-LEEM under the imaging conditions used. Although the divergence determines the spatial coherence of the illumination in microscopy, it has not been possible to characterize this key instrumental parameter in LEEM before.

Period-Wise Phase Unwrapping Method With Two Gray Level Coding Patterns

Fringe projection profilometry is a widely used three-dimensional (3D) optical measurement technique. However, it is quite challenging to quickly obtain the 3D information of objects. Minimizing the number of patterns for phase unwrapping is an efficient way to address the above problem, and many methods have been proposed. This paper reports a period-wise phase unwrapping method with only two gray level coding patterns. Due to a hybrid coding strategy implemented, the number of patterns used in the proposed method reduces by one in comparison with conventional gray level method when generating the same number of codewords. A robust decoding scheme is also developed to determine the fringe order, and its accuracy is guaranteed by using the self-correcting method to remove the phase errors. Some experiments have been conducted, and their results confirm that the success of the proposed method.

A multi-code 3D measurement technique based on deep learning

Benefiting from the merits of low cost, high accuracy and high resolution, fringe projection profilometry has been developing rapidly over the past decades. However, recovering the absolute phase with high accuracy and robustness effectively has always been significant challenge in fringe projection profilometry. In this paper, an intelligent Multi-code Deep Learning (MCDL) technique is developed to solve the high-slope absolute phase from only two patterns with high accuracy and robustness. Two sub-networks are designed for obtaining the wrapped phase and the fringe order. Specially, the proposed MCDL method can solve the high-level fringe orders by only a special multi-code pattern itself through a cooperative multi-connected convolutional neural network. By training the deep network with numerous datasets, the principle of unwrapping phase can be learned by the MCDL approach. Experiments demonstrate that the proposed method has the abilities of high robustness, efficiency and accuracy (measurement error: 0.0189mm, FOV: 250 mm × 200 mm), indicating potential applications for high-speed and high-accuracy three dimensional optical measurement.

Stress Distribution Analysis of Novel Dental Mini-Implant Designs to Support Overdenture Prosthesis.

This study aimed to test and compare 2 novel dental mini-implant designs to support overdentures with a commercial model, regarding the stress distribution, by photoelastic analysis. Three different mini-implant designs (Ø 2.0 mm × 10 mm) were tested: G1-experimental threaded (design with threads and 3 longitudinal and equidistant self-cutting chamfers), G2-experimental helical (design with 2 long self-cutting chamfers in the helical arrangement), and G3-Intra-Lock System. After including the mini-implants in a photoelastic resin, they were subjected to a static load of 100 N under two situations: axial and inclined model (30°). The fringe orders (n), that represents the intensity of stresses were analyzed around the mini-implants body and quantified using Tardy's method that calculates the maximum shear stress (τ) value in each point selected. In axial models, less stress was observed in the cervical third mini-implants, mainly in G1 and G2. In inclined models (30°), higher stresses were generated on the opposite side of the load application, mainly in the cervical third of G2 and G3. All mini-implant models presented lower tensions in the cervical third compared with the middle and apical third. The new mini-implants tested (G1 and G2) showed lower stresses than the G3 in the cervical third under axial load, while loading in the inclined model generated greater stresses in the cervical of G2.

Optimized phase-coding method for absolute phase retrieval based on K-means algorithm

The phase-coding method for absolute phase measurement possesses a strong robustness because its codewords are encoded into phase domain rather than intensity. However, a misalignment problem arises between fringe order and wrapped phase in this method owing to random noises and image blurring, especially in the high-frequency fringes situation. Therefore, the measurement result is unavailable. To overcome this problem, an optimized phase-coding algorithm is proposed in the study. We use the sinusoidal patterns to generate two opposite binary masks, which can locate half of each codeword. Then, the K-means algorithm is used to correct the codewords errors. The accurate fringe order is obtained by merging two halves of codewords and the absolute phase is recovered afterward. The used method is experimentally verified by an established measurement system, and the results show the proposed method is robustness and efficiency.

Error-corrected fringe discrimination using nonary-encoded patterns for phase-shifting projected fringe profilometry

Most 3D profile measurements based on phase-shifting techniques require additional projected patterns to identify fringe orders for the task of phase unwrapping. The total number of projections is usually more than that used for phase extraction. For surfaces with low signal-to-noise ratios, these approaches might further encounter challenges in phase unwrapping. In this study, an error-corrected scheme for fringe discrimination using nonary-encoded patterns is presented. There is no need to take additional projections for phase unwrapping. The fringe patterns used for phase extraction can be analyzed to obtain the absolute phase directly. Any two adjacent fringes on the inspected surface can be discerned. To identify fringes for surfaces which are projected by only two fringes is available. Even though one of the projected fringes is decoded incorrectly, the error-corrected scheme can detect such a mistake and recover the fringe order.

Evaluation of Biomechanical and Stress Distribution of Different Dental Implant Designs: Primary Stability and Photoelastic Analysis

ObjectivesThis study aimed to evaluate and compare the stress distribution and primary stability of three different designs of dental implants. Material and Methods24 implants Neodent® were used (n=8): G1 – Alvim CM; G2 – Drive CM; G3 – Facility, submitted to insertion torque (IT) and pullout test, on 20 PCF (0.24 g/cm3) and 40 PCF (0.64 g/cm3) polyurethane blocks. For the stress distribution, by means of photoelasticity, axial and oblique loads (model at 30° inclination) of 100 N were performed, for reading and quantifying the fringe orders. According to the distribution data, a parametric or non-parametric analysis was performed (α=0.05). ResultsThe IT was lower in G3 (p<0.05) compared to G1 and G2, in 20 and 40 PCF polyurethanes. In the pullout, no difference (p>0.05) was observed between G1 and G2, in both 20 and 40 PCF polyurethanes. In the comparisons between polyurethanes, higher values (p<0.05) were obtained in the 40 PCF for IT and pullout. In the axial loading, lower stresses were observed in the cervical third and higher stresses in the middle and apical third of the implants. With the oblique inclination of the models, higher stresses were generated in the opposite side of the load, in the cervical third of G1, followed by G3 and G2. ConclusionThe results allow to affirm that G1 and G2 exhibit high primary stability and satisfactory stress distribution. Although G3 generates stresses comparable to other implants, its indication is limited in low density bones.

Fringe Order Correction for Fringe Projection Profilometry Based on Robust Principal Component Analysis

Temporal phase unwrapping is among the most robust and efficient phase unwrapping methods in fringe projection profilometry. They can recover the fringe orders even in the presence of surface discontinuities. However, fringe order errors may occur due to phase noise and poor measurement conditions. Such errors often exhibit an impulsive nature and introduce errors to the absolute phase map. Most existing fringe order error correction methods detect and correct the errors in a pixel-by-pixel manner, which may under-utilize the correlation of the fringe orders on different pixels. In this paper, we propose a new method to cope with the fringe order errors associated with temporal phase unwrapping. By exploiting the low-rankness of the fringe order map and sparse nature of the impulsive fringe order errors, we develop a robust principal component analysis (RPCA)-based approach to remove the impulsive fringe order errors. Experiments demonstrate that the proposed method is valid in eliminating the fringe order errors.