Fringe Order Research Articles

Joint Coding Strategy of the Phase Domain and Intensity Domain for Absolute Phase Retrieval

Codewords used to determine fringe orders are significant for absolute phase retrieval based on the phase-coding method. However, because of inevitable interference from image blurring, image noise, and system nonlinearity, it is challenging to significantly increase the number of codewords for high-accuracy phase retrieval. To address this challenge, this article proposes a joint coding strategy to perform the coding of high-density stripes. More specifically, codewords are simultaneously embedded into the phase domain and the intensity domain of composite fringe patterns, which greatly extends the encoding range of valid codewords. Moreover, to improve the anti-interference capability of the proposed coding strategy, a regional correction technique (RCT) is presented to remove jump phase errors induced by the inevitable interference. The results of experiments indicate that the proposed method is effective and accurate for both complex objects and a standard sphere.

Edge-preserved fringe-order correction strategy for code-based fringe projection profilometry

Code-based fringe projection profilometry (CBFPP) is widely used because of its simple structure, robustness, and potential high speed. One of the most important steps in this technique is to obtain the fringe orders correctly. However, fringe orders tend to fail easily, especially around the phase-jump regions. First, this paper analyzes the formation mechanisms of different types of fringe-order noise. Then, an edge-preserved fringe-order correction strategy has been proposed to tackle the fringe order noise problem. Unlike the proprietary denoising algorithms, the correction approach is suitable for all types of CBFPP. Furthermore, the present algorithm is fast and can process in a short time. Moreover, the entire filtering procedure is noninvasive and can deal with dense point artifacts. The simulation and experimental results are presented to verify the feasibility and effectiveness of the proposed method.

Critical phase-transition temperature for freezing stress in thermo-sensitive photopolymers used for visualizing stress fields in solids

Quantitative visualization of the hidden full-field stresses in three-dimensional (3D) solids is crucial for solving various engineering problems; however, it is challenging to achieve using the conventional experimental techniques. Frozen stress technique is an effective method to characterize internal stress fields. However, difficulties in fabricating the complex 3D models impede the extension of this method. The method combining additive manufacturing or 3D printing, printable transparent photopolymers, and frozen stress techniques provides a new approach to overcome these challenges. However, the effects of continuous temperature rise and loading during the frozen stress tests on the stress birefringence of the thermo–sensitive photopolymers have not been studied thoroughly. In this study, the stress birefringence characteristics of the photopolymers were examined using 3D printed transparent disk models and frozen stress tests under various temperatures and radial loads. A reflection polariscope system incorporated with a high-temperature loading chamber was designed to freeze and capture the stress fringes in the printed model. The thermo–optic curve, stability of full-field fringes, and elasticity and plasticity of the photopolymer under high temperatures and remaining loads were investigated. The effects of high temperatures and remaining loads on the stability of the fringe orders were analyzed. The linear relationship between the fringes and stresses in the material was verified using the fringe orders in the central points of the disk models. The critical temperatures that discriminate between the three different thermo–stress states, i.e., glassy state, transition state, and freezing state, were discussed. Our results indicate that the lowest critical temperature for freezing stresses in the tested photopolymer is 80 °C.

Two-Digit Phase-Coding Strategy for Fringe Projection Profilometry

Phase-coding methods have been widely used for three-dimensional (3-D) shape measurement, which use sinusoidal phase-shifting patterns to recover wrapped phase and the stair phase-coding patterns to determine the fringe order. However, due to the system nonlinearity, random noises, and image blurring, the total number of codewords that can be used is limited. In order to increase the number of codewords, this article presents a two-digit phase-coding (TDPC) strategy, in which each fringe of the sinusoidal phase-shifting patterns corresponds to a two-digit codeword encoded in the phase-coding patterns. In this way, more codewords can be generated without increasing additional patterns. Experiments of the cup and sculptures have been carried out, and the results confirm that the TDPC method can recover the 3-D shape of objects more robustly. Meanwhile, the precision experiment of a standard ball proves the high accuracy of the proposed method.

Absolute phase unwrapping with SVM for fringe‐projection profilometry

Phase unwrapping is a fundamental task in phase-based profilometry. Existing spatial and temporal approaches are facing challenges such as error propagation and low efficiency. In this study, the authors propose a learning-based method that uses a support vector machine (SVM) to perform phase unwrapping, where the problem is solved as a classification task. To be specific, seven elements, extracted from the captured patterns and the wrapped phase, form the input feature vector and the fringe order is the output class. Besides, a radial basis function kernel SVM is adopted as the model. The proposed method is conducted independently for every pixel, and does not suffer from error propagation in the spatial unwrapping. Moreover, it needs fewer patterns than temporal unwrapping since only one phase map is required. Simulation and experimental results demonstrate that the proposed scheme produces precise depth maps, which are comparable with the complex quality-guided methods but at a much faster speed.

High-accuracy simultaneous measurement of surface profile and film thickness using line-field white-light dispersive interferometer

White-light dispersive interferometry (WLDI) is an instantaneous, high-resolution optical metrological technique for measuring precise and complicated surfaces. This method enables nondestructive inspection of transparent-film-structure devices that are widely used in semiconductor packaging. We propose in this paper to use a home-built WLDI system with line-by-line spectral calibration, phase-shifting algorithm, and single-wave-number method for high-accuracy, simultaneous measurements of surface profiles and film thickness. By calibrating the relationship between wave-number and pixel position on each line of a two-dimensional detector, the line-by-line calibration method improves the measurement accuracy by correcting the spectral distortion caused by the optical system. Moreover, the spectral signal phase is obtained by the phase-shifting algorithm instead of by the Fourier transform method. The single-wave-number method is applied to the computation process by introducing the fringe order, and the measurement result indicates that it enhances the system immunity to environmental noise. A 1.806-µm-high standard step and a 1052.2-nm-thick standard film are measured to verify the system performance and show that the system is highly accurate and reliable.

Quantification of photoelastic fringe orders using polarized light camera and continuous loading

Quantification of fringe orders is important in visualizing full-field stress in digital photoelasticity. Various methods have been developed to improve the calculated accuracy of fringe orders, such as the phase shifting, carrier, and RGB methods. However, in these methods, fringe orders are calculated using the photoelastic patterns under a certain load but not the patterns in the whole time series; this impedes quantification of the fringe orders in dynamic photoelasticity. In this study, a polarized light camera was employed to simultaneously capture the photoelastic patterns of the dark and bright fields under circular polariscope. Based on the light intensity difference of these patterns in the entire loading process, a method of quantifying fringe orders is proposed. Full-field fringe orders in a disk fabricated by 3D printer and subjected to three compressive loads were calculated using this method. Its good accuracy, improved by removing the background light and choosing a suitable capture frame rate, was verified by comparing the fringe orders calculated by the traditional and proposed methods. Furthermore, the determination of the full-field fringe orders in complex structures indicated that the complexity of tested models had no influence on the calculated accuracy.

Absolute phase measurement with four patterns based on variant shifting phases.

Fringe projection profilometry has been proverbially utilized for measuring the shapes of objects. A common challenge in those systems is to accurately obtain a smooth absolute phase. Many new methods have been proposed to address this challenge. In this paper, we discuss a technique based on variant shifting phases. This approach embeds codewords into the shifting phase and only needs four patterns. However, reliable measurement results are difficult to achieve with a large number of codewords because of the phase errors. To address this shortcoming, we present a robust coding method that embeds a specific code sequence into the shifting phase and can generate more than 36 periods. The fringe order is determined using unique three-adjacent-codes combining the current period and its neighbors. An error correction algorithm is also proposed to optimize the codewords. The proposed method is experimentally verified using an established measurement system. The result shows that the proposed method is robust and efficient.

Spatial pattern-shifting method for complete two-wavelength fringe projection profilometry.

Two-wavelength fringe projection profilometry (FPP) unwraps a phase with the unambiguous phase range (UPR) of the least common multiple (LCM) of the two wavelengths. It is accurate, convenient, and robust, and thus plays an important role in shape measurement. However, when two non-coprime wavelengths are used, only a small UPR can be generated, and the unwrapping performance is compromised. In this Letter, a spatial pattern-shifting method (SPSM) is proposed to generate the maximum UPR (i.e., the product of the two wavelengths) from two non-coprime wavelengths. For the first time, to the best of our knowledge, the SPSM breaks the constraint of wavelength selection and enables a complete (i.e., either coprime or non-coprime) two-wavelength FPP. The SPSM, on the other hand, only requires spatially shift of the low-frequency pattern with the designed amounts and accordingly adjusting the fringe order determination, which is extremely convenient in implementation. Both numerical and experimental analyses verify its flexibility and correctness.

Spatial binary coding method for stripe-wise phase unwrapping.

Binary coding methods have been widely used for phase unwrapping. However, traditional temporal binary coding methods require a sequence of binary patterns to encode the fringe order information. This paper presents a spatial binary coding (SBC) method that encodes the fringe order into only one binary pattern. Each stripe of the sinusoidal phase-shifting patterns is corresponding to an N-bit codeword of the binary pattern. A robust stripe-wise decoding scheme is also developed to extract the N-bit codeword, then fringe order can be determined, and stripe-wise phase unwrapping can be performed. Experiment results confirm that the SBC method can correctly recover the absolute phase of measured objects with only one additional binary pattern.

Effect of Nanographite on Electrical Mechanical and Wear Characteristics of Graphite Epoxy Composites

Effect of weight fraction (WF) of nanographite (NG, 400 nm) on electrical, mechanical and wear and characteristics of graphite epoxy composites (GECs) were investigated. For this purpose, a series of GECs was prepared through dispersion of various WF of NG into epoxy resin, followed by curing with polyamine. Dispersion of NG into epoxy matrix and onward formation of GECs and was revealed through UV, Fourier transformed spectra and atomic force microscopy (AFM). Photoelastic analysis in combination with AFM reveals the presence of uniformly dispersed domain of NG into stress free GECs with fringe order ranging 0.23 - 0.61 under compression of 8 - 20 kgf. GECs have rendered a rising trend in DC conductance ranging 98.32 - 0.54 μS/cm with electrical percolation threshold at 175 WF of NG. GECs have shown enhanced compressive, impact, tensile, strength, Rockwell hardness and wear resistance at 200 WF of NG. In general, GECs has shown a marginal modification in their compressive strength by 5.30 % over cured epoxy. However, their impact and tensile strengths were largely improved to 31.78% and 43.98% over cured epoxy. The present manuscript provides a novel method of modification in electrical, mechanical and wear behaviour epoxy through introducing NG as a novel alternative to traditionally used graphite as filler for development of GECs.

Bicubic interpolation and extrapolation iteration method for high resolution digital holographic reconstruction

Digital holography enables the digitization processing of holograms. The resolution of the reconstructed image is greatly limited by the pixelated imaging detectors. To improve the resolution, a bicubic interpolation and extrapolation iteration (BIPEPI) method is proposed to compensate the limited size of the digital holograms. Based on the prior knowledge of the model of Fresnel zone plate with circular diffraction gratings, the pixel density is increased by the bicubic interpolation (BIP) method inside the hologram to enhance the low-frequency terms of the object. With extrapolation iterations (EPI) method, more high order fringes outside the hologram are generated to enhance the high-frequency terms of the object. The resolution of the reconstructed image can be effectively improved by combining this predicted low- and high-frequency terms. Numerical simulations and optical experiments are presented and the feasibility of the proposed method is quantitatively evaluated.

Inner Shifting-Phase Method for High-Speed High-Resolution 3-D Measurement

Fringe projection profilometry (FPP) is widely used in the 3-D noncontact measurement. In FPP, one of the most important steps is obtaining the absolute phase through fringe orders and wrapped phase. The existing methods usually acquire the fringe orders and wrapped phase independently. Therefore, more patterns are needed to project onto the object, which decreases the measuring speed a lot. We propose an inner shifting-phase method that codes the fringe orders and the wrapped phase into the same four patterns. With the unwrapping algorithm, we obtain the fringe orders and the wrapped phase simultaneously, which decreases the number of required patterns a lot. The proposed method calculates the absolute phase pixel-by-pixel independently without any preacquired information or geometric constraints. Experiment results show that the proposed method achieves almost the same accuracy with only a third of the patterns required by the conventional three-frequency four-step method. Experiment results also verify the validity of the proposed method in measuring both complex and separated objects.

Structured-light-field 3D imaging without phase unwrapping

Directly using wrapped phases may cause a problem of phase ambiguity in fringe-projection-based three-dimensional (3D) imaging. In our previous work, the phase ambiguity was addressed by introducing light-field imaging to associate a wrapped phase-encoded field in the image space with several candidates of spatial points in the object space to identify the correct fringe orders for absolute phase unwrapping. The candidate spatial points with absolute phases can be reconstructed by satisfying the mandatory requirements of system fixation and pre-calibration, which may lack flexibility and applicability. Since we also illustrated that the correspondence cue in an unwrapped phase-encoded field could be used for accurate light-field depth estimation, an instructive question is whether or not depth cues of the light-field imaging can provide constraint conditions to deal with the phase ambiguity without these systematic requirements. To this end, a method for structured-light-field 3D imaging is proposed. The wrapped phase-encoded field was processed to be locally continuous with respect to the phases in specific angular coordinates. After that, the correspondence cue focusing on the local angular variance of the processed wrapped phase-encoded field was used to estimate depths correctly without the requirement of system pre-calibration. Furthermore, comparative experiments under different measurement conditions, including the changes of the fringe period of projected patterns, the focal length of the projector, and the relative orientation among system components, produced the consistent measurement results. Consequently, the proposed method is proved to adapt to the changes in the measurement environment and be a flexible way for structured-light-field 3D imaging without the need for phase unwrapping.

Fringe harmonics elimination in multi-frequency phase-shifting fringe projection profilometry.

In fringe projection profilometry, the purpose of using two- or multi-frequency fringe patterns is to unwrap the measured phase maps temporally. Using the same patterns, this paper presents a least squares algorithm for, simultaneously with phase-unwrapping, eliminating the influences of fringe harmonics induced by various adverse factors. It is demonstrated that, for most of the points over the measured surface, projecting two sequences of phase-shifting fringe patterns having different frequencies enables providing sufficiently many equations for determining the coefficient of a high order fringe harmonic. As a result, solving these equations in the least squares sense results in a phase map having higher accuracy than that depending only on the fringe patterns of a single frequency. For the other few points which have special phases related to the two frequencies, this system of equations becomes under-determined. For coping with this case, this paper suggests an interpolation-based solution which has a low sensitivity to the variations of reflectivity and slope of the measured surface. Simulation and experimental results verify that the proposed method significantly suppresses the ripple-like artifacts in phase maps induced by fringe harmonics without capturing extra many fringe patterns or correcting the non-sinusoidal profiles of fringes. In addition, this method involves a quasi-pointwise operation, enabling correcting position-dependent phase errors and being helpful for protecting the edges and details of the measurement results from being blurred.

An improved gray-level coding method for absolute phase measurement based on half-period correction

Absolute phase retrieval is important for three-dimensional (3D) shape measurement in fringe projection technique. Numerous phase unwrapping methods have been proposed for addressing this issue, and gray-level is one such technique employed to determine fringe orders for wrapped phase. However, the codeword detection can fail due to random noise or cameras/projectors defocus. We propose an improved method to determine the codewords in this paper. Specifically, three sinusoidal fringe patterns are used to obtain the wrapped phase and three n-ary gray-level (nGL) patterns are employed to obtain the fringe order. Two opposite masks can be calculated through wrapped phase binarization. The masks and the nGL patterns are roughly used to obtain codewords. After half-period correction, the codeword is accurately reconstructed, and the fringe order is also determined. Simulations and experiments demonstrated the robustness and effectiveness of the proposed algorithm to measure isolated objects with complex surfaces.

Fringe Order Correction for Number-Theoretical Phase Unwrapping Method via Maximum Likelihood Principle

The number-theoretical phase unwrapping method has recently been widely applied in fringe projection profilometry. But fringe order errors may occur due to noise or distortion, leading to errors in the unwrapped phase map, and eventually affecting the accuracy of the reconstructed object surface. In this paper, we propose a novel fringe order correction method based on the maximum likelihood principle. The direct cause of fringe order error is the deviation of an intermediate variable which in theory should be an integer, and the ground truth of the integer stays unchanged within a valid neighborhood. By modeling the calculated intermediate variable as an observed sample from the normal distribution of the unknown ground truth integer, we can determine a valid neighborhood relative to the observed pixel. Then the ground truth integer can be calculated by maximizing the likelihood function and then the fringe order error is corrected. The simulation results and experimental comparisons have verified the feasibility, robustness, and superiority of the proposed method in contrast with other fringe order correction methods.

基于相位编码的三维测量技术研究进展

Structured light has developed rapidly as a non-contact active three-dimensional measurement method. The phase coding method based on the principle of structured light embeds the codeword into the intensity of the fringe in the form of phase, which is insensitive to surface contrast, ambient light and camera noise due to the use of phase instead of intensity to determine the code word, so it has stronger robustness. The research progress of three dimensional measurement methods of phase-coding was reviewed, and the three-dimensional measurement principles based on phase encoding was summarized, including the design method of initial phase, the generation method of encoded fringes, phase calculation methods, acquisition and correction of fringe order, and acquisition of absolute phase. Some experimental results were given, and the advantages and disadvantages of the phase coding method were pointed out. Finally, the challenges faced by the technology were discussed, and the future development direction of the field was pointed out.

Modification in mechanical, tribological & electrical properties of epoxy at low weight fraction of multiwalled carbon nanotube

Effect of weight fraction (WF, mg/dL) of multiwalled carbon nanotube (MWCNT) on mechanical properties, wear behavior and electrical conductance of epoxy nanocomposites (ENCs) was investigated. For this purpose, a series of ENCs was prepared through curing of epoxy resin with polyamine in presence of various WF of MWCNT ranging 1.0–300, followed by post curing under microwave irradiation to define the ENCs. Effect of WF on dispersion of MWCNT into epoxy matrix and onward formation of ENCs was revealed through spectra, microscopy, stress analysis and DC conductance. Loading of MWCNT up to 200 WF imparts ultimate improvements in Rockwell hardness, compressive, impact, tensile strength and wear resistance of ENCs. Whereas, electrical percolation threshold of ENCs was appeared at 10 WF of MWCNT with electrical insulation at 100 V. Stress analysis under diametric compression ranging 8–20 kgf reveals increase in fringe order of ENCs ranging 0.25–0.45 up to 20 WF of MWCNT. Stress analysis and atomic force microscopy reveals that ENCs with enhanced dispersion and reduced stress may be produced at 20 WF of MWCNT. Present study reveals that ENCs with improved dispersion and reduced internal stress may be produced through loading of 20WF of MWCNT. Whereas, loading of MWCNT up to 200 WF results ENCs with improved mechanical properties, electrical conductance and wear resistance.

基于多级条纹级数修正的相位误差校正方法

基于多级条纹级数修正的相位误差校正方法