Theory and verification of moiréfringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

Establishment and Error Analysis of Model of Interference Fringe Contrast for Laser Tracing Measurement Optical System

A method was proposed to analyze the influences of the non-ideal spectroscopic performance of optical components and orientation errors of a laser tracing measurement optical system on the tracing measurement performance.A comprehensive model of the interference fringe contrast based on the laser tracing system s measurement principle was established in this study.Simulation results based on ZEMAX verified the model.According to the simulation results,the placement angle of the analyzer had a direct influence on the interference fringe contrast.When the angle of the polarized light to the analyzer’s transmission axis increased from 65°to 85°,each contrast of the four-way interference fringes decreased from 0.9996 to 0.3528,the interference fringe contrast is decreased by 65%.Under the split ratio of beam splitters in the interference part(BS 1)of 5∶5,when the splitting ratio of BS 2 changed from 2∶8 to 8∶2,the fringe contrast of the interference signals received by the photodetectors increased,but the injection light intensity onto the PSD reflected by BS 2 decreased.The significant influence of the tracing performance was verified by the experiments.When splitting ratio of BS 2 increased,the contrast of the interference fringes increased.Due to the weakening of the incident light intensity of the PSD caused by the change of BS 2 splitting ratio,the response time of the tracing system is increased by 23.7 ms.As a result,the tracing performance of the laser tracing measurement optical system was degraded.An important theoretical basis was provided to evaluate and improve the accuracy and reliability of laser tracing measurement systems.

Carrier fringe method of moire interferometry for tiny strain measurements in micro-field

In this paper, we demonstrate a new optical method for tiny strain measurements based on the principle of carrier fringes of moire interferometry. A cross-line grating with frequency of 1200 lp/mm is replicated on the specimen surface, and the strain can be deduced from the changes in carrier fringes before and after the deformation of an object. Four coherent laser beams are used to obtain the carrier fringe patterns of field U and V. Both theoretical analysis and numerical simulation indicate that the ideal accuracy of strain can be controlled within a range of ±1με. Case study of a plane extension experiment shows that the measurement accuracy of strain can be controlled within the range of ±10με. The average strain values of every row of field U and every column of field V can be obtained by using this method, and approximated strain of every pixel in the whole-field can be further acquired, and thus it is possible to measure tiny strains occurred in a micro-field. The technology in this paper can provide comprehensive information for analyzing related mechanical content in the field of MEMS.

Fringe Projection Measurement System in Reverse Engineering

Acquisition of physical data with high precision is a key step in reverse engineering (RE). It is an important stimulative for the progress of reverse engineering with which various digitizing devices are invent ed, developed and made applicable. This paper introduces a three dimensional opt ical measurement method based on digital fringe projection technique in RE to im prove the technique through its application. A practical example is presented an d the result demonstrates the applicability and feasibility of the measurement s ystem as well as the reliability and validity of relevant methods and algorithms .

Simultaneous Measurement of Fringe Visibility and Path Predictability of Wave-Particle Duality

An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young＇s double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters.

New Approach for 3D Shape Measurement Based on Color-Coded Fringe and Neural Network

A new 3D surface contouring and ranging system based on digital fringe projection and phase shifting technique is presented. Using the phase-shift technique, points cloud with high spatial resolution and limited accuracy can be generated. Stereo-pair images obtained from two cameras can be used to compute 3D world coordinates of a point using traditional active triangulation approach, yet the camera calibration is crucial. Neural network is a well-known approach to approximate a nonlinear system without an explicit physical model, in this work it is used to train the stereo vision application system to calculating 3D world coordinates such that the camera calibration can be bypassed. The training set for neural network consists of a variety of stereo-pair images and the corresponding 3D world coordinates. The picture elements correspondence problem is solved by using projected color-coded fringes with different orientations. Color imbalance is completely eliminated by the new color-coded method. Once the high accuracy correspondence of 2D images with 3D points is acquired, high precision 3D points cloud can be recognized by the well trained net. The obvious advantage of this approach is that high spatial resolution can be obtained by the phase-shifting technique and high accuracy 3D object point coordinates are achieved by the well trained net which is independent of the camera model works for any type of camera. Some experiments verified the performance of the method.

Measuring the kinematics of a free-flying hawk-moth(Macroglossum stellatarum)by a comb-fringe projection method

We describe a 2D fringe projection method that involves projecting two groups of sharp comb fringes onto a free-flying hawk-moth from different directions and recording the images of distorted fringes by two high speed cameras from two orthogonal views. By calculating the 3D coordinates of the points on the hawk-moth and three-dimensional reconstruction of the wing, the flight trajectory, body attitude and wing kinematics including flapping angle, elevation angle, torsion angle, and camber deformation are obtained.

Optical/Digital Fringe Multiplication in Projection Moire

In this paper, the optical/digital fringe multiplication (O/DFM) is realized in projection moiré using digital image processing (DIP). Both deformed grating and reference grating are captured using a CCD camera. The reference grating can also be produced using DIP. With the O/DFM, the pattern is multiplied with an image processing software, which is developed using MATLAB 6.5. Also with DIP, the phase shifting can become much simpler, and the automation can be adopted. The multiplied pattern is much thinner and easier to read, and sensitivity of measurement can be enhanced.

Precise Measurement of Moving Object by Moiré-Based Image Processing Technique

Moiré images that are generally termed as moiré fringes have been generated due to the interference of two repetitive gratings. These patterns can be applied to many uses in metrology such as the measurements of surface profilometry of aerofoil, stress-strain effects, thermal deformation and so on. Moreover, 3D surface reconstruction as well as movement characterization of linearly and rotary moving objects can be visualized and identified by the moiré imaging technique. Recently it is approached as an emerging tool in the fields of biotechnology-particularly in biomechanics, nanotechnology, broadband communication and optoelectronics as well. Conventional Moiré interferometry evaluates the interference of two light waves being reflected on a reference surface and the object to be profiled. However, satisfactions in the requirements for the current significant issues in obtaining accurate measurements regarding the information of the movements as well as the dimensional deformations of objects dealing with the online inspection in micro-level and nano-level are still challenging. Particularly, for the demand of the present real-time auto-inspection of different precise information of movements objects statistically and dynamically. In that case single light wave system makes the moiré sensing system easier and applicable in real-time imaging. Furthermore, avoiding the employment of expensive conventional imaging facilities in 3-D measurement in mechanical as well as bio-mechanical systems has become a critical problem to be tackled. Therefore, research has been conducted focusing on the objective of developing a simple but precise measuring tool based on a single wave moiré imaging technique for multidimensional motion sensing by employing simple image processing approaches. An experimental set-up with a small CMOS camera has been developed capable of measuring the motion of an object by using a simply ink-printed straight optical grating lines attached to the moving objects. Several model experiments have been conducted for getting the information of movements of an object by adopting several mouse click options only on the moiré image visible at the computer screen. After getting information of the moiré image by the proposed technique, the movements of the object have been accurately identified. The system has been found simple and faster compared to the other conventional methods as well.

A study of making use of computer-aided projection fringe system to measure breast dimension

To measure breast basic dimension by using computer-aided projection fringe system.Methods A system has been developed for measuring breast basic dimension based on computer-aided projection fringe measurement and programming software.Plastic manikins breast’s SN-N (sternal notch to nipple distance),N-ML (nipple to midline distance),N-N (internipple distance),MBW (base width of breast) and N-IMF (nipple to inframammary fold distance) are measured with this system.At the same time,these items are also measured with routine ruler.Results This study indicate that the system has some merits:① non-touching measurement;② it is very rapid,the patient measured need hold his breath only 0.5 second,and all the time it takes is about 2.5 minutes;③ the measurement’s sensitivity is as high as to 0.6 mm,which meets the clinic requirement entirely;④ the measurement’s accuracy of the system is not significantly when comparing to the routine ruler’s.Conclusion Computer-adided projection fringe system for measuring breast basic dimension is feasible and advanced.14 refs,1 fig.

Angle measurement error and compensation for pitched rotation of circular grating

As circular grating is not vertical to the shaft,the angle measurement error of the circular grating is analyzed.Based on the moire fringe equations in pitched condition,the mathematic model of the angle measurement error is derived.The paper comes to the conclusion that the nonorthogonal angle between the circular grating and the shaft leads to the second harmonic error of the angle measurement,and the correctness of the result is proved by the experimental data.The method of the error compensation is presented,and the angle measurement accuracy of the circular grating is improved by the error compensation.

Research and development of fringe projection-based methods in 3D shape reconstruction

This paper discusses current research and development of fringe projection-based techniques. A system based on Fourier transform profilometry (FTP) is proposed for three-dimensional (3D) shape recovery. The system improves the method of phase unwrapping to gain accurate 3D shapes of objects. The method uses a region-growing algorithm for the path prediction guided by the quality map to increase the recovering accuracy and provides a fast and simple tool for 3D shape recovery. The shape measurement and data recovery are integrated to offer a new method of 3D modelling. Examples are presented to verify the feasibility of the proposed method.

Angle measurement error and compensation for decentration rotation of circular gratings

As the geometric center of circular grating does not coincide with the rotation center,the angle measurement error of circular grating is analyzed. Based on the moire fringe equations in decentration condition,the mathematical model of angle measurement error is derived. It is concluded that the decentration between the centre of circular grating and the center of revolving shaft leads to the first-harmonic error of angle measurement. The correctness of the result is proved by experimental data. The method of error compensation is presented,and the angle measurement accuracy of the circular grating is effectively improved by the error compensation.

A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.

MULTIPARAMETER MEASUREMENT FOR RACEWAY GROOVE OF BEARING BASED ON 3D RECONSTRUCTION WITH DIGITAL STRUCTURED LIGHT

A fast 3D reconstruction method based on structured light to measure various parameters of the raceway groove is presented. Digital parallel grating stripes distributed with sine density are projected onto the raceway groove by a DLP projector, and distorting of stripes is happened on the raceway. Simultaneously, aided by three-step phase-shifting approach, three images covered by different stripes are obtained by a high-resolution CCD camera at the same location, thus a more accuracy local topography can be obtained. And then the bearing is rotated on a high precision computer controlled rotational stage. Three images are also obtained as the former step at next planned location triggered by the motor. After one cycle, all images information is combined through the mosaics. As a result, the 3D information of raceway groove can be gained. Not only geometric properties but also surface flaws can be extracted by software. A preliminary hardware system has been built, with which some geometric parameters have been extracted from reconstructed local topography.

High-precision measurement of low reflectivity specular object based on phase measuring deflectometry

Phase measuring deflectometry(PMD)is a robust,noncoherent technique for the characterization of specular surface.For measuring high specular reflectivity surface,PMD can deliver micron radian range local gradient.However,when the measured surface has low specular reflectivity,the accuracy of the measured gradient is low since the captured fringe pattern shows low signal to noise ratio.The phase error characteristics in PMD system when testing low reflectivity surfaces are analyzed.The analysis illustrates that the random phase error increases rapidly while the nonlinear error drops slowly with the decreasing of the tested surface reflectivity.In order to attain high precision measurement of low reflectivity specular surface,a robust error reduction method based on wavelet de-noising is proposed to reduce the phase error.This error reduction method is compared with several other normally used methods in both simulation and experiment work.The method based on the wavelet de-noising shows better performance when measuring the low reflectivity specular surface.

SIMULTANEOUS RECORDING OF FRINGE PATTERNS WITH ONE CAMERA

A novel method to separate and simultaneously record the Moiréinterferometry fringe patterns of three deformation fields with only one CCD camera is developed;details of its operation principle,key points and error analysis are presented.With this technique,the deformation in U,V and W fields can be measured simultaneously,so dynamic test with comprehensive information can be performed.The advantage of this technique over other similar techniques lies in its simplicity,easy implementation and low cost.An application of this technique is given to show its feasibility.Technical problems that may be caused with this technique are also analyzed.

Three-Dimensional Shape Measuring Method Based on Dual-Frequency Digital Moiré Fringe

A dual-frequency digital Moiré measurement method(DFDM) is proposed for the three-dimensional(3D) shape measurement of an object.The high-and low-frequency fringes are modulated separately along orthogonal direction using different carrier frequencies before being projected onto the measured object.After collecting and demodulating the composite fringe,the digital π phase shift is used to remove the DC component of the demodulated fringes,resulting in high-precision Moiré fringes for calculating the wrapped phase.The unwrapping of the high-frequency wrapped phase is guided by the low-frequency phase to further realistically reconstruct the surface of the measured object.When compared with existing single-shot digital Moiré profilometry,DFDM effectively removes the DC component of the fringe and calculates the phase more accurately.

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

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

基于条纹投影三目系统的舌面完整点云获取方法

传统的舌诊过程存在客观性较差的问题,将计算机视觉技术应用于舌诊可以有效推进舌诊客观化。双目立体视觉结合结构光条纹投影技术是三维测量的常用手段,但对于舌诊的测量场景,由于舌体表面常带有津液和口水等,造成条纹图像出现分布随机性较大的高反光区域,导致相位解算错误和点云缺失。本文提出了一种基于光栅投影的三目测量系统,由3个相机构成1个三目和3个双目子系统。在相位和级次约束基础上引入双极线约束,提高三目立体匹配精度,并利用匹配点补充优化三目匹配点集,重建高反光区域点云。结果显示,对比传统双目系统,本系统的匹配精度和重建精度均得到提升,特别是在真实舌面测量中能够生成纹理清晰、特征完整的点云,对舌面高反光区域进行了有效测量,有助于舌诊的客观化进行。