Microscopic phase-shifting profilometry based on digital micromirror device technology

A microscopic three-dimensional (3-D) shape measurement system based on digital fringe projection has been developed and experimentally investigated. A Digital Micromirror Device along with its illumination optics is integrated into a stereomicroscope, which projects computer-generated fringe patterns with a sinusoidal intensity profile through the microscope objective onto the object surface being measured. The fringe patterns deformed by the object surface are recorded by a CCD camera. The microscopic 3-D shape of the object surface is measured and reconstructed by use of a phase-shifting technique. We discuss design considerations and error analysis of the system. Experimental results successfully demonstrate the capability of this technique for surface profile measurement of rough surfaces at the micrometer level.     

Thermal deformation measurement of the solder joints in electronic packages using electron moiré method

In this paper, electron moiré method is used to measure the thermal deformation of electronic packages. In order to observe the electron moiré fringe, a holographic grid was replicated on the cross section of the BGA type package at 150°C. This grid was fabricated on a glass plate using a moving point holographic system, and was replicated to measured area at high temperature. Under SEM, the holographic grid(specimen grid) and a programmed electron beam scan(master grid) interfere and form electron moiré patterns. The shear strain measurement technique using electron moiré method is described. Using the electron moiré method, the shear strains in the different solder joints were measured and analysed. Some useful results were obtained.     

APPLICATION OF GRIDS TO PLASTICS FOR THE MOIRE FRINGE METHOD OF STRAIN MEASUREMENT

There has been considerable interest during recent years on the measurement of strain using the moiré fringe method. This report reviews the techniques of applying grids to specimens and gives details of methods used at NEL. Strain measurements on a simple tensile test specimen using the moiré mismatch technique are compared with those obtained with a Linley extenso-meter.     

Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting

The use of an optical fringe projection method with two-step phase shifting for three-dimensional (3-D) shape measurement of small objects is described. In this method, sinusoidal linear fringes are projected onto an object's surface by a programmable liquid-crystal display (LCD) projector and a long-working-distance microscope (LWDM). The image of the fringe pattern is captured by another LWDM and a CCD camera and processed by a phase-shifting technique. Usually a minimum of three phase-shifted fringe patterns is necessary for extraction of the object shape. In this method, a new algorithm based on a two-step phase-shifting technique produces the 3-D object shape. Unlike in the conventional method, phase unwrapping is performed directly by use of an arccosine function without the need for a wrapped phase map. Hence, shape measurement can be speeded up greatly with this approach. A small coin is evaluated to demonstrate the validity of the proposed measurement method, and the experimental results are compared with those of the four-step phase-shifting method and the conventional mechanical stylus method.     

Intensity range extension method for three-dimensional shape measurement in phase-measuring profilometry using a digital micromirror device camera

Phase-measuring profilometry is an accurate and effective technique for performing three-dimensional (3D) shape and deformation measurements of diffuse objects by fringe projection. However, phase analysis cannot be performed in underexposed or overexposed areas of the detector when an object with wide reflectance is measured. A novel intensity range extension method using a digital micromirror device (DMD) camera is proposed. In the optics of the DMD camera, each pixel of the CCD corresponds exactly to each mirror of the DMD. The phase-shifted fringe patterns with high contrast can be easily captured by programming an inverse intensity pattern that depends on the reflectance of the object. Our method can provide a wider intensity range and higher accuracy for 3D shape measurement than other conventional methods in both underexposed and overexposed areas. The measurements of a replica of a metallic art object and a flat plane are analyzed experimentally to verify the effectiveness of our method. In the experiment, the percentage of invalid points due to underexposure and overexposure can be reduced from 20% to 1%.     

Profile measurement taken with liquid-crystal gratings

Profile measurement taken with liquid-crystal gratings and a phase-shifting technique is proposed, and its effectiveness is verified by experiment. The surface profile is obtained by measurement of the phase distributions of the sinusoidal gratings deformed by an object's surface. The liquid-crystal grating gives an accurate phase shift, an arbitrary projection pitch, and a constant surface brightness compared with conventional gratings such as a laser interference fringe grating and a Ronchi grating. Therefore a flexible measuring system may be developed with it. Two gratings with different pitches are used to measure an object with large steps. A two-color projection system can be used to produce such gratings simultaneously. Locally varying reflectivity on a surface can also be compensated by adjustment of the color component of the projected grating with a liquid-crystal grating. Thus the contrast in the projected grating can be made uniform, and a good profile measurement can be accomplished.     

Control of phase of fringes in speckle interferometry for application of fringe scanning method

The speckle interferometry is an effective technique in the displacement measurement of a structure with a rough surface. However, when the fringe scanning technique is introduced to speckle interferometry for improving the measurement resolution, generally two speckle patterns before and after the deformation of the measurement object and another speckle pattern obtained under different conditions from these two speckle patterns are required at least. So, three speckle patterns are generally required for precise fringe analysis as a minimum condition. In this paper, a method for introducing the fringe scanning method is proposed by controlling the phase of the specklegram as a fringe image using filtering techniques. Then, the temporal fringe analysis method that uses only two speckle patterns are proposed for speckle interferometry. As the result of experiments, it is shown that high precise fringe analysis can be realized by the fringe scanning methods using only two speckle patterns for the displacement measurement with a large deformation.     

High Temperature Gratings for the Moiré and Moiré Interferometry Methods and their Application to Deformation Measurement - A Review

Abstract: This paper gives a general review of the production of high temperature gratings and their application to deformation measurement. The fabrication techniques for gratings and deformation measurement methods using the gratings are discussed. The review is confined to in-plane moiré and moiré interferometry methods. Some typical applications in high temperature deformation measurement are briefly discussed.     

Phase error compensation for three-dimensional shape measurement with projector defocusing

This paper analyzes the phase error for a three-dimensional (3D) shape measurement system that utilizes our recently proposed projector defocusing technique. This technique generates seemingly sinusoidal structured patterns by defocusing binary structured patterns and then uses these patterns to perform 3D shape measurement by fringe analysis. However, significant errors may still exist if an object is within a certain depth range, where the defocused fringe patterns retain binary structure. In this research, we experimentally studied a large depth range of defocused fringe patterns, from near-binary to near-sinusoidal, and analyzed the associated phase errors. We established a mathematical phase error function in terms of the wrapped phase and the depth z. Finally, we calibrated and used the mathematical function to compensate for the phase error at arbitrary depth ranges within the calibration volume. Experimental results will be presented to demonstrate the success of this proposed technique.     

Deformation Data from Thermal Marking

Abstract: A novel experimental technique for strain measurement, named thermal moiré, and based on a combination of thermography and moiré concepts, is presented in this paper. The proposed technique essentially involves the temporary imprinting of a thermal pattern onto the surface of the object of interest as a substitute for conventional gratings, to remove the need for physical printing, etching or bonding. In materials with low diffusivity, the thermal pattern can be observed with an infrared camera and analysed using conventional techniques. Work on the development of suitable laboratory apparatus is described, and preliminary experimental results are presented to illustrate the feasibility of the method.     

Flexible three-dimensional measurement technique based on a digital light processing projector

A new method of 3D measurement based on a digital light processing (DLP) projector is presented. The projection model of the DLP projector is analyzed, and the relationship between the fringe patterns of the DLP and the fringe strips projected into the 3D space is proposed. Then the 3D shape of the object can be obtained by this relationship. Meanwhile a calibration method for this model is presented. Using this calibration method, parameters of the model can be obtained by a calibration plate, and there is no requirement for the plate to move precisely. This new 3D shape measurement method does not require any restrictions as that in the classical methods. The camera and projector can be put in an arbitrary position, and it is unnecessary to arrange the system layout in parallel, vertical, or other stringent geometry conditions. The experiments show that this method is flexible and is easy to carry out. The system calibration can be finished quickly, and the system is applicable to many shape measurement tasks.     

Carrier phase component removal: a generalized least-squares approach

In fringe projection profilometry, an object shape is evaluated through phase distribution extracted from a projected fringe pattern. For parallel illumination geometry, the carrier phase component introduced by the fringes is spatially linear, whereas nonparallel illumination would lead to a nonlinear carrier. In this study, a general approach for the removal of a nonlinear-carrier phase component is proposed. A series expansion technique is used to approximate the carrier phase function, and a least-squares method is developed to estimate the unknown coefficients of the series. The theoretical analysis is given on the basis of a divergent illumination geometry with carrier fringes in the x direction. The method is also extended to include a curved surface-fitting approach, which is applicable to various measurement system geometries.     

Investigation of membrane deformation by a fringe projection method

An optical method has been developed to measure the deformation of a membrane in a microphone. A fringe projector that consists of an optical fiber and an optical wedge is described and analyzed by geometric optics. A three-step phase-shifting technique that involves the introduction of an arbitrary phase is discussed. The fine fringe patterns projected onto a small test surface are captured by a CCD camera mounted on a long-distance microscope. With the aid of a phase-shifting technique and signal-demodulating techniques, the proposed setup is capable of measuring deformation of the membrane of the order of as much as submicrometers.     

基于三次插值坐标变换的反向条纹投影技术

反向条纹投影技术是一种应用于在线或批量检测的快速而稳定的光学三维面形检测技术。本文提出了一种利用分片二元三次多项式插值来确定摄像机和投影器坐标变换关系的方法,它通过在摄像机10个像素点区域内拟和两个二元三次多项式,来求得该区域内投影器像素点对应的摄像机坐标值。计算机模拟和实物的对比实验表明,该方法能有效地提高反向条纹投影的精度。     

Uneven fringe projection for efficient calibration in high-resolution 3D shape metrology

A novel uneven fringe projection technique is presented whereby nonuniformly spaced fringes are generated at a digital video projector to give evenly spaced fringes in the measurement volume. The proposed technique simplifies the relation between the measured phase and the object's depth independent of pixel position. This method needs just one coefficient set for calibration and depth calculation. With uneven fringe projection the shape data are referenced to a virtual plane instead of a physical reference plane, so an improved measurement with lower uncertainty is achieved. Further, the method can be combined with a radial lens distortion model. The theoretical foundation of the method is presented and experimentally validated to demonstrate the advantages of the uneven fringe projection approach compared with existing methods. Measurement results on a National Physical Laboratory (UK) "step standard" confirm the measurement uncertainty using the proposed method.     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

相移条纹投影三维形貌测量技术综述

结构光三维形貌测量系统目前得到了越来越广泛的应用和研究,相移条纹投影三维形貌精密测量技术是其重要的发展方向。对结构光相移条纹投影三维形貌测量系统的应用发展、工作过程、不同系统构成方式、相移条纹的各种形式及特点、相位误差校正方法、不同相位解包裹算法及其优缺点和适用场合、测量系统数学模型的实现方法及其相应的优缺点、高动态范围测量技术等进行了详细的分析。对相移条纹投影系统的工作流程、实现方法、关键技术的发展及其存在问题等进行了比较全面的梳理,为三维形貌精密测量技术进一步满足先进制造中更高精度的要求指出了后续的研究方向。     

Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift

A three-frame phase-shifting algorithm with a constant but unknown phase shift is proposed. The algorithm is based on background-intensity removal prior to phase retrieval to eliminate an undetermined factor in a fringe pattern. The proposed method is validated on three-dimensional profilometry by fringe projection and on deformation measurement by means of digital speckle shearing interferometry. For a fringe pattern with slow-varying background intensity, the background removal is achieved in the frequency domain. For a speckle pattern, a background removal technique is integrated with the three-frame algorithm. In this process, manual intervention is minimal, and high computational speed is achieved. In addition, high-frequency phase signals would not be removed in the noise-reduction process as is the case in the bandpass-filtering technique. Accuracy of the method is discussed.     

Temporal evaluation of fringe patterns with spatial carrier with an improved asynchronous phase demodulation algorithm

Abstract

A method for temporal evaluation of fringe patterns with a spatial carrier is presented. The proposed technique consists in the recording of the temporal irradiance fluctuations obtained when a linear variation of the set-up sensitivity is introduced. In this way, the use of a spatial carrier introduces a linear temporal carrier frequency. This allows the use of fast and low time consuming temporal asynchronous demodulation algorithms, similar to those employed in spatial phase shifting techniques. An existing five-step algorithm has been corrected for asynchronous demodulation. It is shown that it is possible to fix the sensitivity variation in such a way that the algorithm presents optimum behaviour against noise and nonlinearities presented by the temporal irradiance signal. Finally, the technique has been applied to measure the shape of an object, using a fringe projection set-up.