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.     

Difference displacement measurement by digital holography by use of simulated wave fronts

A concept called fringe compensation was first presented in phase-shifting electronic speckle-pattern interferometry. We apply a similar principle to digital holographic interferometry; here the phase of a wave front is known and can be manipulated. The basic mathematical formulation of fringe compensation and some experimental results are shown with relatively large, simple rigid-body rotation and circular membrane deformation.     

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.     

Error analysis of the phase-shifting technique when applied to shadow moiré

An exact solution for the intensity distribution of shadow moiré fringes produced by a broad spectrum light is presented. A mathematical study quantifies errors in fractional fringe orders determined by the phase-shifting technique, and its validity is corroborated experimentally. The errors vary cyclically as the distance between the reference grating and the specimen increases. The amplitude of the maximum error is approximately 0.017 fringe, which defines the theoretical limit of resolution enhancement offered by the phase-shifting technique.     

Phase-shifter calibration and error detection in phase-shifting applications: a new method

The phase-shifting technique is used in optical metrology to evaluate the local phase of a fringe pattern. Accurate calibration of the shifting device is often essential but sometimes hardly possible because of deviations of the fringe pattern from the ideal sinusoidal shape and because of a nonconstant phase shift between consecutive frames. We introduce a new technique for calculating the phase shift between frames even in the presence of high noise and nonsinusoidal fringe patterns. In addition, this technique permits the identification of different error sources such as low signal-to-noise ratio, higher harmonics contained in the fringe pattern, and nonconstant phase shift.     

Derivation of retardation phase in computer-aided photoelasticity by using carrier fringe phase shifting

Previous phase-shifting schemes in computer-aided photoelasticity required the processing of six fringe patterns to derive the phase difference due to retardation. A technique in which a carrier fringe is used is demonstrated to reduce to four the number of fringe patterns required. The use of fewer fringe patterns lowers the computation time and the number of phase-step errors. The basis of the technique is outlined in detail, and experimental results are presented as well.     

十六步相移技术在弹痕条纹图分析中的应用

在三维弹痕测量系统中,为了获取较高的测量精度,为此本文提出一种采用十六步相移技术的条纹图处理算法。首先分析了物体三维形貌相位分布获取原理,然后对采集到的弹痕图像进行自适应维纳滤波,去除一部分系统噪声,再利用小波变换对原始图像进行3层sym4小波分解去噪,本系统在小波软阈值分析法的基础上,加入了3层的小波系数分解,同时结合十六步相移法进行相位主值的计算。实验结果表明,弹痕条纹图的位相值曲线更加平滑,原始图像条纹图位相高度偏差的最大值为1.631μm,在经过十六步相移技术处理后,位相主值最大偏差值仅为0.8674μm,对本系统的精度提高奠定了基础。     

Two-step phase-shifting fringe projection profilometry: intensity derivative approach

A new two-step phase-shifting fringe projection profilometry is proposed. The slowly variable background intensity of fringe patterns is removed by the use of an intensity differential algorithm. The high-resolution differential algorithm is achieved based on global interpolation of fringe gray level on a subpixel scale. Compared with the traditional three- or four-step phase-shifting method, the profile measurement is sped up with this approach. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed measurement method. The experimental results compared with those of the four-step phase-shifting method are presented.     

Two-wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator

A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-microm synthetic wavelength.     

一种改进的基于条纹对比度的三维测量方法

基于条纹对比度的三维测量方法由于具有垂直测量的特点,可用于测量表面有突变的复杂物体的三维信息.本文在现有方法的基础上,提出了一种改进的基于条纹对比度的三维测量方法.该方法利用投影仪将一组相移的正弦条纹依次投射在被测物体上,并使被测物体位于投影仪成像面的前方,CCD相机通过一个半透半反镜从投影方向获取物体表面的条纹图像,...     

Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing

Three-dimensional profilometry by sinusoidal fringe projection using phase-shifting algorithms is usually distorted by the nonlinear intensity response of commercial video projectors. To overcome this problem, several methods including sinusoidal pulse width modulation (SPWM) were proposed to generate sinusoidal fringe patterns with binary ones by defocusing the project to some certain extent. However, the residual errors are usually nonnegligible for highly accurate measurement fields, especially when the defocusing level is insufficient. In this work, we propose two novel methods to further improve the defocusing technique. We find that by properly optimizing SPWM patterns according to some criteria, and combining SPWM technique with four-step phase-shifting algorithm, the dominant undesired harmonics will have no impact on the phase obtained. We also propose a new sinusoidal fringe generation technique called tripolar SPWM, which can generate ideal sinusoidal fringe patterns with a very small degree of defocusing. Simulations and experiments are presented to verify the performance of these two proposed techniques.     

Microelectromechanical system pressure sensor integrated onto optical fiber by anodic bonding

Optical microelectromechanical system pressure sensors based on the principle of Fabry-Perot interferometry have been developed and fabricated using the technique of silicon-to-silicon anodic bonding. The pressure sensor is then integrated onto an optical fiber by a novel technique of anodic bonding without use of any adhesives. In this anodic bonding technique we use ultrathin silicon of thickness 10 microm to bond the optical fiber to the sensor head. The ultrathin silicon plays the role of a stress-reducing layer, which helps the bonding of an optical fiber to silicon having conventional wafer thickness. The pressure-sensing membrane is formed by 8 microm thick ultrathin silicon acting as a membrane, thus eliminating the need for bulk silicon etching. The pressure sensor integrated onto an optical fiber is tested for static response, and experimental results indicate degradation in the fringe visibility of the Fabry-Perot interferometer. This effect was mainly due to divergent light rays from the fiber degrading the fringe visibility. This effect is demonstrated in brief by an analytical model.     

Accurate pixel-to-pixel correspondence adjustment in a digital micromirror device camera by using the phase-shifting moiré method

A camera based on the digital micromirror device (DMD) technology has been previously developed. In this optical system, the correspondence of each mirror of the DMD to each pixel of the CCD cannot readily be done since the pixel sizes of the DMD and the CCD are very small. An accurate pixel-to-pixel correspondence adjustment in the DMD camera by means of the phase-shifting moiré method is proposed. To perform high accurate adjustment of the optical system, the phase distribution of a moiré fringe pattern is analyzed when the CCD pixels and the DMD mirrors have a mismatch and/or misalignment with each other. This technique does not need a complicated setting or complex image processing to generate the moiré fringe pattern, and it needs only one captured image. In the adjustment experiment, the proposed method provided very accurate adjustment whose error was less than 1/25 pixel. An experiment of phase analysis to demonstrate the usefulness was performed.     

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.     

Determination of the zero-order fringe position in digital speckle pattern interferometry

A method for determining the position of the zero-order fringe in a metrological experiment with digital speckle pattern interferometry is proposed. It is based on an averaging procedure with shifted images obtained before and after a load is applied. This technique is a complement to the phase-shifting methods. Experimental examples are shown.     

Measurement of focal length with phase-shifting Talbot interferometry

Phase-shifting interferometry with a Fourier fringe analysis technique is implemented to analyze Talbot interferometric fringes and to evaluate the focal length of a lens. A four-step algorithm is used to obtain the phase map of the lens. The slope of the phase map is related to the focal length, and it is from this relationship that we evaluate the focal length. Experimental results are presented. Our experimental study suggests that phase-shifting Talbot interferometry combined with a Fourier fringe analysis technique can be advantageously used to improve the accuracy of measurement.     

Measurement of a fiber-end surface profile by use of phase-shifting laser interferometry

We describe a laser interferometric system in which two objectives are used to measure surface profile on a connectorized fiber-end surface. By the use of the proposed illumination design a He-Ne laser as a point light source is transformed to an extended light source, which is beneficial to localize interference fringe pattern near the test surface. To obtain an optimal contrast of the interference fringe pattern, the flat mirror with an adjustable reflection ratio is used to suit different test surfaces. A piezoelectric transducer attached on the reference mirror can move precisely along the optical axis of the objective and permits implementation of four-step phase-shifting interferometry without changing the relative position between the CCD sensor and the test surface. Therefore, an absolutely constant optical magnification can be accurately kept to capture the interference fringe patterns resulting from a combination of light reflected from both the reference flat mirror and the test surface. The experimental result shows that surface profile on a fiber-end with surface features such as a small fiber diameter of 125 microm and a low reflection ratio of less than 4% are measurable. Measurements on a standard calibration ball show that the accuracy of the proposed setup is comparable with that of existing white-light interferometers and stylus profilometers.     

Iterative full-bandwidth wavefront reconstruction from a set of low-tilt Fizeau interferograms for high-numerical-aperture surface characterization

Full-bandwidth phase-shifting methods as well as band-limited fringe carrier techniques are both problematic when testing high-NA spherical surfaces in Fizeau interferometers. Phase stepping is usually performed by moving a sample and reference sphere relative to each other along the optical axis. At a high NA the method suffers from phase-shift inhomogeneity across the sample surface. Fringe carrier techniques rely on a minimum fringe frequency and call for an off-axis position of the sample, which in turn introduces condenser aberrations. Distortion of the imaging optics generates further apparent aberrations. We propose to combine both principles. The phase shifts are replaced by a set of very low tilts such that the sample is virtually on axis. Initial wavefront estimates are generated by a fringe carrier method. An adaptive Misell-type algorithm combines the interferometric data and iteratively improves the reconstructed wavefront until full spatial bandwidth is achieved.     

Application of a liquid-crystal spatial light modulator for brightness adaptation in microscopic topometry

Three-dimensional optical topometry of technical surfaces becomes increasingly important for the control of industrial processes. However, the local reflectance of the surface of the investigated sample often varies within a wide range, making accurate measurements by fringe projection difficult. We demonstrate the use of a liquid-crystal spatial light modulator as the fringe-generating element in a standard stereo microscope. With this device the brightness of the projected patterns can be adapted pixelwise. This technique leads to a significant improvement of the results of our measurements with a phase-shifting algorithm.     

Deformation measurement with object-induced dynamic phase shifting

A simple, yet powerful, means of computing the phase of fringe patterns depicting dynamic phenomena is presented. It is shown that the basic principle of the phase-shifting methods can be extended to the case of dynamic situations. The crux is to recognize that the phenomenon under examination can itself provide the necessary incremental phase shifts. This new method possesses a very wide range of applications in the field of deformation measurement.