Surface Shape Measurement Research Articles

Fourier transform profilometry of a single-field fringe for dynamic objects using an interlaced scanning camera

Fourier transform profilometry (FTP) of a single-field fringe is proposed using an interlaced scanning camera in dynamic object's surface shape measurement. The deformed fringe patterns of a measured dynamic object are grabbed by an interlaced scanning camera, every of which is divided into two single-field fringes, each of which is not necessarily deinterlaced, and directly reconstructs a 3D surface shape by using FTP. A conclusion is inferred theoretically that two reconstructed object's shapes are identical using a single-field fringe and its corresponding frame fringe. The simulation and experiment results demonstrate the feasibility and effectiveness of the proposed method. The method not only keeps the advantages of traditional FTP, but also doubles the measured system's time resolution.

Problems in the application of a null lens for precise measurements of aspheric mirrors.

Problems in the application of a null lens for surface shape measurements of aspherical mirrors are discussed using the example of manufacturing an aspherical concave mirror for the beyond extreme ultraviolet nanolithographer. A method for allowing measurement of the surface shape of a sample under study and the aberration of a null lens simultaneously, and for evaluating measurement accuracy, is described. Using this method, we made a mirror with an aspheric surface of the 6th order (i.e., the maximum deviation from the best-fit sphere is 6.6 μm) with the parameters of the deviations from the designed surface PV=5.3 nm and RMS=0.8 nm. An approximation of the surface shape was carried out using Zernike polynomials {Z(n)(m)(r,φ),m+n≤36}. The physical limitations of this technique are analyzed. It is shown that for aspheric measurements to an Angstrom accuracy, one needs to have a null lens with errors of less than 1 nm. For accurate measurements, it is necessary to establish compliance with the coordinates on the sample and on the interferogram.

Three-dimensional microscopic deformation measurements on cellular solids

The increasing interest in small-scale problems demands novel experimental protocols providing dense sets of 3D deformation data of complex shaped microstructures. Obtaining such information is particularly significant for the study of natural and engineered cellular solids for which experimental data collected at macro scale and describing the global mechanical response provide only limited information on their function/structure relationship. Cellular solids, in fact, due their superior mechanical performances to a unique arrangement of the bulk material properties (i.e. anisotropy and heterogeneity) and cell structural features (i.e. pores shape, size and distribution) at the micro- and nano-scales.To address the need for full-field experimental data down to the cell level, this paper proposes a single-camera stereo-Digital Image Correlation (DIC) system that makes use of a wedge prism in series to a telecentric lens for performing surface shape and deformation measurements on microstructures in three dimensions. Although the system possesses a limited measurement volume (FOV~2.8×4.3mm2, error-free DOF ~1mm), large surface areas of cellular samples can be accurately covered by employing a sequential image capturing scheme followed by an optimization-based mosaicing procedure. The basic principles of the proposed method together with the results of the benchmarking of its metrological performances and error analysis are here reported and discussed in detail. Finally, the potential utility of this method is illustrated with micro-resolution three-dimensional measurements on a 3D printed honeycomb and on a block sample of a Luffa sponge under compression.

拼接干涉技术在同步辐射领域的发展现状及趋势

In synchrotron radiation field, the apertures of optical components increase gradually and their surface figure precisions have been demanded to be a nano-radian level. This paper researches the modern surface figure measurement methods in this field, stitching interferometry, to realize the high resolution two-dimensional measurement of optical components. The basic principles of the stitching interferometry are introduced. Then, a series of common optical surface shape measurement instruments in the synchrotron radiation field are overviewed, such as long trace profilers based on laser beams, high precision and auto-collimation measuring machines for nanometer optical components and stitching interferometers. It describes their development history and working characteristics and compares their shortcomings and advantages. Finally, this paper analyzes the main error sources involved in the stitching interferometry, and points out that the application and development trends of the technology are mainly the innovation of the stitching algorithm, the improvement of measuring speeds of interferometers, the commercialization of interferometers and the integration of the interferometry and other science technologies. 漏 2016, Science Press. All right reserved.

Simultaneous measurement of surface shape and optical thickness using wavelength tuning and a polynomial window function.

In this study, a 6N - 5 phase shifting algorithm comprising a polynomial window function and discrete Fourier transform is developed for the simultaneous measurement of the surface shape and optical thickness of a transparent plate with suppression of the coupling errors between the higher harmonics and phase shift error. The characteristics of the 6N - 5 algorithm were estimated by connection with the Fourier representation in the frequency domain. The phase error of the measurements performed using the 6N - 5 algorithm is discussed and compared with those of measurements obtained using other algorithms. Finally, the surface shape and optical thickness of a transparent plate were measured simultaneously using the 6N - 5 algorithm and a wavelength tuning interferometer.

Absolute measurement of optical flat surface shape based on the conjugate differential method.

In this paper the conjugate differential method is proposed to measure the absolute surface shape of the flat mirror using a phase-shifting interferometer. The conjugate differential method is derived from the differential method, which extracts absolute phase differences by introducing the slight transverse shifts of the optic. It employs the measurement schemes making transverse shifts on the orthogonally bilateral symmetry positions. So the measurement procedures have been changed into four-step tests to get the phase difference map instead of three-step tests for the differential method. The precision of the slope approximation is enhanced by reducing couplings between multi-step tests, and the reliability of the measurements can be improved. Several differential wavefront reconstruction methods, such as Fourier transform, Zernike polynomial fitting and Hudgin model method, can be applied to reconstruct the absolute surface shape from the differencing phase maps in four different simulation environment. They were also used to reconstruct the absolute surface shape with the conjugate differential method in the experiment. Our method accords with the classical three-flat test better than the traditional differential method, where the deviation of RMS value between the conjugate differential method and the three-flat test is less than 0.3 nm.

Three-dimensional shape measurement of complex surfaces based on defocusing and phase-shifting coding

Binary fringe defocused projection is a promising method for high-speed, high-accuracy three-dimensional (3D) shape measurement because of the advantages of superfast projection and capability to overcome the nonlinear gamma of the projector. However, the application of this approach for complex surface measurement remains a challenge. Thus, a method that combines binary fringe and phase coding fringe based on defocusing is proposed to achieve fast-speed, high-accuracy 3D shape measurement of complex surfaces. However, in the case of defocusing, as the number of phase coding fringe cycles increases, the fringe order k(x, y) becomes difficult to judge, errors occur in the jump area, and the periodic dislocation problem becomes worse, ultimately leading to phase unwrapping error. A phase-shifting coding method is thus presented to resolve these issues. This method not only alleviates the difficulty in judging the fringe order as a result of defocusing but also resolves the correction problem, and in turn, the periodic dislocation problem. Thus, measurement accuracy is improved. Experimental results demonstrate the feasibility and superiority of the proposed method.

逆光線追跡による柱状透明物体の表面形状と屈折率の同時計測法

逆光線追跡による柱状透明物体の表面形状と屈折率の同時計測法

JPEG 2000-based compression of fringe patterns for digital holographic microscopy

With the advent of modern computing and imaging technologies, digital holography is becoming widespread in various scientific disciplines such as microscopy, interferometry, surface shape measurements, vibration analysis, data encoding, and certification. Therefore, designing an efficient data representation technology is of particular importance. Off-axis holograms have very different signal properties with respect to regular imagery, because they represent a recorded interference pattern with its energy biased toward the high-frequency bands. This causes traditional images’ coders, which assume an underlying 1/f2 power spectral density distribution, to perform suboptimally for this type of imagery. We propose a JPEG 2000-based codec framework that provides a generic architecture suitable for the compression of many types of off-axis holograms. This framework has a JPEG 2000 codec at its core, extended with (1) fully arbitrary wavelet decomposition styles and (2) directional wavelet transforms. Using this codec, we report significant improvements in coding performance for off-axis holography relative to the conventional JPEG 2000 standard, with Bjontegaard delta-peak signal-to-noise ratio improvements ranging from 1.3 to 11.6 dB for lossy compression in the 0.125 to 2.00 bpp range and bit-rate reductions of up to 1.6 bpp for lossless compression.

Challenges in the areal measurement of surface roughness and shape at the micro and nanoscale

Measuring surface roughness accurately at the micro and nano scale presents several challenges. While optical techniques can be used to rapidly measure large areas, significant variations can be found between results from different techniques on similar samples. In the present work, a comparison has been made between the results of two different systems using interference microscopy and AFM to make measurements at the same place on the same sample. Two samples were prepared on silicon wafers by marking them with a multi-scale pattern using a photoresist process of lithography from an optical mask, followed by reactive ion etching. One was left bare and the other was prepared with a rough layer of hydroxyapatite before measuring at the chosen positions. Comparison of the results showed that while the general shapes of the measured surface microstructures were similar, several differences were found. For example, there was a variation of up to 7% between techniques in the measurement of the depths of the etched features and artefacts were also visible at square edges. These results show the need to pay careful attention to instrument calibration and probe/surface interactions in order to improve the accuracy of surface characterization of surface roughness and topography.

집속이온빔 연마에 의한 패턴의 형태에 관한 연구

For the measurements of surface shape milled using FIB (focused ion beam), the silicon bulk, , and Al/Si samples are used and observed the shapes milled from different sputtering rates, incident angles of ions bombardment, beam current, and target material. These conditions also can be influenced the sputtering rate, raster image, and milled shape. The fundamental ion-solid interactions of FIB milling are discussed and explained using TRIM programs (SRIM, TC, and T-dyn). The damaged layers caused by bombarding of ions were observed on the surface of target materials. The simulated results were shown a little bit deviation with the experimental data due to relatively small sputtering rate on the sample surface. The simulation results showed about 10.6% tolerance from the measured data at 200 pA. On the other hand, the improved analytical model of damaged layer was matched well with experimental XTEM (cross-sectional transmission electron microscopy) data.

Modified sinusoidal fringe-pattern projection for variable illuminance in phase-shifting three-dimensional surface-shape metrology

A camera-independent method of avoiding image saturation using modified sinusoidal fringe-pattern projection to reduce surface measurement error and thus accommodate variable illuminance in phase-shifting surface-shape measurement is presented. The maximum input gray level (MIGL) in the projected patterns is reduced to an optimal tradeoff point, below which the intensity modulation, contrast, and signal-to-noise ratio would diminish the advantage of further MIGL reduction. Measurement simulations using 31 MIGL values, from 105 to 255 in increments of 5, demonstrated reductions in root-mean-square errors for ambient illuminance of 400, 500, 600, 700, 800, and 900 lx, from 0.38, 0.56, 0.86, 1.21, 85, and 373 mm, respectively, at 255 MIGL, to 0.31 to 0.32 mm at the optimum MIGL. The advantage of the method was confirmed in real measurements of a flat plate and human masks. The ability to perform camera-independent measurements under variable lighting conditions and surface reflectivity may lead to more practical measurements in uncontrolled environments.

Optical microscope for three-dimensional surface displacement and shape measurements at the microscale.

We report a novel optical microscope for full-field, noncontact measurements of three-dimensional (3D) surface deformation and topography at the microscale. The microscope system is based on a seamless integration of the diffraction-assisted image correlation (DAIC) method with fluorescent microscopy. We experimentally demonstrate the microscope's capability for 3D measurements with submicrometer spatial resolution and subpixel measurement accuracy.

Adaptive fringe-pattern projection for image saturation avoidance in 3D surface-shape measurement.

In fringe-projection 3D surface-shape measurement, image saturation results in incorrect intensities in captured images of fringe patterns, leading to phase and measurement errors. An adaptive fringe-pattern projection (AFPP) method was developed to adapt the maximum input gray level in projected fringe patterns to the local reflectivity of an object surface being measured. The AFPP method demonstrated improved 3D measurement accuracy by avoiding image saturation in highly-reflective surface regions while maintaining high intensity modulation across the entire surface. The AFPP method can avoid image saturation and handle varying surface reflectivity, using only two prior rounds of fringe-pattern projection and image capture to generate the adapted fringe patterns.

Hand-held 3D scanner for surface-shape measurement without sensor pose tracking or surface markers

Current hand-held three-dimensional (3D) scanners for surface-shape measurement require sensor-tracking devices or surface markers to determine the position and orientation (pose) of the sensor at different viewpoints, thus limiting their functionality. This paper presents a hand-held 3D scanner without sensor tracking or surface markers. Multiple planes of light are simultaneously projected onto an object surface to provide sufficient surface information to enable surface fitting and fine interpolation between acquired data points. In surface scanning, the hand-held scanner acquires a sequence of dense overlapping range-images from different viewpoints with enough overlap between range views and abundant information within each range view to permit registration of all acquired data into a single 3D model. Calibration is performed by closed-form surface-fitting to map 2D image coordinates to 3D calibration-object coordinates. Conical diffraction adjustment corrects for projected-line curvature. The measurement accuracy was suitable for applications such as reverse engineering, and virtual and physical prototyping.

An improving fringe analysis method based on the accuracy of S-transform profilometry

The S transform, as a simple and popular technique for space\ ime–frequency analysis, has been introduced in optical three-dimensional surface shape measurement in recent years. Based on the S transform, S transform “ridge” method (STR) and S transform filtering method (STF) have been proposed to extract the phase information from the single deformed fringe pattern. This paper focuses on studying the STR in fringe pattern analysis. In previous researches about the STR, a linear constraint, which assumed that the phase was locally expressed as first-order Taylor expansion with respect to x and y directions, was implicitly added. Actually at least the second-order partial derivatives of the phase in each local area should be taken into account because they are related to the local curvature of the height distribution of the tested object. Therefore, the traditional STR has larger phase measuring errors in those areas with the rapid height variation on the tested object. This paper proposes an improved STR method, in which the phase is approximately expressed as a quadric in each local area. The phase extraction formula based on the quadric is derived, and the phase correction is carried out as well. Both the simulations and the experiments verify that a more accurate phase map can be obtained by the improved method compared with that by the traditional STR, especially in the areas where height variation is steep.

格子投影法を用いたハニカムサンドイッチパネルの表面形状計測

To establish a precise surface shape measurement technique, we improve our three dimensional measurement system using grating projection method. Improved points are 1) using a higher resolution camera, 2) setting supporting jigs with higher stiffness and higher accuracy, and 3) adjusting measurement parameters. Results of measurement experiments confirm effectiveness of our improvements. On the other hand, measurement results using optical method, such as grating projection method, are affected by optical characteristics of measured objects in general. Then, we apply the method to a surface shape measurement of a honeycomb sandwich panel which is widely used in space engineering. In this paper, to verify our measurement method we compare the measurement result with that using laser measurement equipment, and a good agreement is confirmed.

A06 モバイル計測装置を用いた大型構造物の3次元形状計測(宇宙構造物(2))

近年,衛星搭載のアンテナや太陽電池パネルは,観測周波数の高周波化や高感度化,大電力要求に対応するために,大型化かつ高精度化している.そこで,著者らは,地上ならびに軌道上で,大型構造物の形状を高速かつ高精度に計測する技術の研究開発に取り組んできた.しかし,各種地上試験や軌道上で実用に供するためには,計測装置の小型化とロバスト化が必須である.本研究では,格子投影法を用いた可搬型形状計測装置を用いて,圧縮試験時のスキン付きCFRP製ラティス円筒(直径約2m)および,小型衛星搭載を目指した合成開口レーダー用平面スロットアンテナ(700mm×700mm)の形状計測を実施した計測結果について報告する.可搬型形状計測装置は,基準面を用いたキャリブレーションをあらかじめ実験室でおこなっておき,実際の計測には,プロジェクターとカメラから構成される簡便な計測装置のみを用いた.いずれの場合も,表面形状や変形形状の全視野計測に成功し,ひずみゲージやレーザー変位計による計測では判別しにくい全体の変形モードを取得することができた.

Comparison of Progressive Addition Lenses by Direct Measurement of Surface Shape

Comparison of Progressive Addition Lenses by Direct Measurement of Surface Shape

Comparison of Progressive Addition Lenses by Direct Measurement of Surface Shape

To compare the optical properties of five state-of-the-art progressive addition lenses (PALs) by direct physical measurement of surface shape. Five contemporary freeform PALs (Varilux Comfort Enhanced, Varilux Physio Enhanced, Hoya Lifestyle, Shamir Autograph, and Zeiss Individual) with plano distance power and a +2.00-diopter add were measured with a coordinate measuring machine. The front and back surface heights were physically measured, and the optical properties of each surface, and their combination, were calculated with custom MATLAB routines. Surface shape was described as the sum of Zernike polynomials. Progressive addition lenses were represented as contour plots of spherical equivalent power, cylindrical power, and higher order aberrations (HOAs). Maximum power rate, minimum 1.00-DC corridor width, percentage of lens area with less than 1.00 DC, and root mean square of HOAs were also compared. Comfort Enhanced and Physio Enhanced have freeform front surfaces, Shamir Autograph and Zeiss Individual have freeform back surfaces, and Hoya Lifestyle has freeform properties on both surfaces. However, the overall optical properties are similar, regardless of the lens design. The maximum power rate is between 0.08 and 0.12 diopters per millimeter and the minimum corridor width is between 8 and 11 mm. For a 40-mm lens diameter, the percentage of lens area with less than 1.00 DC is between 64 and 76%. The third-order Zernike terms are the dominant high-order terms in HOAs (78 to 93% of overall shape variance). Higher order aberrations are higher along the corridor area and around the near zone. The maximum root mean square of HOAs based on a 4.5-mm pupil size around the corridor area is between 0.05 and 0.06 µm. This nonoptical method using a coordinate measuring machine can be used to evaluate a PAL by surface height measurements, with the optical properties directly related to its front and back surface designs.