Uncertainty of Positioning and Displacement Measurements in Quantum and Thermal Regimes

We analyze the performance of position-sensing devices and of distance- or displacement-measuring instruments, and we find that the ultimate uncertainty at the quantum limit of detected signal is given by the same expression in all cases, namely, a characteristic length L_c divided by radicNph, the square root of the number of photons detected in the time interval of the measurement. We derive the expression of the length L_c for well-known position-sensing devices (the quadrant photodiode and the position-sensing detector) and for several measuring instruments (pulsed and sine-wave-modulated rangefinders, triangulation telemeter, laser interferometer, and the optical rule). We also extend the analysis of the uncertainty results to the thermal regime case of detection, i.e., when the detector dark current and preamplifier noises are dominant with respect to quantum noise.     

Contribution of the cornea and internal surfaces to the change of ocular aberrations with age.

We studied the age dependence of the relative contributions of the aberrations of the cornea and the internal ocular surfaces to the total aberrations of the eye. We measured the wave-front aberration of the eye with a Hartmann-Shack sensor and the aberrations of the anterior corneal surface from the elevation data provided by a corneal topography system. The aberrations of the internal surfaces were obtained by direct subtraction of the ocular and corneal wave-front data. Measurements were obtained for normal healthy subjects with ages ranging from 20 to 70 years. The magnitude of the RMS wave-front aberration (excluding defocus and astigmatism) of the eye increases more than threefold within the age range considered. However, the aberrations of the anterior corneal surface increase only slightly with age. In most of the younger subjects, total ocular aberrations are lower than corneal aberrations, while in the older subjects the reverse condition occurs. Astigmatism, coma, and spherical aberration of the cornea are larger than in the complete eye in younger subjects, whereas the contrary is true for the older subjects. The internal ocular surfaces compensate, at least in part, for the aberrations associated with the cornea in most younger subjects, but this compensation is not present in the older subjects. These results suggest that the degradation of the ocular optics with age can be explained largely by the loss of the balance between the aberrations of the corneal and the internal surfaces.     

Diversity detection of speckles for double-wavelength interferometry on rough surfaces

When the topography of a rough surface is measured with a double-wavelength interferometer, the phase error of the signal corresponding to the synthetic wavelength increases in the vicinity of dark speckles. To overcome this problem we perform an amplitude-dependent averaging of the synthetic phase over independent speckles (diversity detection). We either use spatially neighboring speckles or in the case of depolarizing surfaces, we use speckles of the same spatial mode, but with orthogonal polarizations. For the latter case the lateral resolution stays unaffected. The reduction of the speckle noise is demonstrated experimentally for a laterally scanning double-wavelength interferometer with superheterodyne detection of the synthetic phase.     

Positioning of Noncooperative Objects by use of Joint Transform Correlation Combined with Fringe Projection

Automated assembly and quality control require reliable systems for the detection of the position and the orientation of complicated objects. Correlation methods are well suited, but they are affected by structured backgrounds, varying illumination conditions, and textured or dirty object surfaces. Using fringe projection to exploit the three-dimensional topography of objects, we improve the performance of a nonlinear joint transform correlator. Positioning of noncooperative objects with subpixel accuracy is demonstrated. Additionally, the tilt angle of an arbitrarily shaped object is measured by projection of object-adapted fringes that produce a homogeneous fringe pattern in the image plane. An accuracy of better than 1 degrees is achieved.     

Systematic errors in small deformations measured by use of shadow-moiré topography

Phase-shift shadow-moiré topography is a noncontact optical technique for measuring the shapes of surfaces. Artifactual bands resembling isoheight surface contours are observed during measurement of small changes in shape by use of this technique. The shape-reconstruction algorithm used in shadow-moiré topography is based on a mathematical model of the fringe patterns generated on the surface to be measured. We hypothesize that the observed bands reflect systematic errors caused by ignoring height-dependent terms in the mathematical model of the fringe patterns. We test the assumption by simulating the fringe patterns for a virtual test surface by using a model that contains height-dependent terms and one term that is idealized by ignoring these terms. Small systematic errors in shape are observed only when the surface is reconstructed from fringe patterns simulated with a model containing the height-dependent terms. Shape-error curves are computed as a function of the surface height by the subtraction of the reconstructed shape from the known shape. Simulated shape-error curves agree with experimental measurements in that they show an increase in error with surface height, and both the experimental and the simulated shape-error curves contain ripples. Although the errors are small in comparison with the dimensions of the surface and are negligible in shape measurements and in most deformation measurements, they may show up as noticeable bands in images of small deformations.     

Design and implementation of optical system for Placido-disc topography

Corneal topography provides powerful support in the diagnosis and treatment of corneal disease by displaying the corneal surface topography in data or image format. To realize the precise detection of corneal surface topography, an optical system for the corneal topography that is based on a Placido disc is designed, which includes a ring distribution on a Placido disc, an imaging system and a collimating illumination system. First, a mathematical model that is based on the corneal topography working principles is established with MATLAB to determine the distribution of white-and-black rings on the Placido disc, in which the ellipsoid facial rings-target of the Placido disc is utilized. Second, the imaging lens structure is designed and optimized by Zemax software. Last, the collimating illumination lens structure is designed by paraxial ray trace equations. The quality of the corneal topography, which is based on our designed optical system, is evaluated. The high-contrast image of uniformly distributed white-and-black rings is observed through the CCD camera. Our optical system for the corneal topography has high precision, with a measuring region of the cornea with a diameter of approximately 10 mm. Therefore, the creation of this optical system offers guidance for designing and improving the optical system of Placido-disc topography.     

Optical resonant ultrasound spectroscopy for fluid properties measurement

The properties of fluids are studied using unusually small containment spherical resonators. Proper identification of resonant fluid signatures allows determination of pressure and density of the internal gas with great accuracy using an appropriate equation of state (EOS). Low noise and high sensitivity detection of vibration are critical parameters to characterizing the contained gas when its pressure approaches 1 atm. or less. The benefits of using spherical resonators to determine fluid properties are discussed, and some example calculations of sound speed are presented. In addition to measuring fluids, a comparative experimental approach is taken to explore and, eventually, to optimize vibration detection. In the experiments, two detection methods, a contact piezoelectric transducer (PZT) device and a non-contact optical device, are compared simultaneously and quantitatively. This is done in a unique manner without change in vibration coupling to the sample between tests. A commercially available resonant ultrasound spectroscopy system is used as the contact system, while another commercial device (used as the non-contact vibration detector) combined with the same excitation source (used in the contact system) comprises the other system. The non-contact detector is an optical interferometric receiver that provides adaptation to optically rough surfaces and high sensitivity to acoustic displacements through optical interference in photorefractive GaAs. Both vibration detection systems are compared with particular emphasis on displacement sensitivity, frequency response, and noise level. Furthermore, the results from comparing detection modalities are presented, and their effects on fluid properties measurement are discussed     

Multilevel spatial randomness approach for monitoring changes in 3D topographic surfaces

The 3D surface topography of finished products is a key characteristic for monitoring the quality of products and manufacturing processes. The topography has unique properties in which the topographic values are spatially autocorrelated with their neighbours and the locations of topographic values randomly change from one surface to another under the in-control process behaviour, making the online detection of local topographic changes challenging. Due to the complex structure of topographic data, the existing monitoring approaches lack the detection of local changes. Therefore, we develop a novel online monitoring approach for detecting local changes in 3D topographic surfaces. We introduce a multilevel surface thresholding algorithm for enhancing the representation of topographic values by slicing the 3D surface topography into cumulative levels in reference to the characteristics of the in-control surfaces. The spatial and random properties of topographic values are quantified at each surface level through the proposed spatial randomness profile. After obtaining the spatial randomness profile, an effective monitoring statistic based on the functional principal component analysis is developed for detecting anomaly surfaces. The proposed approach shows superior performance in identifying a wide range of fault patterns and outperforms the existing approaches in both simulated and real-life topographic data.     

三维表面形貌的连通性表征

从集合的角度,运用图像描述方法,提出了三维表面形貌连通性表征的方法,建立了连通数、连通指数的概念以及相应的算法,并结合实际,模拟出一些特征明显的三维表面形貌,确定了评定表面连通性能的基准面,定量分析了表面形貌的连通性随表面高度的变化情况,比较出在传统的表面形貌参数相似的情况下表面连通性能的差异,为表面形貌表征研究开辟了一个新的途径.     

High-accuracy position and orientation measurement of extended two-dimensional surfaces by a phase-sensitive vision method

We introduced recently phase measurements usually performed in interferometry to the domain of image processing and intelligent vision [IEEE Trans. Instrum. Meas. 49, 867 (2000)]. Our purpose is to sense with a high accuracy the position, orientation, and displacement of two-dimensional (2D) surfaces observed by a static vision system. We report on significant improvements of the method. Experimental measurements reveal a peak-valley noise of approximately 10(-2) CCD pixel, corresponding approximately to a 10(-3) period of the phase reference pattern. Then the observation of 10 microm scaled features enables an accuracy of a few nm in the position sensing of the phase reference pattern for the extended 2D measurement range.     

Speckle noise in laser bar-code-scanner systems

We present a theoretical model and its experimental verification for speckle-induced noise in laser-based bar-code-scanner systems. We measured the dependence of the signal-to-speckle-noise ratio on distance, spot size, and detector size. Analyses of the power spectra of both the speckle noise and of the measured surface profiles of different substrates suggest that the paper surface granularity can be approximated by a white Gaussian noise process, thus confirming the assumption of the theoretical model.     

Noise analysis for position-sensitive detectors

A study of the different noise sources in a position sensitive detector (PSD)-transimpedance amplifier (TIA) sensing system is presented and the dominant noise sources are identified. The effect of these noise sources on the position detection capability of the sensing system is analyzed. An expression derived for the position resolution of the phase method of position detection reveals the position resolution depends inversely on the modulation frequency of the light source and the square of the amplitude of the currents flowing through the metal electrodes, and is dependent on the position of the incident light beam. Simulation results show that the best achievable position resolution is at the center of the PSD and becomes worse as one moves away from the center toward the edges. Compared to the 4 nm/√Hz position resolution that is achievable using the amplitude method of position detection, the phase method of position detection provides a resolution of 9 nm/√Hz and 6 nm/√Hz corresponding to a modulation frequency of 50 kHz and 70 kHz respectively     

第一台多功能微纳米级表面特性摩擦显微仪

介绍了一台具有国际发明专利的新型仪器--多功能机械摩擦显微仪(TPM). TPM可用于检测微纳米级工程表面的机械和摩擦性能. 其特点是在一次扫描中可同时检测以下四项功能参数表面轮廓、表面摩擦、表面纳硬度和表面弹性模量. 由于TPM基于点阵扫描, 因此所测得的四项参数在空间和时间上是相关的. TPM是一种可变力触针式扫描仪. 表面接触力由一个永久磁铁和线圈加力装置控制, 加力范围为0.01～30 mN. 扫描平台范围为100 μm×100 μm,该范围通过闭环控制具有纳米级精确度.表面轮廓的范围为20 μm并具有0.1 nm的分辨力. TPM 已经用于各种表面的性能测试中并取得了广泛的认可.TPM 在2001年获得了"Metrology for World Class Manufacturing Awards 2001".     

Localization and Registration of Three-Dimensional Objects in Space-Where are the Limits?

We discuss the accuracy limits for the localization of surfaces in three-dimensional (3-D) space. Such a localization is necessary for the registration of different views of an object, taken by 3-D sensors from several directions. A quantitative analysis shows that the lateral localization accuracy of a small surface area is proportional to the local curvature of the surface. This confirms the intuitive conjecture that our visual system performs localization of 3-D objects via sharp features. The longitudinal localization accuracy depends only on the noise of the data and is usually much better than the lateral localization accuracy, suggesting that surfaces are to be registered only along the longitudinal directions.     

Two-wavelength method for endoscopic shape measurement by spatial phase-shifting speckle-interferometry

A two-wavelength method for endoscopic topography reconstruction is introduced that can be applied to out-of-plane sensitive electronic-speckle-pattern interferometry systems based on rigid endoscope imaging systems. The surface measurement is performed by detection of the phase-difference distribution affected by a change in the applied laser wavelength. Furthermore, the off-axis endoscopic illumination geometry is taken into account by an approximation. Experimental results of the characterization of the endoscopic surface reconstruction technique and the measurement accuracy obtained are described and discussed. Finally, the applicability of the method is demonstrated with results from the topographic reconstruction of a free-form surface.     

Elasticity solution for vibration of 2‐D curved beams with variable curvatures using a spectral‐sampling surface method

An accurate spectral‐sampling surface method for the vibration analysis of 2‐D curved beams with variable curvatures and general boundary conditions is presented. The method combines the advantages of the sampling surface method and spectral method. The formulation is based on the 2‐D elasticity theory, which provides complete accuracy and efficiency for curved beams with arbitrary thicknesses and variable curvatures because no other assumptions on the deformations and stresses along the thickness direction are introduced. Specifically, a set of non‐equally spaced sampling surfaces parallel to the beam's middle surface are primarily collocated along the thickness direction, and the displacements of these surfaces are chosen as fundamental beam unknowns. This fact provides an opportunity to derive elasticity solutions for thick beams with a prescribed accuracy by selecting sufficient sampling surfaces. Each of the fundamental beam unknowns is then invariantly expanded as Chebyshev polynomials of the first kind, and the problems are stated in variational form with the aid of the penalty technique and Lagrange multipliers, which provide complete flexibility to describe any arbitrary boundary conditions. Finally, the desired solutions are obtained by the variational operation. Copyright © 2016 John Wiley & Sons, Ltd.     

人眼角膜参数计量校准与量值溯源方法研究

角膜曲率半径、屈光度和散光轴位是评价人眼角膜形态的关键参数。为解决人眼角膜参数准确测量和量值有效溯源,基于角膜反射成像原理,采用球面和环曲面设计形式,首次研制出人眼角膜参数系列标准。曲率半径测量范围为(5.5~10.0)mm,不确定度U=0.002mm(k=2);轴位测量范围为 0°~180°,不确定度U=1°(k=2)。建立了角膜曲率计工作基准装置国家计量标准,形成了人眼角膜参数量值传递与溯源体系。实验结果表明,该计量标准可以满足人眼角膜参数测量仪器的校准和量值溯源,保证人眼角膜参数的测量准确。     

混沌振子微弱未知信号检测方法的改进

目前普遍应用Duffing混沌振子系统检测噪声背景下微弱信号,由于其具有对周期信号敏感而对干扰信号免疫的特点,所以在检测时常常忽略噪声的影响。然而大量实验发现,系统对某些方差的噪声免疫力很低,容易造成误判。由此,在分析噪声对微弱信号检测影响的基础上,采用互相关检测器对待测信号进行处理,以此抑制噪声。对工程上不易实现的混沌阵列检测法引入实用性强的循环算法,操作简单,仿真结果精度高。     

Precision metrology for studying thin films and surfaces

Evaluation techniques that are appropriate for characterizing the surface topography of optical thin films and surfaces are briefly described. These include microscopes ranging from low power optical microscopes to scanning probe microscopes that can measure topography of individual atoms or groups of atoms, optical non-contact and mechanical contact profilers, some of which can give topographic maps of surface areas, and total integrated scattering and angle-resolved scattering that yield statistical properties of surfaces. Theories are needed to relate scattering to surface topography; these are valid only for certain types of topographies. Examples are given showing how various surface evaluation techniques can be applied to selected surfaces.     

Device for magneto-optic signal detection with a small crystal prism

A device made of a birefringent crystal for signal detection of magneto-optic (MO) disks is presented. The light beam from a MO disk is separated into two orthogonally polarized components at the surface of a birefringent prism. After these two components are reflected by the top and the bottom surfaces of the prism inside, at the detector they become sufficiently separated from each other for discrete detection, even though the prism is small. A method for calculating the light intensities and the positions of focused beams in a birefringent prism and the results of a fundamental experiment are presented.