Paraxial speckle-based metrology systems with an aperture

Digital speckle photography can be used in the analysis of surface motion in combination with an optical linear canonical transform (LCT). Previously [D. P. Kelly et al. Appl. Opt.44, 2720 (2005)] it has been shown that optical fractional Fourier transforms (OFRTs) can be used to vary the range and sensitivity of speckle-based metrology systems, allowing the measurement of both the magnitude and direction of tilting (rotation) and translation motion simultaneously, provided that the motion is captured in two separate OFRT domains. This requires two bulk optical systems. We extend the OFRT analysis to more general LCT systems with a single limiting aperture. The effect of a limiting aperture in LCT systems is examined in more detail by deriving a generalized Yamaguchi correlation factor. We demonstrate the benefits of using an LCT approach to metrology design. Using this technique, we show that by varying the curvature of the illuminating field, we can effectively change the output domain. From a practical perspective this means that estimation of the motion of a target can be achieved by using one bulk optical system and different illuminating conditions. Experimental results are provided to support our theoretical analysis.     

Analysis of imaging properties of a vibrating thin flat mirror

Thin flat mirrors are often used in designing various optical measurement systems. Such mirrors are generally deformed by environmental conditions during measurements. A detailed theory of deformation of a thin flat mirror that oscillates harmonically in the direction of the normal to its surface is introduced in our work. The mirror is treated as a vibrating membrane, and the time-dependent effect of the mirror deformation on the properties of reflected light is studied. A relation is derived for a dynamic wave aberration. On the basis of this relation, calculation of the Strehl definition of the deformed mirror is performed both by exact integration and by approximation. The results obtained can be used for analysis of the influence of mechanical vibrations on the accuracy of optical measurement systems in various practical applications where thin flat mirrors are used.     

Observer for a thick layer of solid deuterium-tritium using backlit optical shadowgraphy and interferometry

Our work is in the context of the French "laser mégajoule" project, about fusion by inertial confinement. The project leads to the problem of characterizing the inner surface, of the approximately spherical target, by optical shadowgraphy techniques. Our work is entirely based on the basic idea that optical shadowgraphy produces "caustics" of systems of optical rays, which contain a great deal of 3D information about the surface to be characterized. We develop a method of 3D reconstruction based upon this idea plus a "small perturbations" technique. Although computations are made in the special "spherical" case, the method is in fact general and may be extended to several other situations.     

Stability of systems of plane reflecting surfaces

A general rule for the stability of plane reflecting surface systems is derived by use of the features of the reflection matrix. It is proved that only two directions can be stable: the forward direction and the backward direction (retroreflection). Examples for the application of this rule in the design of stable reflecting systems for optical communication are given.     

基于网点结构的光学网点扩大特性研究

目的研究印刷品网点扩大中光学网点扩大特性,量化分析不同类型网点结构对光学网点扩大的影响差异,探讨光学网点扩大的一般规律。方法根据网点结构,提出周长对网点面积率敏感度的定义,以此分析光学网点扩大随网点结构特性的变化规律,图象栅格化处理器(RIP)输出多种网点结构,以不同网点胶印样张形式验证光学网点扩大规律。结果对于调幅网点,光学网点扩大大于机械网点扩大;对于调频网点,机械网点扩大大于光学网点扩大。同心圆网点是一种特殊网点结构,兼有调幅、调频光学扩大特性。结论光学网点扩大不可避免,光学网点扩大值与周长对面积率敏感度正相关,研究不同网点结构的光学扩大特性对印刷品质量控制有一定意义。     

A new approach to the definition of power components in three-phasesystems under nonsinusoidal conditions

A method has been proposed for the definition of active and nonactive power components in three-phase systems under nonsinusoidal conditions. The method is more attractive than others since it is not a mere extension of methods employed in single-phase systems, but comes from the application of a quite powerful and synthetic mathematical tool specifically studied for the representation of three-wire three-phase systems in any possible condition: the Park transformation and the Park vectors. It is proven that the application of this method leads to the definition of two quantities, the real and the imaginary power, that are measurable in a quite simpler way than those proposed by other theories. The two satisfy all properties typical of the electrical power and are directly related, under sinusoidal and balanced conditions, to the active and reactive powers. It is shown how this method fits with other proposed methods that can be regarded in terms of this more general theory     

光学表面的分形结构和表征算法

根据光学表面在微观结构上呈现出的统计自相似性，利用与尺度无关的分形模型描述了光学表面的结构特征，采用结构函数法对分形维数进行计算，分析了抛光表面的分形特点。在此基础上，提出了采用一阶自回归分形模型对抛光表面进行模拟的新方法，分析了界定尺度、模型参数对分形特征和分形维数的影响规律。     

Design of lenses with curved Petzval image surfaces

Abstract

Design strategies have been devoted to simplify and miniaturize optical systems. In this paper, by constraining image surface to coincide with the Petzval surface, we achieve a compact f/2.8 lens system design with a curved Petzval image surface. Arc distortion is proposed to accurately measure the distortion relative to a curved image surface. The optical performance of our curved image surface lens is analysed and compared. Results show that modulation transfer function (MTF) of our curved Petzval design over 69% at 100 cycles/mm for entire fields is achievable with 100-mm effective focal length, 40º full field of view, >92.4% edge relative illumination, <0.5% arc distortion. Comparisons with a traditional lens with a planar image plane demonstrate that a curved Petzval image surface is an excellent strategy to simplify and miniaturize optical systems, compensate field curvature and benefit astigmatism correction, increase off-axis illumination and improve MTF. Furthermore, the lens with a curved Petzval image surface has a more uniform optical power distribution and greater degree of lens symmetry.     

Calculation of speckle displacement, decorrelation, and object-point location in imaging systems

My purpose here is to outline a method for calculating the fundamental behavior of speckle patterns in imaging systems. The theory of speckle displacement and decorrelation to include imaging at a general oblique angle is extended to more imaging systems, and explicit formulas are given for the image-point-object-point relationship that is important when defocused speckle is used. The intermediate results can be reused for optical systems other than those presented here. The image-speckle displacement analyzed in the three systems is expressed equivalently. The speckle decorrelation is in general larger in a single-lens system than in a two-lens system and can be minimized by proper design of the system.     

Optical fractional Fourier transforms with complex orders

A definition of real and complex domains for the order of fractional Fourier transforms is introduced in association with diffraction either in free space or through real and complex lenses. The geometrical and the optical conditions that lead to real and complex orders of the fractional Fourier transforms and their relevance to cascading optical systems are discussed.     

Influence of total reflection on the imaging quality of optical systems

In the case of total reflection at a boundary surface between two different optical media, the ray reflected at the boundary is spatially shifted with respect to the point where the incident ray intersects the boundary. The light penetrates into the second medium, and the evanescent electromagnetic wave propagates along the boundary. The described effect is called the Goos-H?nchen effect. Our work describes the influence of the Goos-H?nchen effect on the imaging properties of planar optical systems, and a differential equation of a wave-front meridian that corresponds to a reflected bundle of rays is derived. It is shown that the wave front can be described by the d'Alambert differential equation. This equation makes it possible to determine the coordinates of individual points on the wave-front meridian. The influence of total reflection on the value of the Strehl definition of the reflected ray bundle, is also investigated.     

Threshold values of pavement surface properties for maintenance purposes based on accidents modelling

In general, road authorities recognise the importance of research studies to support the development of maintenance programmes for surface characteristics to be incorporated into pavement management systems. For this purpose, the establishment of threshold values is an essential issue, but the literature concerning this topic is very scarce. The main objective of this paper was to present a methodology for the establishment of threshold values based on safety criteria and concerning skid resistance and macrotexture, represented by International Friction Index, coefficient of friction and texture depth. The methodology consists of two phases: evaluation of the influence of the pavement surface properties on road accidents and establishment of threshold values for each road environment (RE). The analysis of the influence of these parameters on accident occurrence is based on the definition of compound RE, a more appropriate technique for accident modelling. Minimum and safety values of the parameters are recommended in this paper.     

Optical design of freeform two-mirror beam-shaping systems

The problem of design of a two-mirror optical system for reshaping the irradiance distribution of a laser beam in a prescribed manner is considered in the geometrical optics approximation. The presented design equations are derived in a rigorous manner and are applicable to two-mirror optical systems not limited to radiance profiles and beam cross sections that are rotational or rectangular symmetric. The resulting mirrors are free-form surfaces not restricted by a priori constraints. Moreover, the presented approach shows also that even in the general case two different designs are available for the same data. In one of these designs the first mirror is always concave and the second is convex, while in the second design the resulting mirrors may be neither convex nor concave. Since, in general, the surface mirrors are aspherical, the availability of a design with convex and concave mirrors is particularly important for fabrication.     

Surface layer impurities on silicon spheres used in determinationof the Avogadro constant

The Avogadro constant is required to be determined with an uncertainty of less than 1×10^-8 in order to allow an atomic definition of the kilogram. A single-crystal silicon sphere 93.6 mm diameter is used for this determination. A thin surface layer (typically 2 nm to 5 nm thick on flats and 10 nm or more on spheres) of contaminants such as oxide, water and hydrocarbons on the sphere can significantly affect the measurements due to corrections for density changes and to phase change on reflection in the diameter measurement by optical interferometry. The stability of this surface layer as a function of time is also of importance because of ongoing measurements. The nature of this contamination has been investigated using optical ellipsometry and ion beam analysis. It is concluded that the composition and structure of the surface layer are affected by a number of parameters and that the most appropriate method of achieving the desired accuracy is to remove the surface layer by etching and to form a hard stable coating of controlled thickness and composition. This coating may be either silicon dioxide or silicon nitride     

变形反射镜的发展

介绍了我们的变形反射镜（以下简称变形镜）的研制发展过程，叙述了变形镜的主要性能的定义和要求及其测试方法，列举了我们已在自适应光学系统中成功应用的几种变形镜和有关研究工作的进展并指出今后的发展展望。     

Uncertainties in Small-Angle Measurement Systems Used to Calibrate Angle Artifacts

We have studied a number of effects that can give rise to errors in small-angle measurement systems when they are used to calibrate artifacts such as optical polygons. Of these sources of uncertainty, the most difficult to quantify are errors associated with the measurement of imperfect, non-flat faces of the artifact, causing the instrument to misinterpret the average orientation of the surface. In an attempt to shed some light on these errors, we have compared autocollimator measurements to angle measurements made with a Fizeau phase-shifting interferometer. These two instruments have very different operating principles and implement different definitions of the orientation of a surface, but (surprisingly) we have not yet seen any clear differences between results obtained with the autocollimator and with the interferometer. The interferometer is in some respects an attractive alternative to an autocollimator for small-angle measurement; it implements an unambiguous and robust definition of surface orientation in terms of the tilt of a best-fit plane, and it is easier to quantify likely errors of the interferometer measurements than to evaluate autocollimator uncertainty.     

Cover Picture: Functionalization of Crystalline Colloidal Arrays through Click Chemistry (Adv. Mater. 21/2007)

Photonic crystals based on electrostatically‐stabilized colloidal arrays dispersed in a liquid medium are of interest to materials scientists partly because of the optical tuning afforded to theses systems with a variation in interparticle distance. On p. 3507, Stephen Foulger and co‐workers from Clemson University, USA report on a general strategy for the preparation of well‐defined and regioselectively functionalized ordered colloidal particles through the exploitation of “click” chemistry. Click transformations have found utility in the synthesis and/or functionalization of a range of systems. In addition, the solvochromic tuning of the ordered arrays is employed to modify the emission spectra of the surface‐attached photoluminescent dyes.     

Optical Bilinear Transformations: General Properties

Because of the quadratic relation between the optical field and intensity, an inherent non-linearity exists in almost all optical systems. A class of non-linear transformations which we call bilinear (quadratic with memory) is defined; its properties and relevance to optical imaging systems are discussed. For space-invariant systems, a generalized transfer function is defined which characterizes the bilinear system completely. We also examine the approximate linearization of bilinear systems for low-contrast images, and the propagation of noise through such systems. Special emphasis is given to the partially coherent system which is but a special case of this general bilinear system.     

An approach to multilayer microfluidic systems with integrated electrical, optical, and mechanical functionality

A general solution is presented for the realization of microfluidic systems containing multiple compartments with sequential functions. The approach utilizes multilayer plastic/glass/silicon microfluidic system configurations with integrated electrical, optical, and fluid control functionalities. The approach allows for the integration of on-column, on-chip electrical conductivity/impedance detectors and driving electrodes, as well as for the integration of on-column, off-chip optical detection using resonance light scattering. A process-compatible latex microvalve is demonstrated and characterized. The procedure utilizes a novel packaging technique for realizing integrated fluid and electrical interfaces between the microsystem and conventional tubing/instrumentation. The microfluidic system demonstrated in this work contains some of the most commonly used components in bioanalysis systems and can be used as a platform to fabricate more sophisticated microscale bioanalysis systems for a variety of applications.