Measurement of profiles along a circle on two flat surfaces by use of a Fizeau interferometer with no standard

A method for measuring profiles along a circle on a flat surface with no standard is described. For the measurement, two unknown surfaces are placed almost parallel, and the distance between them is measured many times along a circle by rotation of one of the surfaces. Profiles of the two surfaces can be determined from the distance data. In this study the measuring method is explained: The space between two surfaces measured with a Fizeau interferometer. Four measuring experiments are carried out for determining the profile of a precision-grade half-mirror; in each experiment a different ordinary mirror with unknown profile is used as the second mirror. Profiles of the precise mirrors obtained by these experiments agree closely, with deviations of approximately 2 nm. A similar experiment with many concentric circles was carried out with a precise half-mirror and another precise mirror. Although the profiles of many concentric circles were independent of one another, the result shows that the high-frequency component of a whole plane can be estimated.     

Improvements in the accuracy and the repeatability of long trace profiler measurements

Modifications of the long trace profiler at the Advanced Photon Source at Argonne National Laboratory have significantly improved its accuracy and repeatability for measuring the figure of large flat and long-radius mirrors. Use of a Dove prism in the reference beam path corrects phasing problems between mechanical errors and thermally induced system errors. A single reference correction now completely removes both of these error signals from the measured surface profile. The addition of a precision air conditioner keeps the temperature in the metrology enclosure constant to within +/-0.1 degrees C over a 24-h period and has significantly improved the stability and the repeatability of the measurements. Long-radius surface curvatures can now be measured absolutely with a high degree of confidence. These improved capabilities are illustrated with a series of measurements of a 500-mm-long mirror with a 5-km radius of curvature. The standard deviation in the average of ten slope profile scans is 0.3 microrad, and the corresponding standard deviation in the height error is 4.6 nm.     

Laser beam intensity profile transformation with a fabricated mirror

A nonaxisymmetric mirror is designed by the same method as a computer-generated hologram for laser beam intensity profile transformation and is fabricated by plasma chemical vaporization machining. We successfully transformed a circular Gaussian beam of a He-Ne laser into a rectangular uniform beam maintaining spatial coherence and using a nonaxisymmetric surface profile mirror. There are ripples in the intensity profile of the transformed rectangular beam. These ripples in the intensity profile result from small ripples on the mirror surface. These results show that we can perform coordinate transformation using these fabricated mirrors, which has so far been possible only by using computer-generated holograms.     

Influence of Layup and Curing on the Surface Accuracy in the Manufacturing of Carbon Fiber Reinforced Polymer (CFRP) Composite Space Mirrors

Carbon fiber reinforced polymer, CFRP, composite materials have been used to fabricate space mirror. Usually the composite space mirror can completely replicate the high-precision surface of mould by replication process, but the actual surface accuracy of replicated space mirror is always reduced, still needed further study. We emphatically studied the error caused by layup and curing on the surface accuracy of space mirror through comparative experiments and analyses, the layup and curing influence factors include curing temperature, cooling rate of curing, method of prepreg lay-up, and area weight of fiber. Focusing on the four factors, we analyzed the error influence rule and put forward corresponding control measures to improve the surface figure of space mirror. For comparative analysis, six CFRP composite mirrors were fabricated and surface profile of mirrors were measured. Four guiding control measures were described here. Curing process of composite space mirror is our next focus.     

Polarimetric calibration of large-aperture telescopes. I. Beam-expansion method

A concept is described for the high-accuracy absolute calibration of the instrumental polarization introduced by the primary mirror of a large-aperture telescope. This procedure requires a small aperture with polarization-calibration optics (e.g., mounted on the dome) followed by a lens that opens the beam to illuminate the entire surface of the mirror. The Jones matrix corresponding to this calibration setup (with a diverging incident beam) is related to that of the normal observing setup (with a collimated incident beam) by an approximate correction term. Numerical models of parabolic on-axis and off-axis mirrors with surface imperfections are used to explore the accuracy of the procedure.     

Form-Profiling of Optics Using the Geometry Measuring Machine and the M-48 CMM at NIST

We are developing an instrument, the Geometry Measuring Machine (GEMM), to measure the profile errors of aspheric and free form optical surfaces, with measurement uncertainties near 1 nm. Using GEMM, an optical profile is reconstructed from local curvatures of a surface, which are measured at points on the optic’s surface. We will describe a prototype version of GEMM, its repeatability with time, a measurements registry practice, and the calibration practice needed to make nanometer resolution comparisons with other instruments. Over three months, the repeatability of GEMM is 3 nm rms, and is based on the constancy of the measured profile of an elliptical mirror with a radius of curvature of about 83 m. As a demonstration of GEMM’s capabilities for curvature measurement, profiles of that same mirror were measured with GEMM and the NIST Moore M-48 coordinate measuring machine. Although the methods are far different, two reconstructed profiles differ by 22 nm peak-to-valley, or 6 nm rms. This comparability clearly demonstrates that with appropriate calibration, our prototype of the GEMM can measure complex-shaped optics.     

基于立体相位测量偏折术的预应力薄镜面形检测

应力抛光技术通过在镜面上施加预定载荷,将包括自由曲面在内的非球面转化为球面进行加工,对加工镜面的形变进行精准检测是实现高精度应力抛光的关键。利用立体相位测量偏折术对预应力薄镜进行镜面面形和形变检测,获得被测镜表面的连续相位分布,结合表面法线唯一性与梯度分布积分,最终得到被测镜的高度分布和面形。模拟了系统误差成分,同时采用旋转平均法对系统误差进行标定去除,保证和提高了测量精度。对一块口径320 mm,球面半径5200 mm的预应力薄镜面形和变形量进行测量,静态测量结果与三坐标机测量结果对比,动态应变测量结果与有限元仿真结果对比,分别一致吻合,表明本文方法具备微米级的测量精度,相比于干涉仪和三坐标机更适用于大面形变化的预应力薄镜检测。     

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.     

Energy flow of electric dipole radiation in between parallel mirrors

We have studied the energy flow patterns of the radiation emitted by an electric dipole located in between parallel mirrors. It appears that the field lines of the Poynting vector (the flow lines of energy) can have very intricate structures, including many singularities and vortices. The flow line patterns depend on the distance between the mirrors, the distance of the dipole to one of the mirrors and the angle of oscillation of the dipole moment with respect to the normal of the mirror surfaces. Already for the simplest case of a dipole moment oscillating perpendicular to the mirrors, singularities appear at regular intervals along the direction of propagation (parallel to the mirrors). For a parallel dipole, vortices appear in the neighbourhood of the dipole. For a dipole oscillating under a finite angle with the surface normal, the radiating tends to swirl around the dipole before travelling off parallel to the mirrors. For relatively large mirror separations, vortices appear in the pattern. When the dipole is off-centred with respect to the midway point between the mirrors, the flow line structure becomes even more complicated, with numerous vortices in the pattern, and tiny loops near the dipole. We have also investigated the locations of the vortices and singularities, and these can be found without any specific knowledge about the flow lines. This provides an independent means of studying the propagation of dipole radiation between mirrors.     

Cavity with a deformable mirror for tailoring the shape of the eigenmode

We demonstrate an optical cavity that supports an eigenmode with a flattop spatial profile--a profile that has been proposed for the cavities in the Advanced Laser Interferometer Gravitational Wave Observatory, the second-generation laser interferometric gravitational wave observatory--because it provides better averaging of the spatially dependent displacement noise on the surface of the mirror than a Gaussian beam. We describe the deformable mirror that we fabricated to tailor the shape of the eigenmode of the cavity and show that this cavity is a factor of 2 more sensitive to misalignments than a comparable cavity with spherical mirrors supporting an eigenmode with a Gaussian profile.     

白光相移干涉中频谱对测量精度的影响

在相移干涉中有时采用白光干涉来扩大深度测量范围,白光光源的使用,缩短了光束的相干长度,降低了测量精度。本文从干涉理论出发推导了白光相移干涉法测量三维表面形貌的计算公式,通过数值积分的方法分析了干涉光频谱对测量精度的影响。分析表明,在白光相移干涉测量中表面形貌的测量精度与中心波长和频谱宽度有关,白光频谱越宽,测量精度越低,中心波长越大,测量精度越高。     

Precise measuring method for detecting the in situ distortion profile of a high-heat-load mirror for synchrotron radiation by use of a pentaprism long trace profiler

A precise measuring method for detecting the in situ distortion profile of a high-heat-load mirror for synchrotron radiation by use of a pentaprism long trace profiler (LTP) is presented. A maximum distortion of 0.47 microm across a length of 180 mm was measured for an internally water-cooled mirror on an undulator beam line at ELETTRA while exposed to a total emitted power of 600 W. This first successfully tested in situ distortion profile points out the importance and need for this method. Two configurations for performing in situ LTP tests are discussed. For this measurement the configuration with all the equipment external to the vacuum chamber was used. The experiment has an accuracy and a repeatability of 0.04 microm. Suggestions for improving the accuracy and stability are presented.     

Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity.     

Fast scanning method for one-dimensional surface profile measurement by detecting angular deflection of a laser beam

A fast scanning method for one-dimensional surface profile measurement is proposed. The profile is measured by integration of a slope distribution of the surface obtained from angular deflection of a scanning laser beam. A scanning optical system that consists principally of a spherical concave mirror and a rotating scanner mirror has reasonably low cost and is insensitive to mechanical vibration because of its high-speed scanning, of the order of milliseconds. A surface profile of a polygonal mirror along a 5-mm width was measured with the scanning method and with an interferometer. The root-mean-square difference between the two measured results is 0.98 nm.     

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.     

Designing reflectors to generate a line-shaped directivity diagram

A novel method of designing a mirror surface to generate a directivity diagram represented as a vector function of one argument is presented. A general relationship for the mirror surface for an arbitrary illuminating beam wavefront is derived as an envelope of a parametric family of surfaces. Each surface in the family transforms the input beam into a beam with plane wavefront of desired direction. For the spherical illuminating beam the mirror surface is given as the envelope of the family of rotational paraboloids. The envelope is represented as a family of curves given by the intersections of paraboloids with circular cones of rays from the point source.     

Φ1.05 m轻量化反射镜设计与制造

针对Ф1.05 m空间光学系统主镜的设计指标要求,提出了轻量化反射镜结构优化设计的新方法,并建立了反射镜结构自动化仿真分析与优化设计平台,基于此平台确定了性能优异的主镜结构设计方案。主镜重量小于50 kg,轻量化率已接近国外先进水平; 主镜在三球铰支撑下的第一阶模态频率为361.2 Hz,自由状态下的一阶非零模态频率为501.9 Hz; 在1 ℃均匀温度变化下,不去离焦和去除离焦之后的面形RMS分别为0.55 nm和0.10 nm; 主镜在30g过载加速度作用下的最大应力为16.1 MPa,均满足设计要求。采用目前最先进的第三代大口径反射镜加工工艺,路线为超精密铣磨—小磨头数控研抛—离子束精修,实现主镜面形误差的确定性去除。为保证面形检测结果的天地一致性,发展了重力卸载技术和面形误差数据后处理技术,剔除重力和其他系统误差对检测的影响。主镜最终面形精度达到0.011λ RMS,获得了高精度的光学面形,也证明了方案的合理性。     

汽车外廓尺寸测量仪量值溯源方法研究

汽车外廓尺寸测量仪基于先进的计算机实时立体视觉技术,集光学、电子、计算机等高科技于一体,实现全自动、可视化、网络化,而且具有自动控制检测过程,加强对车辆的监督管理。文章主要从监管及安全角度探讨其计量性能要求和量值溯源方法,作为福建省开展校准汽车外廓尺寸测量仪的技术依据。     

Optical diffraction in nonuniform cholesteric liquid crystals: phase-grating mode.

We have worked out the diffraction pattern in the phase-grating mode of a cholesteric liquid crystal (cholesteric) with a pitch gradient. The pitch gradients considered are symmetric and asymmetric with respect to the sample center. For a uniform input beam, the intensity profile of each diffraction order becomes broad. Further, in the symmetric gradient, the profile of each order is irregular, while in the asymmetric gradient it is nearly flat. For a Gaussian input beam, for the symmetrically deformed structure the profile for each order is asymmetric, while for the asymmetrically deformed structure, the profiles just becomes broad. We find that even a 5% nonuniformity in the pitch can drastically alter the diffraction profiles.