Aspheric mirror with constant angular magnification II

Differential equations for a constant-angular-magnification aspheric-mirror surface shape are derived for a general dependence of the camera image height on the camera field angle. The explicit equations of the constant-angular-magnification mirror surface are given for some particular values of the angular magnification. For a series of odd integer values of the angular magnification, 10th-order polynomial approximations of the mirror surface are presented. The imaging performance of such a mirror with an angular magnification of 7 is analyzed and compared with a spherical mirror. The main cause of image blur in all-sky cameras at the edge of the field of view was found to be a strong image curvature. We show that increasing the camera-to-mirror distance and/or stopping down the camera lens reduces the image blur.     

TMC系统主镜的平板补偿自准检验方法

针对TMC(三镜卡塞格林)光学系统凹椭球面主镜的检验,本文提出了一种平板补偿的自准检验方法.该方法克服了OFFENER零位补偿器本身性能难以检验,只能靠加工和装调保证精度的问题.针对TMC主镜面形与抛物面接近的特点,对平板补偿的自准检验方案进行了理论分析,利用二次非球面的法线像差性质推导了检验光路中球差的表达式,并利用最小剩余球差进行补偿平板参数的确定.对某TMC系统顶点曲率1 589mm,二次系数-0.983,口径φ500 mm的主镜检验,设计了尺寸仅为φ34.2 min×9.126 5 mm的补偿平板.在ZEMAX中计算的结果表明,经平板补偿后的检验光路波像差RMS值为0.003λ,可满足TMC主镜的高精度检验要求.对补偿平板的检验方法,以及加工和使用中应当采取的措施也进行了考虑.与常用检验方法相比,本文方法具有容易对平板性能进行检验,成本低、研制周期短等优点.     

Three-dimensional shape measurement of large-aperture aspheric mirrors by off-axis null Ronchi test

An off-axis null Ronchi test is presented to measure the three-dimensional (3D) shape of a large-aperture aspheric mirror. The method designs curved fringe patterns as null sinusoidal gratings by means of phase information and ray tracing. In the process of measurement, the curved fringe patterns are displayed on a transmission-type liquid crystal display (T-LCD) screen, and a CCD camera records the fringe patterns containing the information of deviations of the mirror. The slopes of the deviations of the mirror are obtained by using the recorded fringe patterns. The deviations are restored by integrating, and then the 3D shape of the mirror can be reconstructed. Compared with the classical null Ronchi test, the method can provide enough measured data points and avoid the jagged edges of bands on the null gratings. Moreover, the method can conveniently change period and direction of the curved fringes and accurately control phase shifting. Computer simulations and a preliminary experiment are presented to show the performance of the method.     

Measurement based on fringe reflection for testing aspheric optical axis precisely and flexibly

A method based on fringe reflection is proposed to measure the optical axis of an aspheric mirror precisely and flexibly. In the measurement, a screen displaying a fringe pattern is moved along its normal direction, and a camera is located beside and observes the fringe pattern reflected via a tested surface. This method can test the optical axis of an aspheric mirror quantitatively before measuring the absolute height of the tested surface. And it can be combined with some presented methods that need to fit the aspheric mirror according to the optical axis to measure the surface. To validate the ability of this method, it is combined with one of the presented methods to measure absolute height of an aspheric mirror precisely and flexibly. Computer simulations and preliminary experiment validate the feasibility of this method.     

Efficiency of an elliptically shaped x-ray mirror

Curved reflecting mirrors are widely used as x-ray optical elements for both laboratory and synchrotron radiation sources. In general, the mirror parameters are optimized by numerical simulation. We discuss an analytical approach that is useful for deriving the mirror parameters, including eccentricity, length, angular acceptance, and magnification. We have examined in particular an elliptical surface from which we learned that, given the distance between the foci of the ellipse, the magnification, and the critical angle of total external reflection, it is possible to find analytically the optimal eccentricity that maximizes the angular acceptance and the optimal mirror length. We found that the last-named parameter, in a first approximation, depends only on the distance between the foci of the ellipse and on the magnification factor. We present as well a comparison of optimal parameters obtained with analytical calculation and with ray-tracing simulation that yielded good agreement.     

Correlation-Based Measurements of Camera Magnification and Scale Factor

A correlation method is described whereby the high precision of a commercial translator, which can be $10^{-5}$ or smaller in fractional error, is transferred to the image plane of a camera system through the determination of magnification and scale factor (effective focal length). Key to this method is the averaging of pixel boundary effects with a large-area planar random-dot target. The correlation method is relatively insensitive to camera random errors, target characteristics, illumination nonuniformities and localized imperfections in the camera or the target. Random errors are reduced by the large number of pixels contributing to each correlation sum. Variations of the focal length across the camera field-of-view were measured. Both systematic errors and the angular variation of magnification (lens aberrations) limit the accuracy of the method.      

应力抛光技术加工抛物面的实验研究

大口径非球面加工技术一直是先进光学制造领域研究的前沿课题,本文开展了以大型非球面应力抛光技术(SMP)为核心的相关先进光学制造技术的研究.研究了应力抛光技术的原理及算法,以加工一块口径为φ314mm,F/7的抛物面镜为例,验证应力抛光技术的合理性和有效性.采用干涉仪检测抛光结束的抛物面其峰值(PV)为3.317λ,均方根(rms)为0.489λ.结果表明,应力抛光技术能够以较高精度、快速地形成旋转对称的抛物面,其面形误差满足或接近于非球面面形的精度要求.     

Performance Analysis and Evaluation of Geometric Parameters in Stereo Deflectometry

This paper presents a novel geometric parameters analysis to improve the measurement accuracy of stereo deflectometry. Stereo deflectometry can be used to obtain form information for freeform specular surfaces. A measurement system based on stereo deflectometry typically consists of a fringe-displaying screen, a main camera, and a reference camera. The arrangement of the components of a stereo deflectometry system is important for achieving high-accuracy measurements. In this paper, four geometric parameters of a stereo deflectometry system are analyzed and evaluated: the distance between the main camera and the measured object surface, the angle between the main camera ray and the surface normal, the distance between the fringe-displaying screen and the object, and the angle between the main camera and the reference camera. The influence of the geometric parameters on the measurement accuracy is evaluated. Experiments are performed using simulated and experimental data. The experimental results confirm the impact of these parameters on the measurement accuracy. A measurement system based on the proposed analysis has been set up to measure a stock concave mirror. Through a comparison of the given surface parameters of the concave mirror, a global measurement accuracy of 154.2 nm was achieved.     

大口径光学镜面超精密加工机床的研制

设计制作了最大加工直径为φ880 mm的光学镜面超精密加工机床.该机床采用大理石床身、4轴数控联动、全气浮支承和零传动结构,以实现光学球、非球及自由形面的超精密切削.介绍了机床整体结构特点和性能参数,描述了气浮电主轴、气浮直线导轨、直驱回转工作台等关键技术及部件.该机床主轴回转精度0.05μm,直线伺服轴分辨力1.25 nm,回转工作台角位移分辨力0.009.″在硬铝和无氧铜材料上分别加工出了面形精度0.5μm、表面粗糙度5 nm的φ400 mm球面和面形精度0.5μm/φ100 mm、表面粗糙度8 nm的非球形面.     

Point shifting in the optical testing of fast aspheric concave surfaces by a cylindrical screen

A method for increasing the precision and sensitivity of the quantitative evaluation of fast aspheric surfaces through the null screen method is presented. This consists of applying small displacements to the cylindrical null screen along the optical axis. These movements allow a scan of the image spots over zones that with the analysis of a single image are more difficult to evaluate. The precision of the test is increased due to a greater density of sampling reducing the numerical errors during the integration. Results of the evaluation of an elliptical concave mirror on axis show that the numerical integration errors can be reduced from 20% for short paths to 80% for larger integration paths.     

Photographic optical systems with nonrotational aspheric surfaces

Sections of nonrotational aspheric surfaces can be useful in a variety of optical situations. In several examples, image-forming objectives, as for photographic or electronic camera products, are described in which suitably located asymmetric pairs of refractive surfaces are devised, such that relative rotation about a displaced axis of one with respect to the other can be used to produce a focusing effect that is satisfactory for imaging purposes over reasonable fields of view and for practicable apertures and achromatic corrections. Taylor expansions about assignable reference points in any given surface of a sequence, together with suitable coordinate systems, can be employed to relate performance to shape parameters.     

Quasi-null lens optical system for the fabrication of an oblate convex ellipsoidal mirror: application to the Wide Angle Camera of the Rosetta space mission

The design of a quasi-null lens system for the fabrication of an aspheric oblate convex ellipsoidal mirror is presented. The Performance and tolerance of the system have been analyzed. The system has been applied successfully for the fabrication of the primary mirror of the Wide Angle Camera (WAC), the imaging system onboard the Rosetta, the European Space Agency cornerstone mission dedicated to the exploration of a comet. The WAC is based on an off-axis two-mirror configuration, in which the primary mirror is an oblate convex ellipsoid with a significant conic constant.     

Three-dimensional shape measurement of aspheric mirrors with fringe reflection photogrammetry

Three-dimensional (3D) shape measurement of an aspheric mirror with fringe reflection photogrammetry involves three steps: correspondence matching, triangulation, and bundle adjustment. Correspondence matching is realized by absolute phase tracking and triangulation is computed by the intersection of reflection and incidence rays. The main contribution in this paper is constraint bundle adjustment for carefully dealing with lens distortion in the process of ray intersection, as compared to the well-known grating reflection photogrammetry. Additionally, a free frame is proposed to alleviate troublesome system geometrical calibration, and constraint bundle adjustment is operated in the free frame to refine the 3D shape. Simulation and experiment demonstrate that constraint bundle adjustment can improve absolute measurement accuracy of aspheric mirrors.     

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.     

离轴非球面的条纹反射检测技术

条纹反射测量技术具有动态范围大、灵敏度高的特点,通过高精度的系统标定可以获得很高的测量精度。本文研究将条纹反射测量技术应用于离轴非球面反射镜粗抛光阶段的面形检测,使用激光跟踪仪建立检测系统坐标系,然后将相机和显示屏的实测标定数据代入坐标系并在Zemax软件中建立测量装置的理想模型,通过光线追迹得到理想的屏幕像素点位置,采用相移技术可以得到实测时屏幕像素点位置,从而计算得到被测镜面形的斜率误差,最后积分得到检测结果。文中采用该方法对一块SiC离轴非球面镜进行了实测,并与三坐标测量机的结果进行对比,验证了方法的可行性,可用于指导离轴非球面镜粗抛光阶段的加工。     

Mode-matching Techniques as an Aid to Laser Cavity Alignment

Improvement of the alignment accuracy of an experimental, curved mirror, laser cavity by mode matching of the alignment laser beam to the experimental cavity parameters is discussed. It is shown that the use of a two-lens telescope, giving beam magnification, allows the mode-matched condition to be readily obtained for a wide variety of cavity configurations, and that a particular matching condition optimizes the mirror alignment accuracy, giving equal alignment sensitivity for each mirror of the experimental cavity. The mode-matching procedure avoids the need for large distances to provide high angular sensitivity, and compact alignment systems, suitable for building in to experimental lasers are readily designed. As an example, the alignment of an atomic iodine laser is discussed.     

Spherical primary telescope with aspheric correction at a small internal pupil

The aspheric plate at the center of curvature of a spherical primary is replaced by a small aspheric corrector at a minified pupil located inside a reimaging camera. The correctors are identical for each reimaging camera because the spherical aberration of the primary sphere is identical and symmetrical for all field positions. The magnitude of the field aberrations is evaluated over a range of primary focal ratios and minified pupil diameters. The major term is the increased field angle through the minified aspheric corrector. The field and chromatic aberrations in such a camera are compared with the equivalent full-aperture Schmidt corrector. Field-of-view partitioning enables each subfield to be designed for specific observational requirements, such as multiple-fiber spectrography or CCD imaging. Field partitioning is shown to be a powerful means for the replacement of the large aspheric corrector of a Schmidt telescope by a multiplicity of small reimaging subsystems. The cost to fill the typical wide field of a Schmidt telescope with reimaging modules is approximately 1% the cost of a Schmidt aspheric plate.     

Testing fast aspheric concave surfaces with a cylindrical null screen

A noncontact test procedure to obtain the shape of fast concave surfaces is described. A cylindrical null screen with a curved grid drawn on it in such a way that its image, which is formed by reflection on a perfect concave surface, yields a perfect square grid is proposed. The cylindrical null screen design and the surface evaluation algorithm are presented. Experimental results for the testing of an elliptical mirror of 164 mm in diameter (f/0.232) are shown.     

Fabrication and alignment issues for segmented mirror telescopes

There is a great demand for new telescopes that use larger primary mirrors to collect more light. Because of the difficulty in the fabrication of mirrors larger than 8 m as a single piece, they must be made with numerous smaller segments. The segments must fit together to create the effect of a single mirror, which presents unique challenges for fabrication and testing that are absent for monolithic optics. This is especially true for the case of a highly aspheric mirror required to make a short two-mirror telescope. We develop the relationship between optical performance of the telescope and errors in the manufacture and operation of the individual segments.     

环形子孔径检测技术中测量数据的准确提取方法

环形子孔径拼接测试技术是一种无需辅助元件就能检测旋转对称大口径非球面镜的有效手段。根据该技术的检测原理及基于Zemike多项式的“拼接”算法,提出了一种相应的环形子孔径数据提取方法。该方法基于商用相移干涉仪的CCD成像系统和其数据处理软件提供的Mask编辑功能,利用被测镜面上方的三个可移动的基准标记进行绝对定位,给出了具体的实施方案。对一口径700mm、F2的抛物面主镜进行实验,研究结果表明,该数据提取方法操作简单可行,适合于加工车间的实施,取得了符合“拼接”算法需求的子孔径测试数据和对应环带的内外半径值。