Mirror Figure Research Articles

A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition

In the third- and coming fourth-generation synchrotron radiation facilities, X-rays having both high brightness and high coherency can be utilized. Such X-rays require high accuracy in the reflective optics. In this study, we developed an ultra-precise measurement instrumentation for tangentially long X-ray mirrors using a Fizeau interferometer. In the system, the mirror figure is measured by stitching the subaperture profiles measured by the relative-angle determinable stitching interferometry, which we developed previously. High measurement accuracy of approximately 2 nm (peak to valley) was achieved in the measurement of a 400 mm-long aspherical surface.

Algorithm for ion beam figuring of low-gradient mirrors

Ion beam figuring technology for low-gradient mirrors is discussed. Ion beam figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target workpiece to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional contact polishing processes, are avoided. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer-controlled optical surfacing (CCOS) principle. With the properties of the removal function, the shaping process of low-gradient mirrors can be approximated by the linear model for planar mirrors. With these discussions, the error surface figuring technology for low-gradient mirrors with a linear path is set up. With the near-Gaussian property of the removal function, the figuring process with a spiral path can be described by the conventional linear CCOS principle, and a Bayesian-based iterative algorithm can be used to deconvolute the dwell time. Moreover, the selection criterion of the spiral parameter is given. Ion beam figuring technology with a spiral scan path based on these methods can be used to figure mirrors with non-axis-symmetrical errors. Experiments on SiC chemical vapor deposition planar and Zerodur paraboloid samples are made, and the final surface errors are all below 1/100 lambda.

Research on electrostatic deformation of space membrane mirror

薄膜反射镜将解决反射镜孔径与重量相互制约的问题. 采用静电拉伸法控制薄膜反射镜面形, 具有结构简单、反射镜面形易于控制等优点, 其原理为利用静电场上库仑力作用使薄膜产生面形变化, 生成所需的光学曲面. 由于薄膜变形力学, 以及静电场理论的复杂性, 目前薄膜成形及其面形控制在理论分析上仍未有定量的结果. 本文主要以单电极静电场中的薄膜反射镜面形为考察因素, 通过数值计算的方法得到薄膜反射镜上的静电力分布, 运用有限元分析获得该分布下的反射镜面形, 并将其与理想面形进行比较. 提出采用多电极闭环控制可获得更高的控制精度, 对静电拉伸薄膜的研究具有一定的指导意义.

Bayesian Principle Based Dwell Time Algorithm for Ion Beam Figuring of Low Gradient Mirrors

Ion beam figuring is a technology of figuring mirrors errors of high efficiency. Dwell time algorithm is one of the key problems. Based on the Bayesian principle, an iterative dwell time algorithm for planar mirrors is deduced from the computer controlled optics shaping principle. With the Gaussian extension for the data edge, the edge effect is weakened. The rapid approximate calculation of the velocity for the realization of dwell time is presented, and then the model relation between the realization error and the process parameters is deduced. By the additional smoothing factors from the error model, the realization precision for the dwell time is improved. Based on the properties of the removal function, the shaping process of low gradient mirrors can be approximated to the linear model of planar mirrors. With these discussions, the error surface controlling technology for low gradient mirrors is set up. At last, the figuring experiments on planar and spherical samples are made; the convergence rates of both can reach 9. It is concluded that the linear model is reasonable and the approximate velocity is effective. The ion beam figuring technology based on these algorithms is a deterministic process of high efficiency and can be used to correct the surface error precisely and rapidly.

Optimal light beams and mirror shapes for future LIGO interferometers

We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this minimization is a beam with thermal noise a factor of 2.32 (in power) lower than previously considered Mesa Beams and a factor of 5.45 (in power) lower than the Gaussian beams employed in the current baseline design. Mirrors that confine these beams have been found to be roughly conical in shape, with an average slope approximately equal to the mirror radius divided by arm length, and with mild corrections varying at the Fresnel scale. Such a mirror system, if built, would impact the sensitivity of LIGO, increasing the event rate of observing gravitational waves in the frequency range of maximum sensitivity roughly by a factor of 3 compared to an Advanced LIGO using Mesa beams (assuming all other noises remain unchanged). We discuss the resulting beam and mirror properties and study requirements on mirror tilt, displacement, and figure error, in order for this beam to be used in LIGO detectors.

Optical control of the Advanced Technology Solar Telescope

The Advanced Technology Solar Telescope (ATST) is an off-axis Gregorian astronomical telescope design. The ATST is expected to be subject to thermal and gravitational effects that result in misalignments of its mirrors and warping of its primary mirror. These effects require active, closed-loop correction to maintain its as-designed diffraction-limited optical performance. The simulation and modeling of the ATST with a closed-loop correction strategy are presented. The correction strategy is derived from the linear mathematical properties of two Jacobian, or influence, matrices that map the ATST rigid-body (RB) misalignments and primary mirror figure errors to wavefront sensor (WFS) measurements. The two Jacobian matrices also quantify the sensitivities of the ATST to RB and primary mirror figure perturbations. The modeled active correction strategy results in a decrease of the rms wavefront error averaged over the field of view (FOV) from 500 to 19 nm, subject to 10 nm rms WFS noise. This result is obtained utilizing nine WFSs distributed in the FOV with a 300 nm rms astigmatism figure error on the primary mirror. Correction of the ATST RB perturbations is demonstrated for an optimum subset of three WFSs with corrections improving the ATST rms wavefront error from 340 to 17.8 nm. In addition to the active correction of the ATST, an analytically robust sensitivity analysis that can be generally extended to a wider class of optical systems is presented.

Kirkpatrick-Baez mirrors used in high resolution X-ray microscopy, tomography and fluorescence analysis

The combination of a very brilliant X-ray source and state-ofthe-art X-ray optics opens the way to nano-focusing applications. Dynamically bent graded multilayers set in the KB-geometry are developed at the ESRF as an extremely efficient device to focus undulator radiation to spots below 100 nm [1]. The smallest 2D focus reached so far with this device is of the order of 80 nm in both directions. This has been achieved both on a long, coherent beamline and on a shorter beamline using the concept of a secondary source. The first mirror of the system, coated with a graded multilayer, plays both the role of vertical focusing device and monochromator, resulting in a very high flux (a few 10 11 photons/s) and medium monochromaticity (ΔE/E∼10p). Two different fields benefit particularly from the combination small focus / high flux: projection microscopy (magnified tomography) and X-ray fluorescence mapping. In projection microscopy the sample is set at a small distance (10-100 mm) downstream or upstream of the focus and a magnified Fresnel diffraction pattern is recorded on a medium resolution detector set at a large distance (several meters) from the focus. This approach allows to overcome the spatial resolution limit imposed by the detector in the parallel beam geometry. It was used to give direct evidence of nanometric invasion-like grain boundary penetration in the Al/Ga system [2]. For tomography, scans are acquired at different focussample distances. This yields variable magnifications, but also different effective propagation distances (∼equal to the focussample distance). The principal difficulties in this approach are related to the mirror imperfections and the pronounced refraction effects at the sample edges when going to sub-100 nm pixel sizes. Satisfactory results were however obtained in local tomography mode on aluminium alloys. A correction for mirror figure error and a phase retrieval method adapted to the imaging setup are incorporated in the tomograhic procedure [3]. In fluorescence imaging the sample is scanned through the focal plane while the spectrum of the emitted fluorescence is recorded with an energy dispersive detector. This rich probe, complementary to transmission imaging, provides element specific information and allows to image and quantify trace elements. The possibility to apply this method to the field of neurochemistry at the sub-cellular level has been demonstrated. Finally, the best one dimensional focus reached so far with reflective multilayer optics is 40 nm. The ultimate limits of this focusing approach will be discussed.

Efficient sub 100nm focusing of hard x rays

An x-ray beam with energy of 20.5keV has been efficiently focused down to a spot size as small as 90nm×90nm by a Kirkpatrick–Baez reflecting mirrors device. The first mirror, coated with a graded multilayer, plays both the role of vertical focusing device and monochromator, resulting in a very high flux (2×1011photons∕s) and medium monochromaticity (ΔE∕E∼10−2). Evaluation of the error contributions shows that the vertical focus is presently limited by the mirror figure errors, while the horizontal focus is limited by the horizontal extension of the x-ray source. With a gain in excess of a few million, this device opens up new possibilities in trace element nanoanalysis and fast projection microscopy.

Relative angle determinable stitching interferometry for hard x-ray reflective optics

Metrology plays an important role in surface figuring with subnanometer accuracy. We have developed relative angle determinable stitching interferometry for the surface figuring of elliptical mirrors, in order to realize hard x-ray nanofocusing. In a stitching system, stitching angles are determined not by the general method using a common area between neighboring shots, but by the new method using the mirror’s tilt angles measured at times when profile data are acquired. The high measurement accuracy of approximately 4nm (peak-to-valley) was achieved in the measurement of a cylindrical surface having the same curvature as the elliptically designed shape to enable hard x-ray nanofocusing.

Computerized Assessment of the Ability for Transformation of Visual Mental Images

Transformation of visual mental images according cognitive theories is a subprocess of view imagery. Software test for asseement of the ability for mental rotation includes 24 tasks. Each of them consists of 5 figures, one of wich is a mirror figure of other. The tested person has to discover the mirror figure. The software is designed in two versions for running on any IBM-compatible personal computer operating under MS-DOS or Windows. Object-oriented approach for development of the software has been applied. Classes and their relationships are described.

Thermal and structural deformation and its impact on optical performance of projection optics for extreme ultraviolet lithography

Thermal and structural deformation of mirrors becomes an important consideration for extreme ultraviolet lithography (EUVL) when targeting features of 50 nm and below. Such deformation will contribute to the critical dimension control and decrease the performance of the designed system. Multilayer coated mirrors typically absorb 35%–40% of the in-band radiation, which results in the deformation of mirror figures and degrades the performance of the optics. We have employed several software packages to study these effects. This article presents the results for the EUVL production tool with wafer throughput of eighty 300 mm wafers per hour for the 35 nm technology generation.

Interferometric hartmann wave-front sensing for active optics at the 6.5-m conversion of the multiple mirror telescope.

A little-used interferometric modification to the classical Hartmann optical test is being used for active optics corrections at the 6.5-m Multiple Mirror Telescope (MMT) Observatory. The technique produces compact interference spots whose positions depend on discrete wave-front phase-difference errors. A diffraction model illustrates the formation of interference spots. The limitations on wave-front sampling that are due to atmospheric seeing are estimated. Two data reduction matrix strategies are given. A single correction of collimation and primary mirror figure produces a nearly diffraction-limited telescope image. Wave-front polynomial coefficients ranging from several nanometers to several micrometers in amplitude are reliably detected.

Concepts for a Large‐Aperture, High Dynamic Range Telescope

ABSTRACTThis paper summarizes concept studies for a large telescope capable of wide‐field imaging and of the highest possible dynamic range for photometry and angular resolution.Point‐spread functions (PSFs) and scattered light levels at large offsets are computed and compared for four telescopes of the same light‐gathering power but with different pupil functions:1. a reference monolithic mirror telescope with a 17.4 m primary,2. a segmented mirror telescope (SMT) with a hexagonally segmented primary,3. a hexagonal off‐axis telescope (HOT) with a distributed aperture made of 6 × 6.5 m unobstructed circular mirrors that are identical off‐axis sections of a parent 20 m mirror, and4. a square off‐axis telescope (SOT) whose aperture is made of 4 × 8 m off‐axis mirrors.The characteristics of the PSFs are examined in the diffraction‐ and seeing‐limited regimes, assuming (1) perfect mirror figure and (2) realistic figure errors (edge defects). The implications of field rotation with an altitude‐azimuth mounting are discussed in each case. The implementation of adaptive optics (AO) and the properties of AO‐compensated PSFs having a Strehl ratio of 0.5, and of coronagraphic imaging, are also discussed for the four configurations. It is shown that, in the seeing‐limited regime and as intuitively expected, the optical performance of all four telescopes is comparable. With higher order adaptive optics and for coronagraphic observations, the SOT and HOT are superior to the SMT. This distinction becomes larger with relaxed constraints on mirror edge‐polishing requirements. A full optical design is presented for the novel HOT configuration, and optical fabrication issues are briefly addressed. Finally, science programs and possible instrumentation layouts with the HOT are briefly explored for different modes of operation. It appears that the natural “optical bench” configuration of the HOT can provide a remarkably versatile and convenient environment for instrument deployment.

Cryogenic wavefront correction using membrane deformable mirrors

Micro-machined membrane deformable mirrors (MMDMs) are being evaluated for their suitability as wavefront correctors at cryogenic temperatures. Presented here are experimental results for the change in the initial mirror figure of 37-channel MMDMs from OKO Technologies upon cooling to T=78K. The changes in the influence functions are also explored. Of the sample of 3 mirrors tested, one was found to have sufficiently small initial static aberrations to be useful as a wavefront corrector at this temperature. The influence functions at T=78K were found to be similar in shape to both those at room temperature and theoretical predictions of the MMDMs surface shape. The magnitude of the surface deflection at T=78K was reduced by around 20% compared with room temperature values.

Radial shearing interferometer for in-process measurement of diamond turning

A stable interferometer with two zone plates to measure a concave mirror figure is developed. The principle of the measurement is based on the radial shearing interference in which the measuring wavefront from the entire mirror surface under test is referred to that from the central part. On-machine experiments show that the interferometer is stable and compact enough to be applicable to in-process measurement for diamond turning at about 0.06 ?m p-v accuracy.

Distributed Sensing and Shape Control of Piezoelectric Bimorph Mirrors

Meeting the long term needs of the remote sensing community requires the development of large aperture space-based optical systems to achieve dramatic improvements in resolution and sensitivity. It is possible that ultralarge apertures will be obtained using deployable thin film mirror technology, yet many technological barriers must be overcome to make this approach viable. This paper summarizes an initial research effort into the development of piezoelectric thin film mirrors that can be actively shaped using electric fields applied by an electron flux at selected locations. Recent progress is described in the key areas of mirror figure sensing methods, electron gun excitation, and shape control algorithm development.

Elliptical x-ray microprobe mirrors by differential deposition

A differential coating method is described for fabricating high-performance x-ray microfocusing mirrors. With this method, the figure of ultrasmooth spherical mirrors can be modified to produce elliptical surfaces with low roughness and low figure errors. Submicron focusing is demonstrated with prototype mirrors. The differential deposition method creates stiff monolithic mirrors which are compact, robust, and easy to cool and align. Prototype mirrors have demonstrated gains of more than 104 in beam intensity while maintaining submilliradian divergence on the sample. This method of producing elliptical mirrors is well matched to the requirements of an x-ray microdiffraction Kirkpatrick–Baez focusing system.

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.

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.

ラジアルシェア干渉計によるオンマシン測定

A stable interferometer using two zone plates is developed for on-machine measurement of a concave mirror figure. The principle of measurement is based on the radial shearing interference in which the measuring wavefront from the entire mirror surface under test is referred to that from the central part. On-machine experiments showed that the interferometer is stable enough to be applicable to inprocess measurement for diamond turning at about 0.06 μm P-V accuracy.