Μrad Rms Research Articles

A hybrid surface shape control method for optimizing thermal deformation of FEL reflection mirror

The surface shape errors induced by thermal deformation of the free electron lasers (FEL) beamline reflection mirror directly affect the quality of FEL beam. In order to reduce the thermal deformation and meet the stringent requirements of surface shape error of the FEL reflection mirror, this paper proposes a surface shape control method that combines mirror bending and active thermal control (ATC) technique, aiming to minimize surface shape errors and enhance the overall performance of the FEL beamline. A bending mechanism has been designed to achieve a bending sensitivity of 60 nrad RMS/N using only one bending actuator. It does not obstruct the FEL beam with extremely small incident angle. This mechanism can compensate for thermal deformation by eliminating the cylindrical surface component of the thermal deformation. Additionally, a novel ATC algorithm is proposed based on the Tikhonov regularization method. When combined with the bending mechanism, it proves effective in controlling the surface shape of the reflection mirror. The simulation results indicate that this surface control method can effectively reduce the surface shape errors of the reflection mirror. Taking the 3 nm wavelength FEL as an example, the RMS value of surface slope error of the reflection mirror is substantially reduced from 17.1974 μrad (with heat load) to 0.0913 μrad after bending. Based on the bending result, the ATC technique further reduces the slope error to 0.0303 μrad RMS. For 1 nm and 2 nm wavelength FELs, the mirror slope errors ultimately reach 0.0147 μrad RMS and 0.0295 μrad RMS respectively. This surface shape control method ensures that the reflection mirror slope errors meet the beamline requirement, which is 0.05 μrad RMS, thereby guaranteeing the beam quality.

Unified Parameterization and Calibration of Serial, Parallel, and Hybrid Manipulators

In this work, we present methods allowing parallel, hybrid, and serial manipulators to be analyzed, calibrated, and controlled with the same analytical tools. We introduce a general approach to describe any robotic manipulator using established serial-link representations. We use this framework to generate analytical kinematic and calibration Jacobians for general manipulator constructions using null space constraints and extend the methods to hybrid manipulator types with complex geometry. We leverage the analytical Jacobians to develop detailed expressions for post-calibration pose uncertainties that are applied to describe the relationship between data set size and post-calibration uncertainty. We demonstrate the calibration of a hybrid manipulator assembled from high precision calibrated industrial components resulting in 91.1 μm RMS position error and 71.2 μrad RMS rotation error, representing a 46.7% reduction compared to the baseline calibration of assembly offsets.

Development of a long trace profiler in situ at National Synchrotron Radiation Research Center.

To achieve an ultrahigh resolution of a beamline for soft X-rays at the Taiwan Photon Source (TPS), the profile of a highly precise grating is required at various curvatures. The slope error could be decreased to 0.1 µrad (rms) at a thermal load with a specially designed bender having 25 actuators. In the meantime, a long-trace profiler (LTP) was developed in situ to monitor the grating profile under a thermal load; it consists of a moving optical head, an air-bearing slide, an adjustable stand, and a glass viewport on the vacuum chamber. In the design of this system, a test chamber with an interior mirror was designed to simulate the chamber in the beamline. To prevent an error induced from a commercial viewport, a precision glass viewport (150CF, flatness 1/150 λ rms at 632.8 nm) was designed. The error induced from the slope error of the glass surface and the vacuum deformation was also simulated. The performance of the optical head of the LTP in situ (ISLTP) has been tested in the metrology laboratory. The sources of error of this LTP including the linearity and the glass viewport were corrected after the measurement. For the beamline measurement, an optical head was mounted outside the vacuum chamber; the measuring beam passed through the glass viewport to measure the grating profile in vacuum. The measurement of the LTP after correction of the above errors yielded a precision about 0.2 µrad (rms). In a preliminary test, an ISLTP was used to measure the grating profile at soft X-ray beamline TPS45A. The measured profile was for the bending mechanism to optimize the slope profile. From the measured energy spectrum, the slope error of the grating was estimated with software for optical simulation to be about 0.3 µrad (rms), consistent with our estimate of the ISLTP. In the future, it will be used to monitor the thermal bump under a large thermal load. In addition, an ISLTP was used to monitor the properties of optical elements-the twist and radius in the beamline during the installation phase.

Metrology for optical components of Taiwan Photon Source beamlines.

To ensure the high performance of beamlines in Taiwan Photon Source, the metrology of the beamline optical components is essential to realize the theoretical optical simulation. The design and performance of a long-trace profiler (LTP) with moving optical head is described. A LTP is used as a metrological tool for the assembly and correction of optical components at the beamline. For a water-cooled mirror, a LTP serves to optimize the surface profile to a slope error of 0.1 µrad (rms) and adequate thermal conductance. To correct a bendable cooling mirror in a twisted condition, the sagittal slope is decreased by a screw adjustment through the LTP measurement. For the double-crystal monochromator (DCM) with flow-induced vibrations, we proposed an approach to stiffen the bellows hose partially inside the vacuum chamber. From an investigation of the vibrational spectra of the DCM before and after the treatment with the aid of the autocollimator, the current approach is confirmed to be an effective solution for suppression of vibration.

A Fast Piezo Actuated Tip/Tilt Mirror for raster scan applications

This paper presents the system and control design of a novel high performance piezo-actuated fast steering mirror (FSM) for high speed optical scanning which is centered around an easy-to-manufacture membrane-like mechanical flexure and uses an optical sensor system for position measurement. With the membrane flexure the first fundamental resonance mode of the actuator is placed as high as 6.7 kHz, while still enabling an optical angular range of ±4.8 mrad. Using a PI controller together with three notch filters designed in a loop shaping approach for maximizing the system bandwidth and tracking of high resolution raster trajectories, a closed-loop bandwidth as high as 2.7 kHz and a positioning uncertainty of 3.8 µrad rms is obtained. The obtained tracking error when tracking a 250 Hz raster scanning trajectory with a scan amplitude of 2.2 mrad is as small as 73.8 µrad rms (3.6% of scan amplitude).

X-ray metrology and performance of a 45-cm long x-ray deformable mirror.

We describe experiments with a 45-cm long x-ray deformable mirror (XDM) that have been conducted in End Station 2, Beamline 5.3.1 at the Advanced Light Source. A detailed description of the hardware implementation is provided. We explain our one-dimensional Fresnel propagation code that correctly handles grazing incidence and includes a model of the XDM. This code is used to simulate and verify experimental results. Initial long trace profiler metrology of the XDM at 7.5 keV is presented. The ability to measure a large (150-nm amplitude) height change on the XDM is demonstrated. The results agree well with the simulated experiment at an error level of 1 μrad RMS. Direct imaging of the x-ray beam also shows the expected change in intensity profile at the detector.

High-energy, kHz, picosecond hybrid Yb-doped chirped-pulse amplifier

We report on a diode-pumped, hybrid Yb-doped chirped-pulse amplification (CPA) laser system with a compact pulse stretcher and compressor, consisting of Yb-doped fiber preamplifiers, a room-temperature Yb:KYW regenerative amplifier (RGA), and cryogenic Yb:YAG multi-pass amplifiers. The RGA provides a relatively broad amplification bandwidth and thereby a long pulse duration to mitigate B-integral in the CPA chain. The ~1030-nm laser pulses are amplified up to 70 mJ at 1-kHz repetition rate, currently limited by available optics apertures, and then compressed to ~6 ps with high efficiency. The near-diffraction-limited beam focusing quality is demonstrated with M(x)(2) = 1.1 and M(y)(2) = 1.2. The shot-to-shot energy fluctuation is as low as ~1% (rms), and the long-term energy drift and beam pointing stability for over 8 hours measurement are ~3.5% and <6 μrad (rms), respectively. To the best of our knowledge, this hybrid laser system produces the most energetic picosecond pulses at kHz repetition rates among rod-type laser amplifiers. With an optically synchronized Ti:sapphire seed laser, it provides a versatile platform optimized for pumping optical parametric chirped-pulse amplification systems as well as driving inverse Compton scattered X-rays.

High-power Ti:sapphire laser at 820 nm for scanning ground-based water–vapor differential absorption lidar

The Ti:sapphire (TISA) laser transmitter of the mobile, three-dimensional-scanning water-vapor differential absorption lidar (DIAL) of the University of Hohenheim is described in detail. The dynamically-stable, unidirectional ring resonator contains a single Brewster-cut TISA crystal, which is pumped from both sides with 250 Hz using a diode-pumped frequency-doubled Nd:YAG laser. The resonator is injection seeded and actively frequency-stabilized using a phase-sensitive technique. The TISA laser is operating near 820 nm, which is optimum for ground-based water-vapor DIAL measurements. An average output power of up to 6.75 W with a beam quality factor of M2<2 is reached. The pointing stability is <13 μrad (rms), the depolarization <1%. The overall optical-optical conversion efficiency is up to 19%. The pulse length is 40 ns with a pulse linewidth of <157 MHz. The short- and long-term frequency stabilities are 10 MHz (rms). A spectral purity of 99.9% was determined by pointing to a stratus cloud in low-elevation scanning mode with a cloud bottom height of ≈2.4 km.

Metrology, Mirrors and Gratings – Advances and Challenges in Synchrotron Optics

Ultra-precise reflective and diffractive optical elements like blazed diffraction gratings or ultra-precise mirrors of flat, elliptic, parabolic, or other shapes have become key components in today's synchrotron optics. These optical components feature nanometre accuracy on a macroscopic length scale. Beamlines with extreme lengths of 100m to 1km or more (as planned for the European XFEL) will require plane mirrors characterized by a residual slope error of 50nrad rms and a curvature radius of > 1000km on a length of 800mm or even more. Diffraction limited focusing mirrors for hard X-ray application show residual slope deviations of 50nrad rms on a length of 350mm. The current slope limit for focusing mirrors in VUV-application lies at around 0.5μrad rms, one order of magnitude inferior compared to hard X-ray focusing optics, and it can still not be exceeded due to technological restrictions. The requirements for diffraction gratings are even more challenging. In addition to the challenges posed by perfect substrate quality, special attention is needed to guaranty a precise positioning of the grooves along the full aperture length. A positioning accuracy of about 20nm for the carriage system of a ruling engine is mandatory to meet the Marechal tolerance for gratings. For the manufacture of blazed and laminar gratings, we are currently establishing a new technological laboratory at the Helmholtz Zentrum Berlin (HZB), including instrumentation from Carl Zeiss. Besides the present Zeiss technology, we are also developing an advanced technology line, including a new ultra-precise ruling machine, ion etching technology as well as laser holography.

Performance of the APS optical slope measuring system

An optical slope measuring system (OSMS) was recently brought into operation at the Advanced Photon Source of the Argonne National Laboratory. This system is equipped with a precision autocollimator and a very accurate mirror-based pentaprism on a scanning stage and kept in an environment-controlled enclosure. This system has the capability to measure precision optics with sub-microradian rms slope errors as documented with a series of tests demonstrating accuracy, stability, reliability and repeatability. Measurements of a flat mirror with 0.2μrad rms slope error are presented which show that the variation of the slope profile measurements with the mirror setting at different locations along the scanning direction is only 60nrad and the corresponding height error profile has 2nmrms.

Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry

We present recent results on the inspection of a first diffraction-limited hard X-ray Kirkpatrick-Baez (KB) mirror pair for the Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS). The full KB system - mirrors and holders - was under inspection by use of high resolution slope measuring deflectometry. The tests confirmed that KB mirrors of 350mm aperture length characterized by an outstanding residual figure error of <1 nm rms has been realized. This corresponds to the residual figure slope error of about 0.05µrad rms, unprecedented on such long elliptical mirrors. Additional measurements show the clamping of the mirrors to be a critical step for the final - shape preserving installation of such outstanding optics.

Scanning Optical Head with Nontilted Reference Beam: Assuring Nanoradian Accuracy for a New Generation Surface Profiler in the Large-Slope Testing Range

Nanoradian Surface Profilers (NSPs) are required for state-of-the-art synchrotron radiation optics and high-precision optical measurements. Nano-radian accuracy must be maintained in the large-angle test range. However, the beams' notable lateral motions during tests of most operating profilers, combined with the insufficiencies of their optical components, generate significant errors of∼1 μrad rms in the measurements. The solution to nano-radian accuracy for the new generation of surface profilers in this range is to apply a scanning optical head, combined with nontilted reference beam. I describe here my comparison of different scan modes and discuss some test results.

Sub-nm accuracy metrology for ultra-precise reflective X-ray optics

The transport and monochromatization of synchrotron light from a high brilliant laser-like source to the experimental station without significant loss of brilliance and coherence is a challenging task in X-ray optics and requires optical elements of utmost accuracy. These are wave-front preserving plane mirrors with lengths of up to 1 m characterized by residual slope errors in the range of 0.05 μrad (rms) and values of 0.1 nm (rms) for micro-roughness. In the case of focusing optical elements like elliptical cylinders the required residual slope error is in the range of 0.25 μrad rms and better. In addition the alignment of optical elements is a critical and beamline performance limiting topic. Thus the characterization of ultra-precise reflective optical elements for FEL-beamline application in the free and mounted states is of significant importance. We will discuss recent results in the field of metrology achieved at the BESSY-II Optics Laboratory (BOL) of the Helmholtz Zentrum Berlin (HZB) by use of the Nanometer Optical Component Measuring Machine (NOM). Different types of mirror have been inspected by line-scan and slope mapping in the free and mounted states. Based on these results the mirror clamping of a combined mirror/grating set-up for the BL-beamlines at FLASH was improved.

Characterization and calibration of 2nd generation slope measuring profiler

High spectral resolution and nanometer sized foci of 3rd generation SR beamlines can only be achieved by means of ultra precise optical elements. The improved brilliance and the coherence of free electron lasers (FEL) even push the accuracy limits and make the development of a new generation of ultra precise reflective optical elements mandatory. Typical elements are wave front preserving plane mirrors (lengths of up to 1 m, residual slope errors ∼0.05 μrad (rms) and values of 0.1 nm (rms) for the micro-roughness) and curved optical elements like spheres, toroids or elliptical cylinder (residual slope error ∼0.25 μrad (rms) and better). These challenging specifications and the ongoing progress in finishing technology need to be matched by improved accuracy metrology instruments. We will discuss the results of recent developments in the field of metrology made in the BESSY-II-optics laboratory (BOL) at the Helmholtz Zentrum Berlin (HZB), by the use of vertical angle comparator (VAC) in use to calibrate the nanometer optical component measuring machine (NOM). The BESSY-NOM represents an ultra accurate type of slope measuring instruments characterized by an accuracy of 0.05 μrad (rms) for plane substrates and 0.2 μrad (rms) for significant curved surfaces.

An LTP stitching procedure with compensation of instrument errors: Comparison of SOLEIL and ESRF results on strongly curved mirrors

Unknown linearity errors of long trace profilers (LTP) are a troublesome source of measurement errors and discrepancies from instrument to instrument, especially on strongly curved surfaces. This article describes a complete procedure of LTP data acquisition and data processing, which allow to, simultaneously, evaluate the linearity error and reconstruct a corrected slope profile. The method has been tested by performing independent measurements of the same mirrors on SOLEIL and ESRF LTP. Results show that independent measurements using this procedure are in agreement down to 0.2 μrad RMS in slope and 1.6 nm in height.

The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability

We present design and implementation details of the Diamond-NOM (nanometre optical metrology)—a non-contact profiler capable of measuring the surface topography of large (up to 1500 mm long) and heavy (up to 150 kg) optical assemblies with sub-nanometre resolution and repeatability. These levels of performance are essential to fabricate and optimize next generation optics. The capabilities of the Diamond-NOM have already enabled collaborations with optic manufacturers, including production of a preferentially deposited, large (1.2 m), synchrotron mirror with a slope error of ∼0.44 μrad rms and using bimorph technology to reduce figure error of a super-polished (elastic emission machining) optic to <1 nm peak to valley. We demonstrate that the BESSY-NOM scanning pentaprism and autocollimator concept is robust, easily transferable, and repeatable.

A preferential coating technique for fabricating large, high quality optics

A major challenge facing optic manufacturers is the fabrication of large mirrors (>1 m) with minimal residual slope errors (<0.5 μrad rms). We present a differential coating method with the potential to satisfy such exacting technical demands. Iterative cycles of measurement using the Diamond-NOM, followed by preferential deposition, were performed on a 1200 mm long, silicon mirror. The applied coatings were observed to reduce the optical slope and figure errors from 1.62 to 0.44 μrad rms, and from 208 to 13 nm rms, respectively. It is hoped that this research will lead to commercially available products, of direct benefit to the Synchrotron, Free Electron Laser, Astronomy, Space, and Laser communities, who all require state-of-the-art optics.

A local control system for the test masses of the Virgo gravitational wave detector

The mirrors of interferometric detectors of gravitational waves (GW) are suspended in order to be isolated from external disturbances. A local control system able to keep them correctly aligned and to damp the angular modes of the suspension is necessary. In this paper we present the solution adopted for Virgo based on a CCD camera sensor and on digital controls. With this solution the mirrors are kept aligned at the level of less than 1 μrad rms, enough to lock the interferometer and start the automatic alignment system.

An advanced KB mirror pair for microfocusing

A new range of micro-focusing mirrors based on KB pairs has been developed by SESO for Beamline Nanospectroscopy at the Elettra Storage Ring in Trieste, Italy. Both the focusing and the aspheric shape are adjustable with stepper motors. The goal of the beamline is to have a high photon density spot with a variable size in the experimental chamber over the whole soft X-ray range. The estimated dimension of the final spot should be smaller than 4 μm 2 FWHM, with a photon density of the order of 10 13 photons/s μm 2; this may be achieved only by accepting an angular divergence on these mirrors of between 5 and 10 mrad. This condition can be fulfilled only with elliptical (or plane elliptical) mirrors with very limited residual slope errors (below 1 μrad RMS) that are able to correct even small focal distance errors.

Design and fabrication of an active polynomial grating for soft-X-ray monochromators and spectrometers

An active polynomial grating has been designed for use in synchrotron radiation soft-X-ray monochromators and spectrometers. The grating can be dynamically adjusted to obtain the third-order-polynomial surface needed to eliminate the defocus and coma aberrations at any photon energy. Ray-tracing results confirm that a monochromator or spectrometer based on this active grating has nearly no aberration limit to the overall spectral resolution in the entire soft-X-ray region. The grating substrate is made of a precisely milled 17-4 PH stainless steel parallel plate, which is joined to a flexure-hinge bender shaped by wire electrical discharge machining. The substrate is grounded into a concave cylindrical shape with a nominal radius and then polished to achieve a roughness of 0.45 nm and a slope error of 1.2 μrad rms. The long trace profiler measurements show that the active grating can reach the desired third-order polynomial with a high degree of figure accuracy.