188 A Rommeveaux et al be shown that the spurious signal resulting from a slightly offset sinusoidal fringe is in quadrature with the signal resulting from the centered fringe The depth of the image minimum is affected but its position does not change The position of the minimum is interpolated from nine bracketing points In some cases, namely when measuring gratings [7–9], the SUT reflectivity will be different for polarization along or perpendicular to the track direction In order to minimize the loss of fringe contrast in this case we use a specially cut Wollaston prism arrangement where the optical axes of the two prisms are set at 45◦ to the wedge direction and therefore parallel to the quarterwave plate axes, instead of being parallel and perpendicular to the wedge as it is usually constructed Due to the symmetry, the reflected components for the two principal directions of polarization are equal and the fringe contrast is preserved Finally the direction of the probe beam can be chosen by different arrangements of the mirrors and prisms in the moving head By rotating P2 by 180◦ around the X-axis before gluing, we obtain an upward pointing stabilized beam The actual configuration used to measure downward facing surfaces is obtained by inserting between M1 and P1 a periscope composed of two flat and parallel mirrors which brings the beam up without changing its direction Side illumination is realized using the same principle with M1 and the following prisms in an upward pointing configuration, turned 90◦ around the incoming beam so that the lateral direction of the equivalent roof reflector is now along Y instead of Z A 500 m long instrument of the type described above is able to measure slopes in the range of about ±5 mrad corresponding to a radius of 10 m in a 100 mm long mirror [14, 15] When this range is not enough, it is still possible to extend the measurement length by stitching a series of successive scans with different inclinations of the surface A limited number of scans can be stitched without degrading the accuracy as they can be overlapped sufficiently Another important issue is to be able to measure very long mirrors, up to m With this target in mind, the European Synchrotron Radiation Facility (ESRF) constructed its own trace profiler The ESRF LTP is a homemade instrument The first version was built in 1993 with the help of Takacs to measure long mirrors up to 1.5 m [3] Many modifications have been made to the original design: the source and the detector are now separate from the moving optical head and fixed to the table (Fig 10.6), the source is a helium–neon stabilized laser fitted to the optics head through a polarization-preserving optics fiber, a mirror assembly equivalent to a pentaprism is carried by the linear motor stage guided by the 2.5 m long ceramic beam The error in the linearity of the translation is optically corrected by the pentaprism A fixed reference mirror corrects for any source instabilities The detector is a 1,024 pixels photodiode linear array from Hamamatsu which gives a maximum measurable range of 12 mrad Placed at the focal plane of the lens (800 mm focal lens), the sensor detects a fringe pattern intensity profile resulting from the interference of the two beams coming from the Michelson 10 The Long Trace Profilers 189 Fig 10.6 Optical setup of the ESRF long trace profiler Fig 10.7 ESRF LTP calibration setup interferometer The algorithm used to define its position on the detector is based on a fast Fourier transform calculation The software has been developed using Labview R as programming language and can be easily adapted for specific needs In the standard measurement configuration, the sample under test is reflecting upward but an optical bracket can be added to this setup if the SUT is reflecting downward Measurements are taken “on the fly”; the data are collected while the optical head is smoothly moving above the mirror at a constant speed of 40 mm s−1 The LTP is surrounded by a Plexiglas enclosure which reduces greatly the air turbulence Measurements can be carried out faster, thus repeatability has been improved and is better than 0.05 μrad rms, while the slope accuracy on flat mirrors is better than 0.2 μrad To ensure a reliable measurement, an important issue is the determination of the calibration factor At the ESRF a method based on the well-known wedge angle technique is used; Fig 10.7 shows the setup used for calibration A motor displacement of μm induces a μrad angular deviation The precision achieved is 0.1 μrad The mirror to be characterized may be integrated on a static or bending holder system When no mechanical mounting system is provided, the mirror 190 A Rommeveaux et al Fig 10.8 Left: mirror facing down under LTP measurement – Right: detail of the split retro reflector is lying with its surface facing up on three balls or two cylinders separated by a well-known distance Thus the deformation induced by gravity can be analytically calculated and subtracted from the measurement Gravity can have a strong influence on the slope error profile Nevertheless it is always preferable to measure a mirror as close as possible to its future working conditions on the beamline in terms of mounting and the X-ray beam reflecting direction For mirrors reflecting downward an additional bracket with a split retro reflector is added to on the LTP moving head (Fig 10.8) in order to redirect the beam toward the surface through a roof prism and a right angle prism This combination keeps the number of reflections needed to preserve the pentaprism correction For further details on the characteristics of this instrument, please see [16] References 10 11 K Von Bieren, Proc SPIE, 343, 101 (1982) P.Z Takacs, S.N Qian, J Colbert, Proc SPIE, 749, 59 (1987) P.Z Takacs, S.N Qian, U.S Patent 4,884,697, Dec 1989 S.C Irick, W Mckinney, D.J Lunt, P.Z Takacs, Rev Sci Instrum 63, 1436 (1992) http://www.oceanoptics.com/ G Sostero, A Bianco, M Zangrando, D Cocco, Proc SPIE, 4501, 24 (2001) D Cocco, G Sostero, M Zangrando, Technique for measuring the groove density of diffraction gratings using the long trace profiler, Rev Sci Instrum 74–7, 3544 (2003) S.C Irick, W.R McKinney, AIP Conf Proc 417, 118 (1997) J Lim, S Rah, Rev Sci Ins 75(3), 780 (2004) S Qian, W Jark, P Takacs, Rev Sci Ins 66(3), 2562 (1995) S.N Qian, G Sostero, P.Z Takacs, Opt Eng 39–1, 304 (2000) 10 The Long Trace Profilers 191 12 A Rommeveaux, D Cocco, V Schoenherr, F Siewert, M Thomasset, Proc SPIE, 5921, (2005) 13 http://costp7.free.fr/ 14 M Thomasset, S Brochet, F Polack, Proc SPIE, 5921–2, 2005 15 J Floriot et al., in European Optical Society Annual Meeting, Paris, 2006 16 A Rommeveaux, O Hignette, C Morawe, Proc SPIE, 5921 (2005) 11 The Nanometer Optical Component Measuring Machine F Siewert, H Lammert, and T Zeschke Abstract The Nanometer Optical component measuring Machine (NOM) has been developed at BESSY for inspection of the surface figures of grazing incidence optical components up to 1.2 m in length as in synchrotron radiation beam lines It is possible to acquire information about slope and height deviations and the radius of curvature of a sample in the form of line scans and in a three dimensional display format For plane surfaces the estimated root mean square measuring uncertainty of the NOM is in the range of 0.01arcsec The engineering conception, the design of the NOM and the first measurements are discussed in detail 11.1 Engineering Conception and Design The nanometer optical component measuring machine (NOM) (Fig 11.1) was developed at BESSY for the purpose of measuring the surface figure of optical components up to 1.2 m in length used at grazing incidence in synchrotron radiation beamlines [1–3] With it, it is possible to determine slope and height deviations from an ideal surface and the radius of curvature of a sample in the form of line scans and in a three-dimensional display format With the NOM surfaces, up to 600 cm2 have been measured with an estimated measuring uncertainty in the range of 0.05 μrad rms and with a high reproducibility This is a five- to tenfold improvement over the previous state of the art of surface measuring techniques such as achieved using the Long Trace Profiler (LTPII) [3,4] The NOM is basically a hybrid of two angle measuring sensor units, a Long Trace Profiler (LTP-III) and a modified high resolution autocollimating telescope (ACT) The latter (ACT) has been developed with a very small aperture of about d = mm [1] (Fig 11.2) The measuring principle of both sensors is noncontact deflectometry In both cases, no reference surface is needed The LTP III head is a BESSY-specified development by Ocean Optics Ltd in cooperation with Peter Takacs (BNL) who created the optical design The autocollimator used is a special development by Măller Wedel Optical o GmbH The two sensors are mounted stationary and opposite to each other on a compact stone base (Fig 11.2) [1,3] The two test beams are adjusted in a 194 F Siewert et al Fig 11.1 The nano optic measuring machine NOM at BESSY To insure stable environmental conditions the instrument is enclosed in a double walled housing Fig 11.2 Optical set up of the NOM straight line to each other and are guided by a pentaprism or double reflectors to and from the specimen The influence of the pitch tilt on the measurement is compensated for by the 45◦ -pentaprism design The reflector unit is mounted on a movable air-bearing carriage system on the upper member of the stone frame It consists of two parts: (a) one carriage for the motor, which is linked 11 The Nanometer Optical Component Measuring Machine 195 Fig 11.3 Thermal stability at the BESSY metrology-Laboratory (blue line) and inside the NOM housing (green line) by a torque-free coupling to the second, (b) the main carriage with the open pentaprism A second air-bearing movable Y-table below positions the sample laterally The drive units are linear motors Both a step-by-step and an onthe-fly modus are available for data acquisition To guarantee a maximum of thermal stability, the complete heat load of the NOM is limited to less than W Furthermore, the NOM is enclosed by a thermally stable, double-walled, and thermal-bridge-free housing in a temperature controlled measuring lab The housing also limits the influence of air turbulence on the measurement During measurement a temperature stability of 0.1 mK min−1 is maintained The material of choice for the mechanical part of the NOM is stone (Gabbro) characterized by a sluggish response for thermal change The use of metallic parts among the mechanical parts is avoided as far as possible The weight of the compact stone parts of about 4,000 kg is a simple but very useful technique to damp the influence of vibrations on the measurement over a wide range of frequencies A monitoring system recording the mean environmental data such as temperature, air pressure, humidity, and vibrations, as detected on the measurement table close to the specimen, is part of the established conception of metrology at BESSY The measured temperature stability inside the test housing of the NOM is as low as 15 mK per 24 h (Fig 11.3) 11.2 Technical Parameters The measuring area of the NOM covers 1,200 mm in length and 300 mm laterally The accuracy of guidance of the scanning carriage system is about ±1 μm for a range of motion of 1.3 m A correspondingly high accuracy of guidance is also achieved with the y-positioning carriage over 0.3 m The reproducibility of the scanning-carriage movement is in the range of 0.05 μrad rms This 196 F Siewert et al Table 11.1 Technical parameters of the NOM sensors LTP height [nm] View angle Measurable radius of curvature Spatial resolution Autocollimator ±6.6 mrad 1m ±5 mrad 10 m about mm mm 30 25 20 15 10 0 100 200 300 400 x - position [mm] Fig 11.4 Height profile of the center line of a 510 mm reference mirror (substrate material Zerodur∗ ) Scan length = 480 mm Peak to valley = 26.5 ± 0.6 nm Spatial resolution for this measurement: mm reproducibility, combined with the insensitivity of the 45◦ -double-reflector for pitch, is an essential condition for the excellent measurement uncertainty achieved Table 11.1 shows the parameters of the two optical heads Both offer the possibility to scan plane, spherical, or aspherical surfaces In the case of a surface curvature of 10 m or less the specimen is scanned by the LTP alone 11.3 Measurement Accuracy of the NOM To minimize the measurement uncertainty, possible systematic errors of the measuring device must be determined Systematic errors can be determined by making a cross check using different methods for the measurement This approach has been realized here [7, 8] A plane reference surface of 510 mm in length (substrate material Zerodur∗ ) has been measured using the NOM at BESSY by the PTB (Physikalisch Technische Bundesanstalt) with the extended shear angle difference (ESAD) method [9] and by stitching interferometry at Berliner Glas KG, the manufacturer of the reference The ESAD method is the national reference for flatness in Germany Additionally, two different measuring heads, based on different measuring principles, are an integral part of the NOM itself The influence of random deviations such as mechanical vibration, instabilities caused by thermal effects, electronic noise, changes of the refraction index by thermal change, variation of air pressure, and humidity has been determined by comparing measurement data gained under essentially identical conditions The reproducibility achieved is better than 0.01 μrad rms or 0.5 nm rms in height over a scan length of 480 mm at the center line of the sample (Fig 11.4) 11 The Nanometer Optical Component Measuring Machine 197 Table 11.2 Summary of uncertainty terms for a 480 mm line scan at the NOM on a plane reference surface (substrate material: Zerodur1 ) Error source ACT Air turbulence Beam guiding optics Mechanical instability Other random noise Uncertainty overall uc expanded uncertainty: (k = 2) Zerodur is a trade mark of Schott 0.015 μrad rms 0.015 μrad rms 0.005 μrad rms 0.005 μrad rms 0.010 μrad rms 0.025 μrad rms 0.05 μrad rms Glass Mainz/Germany height [nm] 60 NOM- ACT NOM- LTP 40 20 0 50 100 150 200 x - position [mm] slope [mrad] 3,0 NOM - Autocollimator NOM - LTP 1,0 −1,0 −3,0 40 80 120 x - position [mm] 160 200 Fig 11.5 Slope profile (above) and height profile (below) of NOM-ACT and NOMLTP line scans, step size 0.5 mm on a 200 mm plane mirror The LTP-slope profile is the result of 26 averaged line scans The reproducibility is about 0.12 μrad rms The ACT measurement consists of 14 averaged line scans with a reproducibility of 0.03 μrad rms The estimated measurement uncertainty is 0.25 μrad rms for the LTP and 0.05 μrad rms for the ACT result It is difficult to eliminate all sources of systematic errors However, comparing fundamentally different methods, NOM, ESAD, and interferometry, is a very reliable test The measurement uncertainty determined for the NOM measurement is in the range of 0.05 μrad rms Table 11.2 shows the estimated uncertainty budget for the measurement result Compared with the measurements of the other partners in the round-robin procedure, a 198 F Siewert et al Fourier amplitude [arcsec ] 1,0E-01 NOM -LTP NOM -ACT 1,0E-02 1,0E-03 1,0E-04 1,0E-05 1,0E-06 1,0E-07 0,001 0,01 0,1 spatial frequency [1 / mm] 10 Fig 11.6 Power surface density (PSD) curve of NOM-ACT and NOM-LTP line scans on a 200 mm plane mirror conformity in the range of 0.7 nm rms compared to ESAD and of 1.3 nm rms to the result of the stitching interferometry has been achieved [10] Figures 11.5 and 11.6 show the results of slope measurements on a 200mm-long plane mirror (substrate material: single crystal silicon) by use of the two optical sensor units of the NOM For both measurements a measuring point spacing of dx = 0.5 mm was chosen The conformity of both unfitted results is in the range about 0.3 or 1.1 nm rms The reproducibility of 0.03 μrad rms for the NOM-ACT measurement is about four times better than the reproducibility of 0.12 μrad rms achieved for the NOM-LTP 11.4 Surface Mapping Highly accurate topography measurements of an optical surface are required if optical elements are to be characterized in detail or to be reworked to a more perfect shape Figure 11.7 demonstrates in principle a three-step “union jack” like method to scan the complete surface of a rectangular sample To generate a 3D-data matrix two sets of surface scans, each consisting of a multitude of equidistant parallel sampled line scans, are traced orthogonally to each other in the meridional and in the sagittal direction successively Each single surface line scan is taken on the fly Between two single line scans the sample is moved laterally by the Y -position table The scan velocity selected determines the measuring point spacing of the traced line The lateral step size is defined by selecting the lateral shift between the lines scans in the start menu of the scanning software In a final step the two diagonals have to be measured as two individual line scans After taking the data of the two surface mapping scans, the root mean squares of the height data, obtained by integration of the slope measurements, are minimized and the points of the topography that lie on each of the measured diagonals are selected Using the directly measured diagonal as a reference, the rms values of the difference between these two are obtained In this way, a twisting of the surface, which is recognized and measured in the direct measurement, is superimposed onto the generated diagonal and correspondingly onto the entire array of x- and ydata, yielding the genuine shape of the sample The agreement of the diagonals 400 × 60 × 80 Plane ≈0.7 μrad 310 × 30 × 60 Zerodur none Plane ≈1.1 μrad 290 Dimensions L × W × H (mm3 ) Bulk material Coating Shape Residual slope error rms Scan length 390 Gold Zerodur Elettra BESSY Owner P2 P1 Label 240 ≈1 μrad Spherical R = 83 m Gold Fused silica 270 × 40 × 30 Elettra S1 198 ≈1 μrad Spherical R = 44 m None Zerodur 210 × 40 × 40 BESSY S2 Table 14.1 Characteristics of the mirrors tested 110 ≈0.5 μrad Spherical R = 1,280 m None Silicon 120 × 20 × 50 Soleil S3 14 The COST P7 Round Robin for Slope Measuring Profilers 215 216 A Rommeveaux et al Table 14.2 Measurement parameters and scanning conditions BESSY Instrument Mirror position Number of scans averaged Systematic errors correction Scanning method Scanning velocity ELETTRA ESRF SOLEIL Autocollimator Face up LTP On the side LTP Face up LTP Face up By mirror rotation Not applied On fly over sampling 0.2 mm s−1 10 with mirror tilt By mirror rotation Not applied Point by point Point by point On fly mm s−1 mm s−1 40 mm s−1 Table 14.3 Statistical results obtained for P1 and P2 mirror P1 mirror R (km) Slope error rms (μrad) BESSY ELETTRA ESRF SOLEIL 427 454 136 193 P2 mirror Height error rms (nm) R (km) Slope error rms (μrad) Height error rms (nm) 24 23 24 17 −1,951 753 242 −100 0.88 0.81 0.97 1.64 24 19 28 52 1.16 1.12 1.12 0.88 ELETTRA BESSY SOLEIL ESRF slope error (μrad) −1 −2 −3 50 100 150 200 250 mirror coordinates (mm) Fig 14.1 P1 residual slopes after best sphere subtraction 300 14 The COST P7 Round Robin for Slope Measuring Profilers 217 in the internal optics Table 14.4 shows the statistical results obtained for the three spherical mirrors The values for radius of curvature is in agreement by better than 0.3% The concordance of residual errors is better for S3, which has the shortest length and the longest radius, than for S2 which has the opposite features The rms agreement of the slope errors varies from 0.13 μrad (1.6 nm) for S3 to 0.26 μrad (4.1 nm) for S2 A gain, the residual slope profiles obtained at each facility are in excellent agreement in particular between BESSY, using the autocollimator sensor of the NOM, and LTP at the ESRF (Figs 14.2–14.4) Table 14.4 Statistical results obtained for S1, S2, and S3 spherical mirrors S3 R (m) BESSY Elettra ESRF Soleil 1,280 1,274 1,278 1,272 S1 S2 Slope Height R (m) Slope Height R (m) Slope Height error error error error error error rms rms rms rms rms rms (μrad) (nm) (μrad) (nm) (μrad) (nm) 0.44 0.53 0.40 0.51 3.2 4.6 3.0 2.8 83.01 83.21 83.34 83.11 0.87 1.05 0.99 0.92 11.7 15.4 15 12.7 44.52 44.67 44.76 44.63 1.08 0.86 0.82 1.41 17.4 13.3 13.3 20.3 Reference Mirror S2 Residual slopes (after best sphere subtraction) slope error (mrad) 0 20 40 60 80 100 120 140 160 180 −1 −2 −3 mirror coordinates (mm) Fig 14.2 S3 (R ≈ 1.3 km) residual slopes after best sphere subtraction ELETTRA slope error (μrad) 1.5 BESSY SOLEIL ESRF 0.5 − 0.5 −1 −1.5 20 60 40 mirror coordinates (mm) 80 100 Fig 14.3 S1 (R ≈ 83 m) residual slopes after best sphere subtraction 200 218 A Rommeveaux et al slope error (urad) 0 50 100 150 200 250 −1 −2 −3 −4 mirror coordinates (mm) Fig 14.4 S2 (R ≈ 44 m) residual slopes after best sphere subtraction 14.4 Conclusions The five mirrors involved in this Round-Robin are good representatives of the kinds of SR optical components to be characterized by slope measuring instruments These results are in very good agreement with each other, despite the fact that different instruments have been used, in terms of optical setup, hardware, and environmental conditions Even for the spherical mirrors with a short radius of curvature, which push the measurement accuracy of the instruments to their respective limit, due to the quality of their optical components (mirrors, prisms, lenses), the radii determined agreed better than 0.3% The curves of the residual slopes after best sphere subtraction are quite superimposable These five mirrors cross measured with high consistency can be considered as reference mirrors for instrument calibration The round-robin is going to be continued, including additional facilities and increasing the number of reference mirrors to be tested [2] Acknowledgments The authors wish to thank all their respective colleagues for their help, in particular Sylvain Brochet, Heiner Lammert, Thomas Zeschke, and Giovanni Sostero They are grateful to the mirror owners for lending them during this round-robin References P.Z Takacs, S.N Qian, J Colbert, Proc SPIE 749, 59 (1987) F Siewert et al., in SRI 2006 AIP Conference Proceedings, Mellville, New York, 879, 706 (2007) 15 Hartmann and Shack–Hartmann Wavefront Sensors for Sub-nanometric Metrology P Merc`re, M Idir, J Floriot, and X Levecq e Abstract The recent development of third generation synchrotron radiation facilities has led to unprecedented progresse in X-ray applications such as microscopy and photolithography To optimize performance in such research metrology tools with capabilities in the nanometre and even the sub-nanometre range, in order to characterize the surface figure errors of the optics used to focus or collimate the Xray beams, to align them on the beam lines and to perform diagnostics of the beam spatial profile To answer these needs, Synchrotron Soleil and Imagine Optic have developed in partnership a Shack-Hartmann long trace profiler (SH-LTP) which performs the bidimensional surface figure measurement of X-ray mirrors with nanometer precision and an increased dynamic range compared to earlier instruments The SH-LTP offers a more complete diagnostic for highly curved surfaces compared to standard LTPs This partnership has also led to the development of X-ray Hartmann wavefront sensors to measure and control the spatial quality of X-ray beams Compared to interferometric tools, these sensors have better flexibility and can be integrated into closed-loop adaptive optical systems 15.1 Introduction Recent evolution of X-ray sources has opened a large field of research and applications in this spectral range As in the visible range, one can distinguish two main centers of interest: high resolution X-ray imaging on the one hand, and improvement of the spatial quality of collimated X-ray beams on the other hand Applications are, for example, EUV photolithography, X-ray microscopy, tomography, phase contrast imaging, or material probing With the development of such applications, an increasing need of optical components with better surface figures has appeared Today, optical shape requirements in terms of slope errors are typically in the microradian and sub-microradian ranges For the characterization of such high-quality components, the long trace profiler (LTP), used in mostly all synchrotron radiation facilities, has become the state-of-the-art off-line metrology tool However, this instrument presents some drawbacks: 1D measurement, limited dynamic 220 P Merc`re et al e range (small radii of curvature below m cannot be measured), and poor flexibility To overcome these drawbacks, a stitching Shack–Hartmann long trace profiler (SH-LTP) has been developed Resulting from a joint collaboration between Imagine Optic and SOLEIL, this new technology fulfils all the new requirements of an enhanced metrology Bidimensional sub-nanometric characterization of optical surfaces, high precision, high sensitivity, and large dynamic are among the main advantages of the SH-LTP First section of this chapter will be devoted to a description of this new instrument and the latest results obtained at the Optical Metrology Laboratory of SOLEIL will be presented Although off-line characterization of optical components is important (to know exactly if an optic is suitable for the requirements of one’s application, or to know exactly what one is putting on the beamline), it cannot replace “at wavelength” metrology A fact is that “at wavelength” metrology is increasingly required on EUV and X-ray beamlines, not only for in situ characterization of individual optics or optical systems, but also for their precise alignment with respect to the beam Many kinds of wavefront sensors, mostly based on interferometry, have been developed so far Up to now, the phase-shifting point diffraction interferometer (PSPDI) and the shearing interferometer (SI) are among the most effective interferometric tools The PSPDI benefits from a very high precision (