X-ray mirror metrology using SCOTS/deflectometry Run Huang a, Peng Su a*, James H. Burge a and Mourad Idir b a College of Optical Sciences, the University of Arizona, Tucson, AZ 85721, U.S.A. b Brookhaven National Laboratory NSLS II 50 Rutherford Dr. Upton, NY 11973-5000 USA ABSTRACT SCOTS is a high precision slope measurement technology based on deflectometry. Light pattern on a LCD display illuminates the test surface and its reflected image is used to calculate the surface slope. SCOTS provides a high dynamic range full field measurement of the optics without null optics required. We report SCOTS tests on X-ray mirrors to nm and even sub nm level with precise calibration of the test system. A LCD screen with dots/check board pattern was aligned into the system at the test mirror position to calibrate camera imaging distortion in-situ. System errors were further eliminated by testing and subtracting a reference flat which was also aligned at the same position as the test mirror. A virtual reference based on the ideal shape of the test surface was calculated and subtracted from the test raw data. This makes the test a virtual null test. Two X-ray mirrors were tested with SCOTS. 0.1µrad (rms) slope precision and sub nm (rms) surface accuracy were achieved. Keywords: X-ray optics, Optical metrology, 1. INTRODUCTION Transporting lights at X-ray, soft X-ray and EUV wavelengths from synchrotron sources to sample station while preserving high brightness and diffraction limited focus requires high precision optics in transporting beamline. Manufacturing of those high precision focusing optics in X-ray is a challenging task since fabrication process needs accurate metrology feedback to control the polishing program [1]. Thus, the improvement of the fabrication must be accompanied by the improvement of the metrology, as the measurement accuracy determines the final figure accuracy of the fabricated mirror. In the field of optical metrology, there are many metrology technologies and tools developed with different pros and cons. Interferometers typically have sub wavelength accuracy but they require specially designed null optics when the test optics is not spherical. Slope measurement technologies like long trace profiler (LTP) use deflectrometry method to inspect the reflective optical surfaces without null lens or computer generate holograms (CGH). Some of these instruments have reported 0.05 µrad slope accuracy [2,3]. However, LTP only measures a single line profile at a time and scanning mechanism is needed to obtain full field measurement of the test optics. The University of Arizona developed a Software Configurable Optical Test System (SCOTS) [4] which is also based on reflection deflectrometry, different from LTP, SCOTS provides a full field measurement with no stitching or scanning. This technology has been successfully applied to many astronomy large telescopes and right now it is being pushed to higher accuracy of nm and even sub nm surface rms. In this paper, we present our recent SCOTS test results on the metrology of two high precision X-ray mirrors. Careful calibrations of the system were implemented. Accurate measurements on these two X-ray mirrors, where one is a spherical mirror and the other is an off-axis elliptical mirror, prove the capability of SCOTS to measure spherical, aspherical and even freeform optics with comparable results with interferometry and LTP. The paper is organized as follows. We first describe the principle of SCOTS and the Zemax model we used in our measurement, and in section 3, we give a detailed discussion about the SCOTS setup and calibrations for the measurements of the two X-ray mirrors and give the test results. Summary is given in section 4. 2. PRINCIPAL SCOTS is a deflectometry method to measure the surface slope by triangulations. Fig. 1(a) is the schematic setup of a SCOTS test. The SCOTS test can be treated as a Hartmann test with the light path in reverse. The point source in Advances in X-Ray/EUV Optics and Components VIII, edited by Ali Khounsary, Shunji Goto, Christian Morawe, Proc. of SPIE Vol. 8848, 88480G 2013 SPIE CCC code: 0277-786X/13/$18 doi: 10.1117/12.2024500 Proc. of SPIE Vol. 8848 88480G-1
Hartmann test is replaced by a pinhole camera looking at the test mirror. The Hartmann plate on the mirror aperture is removed and the detector in Hartmann test is replaced by a LCD screen sending the light backwards. In SCOTS, both the camera and LCD screen are set up near the center of curvature of the test mirror. If we light up certain pixel on the LCD screen to illuminate the test mirror, on the detector image plane where the mirror image is formed there will be a corresponding bright region. The illuminating screen pixel, reflection region on the mirror and camera aperture center uniquely define an incident ray and its reflected ray. The local surface slope (Wx, Wy) of test optics can then be calculated by equation (1): (a) (b) surface under test camera aperture Image plane Point source(camera) \ Test mirror 1 illumination screen 1\ Image plane (illumination screen) Fig. 1. (a) Schematic setup of a SCOTS test. (b) Reversed model of the SCOTS test in Zemax xm xscreen xm xcamera dm2screen dm2camera wx( xm, ym) = z w x y z w x y dm2screen dm2camera ym yscreen ym ycamera dm2screen dm2camera wx( xm, ym) = z w x y z w x y d d (, ) (, ) m2screen m m m2camera m m (, ) (, ) m2screen m m m2camera m m m2screen m2camera Where x m and y m are the coordinates of the mirror surface, x screen and y screen are the coordinates of the LCD screen pixel that illuminate the corresponding mirror surface x m and y m. x camera and y camera are the coordinates of the camera aperture center. d m2screen and d m2camera are the distances from mirror pixel to illuminating screen pixel and camera aperture respectively. z m2screen and z m2camera are the z direction (starts from mirror vertex) distances from mirror to illuminating screen pixel and camera aperture respectively. Further integration of the slope will give the surface shape of the test optics. Instead of using the complete triangulation equation, eq.(1), to calculate the absolute local surface slope and sag of the test optics, we calculate the surface departure of the test optics from its ideal shape directly. We achieve this by comparing the experiment raw data with a virtual SCOTS test result from Zemax, where the testing surface is assumed to have its ideal shape. The Zemax model is shown in Fig 1(b). The camera position, screen position and mirror position in the model are very well matched with real measurement geometry which are precisely measured and calibrated with Laser tracker to hundred-µm accuracy. Since we calculate the surface departure, the test model can be simplified as a comparison between the ideal transverse ray aberration from Zemax and the measured transverse ray. The transverse ray aberration can be transferred to system wavefront aberration with Eq. (2). (1) W( x, y) xscreen W( x, y) y, x d y d screen m2screen m2screen (2) Proc. of SPIE Vol. 8848 88480G-2
Where W(x,y) is the wavefront aberration, x and y are the exit pupil coordinates of the system. d m2screen is the measured mirror-to-screen distance. Different methods such as line-scanning and phase shifting sinusoidal fringes have been applied on SCOTS to calculate the screen coordinate x screen and y screen. A detailed comparison of line scanning and phase shifting methods can be found in [4]. 3. SCOTS TEST ON X-RAY OPTICS 3.1 Test setup Two X-ray mirrors were measured with SCOTS. One of the mirrors is spherical with 54.29 meter radius of curvature. The second one is an off-axis elliptical mirror with around 260 meter local radius of curvature. Both mirrors are about 100 mm long and 40-50 mm wide. The two tests shared very similar test geometry as shown in Fig. 2 (a). A 19 LCD screen was chosen to give enough illumination area for the mirrors. The screen was set up around 2.6 meter away from the mirror and generated sinusoidal fringe patterns in x and y directions to illuminate the mirror. A 1/3 CCD and a commercial camera lens of 50mm focal length with /- 2 FOV were set next to the LCD screen to capture the reflected fringe pattern. The reflected pattern was shown in Fig.3. Phase shifting algorithm was used to calculate the phase map to register the mirror pixel and screen pixel. The camera perspective and distortion was calibrated in-situ by putting a mini LCD screen with dots pattern at the test mirror position, as shown in Fig 2 (b) and using a set of orthogonal vector polynomial [5,6] to fit the mapping coefficients between the centroid dots position and ideal dots position. camera Fig 2. (a) System setup for the SCOTS test. (b) Camera perspective and distortion calibration with a calibration screen displaying dots pattern Fig.3. Fringe pattern reflected from test mirror. 11111111111111 distortion calibration screen i. Proc. of SPIE Vol. 8848 88480G-3
(a) Spherical mirror: rms = 8.0nm 25 (b) Elliptical mirror: rms = 1.2 nm 2 dorm lib o -25 F ri. Fig. 4 (a) surface departure( power and astigmatism removed) of the spherical mirror. rms = 8.0nm (b) Surface departure (power removed) of the elliptical mirror. rms = 1.2 nm 4 o 3.2 Calibration of camera inherent error Many previous measurements show that inherent imaging aberration from the camera lens affects the test results as a function of camera field of view. In the test, the calibration of camera lens aberration is done by measuring a 4 interferometry reference flat, as shown in Fig. 5(a) [7]. The interferometric test of the reference flat shows a peakvalley of 20nm power, 40nm astigmatism and 2nm rms other surface errors. After taking a measurement of the test mirrors, the reference flat was inserted into the test mirrors position with precise alignment control. e.g., when measuring the elliptical mirror, the reference flat position was controlled by using a laser displacement sensor from Keyence with 1um distance measurement accuracy and centroid of a return alignment laser beam with 10urad tip/tilt accuracy. Fig. 5(b) is the raw fringe pattern reflected from the flat. (a) Fig. 5 (a) Interferometry reference flat used in SCOTS system calibration (b) Fringe pattern reflected from the flat under the area of X-ray mirror With the reference flat calibration, the measured surface departure of the spherical mirror is shown in Fig. 6(a) and the surface departure of elliptical mirror is shown in Fig 6(b). The manufacturer s report indicates the spherical mirror has 3.4nm rms surface error after removing best fit sphere, and SCOTS measured 4.0 nm rms surface error. The elliptical mirror has less than 1 nm rms surface error and SOCTS measured 0.74nm rms. (a) Spherical mirror: rms = 4.0nm 25 (b) Elliptical mirror: rms = 0.74nm 0-25 Fig. 6 (a) surface departure( power and astigmatism removed) of the spherical mirror with reference flat calibration applied. rms = 4.0nm (b) Surface departure (power removed) of elliptical mirror with reference flat calibration applied. rms = 0.74nm Proc. of SPIE Vol. 8848 88480G-4
10 8 6 Center Profile SCOTS LTP 4 Height(nm) 2 0-2 -4-6 -8-10 -50-40 -30-20 -10 0 10 20 30 40 50 Position on the mirror (mm) Fig 7. Center line profiles of the spherical X-ray mirror from the SCOTS and LTP measurement. Fig. 7 shows the comparison of the center line profile of the spherical mirror from SCOTS and manufacture s LTP measurement [7]. The test results from these two methods have great agreement. The difference between the two test methods can come from the following sources: 1) uncertainty from both test methods; 2) registration uncertainty between the SCOTS map and the LTP profile; 3) quality of the calibration reference flat; 4) SCOTS system stability. It is worth noticing that surface error from the reference flat was not separated from the final surface maps of the two X- ray mirror as shown in Fig. 6(a) and (b). The quality of the reference flat limits the accuracy of the test. Translation test of the reference flat is a possible solution to separate the inherent surface error from the reference flat and further increase the test accuracy. 3.3 Precision test 0.1µrad slope precison was achieved with our SCOTS system by testing the 4 interferometer reference flat and comparing the slope difference from two separate tests. Each test was averaged with 800 single measurments. The rms error of the slope difference is 0.13µrad in both x and y directions. Integration of these slope errors showed 0.35nm rms surface error which was dominated by low order aberration, astigmatism. We are currently investigating this problem to increase the stability of the test system for higher accuracy measurements. SUMMARY In comparison with metrology commonly used for X-ray optics such as sub-aperture stitching interferometry and long trace profilometer (LTP), SCOTS provides a full-field measurement solution and with comparable precision. SCOTS test can also easily accommodate to measure much steeper aspheric or free-form surfaces owing the advantage of high dynamic test range. Calibrations of SCOTS system, i.e. camera perspective, camera aberration are important and can help to increase the test accuracy to nm and even sub nm. When the testing optics has equivalent or higher surface quality to the calibration reference, it is necessary to separate the surface error from the reference to get higher accuracy. REFERENCES [1] Mourad Idir, Konstantine Kaznatcheev,Shinan Qian, and Ray Conley. Current status of the NSLS-II optical metrology laboratory Nucl.Instrum.Methods Phys.Rev.A 710,17-23(2013) [2] F. Siewert, J. Buchheim, Sébastien Boutet, Garth J. Williams, Paul A. Montanez, Jacek Krzywinski, and Riccardo Signorato, Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry, Opt. Exp., 20, 4525-4536 (2012) Proc. of SPIE Vol. 8848 88480G-5
[3] Y.Senba, H.Kishimoto, H.Ohashi, H.Yumoto, T.Zeschke, F.Siewert, S.Goto, T.Ishikawa, Upgrade of long trace profiler for characterization of high-precision X-ray mirrors at SPring-8, Nucl.Instr. and Meth. A 616,237-240 (2010). [4] Peng Su, Robert E. Parks, Lirong Wang, Roger P. Angel, and James H. Burge, Software configurable optical test system: a computerized reverse Hartmann test, Applied Optics, Vol.49, Issue 23, pp.4404-4412 (2010). [5] C. Zhao, and J. H. Burge, Orthonormal vector polynomials in a unit circle, Part I: basis set derived from gradients of Zernike polynomials, Opt. Exp., 15(26), 18014-18024 (2007). [6] C. Zhao, and J. H. Burge, Orthonormal vector polynomials in a unit circle, Part II: completing the basis set, Opt. Exp., 16(9), 6586-6590 (2008). [7] Peng Su, Yuhao Wang, James H. Burge, Mourad Idir, Konstantine Kaznatcheev, Non-null full field X-ray mirror metrology using SCOTS: A reflection deflectometry approach, Opt. Exp. 20, 12393-12407. (2012). Proc. of SPIE Vol. 8848 88480G-6