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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 3 — Feb. 10, 2014
  • pp: 2770–2781
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A 2 D high accuracy slope measuring system based on a Stitching Shack Hartmann Optical Head

Mourad Idir, Konstantine Kaznatcheev, Guillaume Dovillaire, Jerome Legrand, and Rakchanok Rungsawang  »View Author Affiliations


Optics Express, Vol. 22, Issue 3, pp. 2770-2781 (2014)
http://dx.doi.org/10.1364/OE.22.002770


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Abstract

We present a 2D Slope measuring System based on a Stitching Shack Hartmann Optical Head (SSH-OH) aiming to perform high accuracy optical metrology for X-ray mirrors. This system was developed to perform high-accuracy automated metrology for extremely high quality optical components needed for synchrotrons or Free Electrons Lasers (FEL), EUV lithography and x-ray astronomy with slope error accuracy better than 50 nrad rms.

© 2014 Optical Society of America

1. Introduction

Today, manufacturing techniques allow for figuring arbitrary optical surfaces. The form of these elements can be corrected at the nanometer level by computer controlled polishing or deterministic polishing processes (like ion beam figuring or Elastic Emission Machining for example) but the accuracy of absolute form metrology limits the possibilities of the manufacture of modern optical elements. This makes new metrology developments necessary. The actual state-of-the-art optical instruments available in optical metrology laboratory do not have adequate sensitivity for highly curved mirror and do not cover a wide range of spatial frequencies to provide the manufacturer with useful information necessary to feedback the polishing process to improve the quality of the optical component. Metrology plays a critical role in modern figuring because computer-controlled figuring is performed using the measured surface profiles. Thus, the key point for fabricating elliptically curved surfaces is the improvement of the metrology, as the measurement accuracy determines the final figure accuracy of the fabricated mirror.

Over the last decade, X-ray mirrors have evolved rapidly accelerated by the intense use of extremely brilliant 3rd generation synchrotron and Free Electrons Laser (FEL) radiation sources. These X-ray mirrors, planes or off axis ellipses with lengths of up to 1 m, must preserve the incoming wavefront are characterized by residual slope errors in the range of 50 nrad rms and values of 0.3 nm rms or less for micro-roughness [1

1. H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, K. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of x-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013). [CrossRef]

5

5. H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009). [CrossRef]

].

2. Description and principle of the SSHOH optical head

2.1 Generalities and principle of Shack–Hartmann Wavefront Sensors (SHWS)

The basic measurement principle of a Hartmann test from the early 1900s [6

6. J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenkunde 24, 1–21 (1904).

] is quite simple: in this test, a mask with holes was placed in front of the lens to be tested. Light passing through the holes was examined at two planes, typically before and after the focal plane. By examining the shift in position of the rays compared to that of an ideal lens, the aberrations, wavefront map, and other parameters could be determined. In the late 1960s, Roland Shack proposed first shifting the measurement plane to the pupil plane and then using of a grid of lenslets to sample larger areas, while still providing measurements over a localized area [7

7. R. V. Shack, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

]. A (Shack-) Hartmann sensor divides up the incoming beam into sub-beams, dividing up the wavefront into separate beamlets, each focused by pinholes (microlens) onto a sub array of CCD camera pixels. These sensors are based, not on interferometry, but on geometric properties of light that allow robust determination of the wavefront slope. Depending upon where the focal spot from each facet strikes its sub array of pixels, it is then possible to determine the local wavefront inclination (or tilt). Subsequent analysis of all beamlets together leads to determination of the overall wavefront form. The positions of the individual spot centroids are then measured and compared with reference positions. This enables the local slopes of the wavefront (i.e., its derivative) to be measured at a large number of points within the beam. Critical aspects of sensor design include having sufficient resolution over the whole wavefront for the application in mind and simultaneously providing enough CCD pixels per beamlet to accurately determine the spot “center of mass” and the local inclination of the wavefront. Once these resolution issues have been decided, the overall range of measurable wavefront distortion is then a question of balancing sensor geometry against diffraction issues. Any predetermined wavefront later modified by reflection or transmission can then be analyzed and the information used to determine the surface shape or the transmissive optical quality, respectively, of the optical component responsible for the wavefront change. More details on SHWS can be found in the following literature [8

8. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001). [PubMed]

, 9

9. D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 361–397.

].

2.2 Description of the Stitching Shack Hartmann Optical Head (SSH-OH)

The characterization of optical surfaces in generally done with interferometers. They can perform precise measurements for a large range of radii of curvature but they need reference surfaces or holograms to produce ultra-stable and high-quality reference wavefronts so they are limited in dynamic range. For the characterization of high-quality x-ray mirrors, the long trace profiler (LTP) [10

10. S. N. Qian and P. Z. Takacs, “Nano-accuracy surface figure metrology of precision optics,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), pp. 77–114.

16

16. P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y (2009). [CrossRef]

] or the NOM [17

17. F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods A 616(2–3), 119–127 (2010). [CrossRef]

19

19. L. Assoufid, N. Brown, D. Crews, J. Sullivan, M. Erdmann, J. Qian, P. Jemian, V. V. Yashchuk, P. Z. Takacs, N. A. Artemiev, D. J. Merthe, W. R. McKinney, F. Siewert, and T. Zeschke, “Development of a high-performance gantry system for a new generation of optical slope measuring profilers,” Nucl. Instrum. Methods A 710, 31–36 (2013). [CrossRef]

], used in most of the synchrotron radiation facilities, has become the state-of-the-art off-line metrology tool. However, these instruments present some drawbacks: 1D measurement (slope along one single direction and only on a profile), some 2D tests have been reported but with very long measuring time [20

20. F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” in AIP Conference Proceedings (American Institute of Physics, 2004), pp. 847–850.

, 21

21. F. Siewert, H. Lammert, T. Noll, T. Schlegel, T. Zeschke, T. Hänsel, A. Nickel, A. Schindler, B. Grubert, and C. Schlewitt, “Advanced metrology: an essential support fort the surface finishing of high performance x-ray optics,” Proc. SPIE 5921, 592101 (2005). [CrossRef]

], limited dynamic range and relatively slow measurement time.

The NSLSII SSH-OH provides a measurement of the slope profile of the surface under test by scanning a High accuracy Shack Hartman wavefront sensor (SHWS) along the mirror surface. At each point of the mirror, the SHWS measures the 2D local deflection of the beam: both mirror shape derivatives (X and Y) are measured simultaneously. These slopes are measured on each microlens hence the 2D derivatives maps are obtained. The mirror topography is then obtained by integration. The first idea to use a SHWS to characterize x-ray mirror was proposed by Imagine Optic [22] and SOLEIL synchrotron [23

23. J. Floriot, X. Levecq, S. Bucourt, M. Thomasset, F. Polack, M. Idir, P. Mercère, T. Moreno, and S. Brochet, “A Shack-Hartmann measuring head for the two-dimensional characterization of X-ray mirrors,” J. Synchrotron Radiat. 15(2), 134–139 (2008). [CrossRef] [PubMed]

, 24

24. J. Floriot, X. Levecq, S. Bucourt, M. Thomasset, F. Polack, M. Idir, P. Mercère, S. Brochet, and T. Moreno, “Surface metrology with a stitching Shack-Hartmann profilometric head,” Proc. SPIE 6616, 66162A (2007). [CrossRef]

].

The innovative metrology technology proposed here consists of three main improved key components:

  • The first one is a Shack Hartmann wavefront sensor as optical head with very high precision (more than lambda/1500), sensibility, repeatability and large dynamics range.
  • The second component is a high precision positioning system for scanning/positioning large and heavy surfaces. The SHWS optical head is mounted on the translation stage to perform bidimensional mappings by stitching together successive sub-aperture acquisitions.
  • The third component is a robust metrology software for accurate reconstruction of large surfaces, correction of residual imperfections of the motion platform, as well as analyzing and treating the collected data.

The innovative approach of this project is to combine those described three main elements in order to construct a stand-alone non-contact optical large surface metrology system with the following properties: (see Table 1

Table 1. Performances for the new Stitching Shack Hartmann Optical Head.

table-icon
View This Table
)

The minimum mirror radius of 1.2 m is determined by considering the slope measurement accuracy of the Shack-Hartmann wavefront sensor. In order to keep the high accuracy, the focal spots on the CCD camera must not be too close otherwise the slope calculation is not accurate. The smallest distance between adjacent spots that still gives the precision more than lambda/1500 was used to estimate the dynamic range of SSH-OH. A radius of curvature less than 1.2m will create a very strong converging beam onto the Shack-Hartmann. The curvature will be large enough at the scale of a single microlens to create a defocus image on the CCD. The spots on the CCD will then not be a (Sinc2) as expected but defocused. On such spot shapes, the centroid calculation will not be accurate anymore.

In general, space and X/EUV optics have dimensions much larger than the dimensions of the entrance pupil of the profilometric head used to perform the measurement. Obtaining a complete surface mapping requires translation stages to shift the surface under test or the profilometric head. For the characterization of long mirrors and/or improvement of the spatial resolution, a stitching process has to be applied. Well known using interferometer [25

25. J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003). [CrossRef]

27

27. J. H. Burge and C. Zhao, “Applications of subaperture stitching interferometry for very large mirrors,” Proc. SPIE 8450, 84500X (2013).

], it consists in the overlapping of adjacent surface measurements by translation of the optical head or of the mirror under test. Redundancy of the information is used to subtract all systematic errors including measurement errors induced by the imperfections of the translation stage. In our case, the slope measurements in the overlap regions are used in a linear squares fitting routine to determine the relative tilts between frames of data. These relative tilts are then used to correct the data and to construct a stitched gradient map for the mirror under test (MUT). Once the map of the surface gradient is reconstructed, the surface itself is reconstructed using a wavefront reconstructor algorithm such as that described by Southwell [28

28. W. H. Southwell, “Wave front estimation from wave front slope measurements,” J. Opt. Soc. Am. 70(8), 998–1006 (1980). [CrossRef]

].

In our system, the wavefront sensor was designed based on the need for high spatial resolution, but also high accuracy. A summary of the optical head parameters is given in Table 1. The source is a 405 nm diode laser, pigtail coupled to a single mode fiber. This light is collimated and then injected into the optical path through a beam splitter cube. A relay beam expander is used so that the lenslet array is in conjugation to the test optic (Fig. 1
Fig. 1 SSH-OH principle (top) – Actual system at NSLS II (bottom). A 45° mirror can be easily added to change the measurement configuration from vertical to horizontal geometry (top image).
). The dimension of the optical head is L = 545 mm x W = 280 mm x h = 122 mm. Its weight is about 7 kg.

The basic principle of the SSH-OH is roughly the same as for a conventional Long Trace Profile (LTP) or a NOM. However, the analysis pupil size of the sensor is 18 × 13.2 mm2, with a spatial resolution of 1.2 mm (size of the microlenses) and at each point the local slopes are measured in both directions X and Y. These slopes maps are the two derivatives of the mirror surface height. We have then redundancy that can be used to reduce the measurement noise and systematic errors. Moreover, the 2D integration is less noisy than 1D integration as several paths can be considered to calculate the mirror height by integration of the slope maps.

The measuring area of the NSLSII/SSH-OH covers 1,500 mm in length and 300 mm laterally thanks to a 5.5 T granite two axis gantry design by Q-SYS [29]. The accuracy of guidance of the scanning carriage system is about ± 1 μm for a range of motion of 1.5 m. The optics platform can carry a 200 kg load and the optical head motion system is able to accommodate several different optical head with a total load of more than 30 kg (Fig. 2
Fig. 2 NSLS II SSH-OH installed in the optical Metrology Laboratory. (Horizontal geometry).
).

From Fig. 1 (top), the deflecting mirror (bottom part of the picture) allows the SSH-OH to work both for Horizontal and Vertical geometry in order to test the x-ray mirror in the beamline working condition. The change from Horizontal to Vertical testing mirror geometry can be done in less than 1 minute.

In order to provide stable measurement conditions, the whole system is contained in a thermally isolated enclosure. The temperature in the enclosure is not actively stabilized, and it relies simply on the huge heat capacity of the granite bench and the very small power dissipation inside it. The enclosure itself is installed in the class 10,000 clean room of the Optics Laboratory of NSLSII, which is stabilized in temperature within 0.1 °C by the air conditioning system [30

30. M. Idir, K. Kaznatcheev, S. Qian, and R. Conley, “Current status of the NSLS-II optical metrology laboratory,” Nucl. Instrum. Methods Phys. Res. A 710, 17–23 (2013). [CrossRef]

]. Figure 3
Fig. 3 NSLS II Optical Metrology Laboratory Thermal stability.
shows a record of the temperature inside the enclosure over more than 12 hours.

3. Application of the SSH-OH to x-ray mirror metrology

To demonstrate the capabilities of the SSH-OH, we characterized x-ray mirrors with flat, spherical and elliptical shape.

Figure 4
Fig. 4 Spherical mirror measured with the SSS-OH. 2D Map and 1 D lines of Residual slope error of the mirror (power removed).
represents the 2D slope map of a spherical mirror (R ~140 m, L = 250 mm). After best fit removed (radius of 140 m) and comparing the 10 scans measured during the test, a repeatability of 50 nrad rms have been achieved. Figure 4 (top) represents the 2D slope map obtain with the SSH-OH. If we extract a 1D profile from this 2D map for example following A and B lines in Fig. 4, it is clear that the 1 D result will be different (Fig. 4, bottom). This illustrates the importance to have a 2D map of the mirror under test instead of a single line.

Figure 5
Fig. 5 Systematic error estimation (Plane ellipse from JTEC). Same elliptical mirror measured at different angles from 0 to 1 mrad.
represents the measurements done on an elliptical mirror with an inspected aperture length of 100 mm. The local radii of curvature is varying from R = 250 m down to R = 150 m. To have an idea on the systematic error of the instrument, four measurements were taken at different angle between the optical head and the mirror surface from 0 to 1 mrad in horizontal geometry. The rms variation of these four different measurements is around 20 nrad proving the very high repeatability of our instrument. With the best polynomial fit removed, this ellipse is at 54 nrad rms slope error (JTEC Fabrication [31]).

The SSH-OH is also used to measure very large optical component. Figure 6
Fig. 6 1.4 m silicon bendable mirror developed by WinlightX/ France for the NSLS II XPD beamline under the SSH-OH in the NSLS II Optical Laboratory (vertical geometry).
shows a 1.4 m silicon bendable mirror developed by WinlightX/ France for the NSLS II XPD beamline.

Figure 7
Fig. 7 Top part 2D map obtain for R = 16 kms with the SSH-OH. Bottom part 1D residual slope error (best sphere removed) (average of all lines from the 2D map).
(top) is a 2D slope map obtain for a radis of curvature of R = 16 kms. A single line (average of the 2D map in one direction) with the best radius removed is shown in Fig. 7 (bottom part). The scanning time to get the 2D map (forward + backward measurements) is less than 2 hours for a length of 1200 mm (the number of measured points in this 2D map is 11 x 1200 points).

Figure 8
Fig. 8 Measurements for different radius of curvature from flat to 15 km made in order to calibrate the bender using the SSH-OH.
shows several measurements made on this mirror for different radius of curvature from flat (0 steps: curve green) to R~9.2 km (135000 steps: black curve).

Using these measurements, we can determine the calibration curve (curvature versus actuator motion) of this bendable mirror (Fig. 9
Fig. 9 Variation of the curvature (1/R) versus the actuators motion.
).

In Fig. 10
Fig. 10 AB and BA measurement on a flat mirror.
, the measurement of a 100 mm long silicon flat mirror was done in forward direction (from edge A to edge B) and after 180° rotation and re alignment in reverse direction (from edge B to A). From the results in Fig. 10 (top), the agreement of both measurements is excellent. In Fig. 10 (bottom), the difference between AB and BA measurements is in the range of 34 nrad rms which is close to the noise level of our instrument. This slope error translates after integration to 0.3 nm rms height difference between both scans. This result can be taken as indication for the achieved measurement accuracy in terms of slope and height measurement.

5. Conclusions

The NSLSII SSH-OH, the last generation deflectometric instrument, is operational and fully characterized at the Laboratory of Optics and Metrology of NSLS II. The SSH-OH makes possible precise noncontact bidimensional measurement of the surface slope and it is proven to be capable of reaching accuracies limited to a few tens of nanoradians. At a conventional working wavelength (λ = 405 nm), high accuracy (below 50 nrad), high repeatability (below 50 nrad), high dynamic, high-spatial resolution and insensitivity to vibrations are among the main advantages of this new instrument. Radii of curvature down to 1.2 m can be measured with 0.1% accuracy, and large optics can be measured with sub-microradian performances thanks to the stitching approach.

In this paper, we have shown the successful applications of the SSH-OH to rapidly and robustly measure the profile of an X-ray reflective optics. This new, simple, non-contact measurement system offers the characteristics desired for a high-end, single-piece, freeform optics metrology tool. Future calibrations and development of the control and data-processing software will certainly further improve the potential performances of this instrument.

Acknowledgments

The authors would like to thanks WinlightX/France, JTEC corporation/Japan, Q-SYS/Netherlands and all colleagues from Imagine Optic/France and NSLSII for useful discussions and contributions to this project. This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy sciences, under contract No. DE-AC-02-98CH10886.

References and links

1.

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, K. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of x-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013). [CrossRef]

2.

F. Siewert, J. Buchheim, S. Boutet, G. J. Williams, P. A. Montanez, J. Krzywinski, and R. Signorato, “Ultra-precise characterization of LCLS hard X-ray focusing mirrors by high resolution slope measuring deflectometry,” Opt. Express 20(4), 4525–4536 (2012). [CrossRef] [PubMed]

3.

S. Matsuyama, T. Wakioka, N. Kidani, T. Kimura, H. Mimura, Y. Sano, Y. Nishino, M. Yabashi, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “One-dimensional Wolter optics with a sub-50 nm spatial resolution,” Opt. Lett. 35(21), 3583–3585 (2010). [CrossRef] [PubMed]

4.

H. Mimura, H. Yumoto, S. Matsuyama, Y. Sano, K. Yamamura, Y. Mori, M. Yabashi, Y. Nishino, K. Tamasaku, T. Ishikawa, and K. Yamauchi, “Efficient focusing of hard x rays to 25 nm by a total reflection mirror,” Appl. Phys. Lett. 90(5), 051903 (2007). [CrossRef]

5.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2009). [CrossRef]

6.

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenkunde 24, 1–21 (1904).

7.

R. V. Shack, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

8.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001). [PubMed]

9.

D. Malacara-Doblado and I. Ghozeil, “Hartmann, Hartmann-Shack, and other screen tests,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 361–397.

10.

S. N. Qian and P. Z. Takacs, “Nano-accuracy surface figure metrology of precision optics,” in Modern Metrology Concerns, L. Cocco, ed. (InTech, 2012), pp. 77–114.

11.

S. N. Qian and P. Z. Takacs, “Design of multiple-function long trace profiler,” Opt. Eng. 46(4), 043602 (2007).

12.

M. Thomasset, S. Brochet, and F. Polack, “Latest metrology results with the SOLEIL synchrotron LTP,” Proc. SPIE 5921, 592102 (2005). [CrossRef]

13.

P. Z. Takacs, S. N. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 749, 59–64 (1987). [CrossRef]

14.

S. N. Qian, W. Jark, and P. Z. Takacs, “The penta-prism LTP: A long-trace-profiler with stationary optical head and moving penta prism,” Rev. Sci. Instrum. 66(3), 2562–2569 (1995). [CrossRef]

15.

P. Su, J. H. Burge, B. Cuerden, J. Sasian, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics,” Proc. SPIE 7018, 70183T (2008). [CrossRef]

16.

P. Su, J. H. Burge, B. Cuerden, R. Allen, and H. M. Martin, “Scanning pentaprism measurements of off-axis aspherics II,” Proc. SPIE 7426, 74260Y (2009). [CrossRef]

17.

F. Siewert, J. Buchheim, and T. Zeschke, “Characterization and calibration of 2nd generation slope measuring profiler,” Nucl. Instrum. Methods A 616(2–3), 119–127 (2010). [CrossRef]

18.

S. G. Alcock, K. J. S. Sawhney, S. Scott, U. Pedersen, R. Walton, F. Siewert, T. Zeschke, F. Senf, T. Noll, and H. Lammert, “The Diamond-NOM: A non-contact profiler capable of characterizing optical figure error with sub-nanometre repeatability,” Nucl. Instrum. Methods A 616(2-3), 224–228 (2010). [CrossRef]

19.

L. Assoufid, N. Brown, D. Crews, J. Sullivan, M. Erdmann, J. Qian, P. Jemian, V. V. Yashchuk, P. Z. Takacs, N. A. Artemiev, D. J. Merthe, W. R. McKinney, F. Siewert, and T. Zeschke, “Development of a high-performance gantry system for a new generation of optical slope measuring profilers,” Nucl. Instrum. Methods A 710, 31–36 (2013). [CrossRef]

20.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” in AIP Conference Proceedings (American Institute of Physics, 2004), pp. 847–850.

21.

F. Siewert, H. Lammert, T. Noll, T. Schlegel, T. Zeschke, T. Hänsel, A. Nickel, A. Schindler, B. Grubert, and C. Schlewitt, “Advanced metrology: an essential support fort the surface finishing of high performance x-ray optics,” Proc. SPIE 5921, 592101 (2005). [CrossRef]

22.

http://www.imagine-optic.com/

23.

J. Floriot, X. Levecq, S. Bucourt, M. Thomasset, F. Polack, M. Idir, P. Mercère, T. Moreno, and S. Brochet, “A Shack-Hartmann measuring head for the two-dimensional characterization of X-ray mirrors,” J. Synchrotron Radiat. 15(2), 134–139 (2008). [CrossRef] [PubMed]

24.

J. Floriot, X. Levecq, S. Bucourt, M. Thomasset, F. Polack, M. Idir, P. Mercère, S. Brochet, and T. Moreno, “Surface metrology with a stitching Shack-Hartmann profilometric head,” Proc. SPIE 6616, 66162A (2007). [CrossRef]

25.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003). [CrossRef]

26.

http://qedmrf.com/metrology/ssi-technology/advantages/advantages-of-stitching

27.

J. H. Burge and C. Zhao, “Applications of subaperture stitching interferometry for very large mirrors,” Proc. SPIE 8450, 84500X (2013).

28.

W. H. Southwell, “Wave front estimation from wave front slope measurements,” J. Opt. Soc. Am. 70(8), 998–1006 (1980). [CrossRef]

29.

http://www.q-sys.eu/indexEN.html

30.

M. Idir, K. Kaznatcheev, S. Qian, and R. Conley, “Current status of the NSLS-II optical metrology laboratory,” Nucl. Instrum. Methods Phys. Res. A 710, 17–23 (2013). [CrossRef]

31.

http://www.j-tec.co.jp

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(340.0340) X-ray optics : X-ray optics
(340.6720) X-ray optics : Synchrotron radiation
(340.7470) X-ray optics : X-ray mirrors

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: December 26, 2013
Revised Manuscript: January 16, 2014
Manuscript Accepted: January 17, 2014
Published: January 30, 2014

Citation
Mourad Idir, Konstantine Kaznatcheev, Guillaume Dovillaire, Jerome Legrand, and Rakchanok Rungsawang, "A 2 D high accuracy slope measuring system based on a Stitching Shack Hartmann Optical Head," Opt. Express 22, 2770-2781 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2770


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References

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