Abstract

A method to provide absolute planarity measurements through an interferometric oblique incidence setup and an iterative algorithm is presented. With only three measurements, the calibration of absolute planarity is achieved in a fast and effective manner. Demonstration with synthetic data is provided, and the possible application to very long flat mirrors is pointed out.

© 2014 Optical Society of America

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  1. M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing,” Optik & Photonik 7(2), 56–58 (2012).
  2. M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res. B 267(8-9), 1390–1393 (2009).
  3. J. Arkwright, J. Burke, and M. Gross, “A deterministic optical figure correction technique that preserves precision-polished surface quality,” Opt. Express 16(18), 13901–13907 (2008).
  4. A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).
  5. T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).
  6. Y. Mori, K. Yamauchi, and K. Endo, “Elastic emission machining,” Precis. Eng. 9(3), 123–128 (1987).
  7. 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).
  8. W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).
  9. M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45(6), 060503 (2006).
  10. R. D. Geckeler, “Optimal use of pentaprism in highly accurate deflectometric scanning,” Meas. Sci. Technol. 18(1), 115–125 (2007).
  11. P. C. V. Mallik, C. Zhao, and J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).
  12. 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).
  13. J. Yellowhair and J. H. Burge, “Analysis of a scanning pentaprism system for measurements of large flat mirrors,” Appl. Opt. 46(35), 8466–8474 (2007).
  14. J. Ojeda-Castañeda, “Foucault, wire and phase modulation tests,” in Optical Shop Testing, third edn., D. Malacara ed., (Wiley and Sons, Hoboken 2007), pp. 310–312.
  15. L. Rayleigh, “Interference bands and their applications,” Nature 48(1235), 212–214 (1893).
  16. B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 234379 (1984).
  17. R. E. Parks, L.-Z. Shao, and C. J. Evans, “Pixel-based absolute topography test for three flats,” Appl. Opt. 37(25), 5951–5956 (1998).
  18. M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Stuttg.) 112(9), 381–391 (2001).
  19. U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).
  20. V. Greco and G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7(6), 1341–1346 (1998).
  21. V. Greco, R. Tronconi, C. Del Vecchio, M. Trivi, and G. Molesini, “Absolute measurement of planarity with Fritz’s method: uncertainty evaluation,” Appl. Opt. 38(10), 2018–2027 (1999).
  22. L. Zhang, B. Xuan, and J. Xie, “Combination of skip-flat test with Ritchey-Common test for the large rectangular flat,” Proc. SPIE 7656, 76564W (2010).
  23. P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36(9), 2478–2481 (1997).
  24. D. Malacara, “Twyman-Green interferometer,” in Optical Shop Testing, third edn., D. Malacara ed., (Wiley and Sons, Hoboken 2007), pp. 78–79.
  25. Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).
  26. M. Vannoni, A. Sordini, and G. Molesini, “Calibration of absolute planarity flats: generalized iterative approach,” Opt. Eng. 51(8), 081510 (2012).
  27. V. B. Gubin and V. N. Sharonov, “Algorithm for reconstructing the shape of optical surfaces from the results of experimental data,” Sov. J. Opt. Technol. 57, 147–148 (1990).
  28. M. Vannoni and G. Molesini, “Iterative algorithm for three flat test,” Opt. Express 15(11), 6809–6816 (2007).
  29. M. Vannoni and G. Molesini, “Absolute planarity with three-flat test: an iterative approach with Zernike polynomials,” Opt. Express 16(1), 340–354 (2008).
  30. M. Vannoni and G. Molesini, “Three-flat test with plates in horizontal posture,” Appl. Opt. 47(12), 2133–2145 (2008).
  31. C. Morin and S. Bouillet, “Absolute calibration of three reference flats based on an iterative algorithm: study and implementation,” Proc. Soc. Photo Opt. Instrum. Eng. 8169, 816915 (2011).
  32. M. Vannoni, A. Sordini, and G. Molesini, “Long-term deformation at room temperature observed in fused silica,” Opt. Express 18(5), 5114–5123 (2010).
  33. M. Vannoni, A. Sordini, and G. Molesini, “Relaxation time and viscosity of fused silica glass at room temperature,” Eur Phys J E Soft Matter 34(9), 92 (2011).

2013 (1)

Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).

2012 (3)

M. Vannoni, A. Sordini, and G. Molesini, “Calibration of absolute planarity flats: generalized iterative approach,” Opt. Eng. 51(8), 081510 (2012).

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing,” Optik & Photonik 7(2), 56–58 (2012).

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).

2011 (2)

C. Morin and S. Bouillet, “Absolute calibration of three reference flats based on an iterative algorithm: study and implementation,” Proc. Soc. Photo Opt. Instrum. Eng. 8169, 816915 (2011).

M. Vannoni, A. Sordini, and G. Molesini, “Relaxation time and viscosity of fused silica glass at room temperature,” Eur Phys J E Soft Matter 34(9), 92 (2011).

2010 (4)

M. Vannoni, A. Sordini, and G. Molesini, “Long-term deformation at room temperature observed in fused silica,” Opt. Express 18(5), 5114–5123 (2010).

L. Zhang, B. Xuan, and J. Xie, “Combination of skip-flat test with Ritchey-Common test for the large rectangular flat,” Proc. SPIE 7656, 76564W (2010).

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

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).

2009 (1)

M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res. B 267(8-9), 1390–1393 (2009).

2008 (3)

2007 (5)

U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).

M. Vannoni and G. Molesini, “Iterative algorithm for three flat test,” Opt. Express 15(11), 6809–6816 (2007).

J. Yellowhair and J. H. Burge, “Analysis of a scanning pentaprism system for measurements of large flat mirrors,” Appl. Opt. 46(35), 8466–8474 (2007).

R. D. Geckeler, “Optimal use of pentaprism in highly accurate deflectometric scanning,” Meas. Sci. Technol. 18(1), 115–125 (2007).

P. C. V. Mallik, C. Zhao, and J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).

2006 (1)

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45(6), 060503 (2006).

2002 (1)

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).

2001 (1)

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Stuttg.) 112(9), 381–391 (2001).

1999 (1)

1998 (3)

V. Greco and G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7(6), 1341–1346 (1998).

R. E. Parks, L.-Z. Shao, and C. J. Evans, “Pixel-based absolute topography test for three flats,” Appl. Opt. 37(25), 5951–5956 (1998).

A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

1997 (1)

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36(9), 2478–2481 (1997).

1990 (1)

V. B. Gubin and V. N. Sharonov, “Algorithm for reconstructing the shape of optical surfaces from the results of experimental data,” Sov. J. Opt. Technol. 57, 147–148 (1990).

1987 (1)

Y. Mori, K. Yamauchi, and K. Endo, “Elastic emission machining,” Precis. Eng. 9(3), 123–128 (1987).

1984 (1)

B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 234379 (1984).

1893 (1)

L. Rayleigh, “Interference bands and their applications,” Nature 48(1235), 212–214 (1893).

Arkwright, J.

Arnold, T.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Babayan, S. E.

A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

Böhm, G.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Bouillet, S.

C. Morin and S. Bouillet, “Absolute calibration of three reference flats based on an iterative algorithm: study and implementation,” Proc. Soc. Photo Opt. Instrum. Eng. 8169, 816915 (2011).

Boutet, S.

Buchheim, J.

Burge, J. H.

J. Yellowhair and J. H. Burge, “Analysis of a scanning pentaprism system for measurements of large flat mirrors,” Appl. Opt. 46(35), 8466–8474 (2007).

P. C. V. Mallik, C. Zhao, and J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).

Burke, J.

Chen, L.

Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).

Del Vecchio, C.

Elster, C.

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45(6), 060503 (2006).

Endo, K.

Y. Mori, K. Yamauchi, and K. Endo, “Elastic emission machining,” Precis. Eng. 9(3), 123–128 (1987).

Evans, C. J.

Fechner, R.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Fritz, B. S.

B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 234379 (1984).

Frost, F.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Gao, W.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).

Geckeler, R. D.

R. D. Geckeler, “Optimal use of pentaprism in highly accurate deflectometric scanning,” Meas. Sci. Technol. 18(1), 115–125 (2007).

Greco, V.

V. Greco, R. Tronconi, C. Del Vecchio, M. Trivi, and G. Molesini, “Absolute measurement of planarity with Fritz’s method: uncertainty evaluation,” Appl. Opt. 38(10), 2018–2027 (1999).

V. Greco and G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7(6), 1341–1346 (1998).

Griesmann, U.

U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).

Gross, M.

Gubin, V. B.

V. B. Gubin and V. N. Sharonov, “Algorithm for reconstructing the shape of optical surfaces from the results of experimental data,” Sov. J. Opt. Technol. 57, 147–148 (1990).

Han, Z.

Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).

Hänsel, T.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Hariharan, P.

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36(9), 2478–2481 (1997).

Huang, P. S.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).

Ishikawa, T.

Jeong, J. Y.

A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

Kidani, N.

Kimura, T.

Kiontke, S.

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing,” Optik & Photonik 7(2), 56–58 (2012).

Kiyono, S.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).

Krzywinski, J.

Küchel, M. F.

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Stuttg.) 112(9), 381–391 (2001).

Mallik, P. C. V.

P. C. V. Mallik, C. Zhao, and J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).

Matsuyama, S.

Meister, J.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Mimura, H.

Molesini, G.

Montanez, P. A.

Mori, Y.

Y. Mori, K. Yamauchi, and K. Endo, “Elastic emission machining,” Precis. Eng. 9(3), 123–128 (1987).

Morin, C.

C. Morin and S. Bouillet, “Absolute calibration of three reference flats based on an iterative algorithm: study and implementation,” Proc. Soc. Photo Opt. Instrum. Eng. 8169, 816915 (2011).

Nickel, A.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Nishino, Y.

Park, J.

A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

Parks, R. E.

Rayleigh, L.

L. Rayleigh, “Interference bands and their applications,” Nature 48(1235), 212–214 (1893).

Sano, Y.

Schindler, A.

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Schulz, M.

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45(6), 060503 (2006).

Schutze, A.

A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

Shao, L.-Z.

Sharonov, V. N.

V. B. Gubin and V. N. Sharonov, “Algorithm for reconstructing the shape of optical surfaces from the results of experimental data,” Sov. J. Opt. Technol. 57, 147–148 (1990).

Siewert, F.

Signorato, R.

Soons, J.

U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).

Sordini, A.

M. Vannoni, A. Sordini, and G. Molesini, “Calibration of absolute planarity flats: generalized iterative approach,” Opt. Eng. 51(8), 081510 (2012).

M. Vannoni, A. Sordini, and G. Molesini, “Relaxation time and viscosity of fused silica glass at room temperature,” Eur Phys J E Soft Matter 34(9), 92 (2011).

M. Vannoni, A. Sordini, and G. Molesini, “Long-term deformation at room temperature observed in fused silica,” Opt. Express 18(5), 5114–5123 (2010).

Tamasaku, K.

Trivi, M.

Tronconi, R.

Vannoni, M.

Wakioka, T.

Wang, Q.

U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).

Weiser, M.

M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res. B 267(8-9), 1390–1393 (2009).

Williams, G. J.

Wulan, T.

Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).

Xie, J.

L. Zhang, B. Xuan, and J. Xie, “Combination of skip-flat test with Ritchey-Common test for the large rectangular flat,” Proc. SPIE 7656, 76564W (2010).

Xuan, B.

L. Zhang, B. Xuan, and J. Xie, “Combination of skip-flat test with Ritchey-Common test for the large rectangular flat,” Proc. SPIE 7656, 76564W (2010).

Yabashi, M.

Yamada, T.

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).

Yamauchi, K.

Yellowhair, J.

Zeuner, M.

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing,” Optik & Photonik 7(2), 56–58 (2012).

Zhang, L.

L. Zhang, B. Xuan, and J. Xie, “Combination of skip-flat test with Ritchey-Common test for the large rectangular flat,” Proc. SPIE 7656, 76564W (2010).

Zhao, C.

P. C. V. Mallik, C. Zhao, and J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).

Zhu, R.

Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).

Appl. Opt. (4)

Eur Phys J E Soft Matter (1)

M. Vannoni, A. Sordini, and G. Molesini, “Relaxation time and viscosity of fused silica glass at room temperature,” Eur Phys J E Soft Matter 34(9), 92 (2011).

IEEE Trans. Plasma Sci. (1)

A. Schutze, J. Y. Jeong, S. E. Babayan, and J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

Meas. Sci. Technol. (1)

R. D. Geckeler, “Optimal use of pentaprism in highly accurate deflectometric scanning,” Meas. Sci. Technol. 18(1), 115–125 (2007).

Nature (1)

L. Rayleigh, “Interference bands and their applications,” Nature 48(1235), 212–214 (1893).

Nucl. Instrum. Meth. A (1)

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, and A. Schindler, “Ultra-precision surface finishing by ion beam and plasma jet techniques—status and outlook,” Nucl. Instrum. Meth. A 616(2-3), 147–156 (2010).

Nucl. Instrum. Methods Phys. Res. B (1)

M. Weiser, “Ion beam figuring for lithography optics,” Nucl. Instrum. Methods Phys. Res. B 267(8-9), 1390–1393 (2009).

Opt. Eng. (6)

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45(6), 060503 (2006).

B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 234379 (1984).

P. C. V. Mallik, C. Zhao, and J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).

U. Griesmann, Q. Wang, and J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).

P. Hariharan, “Interferometric testing of optical surfaces: absolute measurements of flatness,” Opt. Eng. 36(9), 2478–2481 (1997).

M. Vannoni, A. Sordini, and G. Molesini, “Calibration of absolute planarity flats: generalized iterative approach,” Opt. Eng. 51(8), 081510 (2012).

Opt. Express (5)

Opt. Lett. (1)

Optik & Photonik (1)

M. Zeuner and S. Kiontke, “Ion beam figuring technology in optics manufacturing,” Optik & Photonik 7(2), 56–58 (2012).

Optik (Stuttg.) (2)

M. F. Küchel, “A new approach to solve the three flat problem,” Optik (Stuttg.) 112(9), 381–391 (2001).

Z. Han, L. Chen, T. Wulan, and R. Zhu, “The absolute flatness measurements of two aluminum coated mirrors based on the skip flat test,” Optik (Stuttg.) 124(19), 3781–3785 (2013).

Precis. Eng. (2)

W. Gao, P. S. Huang, T. Yamada, and S. Kiyono, “A compact and sensitive two-dimensional angle probe for flatness measurement of large silicon wafers,” Precis. Eng. 26(4), 396–404 (2002).

Y. Mori, K. Yamauchi, and K. Endo, “Elastic emission machining,” Precis. Eng. 9(3), 123–128 (1987).

Proc. Soc. Photo Opt. Instrum. Eng. (1)

C. Morin and S. Bouillet, “Absolute calibration of three reference flats based on an iterative algorithm: study and implementation,” Proc. Soc. Photo Opt. Instrum. Eng. 8169, 816915 (2011).

Proc. SPIE (1)

L. Zhang, B. Xuan, and J. Xie, “Combination of skip-flat test with Ritchey-Common test for the large rectangular flat,” Proc. SPIE 7656, 76564W (2010).

Pure Appl. Opt. (1)

V. Greco and G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7(6), 1341–1346 (1998).

Sov. J. Opt. Technol. (1)

V. B. Gubin and V. N. Sharonov, “Algorithm for reconstructing the shape of optical surfaces from the results of experimental data,” Sov. J. Opt. Technol. 57, 147–148 (1990).

Other (2)

D. Malacara, “Twyman-Green interferometer,” in Optical Shop Testing, third edn., D. Malacara ed., (Wiley and Sons, Hoboken 2007), pp. 78–79.

J. Ojeda-Castañeda, “Foucault, wire and phase modulation tests,” in Optical Shop Testing, third edn., D. Malacara ed., (Wiley and Sons, Hoboken 2007), pp. 310–312.

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Figures (4)

Fig. 1
Fig. 1

Optical setup and measuring steps for absolute flatness measurement: (a), cavity including the test surface; (b), cavity in the absence of the test surface; (c), same cavity with the reference flat M rotated on its plane.

Fig. 2
Fig. 2

Optical path difference 2 cosα Δz introduced on oblique reflection by a step of height Δz.

Fig. 3
Fig. 3

Example of synthetic surfaces K, L, M and simulated OPD maps KLM, KM, KMβ.

Fig. 4
Fig. 4

Retrieved surfaces K, L (oblique), M, after the application of the iterative algorithm. The error maps with respect to the starting surfaces are also presented.

Tables (1)

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Table 1 Operators acting on the flats and accounting for the data maps

Equations (11)

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KLM(x,y)= F y K+ S y,α L+ F y M
KM(x,y)= F y K+M
K M β (x,y)= F y K+ R β M
S y,α L(i,j)=2cosαL[ (i i 0 )cosα+ i 0 ,j ]
KLM(x,y)KM(x,y)= S y,α L+ F y MM
Δ(KM)= (KM) exp KM ,
Δ(K M β )= (K M β ) exp K M β .
K new =K+ 1 2 1 10 F y Δ(KM)+ 1 2 1 10 F y Δ(K M β ) ,
M new =M+ 1 2 1 10 Δ(KM)+ 1 2 1 10 R β 1 Δ(K M β ) .
S y,α L=KLMKM( F y MM) .
rms (α)= cos(π/4) cosα 0.47nm= X D 2 2 0.47nm.

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