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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References

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  1. M. Zeuner, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).
  20. V. Greco, 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, G. Molesini, “Absolute measurement of planarity with Fritz’s method: uncertainty evaluation,” Appl. Opt. 38(10), 2018–2027 (1999).
  22. L. Zhang, B. Xuan, 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, 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, G. Molesini, “Calibration of absolute planarity flats: generalized iterative approach,” Opt. Eng. 51(8), 081510 (2012).
  27. V. B. Gubin, 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, G. Molesini, “Iterative algorithm for three flat test,” Opt. Express 15(11), 6809–6816 (2007).
  29. M. Vannoni, G. Molesini, “Absolute planarity with three-flat test: an iterative approach with Zernike polynomials,” Opt. Express 16(1), 340–354 (2008).
  30. M. Vannoni, G. Molesini, “Three-flat test with plates in horizontal posture,” Appl. Opt. 47(12), 2133–2145 (2008).
  31. C. Morin, 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, G. Molesini, “Long-term deformation at room temperature observed in fused silica,” Opt. Express 18(5), 5114–5123 (2010).
  33. M. Vannoni, A. Sordini, 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, 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, G. Molesini, “Calibration of absolute planarity flats: generalized iterative approach,” Opt. Eng. 51(8), 081510 (2012).

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

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

T. Arnold, G. Böhm, R. Fechner, J. Meister, A. Nickel, F. Frost, T. Hänsel, 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).

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

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

J. Yellowhair, 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, J. H. Burge, “Measurement of a 2m flat using a pentaprism scanning system,” Opt. Eng. 46, 023602 (2007).

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

2006 (1)

M. Schulz, 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, 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)

R. E. Parks, L.-Z. Shao, 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, J. Park, “The atmospheric-pressure plasma jet: a review and comparison to other plasma sources,” IEEE Trans. Plasma Sci. 26(6), 1685–1694 (1998).

V. Greco, G. Molesini, “Micro-temperature effects on absolute flatness test plates,” Pure Appl. Opt. 7(6), 1341–1346 (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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, G. Molesini, “Absolute measurement of planarity with Fritz’s method: uncertainty evaluation,” Appl. Opt. 38(10), 2018–2027 (1999).

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

Griesmann, U.

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

Gross, M.

Gubin, V. B.

V. B. Gubin, 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, 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, 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, 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, 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, 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, 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, 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, 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, K. Endo, “Elastic emission machining,” Precis. Eng. 9(3), 123–128 (1987).

Morin, C.

C. Morin, 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, 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, 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, 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, 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, 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, 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, J. Soons, “Three-flat tests including mounting-induced deformations,” Opt. Eng. 46(9), 093601 (2007).

Sordini, A.

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

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

Zhang, L.

L. Zhang, B. Xuan, 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, 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, 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, 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, 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, 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)

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

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

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

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

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

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

Optik (Stuttg.) (2)

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

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

Precis. Eng. (2)

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

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

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

C. Morin, 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, 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, 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, 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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