Abstract

It is a key issue to measure the point-diffraction wavefront error, which determines the achievable accuracy of point-diffraction interferometer (PDI). A high-precision method based on shearing interferometry is proposed to measure submicron-aperture fiber point-diffraction wavefront with high numerical aperture (NA). To obtain the true shearing point-diffraction wavefront, a double-step calibration method based on three-dimensional coordinate reconstruction and symmetric lateral displacement compensation is proposed to calibrate the geometric aberration in the case of high NA and large lateral wavefront displacement. The calibration can be carried out without any prior knowledge about the system configuration parameters. With the true shearing wavefront, the differential Zernike polynomials fitting method is applied to reconstruct the point-diffraction wavefront. Numerical simulation and experiments have been carried out to demonstrate the accuracy and feasibility of the proposed measurement method, and a good measurement accuracy is achieved.

© 2016 Optical Society of America

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References

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    [Crossref]
  6. S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
    [Crossref]
  7. H.-G. Rhee and S. W. Kim, “Absolute distance measurement by two-point-diffraction interferometry,” Appl. Opt. 41(28), 5921–5928 (2002).
    [Crossref] [PubMed]
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  13. N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
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  22. X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
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    [Crossref]

2015 (4)

2014 (1)

2013 (4)

J. C. Aguilar, L. R. Berriel-Valdos, and J. F. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).
[Crossref]

D. Wang, F. Wang, H. Zou, and B. Zhang, “Analysis of diffraction wavefront in visible-light point-diffraction interferometer,” Appl. Opt. 52(31), 7602–7608 (2013).
[Crossref] [PubMed]

D. Wang, F. Wang, Y. Yang, and Y. Zhuo, “Modified polarization point diffraction interferometer with extended measurable NA for spherical surface testing,” Optik (Stuttg.) 124(22), 5481–5485 (2013).
[Crossref]

T. Ling, D. Liu, L. Sun, Y. Yang, and Z. Cheng, “Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting,” Proc. SPIE 8838, 88380J (2013).
[Crossref]

2012 (1)

2011 (3)

2010 (2)

N. N. Salashchenko, M. N. Toporov, and N. I. Chkhalo, “Physical limitations of measurement accuracy of the diffraction reference wave interferometers,” Bull. Russ. Acad. Sci., Physics 74(1), 53–56 (2010).
[Crossref]

H. Kihm and Y.-W. Lee, “Double-pass point diffraction interferometer,” Meas. Sci. Technol. 21(10), 105307 (2010).
[Crossref]

2008 (1)

N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

J. Chu and S.-W. Kim, “Absolute distance measurement by lateral shearing interferometry of point-diffracted spherical waves,” Opt. Express 14(13), 5961–5967 (2006).
[Crossref] [PubMed]

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

2004 (1)

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

2002 (2)

H.-G. Rhee and S. W. Kim, “Absolute distance measurement by two-point-diffraction interferometry,” Appl. Opt. 41(28), 5921–5928 (2002).
[Crossref] [PubMed]

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

1998 (1)

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Aguilar, J. C.

J. C. Aguilar, L. R. Berriel-Valdos, and J. F. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).
[Crossref]

Aguilar, J. F.

J. C. Aguilar, L. R. Berriel-Valdos, and J. F. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).
[Crossref]

Attwood, D.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Bai, J.

Batson, P.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Berriel-Valdos, L. R.

J. C. Aguilar, L. R. Berriel-Valdos, and J. F. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).
[Crossref]

Bokor, J.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Bresloff, C.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Chang, C.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Chen, C.

Chen, X.

Cheng, Z.

T. Ling, D. Liu, L. Sun, Y. Yang, and Z. Cheng, “Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting,” Proc. SPIE 8838, 88380J (2013).
[Crossref]

Chkhalo, N. I.

M. V. Svechnikov, N. I. Chkhalo, M. N. Toropov, N. N. Salashchenko, and M. V. Zorina, “Application of point diffraction interferometry for middle spatial frequency roughness detection,” Opt. Lett. 40(2), 159–162 (2015).
[Crossref] [PubMed]

N. N. Salashchenko, M. N. Toporov, and N. I. Chkhalo, “Physical limitations of measurement accuracy of the diffraction reference wave interferometers,” Bull. Russ. Acad. Sci., Physics 74(1), 53–56 (2010).
[Crossref]

N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
[Crossref] [PubMed]

Chu, J.

Dai, F.

Decker, T. A.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Feng, P.

Fukuda, Y.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Gemma, T.

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

Goldberg, K.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Gomei, Y.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Guo, T.

X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
[Crossref]

Ishii, M.

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

Jiang, J.

Johnson, M. A.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Kakuchi, O.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Kihm, H.

H. Kihm and Y.-W. Lee, “Double-pass point diffraction interferometer,” Meas. Sci. Technol. 21(10), 105307 (2010).
[Crossref]

Kim, S. W.

Kim, S.-W.

Klimov, A. Y.

N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
[Crossref] [PubMed]

Kong, M.

X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
[Crossref]

D. Wang, X. Chen, Y. Xu, F. Wang, M. Kong, J. Zhao, and B. Zhang, “High-NA fiber point-diffraction interferometer for three-dimensional coordinate measurement,” Opt. Express 22(21), 25550–25559 (2014).
[Crossref] [PubMed]

Lee, S.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Lee, Y.-W.

Ling, T.

T. Ling, Y. Yang, D. Liu, X. Yue, J. Jiang, J. Bai, and Y. Shen, “General measurement of optical system aberrations with a continuously variable lateral shear ratio by a randomly encoded hybrid grating,” Appl. Opt. 54(30), 8913–8920 (2015).
[Crossref] [PubMed]

T. Ling, D. Liu, L. Sun, Y. Yang, and Z. Cheng, “Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting,” Proc. SPIE 8838, 88380J (2013).
[Crossref]

Liu, D.

Murakami, K.

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

Nakayama, S.

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

Naulleau, P.

P. Naulleau, K. Goldberg, S. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, and J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998).
[Crossref]

Nishiyama, I.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Okazaki, S.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Ota, K.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Otaki, K.

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Phillion, D. W.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Rhee, H.-G.

Rogov, V. V.

N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
[Crossref] [PubMed]

Salashchenko, N. N.

M. V. Svechnikov, N. I. Chkhalo, M. N. Toropov, N. N. Salashchenko, and M. V. Zorina, “Application of point diffraction interferometry for middle spatial frequency roughness detection,” Opt. Lett. 40(2), 159–162 (2015).
[Crossref] [PubMed]

N. N. Salashchenko, M. N. Toporov, and N. I. Chkhalo, “Physical limitations of measurement accuracy of the diffraction reference wave interferometers,” Bull. Russ. Acad. Sci., Physics 74(1), 53–56 (2010).
[Crossref]

N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
[Crossref] [PubMed]

Sasaki, O.

Shen, Y.

Sun, L.

T. Ling, D. Liu, L. Sun, Y. Yang, and Z. Cheng, “Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting,” Proc. SPIE 8838, 88380J (2013).
[Crossref]

Svechnikov, M. V.

Takeuchi, S.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Tang, F.

Taylor, J. S.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Toporov, M. N.

N. N. Salashchenko, M. N. Toporov, and N. I. Chkhalo, “Physical limitations of measurement accuracy of the diffraction reference wave interferometers,” Bull. Russ. Acad. Sci., Physics 74(1), 53–56 (2010).
[Crossref]

Toropov, M. N.

M. V. Svechnikov, N. I. Chkhalo, M. N. Toropov, N. N. Salashchenko, and M. V. Zorina, “Application of point diffraction interferometry for middle spatial frequency roughness detection,” Opt. Lett. 40(2), 159–162 (2015).
[Crossref] [PubMed]

N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
[Crossref] [PubMed]

Wang, C.

Wang, D.

Wang, F.

Wang, X.

Xing, T.

T. Xing, J. Xu, and F. Xu, “A 3D numerical study of pinhole diffraction in visible-light point diffraction interferometry,” Proc. SPIE 8321, 83211O (2011).
[Crossref]

Xu, F.

T. Xing, J. Xu, and F. Xu, “A 3D numerical study of pinhole diffraction in visible-light point diffraction interferometry,” Proc. SPIE 8321, 83211O (2011).
[Crossref]

Xu, J.

T. Xing, J. Xu, and F. Xu, “A 3D numerical study of pinhole diffraction in visible-light point diffraction interferometry,” Proc. SPIE 8321, 83211O (2011).
[Crossref]

Xu, Y.

X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
[Crossref]

D. Wang, X. Chen, Y. Xu, F. Wang, M. Kong, J. Zhao, and B. Zhang, “High-NA fiber point-diffraction interferometer for three-dimensional coordinate measurement,” Opt. Express 22(21), 25550–25559 (2014).
[Crossref] [PubMed]

Yamamoto, T.

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Yamazoe, K.

S. Takeuchi, O. Kakuchi, K. Yamazoe, Y. Gomei, T. A. Decker, M. A. Johnson, D. W. Phillion, and J. S. Taylor, “Visible light point-diffraction interferometer for testing of EUVL optics,” Proc. SPIE 6151, 61510E (2006).
[Crossref]

Yang, Y.

Yue, X.

Zhang, B.

Zhao, J.

X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
[Crossref]

D. Wang, X. Chen, Y. Xu, F. Wang, M. Kong, J. Zhao, and B. Zhang, “High-NA fiber point-diffraction interferometer for three-dimensional coordinate measurement,” Opt. Express 22(21), 25550–25559 (2014).
[Crossref] [PubMed]

Zhu, B.

X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
[Crossref]

Zhu, Y.

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

Zhuo, Y.

Zorina, M. V.

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Acta Opt. Sin. (1)

X. Chen, D. Wang, Y. Xu, M. Kong, T. Guo, J. Zhao, and B. Zhu, “Analysis of point-diffraction wavefront with sub-wavelength-aperture fiber,” Acta Opt. Sin. 35(9), 0912004 (2015).
[Crossref]

Appl. Opt. (7)

Bull. Russ. Acad. Sci., Physics (1)

N. N. Salashchenko, M. N. Toporov, and N. I. Chkhalo, “Physical limitations of measurement accuracy of the diffraction reference wave interferometers,” Bull. Russ. Acad. Sci., Physics 74(1), 53–56 (2010).
[Crossref]

J. Vac. Sci. Technol. B (1)

K. Otaki, T. Yamamoto, Y. Fukuda, K. Ota, I. Nishiyama, and S. Okazaki, “Accuracy evaluation of the point diffraction interferometer for extreme ultraviolet lithography aspheric mirror,” J. Vac. Sci. Technol. B 20(1), 295–300 (2002).
[Crossref]

Meas. Sci. Technol. (1)

H. Kihm and Y.-W. Lee, “Double-pass point diffraction interferometer,” Meas. Sci. Technol. 21(10), 105307 (2010).
[Crossref]

Opt. Eng. (1)

J. C. Aguilar, L. R. Berriel-Valdos, and J. F. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (1)

D. Wang, F. Wang, Y. Yang, and Y. Zhuo, “Modified polarization point diffraction interferometer with extended measurable NA for spherical surface testing,” Optik (Stuttg.) 124(22), 5481–5485 (2013).
[Crossref]

Proc. SPIE (5)

K. Otaki, Y. Zhu, M. Ishii, S. Nakayama, K. Murakami, and T. Gemma, “Rigorous wavefront analysis of the visible-light point diffraction interferometer for EUVL,” Proc. SPIE 5193, 182–190 (2004).
[Crossref]

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N. I. Chkhalo, A. Y. Klimov, V. V. Rogov, N. N. Salashchenko, and M. N. Toropov, “A source of a reference spherical wave based on a single mode optical fiber with a narrowed exit aperture,” Rev. Sci. Instrum. 79(3), 033107 (2008).
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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of SMA fiber point-diffraction wavefront measurement system. (a) Structure of SMA fiber projector and (b) schematic diagram of SMA fiber point-diffraction wavefront measurement.

Fig. 2
Fig. 2

Geometry for systematic error analysis.

Fig. 3
Fig. 3

Procedure for retrieval of SMA fiber point-diffraction wavefront. (a) The whole retrieval procedure, and (b) procedure for double-step calibration of systematic error.

Fig. 4
Fig. 4

Simulation results of systematic error calibration. (a) Residual error obtained with traditional misalignment calibration method, residual error after (b) the first-step calibration and (c) the second-step calibration in the proposed method.

Fig. 5
Fig. 5

Residual errors in the calibration of systematic error under various lateral displacements and NAs in computer simulation. (a) RMS value with traditional method and (b) RMS value with the proposed double-step calibration method.

Fig. 6
Fig. 6

Simulation results of shearing wavefront retrieval based on the differential Zernike polynomials fitting method. (a) Original input wavefront, (b) reconstructed wavefront and (c) the residual error between the original and reconstructed wavefronts.

Fig. 7
Fig. 7

System layout of the SMA fiber point-diffraction interferometer for point-diffraction wavefront measurement. HWP1 and HWP2: half-wave plate; PBS: polarized beam splitter; BS1 and BS2: beam splitter; QWP: quarter-wave plate; FC1, FC2, FC3 and FC4: fiber coupler; S1, S2, S3 and S4: SMA fiber.

Fig. 8
Fig. 8

Measurement results about shearing wavefront retrieval. Unwrapped original wavefront (a) before and (b) after 180-degree rotation in x direction, original wavefront (c) before and (d) after 180-degree rotation in y direction; pre-calibrated shearing wavefronts with the first-step calibration in the proposed method (f) before and (g) after 180-degree rotation in x direction, pre-calibrated shearing wavefronts (h) before and (i) after 180-degree rotation in y direction; final retrieved shearing wavefronts in (e) x and (j) y directions obtained with the double-step calibration method.

Fig. 9
Fig. 9

Experimental result of point-diffraction wavefront measurement. (a) Measured point-diffraction wavefront in original position, (b) measured wavefront after 45° projector rotation, (c) measured wavefront after projector translation.

Tables (2)

Tables Icon

Table 1 Experimental results of shearing wavefront retrieval.

Tables Icon

Table 2 Experimental results of point-diffraction wavefront measurement.

Equations (18)

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{ Δ W x (x,y)=W(x,y)W(x+s,y) Δ W y (x,y)=W(x,y)W(x,y+s) ,
W(x,y)= i=1 N a i Z i (x,y) .
{ Δ W x (x,y)= i=1 N a i Δ Z i, x (x,y) Δ W y (x,y)= i=1 N a i Δ Z i, y (x,y) ,
{ Δ Z i, x (x,y)= Z i (x,y) Z i (x+s,y) Δ Z i, y (x,y)= Z i (x,y) Z i (x,y+s) .
ΔW=ΔZa.
a= (Δ Z T ΔZ) 1 Δ Z T ΔW.
OPD= R 1 ( x 1 , y 1 , z 1 ;x,y,z) R 2 ( x 2 , y 2 , z 2 ;x,y,z),
OPD= x 2 + y 2 + D 2 (x+s) 2 + y 2 + D 2 .
F(Φ)= k f k 2 (Φ) = k ( OPD k ξ k ) 2 ,
OPD 1 =OPD(Φ)OPD( Φ * ).
OPD=D 1+ (r/D ) 2 D 1+ (r/D ) 2 + 2srcosθ / D 2 + (s/D ) 2 .
OPD a 2 Z 2 + a 9 Z 9 + a 19 Z 19 + a 33 Z 33 ,
{ Z 2 =ρcosθ Z 9 =(3 ρ 3 2ρ)cosθ Z 19 =(10 ρ 5 12 ρ 3 +3ρ)cosθ Z 33 =(35 ρ 7 60 ρ 5 +30 ρ 3 4ρ)cosθ ,
{ a 2 =s[t t s 2 / (2 D 2 ) + t 3 /3 + 3 t 3 s 2 / (4 D 2 ) 3 t 5 / 16 15 t 5 s 2 / (16 D 2 ) + t 7 /8 ] a 9 =s[ t 3 /6 + 3 t 3 s 2 / (8 D 2 ) 3 t 5 / 20 15 t 5 s 2 / (20 D 2 ) + t 7 /8 ] a 19 =s[3 t 5 /80 3 t 5 s 2 / (16 D 2 ) +3 t 7 /56] a 33 =s( t 7 / 112 ) .
OPD 1 Δ a 2 Z 2 +Δ a 9 Z 9 +Δ a 19 Z 19 +Δ a 33 Z 33 ,
OPD (s) + OPD (s) 0.
{ W m1 (s) =ΔW+ OPD 1 (s) W m1 (s) =ΔW+ OPD 1 (s) .
ΔW ( W m1 (s) + W m1 (s) ) /2 .

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