Abstract

The numerical aperture (NA) and power of diffraction wave in point-diffraction interferometer (PDI) could significantly limit the measurement range of the system. A fiber point-diffraction interferometer with high NA is proposed for the measurement of absolute three-dimensional coordinates. Based on the single-mode fiber with submicron aperture, the diffraction wave with both high NA and high power is obtained, by which the achievable measurement range of the PDI can be extended. A double-iterative method based on Levenbery-Marquardt algorithm is proposed to determine the three-dimensional coordinates under measurement. Numerical simulation and comparison experiments have been carried out to demonstrate the accuracy and feasibility of the proposed PDI system, with both high measurement precision and nice repeatability achieved.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  5. J. Chu and S.-W. Kim, “Absolute distance measurements using point-diffracted spherical waves,” Proc. SPIE 6293, 62930P (2006).
    [Crossref]
  6. 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).
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  9. 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).
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    [Crossref]
  20. B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
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2014 (1)

O. Onalaja, M. Adjrad, and M. Ghavami, “Ultra-wideband-based multilateration technique for indoor localisation,” IET Commun. 8(10), 1800–1809 (2014).
[Crossref]

2013 (2)

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

2011 (1)

2010 (3)

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

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Polarization point-diffraction interferometer for high-precision testing of spherical surface,” Proc. SPIE 7656, 76560F (2010).
[Crossref]

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

2007 (2)

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[Crossref]

H.-G. Rhee, J. Chu, and Y.-W. Lee, “Absolute three-dimensional coordinate measurement by the two-point diffraction interferometry,” Opt. Express 15(8), 4435–4444 (2007).
[Crossref] [PubMed]

2006 (3)

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]

J. Chu and S.-W. Kim, “Absolute distance measurements using point-diffracted spherical waves,” Proc. SPIE 6293, 62930P (2006).
[Crossref]

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 (2)

S.-W. Kim, H.-G. Rhee, J. Joo, and Y. J. Kim, “Two-point diffraction interferometer for absolute distance measurement,” Proc. SPIE 5531, 162–169 (2004).
[Crossref]

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 (3)

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

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

2001 (1)

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[Crossref]

2000 (1)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

1996 (1)

K. A. Goldberg, E. Tejnil, and J. Bokor, “A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry,” OSA Trends in Optics and Photonics 4, 133–137 (1996).

Adjrad, M.

O. Onalaja, M. Adjrad, and M. Ghavami, “Ultra-wideband-based multilateration technique for indoor localisation,” IET Commun. 8(10), 1800–1809 (2014).
[Crossref]

Bokor, J.

K. A. Goldberg, E. Tejnil, and J. Bokor, “A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry,” OSA Trends in Optics and Photonics 4, 133–137 (1996).

Chen, C.

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Polarization point-diffraction interferometer for high-precision testing of spherical surface,” Proc. SPIE 7656, 76560F (2010).
[Crossref]

Chu, J.

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]

Deckert, V.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Fukuda, Y.

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[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]

Ghavami, M.

O. Onalaja, M. Adjrad, and M. Ghavami, “Ultra-wideband-based multilateration technique for indoor localisation,” IET Commun. 8(10), 1800–1809 (2014).
[Crossref]

Goldberg, K. A.

K. A. Goldberg, E. Tejnil, and J. Bokor, “A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry,” OSA Trends in Optics and Photonics 4, 133–137 (1996).

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]

Hecht, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Inoue, H.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[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, H.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

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]

Joo, J.

S.-W. Kim, H.-G. Rhee, J. Joo, and Y. J. Kim, “Two-point diffraction interferometer for absolute distance measurement,” Proc. SPIE 5531, 162–169 (2004).
[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]

Kataoka, T.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[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.

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]

J. Chu and S.-W. Kim, “Absolute distance measurements using point-diffracted spherical waves,” Proc. SPIE 6293, 62930P (2006).
[Crossref]

S.-W. Kim, H.-G. Rhee, J. Joo, and Y. J. Kim, “Two-point diffraction interferometer for absolute distance measurement,” Proc. SPIE 5531, 162–169 (2004).
[Crossref]

Kim, Y. J.

S.-W. Kim, H.-G. Rhee, J. Joo, and Y. J. Kim, “Two-point diffraction interferometer for absolute distance measurement,” Proc. SPIE 5531, 162–169 (2004).
[Crossref]

Kurosawa, T.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

Lee, Y.-W.

Martin, O. J. F.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Matsuura, T.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[Crossref]

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]

Nakamura, T.

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[Crossref]

Nakano, M.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[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]

Nishiyama, I.

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[Crossref]

Noguchi, H.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

Okagaki, S.

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[Crossref]

Okazaki, S.

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[Crossref]

Onalaja, O.

O. Onalaja, M. Adjrad, and M. Ghavami, “Ultra-wideband-based multilateration technique for indoor localisation,” IET Commun. 8(10), 1800–1809 (2014).
[Crossref]

Osawa, S.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

Oshikane, Y.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[Crossref]

Ota, K.

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[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, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[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]

Pohl, D. W.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Rhee, H.-G.

Sick, B.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Takatsuji, T.

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

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]

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]

Tejnil, E.

K. A. Goldberg, E. Tejnil, and J. Bokor, “A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry,” OSA Trends in Optics and Photonics 4, 133–137 (1996).

Udaka, K.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

Wang, D.

D. Wang, F. Wang, Y. Yang, and Y. Zhuo, “Modified polarization point diffraction interferometer with extended measurable NA for spherical surface testing,” Optik 124(22), 5481–5485 (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, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Polarization point-diffraction interferometer for high-precision testing of spherical surface,” Proc. SPIE 7656, 76560F (2010).
[Crossref]

Wang, F.

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

Wild, U. P.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Yamamoto, T.

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[Crossref]

Yamauchi, K.

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[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.

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

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Polarization point-diffraction interferometer for high-precision testing of spherical surface,” Proc. SPIE 7656, 76560F (2010).
[Crossref]

Zenobi, R.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

Zhang, B.

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.

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

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Polarization point-diffraction interferometer for high-precision testing of spherical surface,” Proc. SPIE 7656, 76560F (2010).
[Crossref]

Zou, H.

Appl. Opt. (3)

IET Commun. (1)

O. Onalaja, M. Adjrad, and M. Ghavami, “Ultra-wideband-based multilateration technique for indoor localisation,” IET Commun. 8(10), 1800–1809 (2014).
[Crossref]

J. Chem. Phys. (1)

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000).
[Crossref]

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

K. Otaki, K. Ota, I. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (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]

Nucl. Instrum. Meth. A. (1)

T. Matsuura, K. Udaka, Y. Oshikane, H. Inoue, M. Nakano, K. Yamauchi, and T. Kataoka, “Spherical concave mirror measurement by phase-shifting point diffraction interferometer with two optical fibers,” Nucl. Instrum. Meth. A. 616(2-3), 233–236 (2010).
[Crossref]

Opt. Eng. (1)

H. Jiang, S. Osawa, T. Takatsuji, H. Noguchi, and T. Kurosawa, “High-performance laser tracker using an articulating mirror for the calibration of coordinate measuring machine,” Opt. Eng. 41(3), 632–637 (2002).
[Crossref]

Opt. Express (2)

Opt. Rev. (1)

T. Matsuura, S. Okagaki, T. Nakamura, Y. Oshikane, H. Inoue, M. Nakano, and T. Kataoka, “Measurement accuracy in phase-shifting point diffraction interferometer with two optical fibers,” Opt. Rev. 14(6), 401–405 (2007).
[Crossref]

Optik (1)

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

OSA Trends in Optics and Photonics (1)

K. A. Goldberg, E. Tejnil, and J. Bokor, “A 3-D numerical study of pinhole diffraction to predict the accuracy of EUV point diffraction interferometry,” OSA Trends in Optics and Photonics 4, 133–137 (1996).

Proc. SPIE (6)

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]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Polarization point-diffraction interferometer for high-precision testing of spherical surface,” Proc. SPIE 7656, 76560F (2010).
[Crossref]

K. Ota, T. Yamamoto, Y. Fukuda, K. Otaki, I. Nishiyama, and S. Okazaki, “Advanced point diffraction interferometer for EUV aspherical mirrors,” Proc. SPIE 4343, 543–550 (2001).
[Crossref]

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]

S.-W. Kim, H.-G. Rhee, J. Joo, and Y. J. Kim, “Two-point diffraction interferometer for absolute distance measurement,” Proc. SPIE 5531, 162–169 (2004).
[Crossref]

J. Chu and S.-W. Kim, “Absolute distance measurements using point-diffracted spherical waves,” Proc. SPIE 6293, 62930P (2006).
[Crossref]

Other (1)

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1986).

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Figures (10)

Fig. 1
Fig. 1 System layout of the submicron-aperture fiber PDI for absolute three-dimensional coordinate measurement.
Fig. 2
Fig. 2 Single-mode fiber with submicron aperture. (a) SEM photo of submicron-aperture fiber, (b) structure of target in the PDI for coordinate measurement.
Fig. 3
Fig. 3 Model for three-dimensional coordinate reconstruction.
Fig. 4
Fig. 4 Procedure for double-iterative method based on L-M algorithm for three-coordinate reconstruction.
Fig. 5
Fig. 5 Aperture angle of diffraction wave and light transmittance for various fiber apertures.
Fig. 6
Fig. 6 Diffraction wavefront error within various NA ranges for different fiber apertures.
Fig. 7
Fig. 7 Coordinate measurement error in various CCD pixel areas.
Fig. 8
Fig. 8 Three-coordinate measurement error with random noise of λ/100 RMS in numerical simulation. Errors in (a) x and y directions, (b) z direction corresponding to the initial target position (−0.375 mm, 15 mm, 200 mm).
Fig. 9
Fig. 9 Three-coordinate measurement error in experimental validation. Errors in (a) x direction, and (b) z direction corresponding to the initial target position (−0.375 mm, 15 mm, 200 mm).
Fig. 10
Fig. 10 Repeated measurement error in experimental validation. Errors in (a) x direction and (b) z direction.

Equations (5)

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φ ( x , y , z ) = 2 π λ [ r 1 ( x 1 , y 1 , z 1 ; x , y , z ) r 2 ( x 2 , y 2 , z 2 ; x , y , z ) ] ,
f k ( Φ ) = 2 π λ ( φ k φ 0 ) ξ k ,
{ φ k ( x k , y k , z k ) = 2 π λ [ r 1 ( x 1 , y 1 , z 1 ; x k , y k , z k ) r 2 ( x 2 , y 2 , z 2 ; x k , y k , z k ) ] , φ 0 ( x 0 , y 0 , z 0 ) = 2 π λ [ r 1 ( x 1 , y 1 , z 1 ; x 0 , y 0 , z 0 ) r 2 ( x 2 , y 2 , z 2 ; x 0 , y 0 , z 0 ) ] ,
f ( Φ ) = { f k ( Φ ) } = { 2 π λ ( φ 1 φ 0 ) ξ 1 2 π λ ( φ k φ 0 ) ξ k 2 π λ ( φ m φ 0 ) ξ m .
F ( Φ ) = 1 2 f ( Φ ) T f ( Φ ) = 1 2 k = 1 m f k 2 .

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