Abstract

3-D profiles of discontinuous surfaces patterned with high step structures are measured using four wavelengths generated by phase-locking to the frequency comb of an Er-doped fiber femtosecond laser stabilized to the Rb atomic clock. This frequency-comb-referenced method of multi-wavelength interferometry permits extending the phase non-ambiguity range by a factor of 64,500 while maintaining the sub-wavelength measurement precision of single-wavelength interferometry. Experimental results show a repeatability of 3.13 nm (one-sigma) in measuring step heights of 1800, 500, and 70 μm. The proposed method is accurate enough for the standard calibration of gauge blocks and also fast to be suited for the industrial inspection of microelectronics products.

©2013 Optical Society of America

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    [Crossref]

2012 (3)

2011 (2)

2010 (4)

S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B 27(11), B51 (2010).
[Crossref]

Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” Annals of CIRP 59(1), 555–558 (2010).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

2009 (5)

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S.-H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging.,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
[Crossref] [PubMed]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

S.-W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

Y.-J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S.-W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009).
[Crossref] [PubMed]

2008 (1)

2006 (3)

2005 (1)

2004 (1)

2003 (1)

2002 (2)

J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express 10(12), 515–520 (2002).
[Crossref] [PubMed]

R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
[Crossref]

2001 (1)

R. J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86(15), 3288–3291 (2001).
[Crossref] [PubMed]

2000 (1)

1999 (2)

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6(5), 449–454 (1999).
[Crossref]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the Cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82(18), 3568–3571 (1999).
[Crossref]

1998 (1)

D. Xiaoli and S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9(7), 1031–1035 (1998).
[Crossref]

1997 (2)

1996 (1)

1995 (3)

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34(1), 183–188 (1995).
[Crossref]

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16(1), 1–6 (1995).
[Crossref]

R. Dändliker, K. Hug, J. Politch, and E. Zimmermann, “High accuracy distance measurement with multiple-wavelength interferometry,” Opt. Eng. 34(8), 2407–2412 (1995).
[Crossref]

1993 (1)

1988 (1)

1982 (1)

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).

Ai, C.

Bouma, B. E.

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S.-H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging.,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
[Crossref] [PubMed]

Bustraan, K.

Chen, L.

R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
[Crossref]

Cheng, W.-Y.

R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
[Crossref]

Choi, S.

Chun, B. J.

Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
[Crossref]

Y.-J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S.-W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009).
[Crossref] [PubMed]

Ciddor, P. E.

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

Dändliker, R.

de Bonth, S.

de Groot, P.

Deck, L.

Decker, J. E.

Desjardins, A. E.

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S.-H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging.,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
[Crossref] [PubMed]

Diddams, S. A.

Diels, J.-C.

R. J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86(15), 3288–3291 (2001).
[Crossref] [PubMed]

Falaggis, K.

Hall, J. L.

J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express 10(12), 515–520 (2002).
[Crossref] [PubMed]

R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
[Crossref]

Hänsch, T. W.

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the Cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82(18), 3568–3571 (1999).
[Crossref]

Hartmann, M.

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16(1), 1–6 (1995).
[Crossref]

Holman, K. W.

R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
[Crossref]

Holzwarth, R.

N. Schuhler, Y. Salvadé, S. Lévêque, R. Dändliker, and R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. 31(21), 3101–3103 (2006).
[Crossref] [PubMed]

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the Cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82(18), 3568–3571 (1999).
[Crossref]

Huang, H.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6(5), 449–454 (1999).
[Crossref]

Hug, K.

R. Dändliker, K. Hug, J. Politch, and E. Zimmermann, “High accuracy distance measurement with multiple-wavelength interferometry,” Opt. Eng. 34(8), 2407–2412 (1995).
[Crossref]

Hyun, S.

Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” Annals of CIRP 59(1), 555–558 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Y.-J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S.-W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009).
[Crossref] [PubMed]

Y.-J. Kim, J. Jin, Y. Kim, S. Hyun, and S.-W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express 16(1), 258–264 (2008).
[Crossref] [PubMed]

Itoh, M.

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6(5), 449–454 (1999).
[Crossref]

Jin, J.

Jones, R. J.

R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
[Crossref]

R. J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86(15), 3288–3291 (2001).
[Crossref] [PubMed]

Joo, K.-N.

Jost, J. D.

Kang, C.-S.

Kasiwagi, K.

Kasuya, Y.

Katuo, S.

D. Xiaoli and S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9(7), 1031–1035 (1998).
[Crossref]

Kim, J. W.

Kim, J.-A.

Kim, S.-W.

J. You, Y.-J. Kim, and S.-W. Kim, “GPU-accelerated white-light scanning interferometer for large-area, high-speed surface profile measurements,” Int. J. Nanomanufacturing 8(1/2), 31 (2012).
[Crossref]

Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” Annals of CIRP 59(1), 555–558 (2010).
[Crossref]

S.-W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Y.-J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S.-W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009).
[Crossref] [PubMed]

Y.-J. Kim, J. Jin, Y. Kim, S. Hyun, and S.-W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express 16(1), 258–264 (2008).
[Crossref] [PubMed]

J. Jin, Y.-J. Kim, Y. Kim, S.-W. Kim, and C.-S. Kang, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
[Crossref] [PubMed]

K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006).
[Crossref] [PubMed]

J. S. Oh and S.-W. Kim, “Femtosecond laser pulses for surface-profile metrology,” Opt. Lett. 30(19), 2650–2652 (2005).
[Crossref] [PubMed]

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34(1), 183–188 (1995).
[Crossref]

Kim, Y.

S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” Annals of CIRP 59(1), 555–558 (2010).
[Crossref]

Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Y.-J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S.-W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009).
[Crossref] [PubMed]

Y.-J. Kim, J. Jin, Y. Kim, S. Hyun, and S.-W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express 16(1), 258–264 (2008).
[Crossref] [PubMed]

J. Jin, Y.-J. Kim, Y. Kim, S.-W. Kim, and C.-S. Kang, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
[Crossref] [PubMed]

Kim, Y.-J.

J. You, Y.-J. Kim, and S.-W. Kim, “GPU-accelerated white-light scanning interferometer for large-area, high-speed surface profile measurements,” Int. J. Nanomanufacturing 8(1/2), 31 (2012).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” Annals of CIRP 59(1), 555–558 (2010).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
[Crossref]

S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
[Crossref]

Y.-J. Kim, Y. Kim, B. J. Chun, S. Hyun, and S.-W. Kim, “All-fiber-based optical frequency generation from an Er-doped fiber femtosecond laser,” Opt. Express 17(13), 10939–10945 (2009).
[Crossref] [PubMed]

Y.-J. Kim, J. Jin, Y. Kim, S. Hyun, and S.-W. Kim, “A wide-range optical frequency generator based on the frequency comb of a femtosecond laser,” Opt. Express 16(1), 258–264 (2008).
[Crossref] [PubMed]

J. Jin, Y.-J. Kim, Y. Kim, S.-W. Kim, and C.-S. Kang, “Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser,” Opt. Express 14(13), 5968–5974 (2006).
[Crossref] [PubMed]

Kojima, S.

Kong, I.-B.

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34(1), 183–188 (1995).
[Crossref]

Kurokawa, T.

Lee, J.

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
[Crossref]

Lee, K.

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[Crossref]

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M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6(5), 449–454 (1999).
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S. Hyun, Y.-J. Kim, Y. Kim, and S.-W. Kim, “Absolute distance measurement using the frequency comb of a femtosecond laser,” Annals of CIRP 59(1), 555–558 (2010).
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Appl. Opt. (6)

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R. J. Jones, W.-Y. Cheng, K. W. Holman, L. Chen, J. L. Hall, and J. Ye, “Absolute-frequency measurement of the iodine-based length standard at 514.67 nm,” Appl. Phys. B 74(6), 597–601 (2002).
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IEEE Trans. Med. Imaging (1)

A. E. Desjardins, B. J. Vakoc, M. J. Suter, S.-H. Yun, G. J. Tearney, and B. E. Bouma, “Real-time FPGA processing for high-speed optical frequency domain imaging.,” IEEE Trans. Med. Imaging 28(9), 1468–1472 (2009).
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Int. J. Nanomanufacturing (1)

J. You, Y.-J. Kim, and S.-W. Kim, “GPU-accelerated white-light scanning interferometer for large-area, high-speed surface profile measurements,” Int. J. Nanomanufacturing 8(1/2), 31 (2012).
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J. Opt. Soc. Am. B (1)

Laser Focus (1)

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).

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Y.-J. Kim, B. J. Chun, Y. Kim, S. Hyun, and S.-W. Kim, “Generation of optical frequencies out of the frequency comb of a femtosecond laser for DWDM telecommunication,” Laser Phys. Lett. 7(7), 522–527 (2010).
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S. Hyun, Y.-J. Kim, Y. Kim, J. Jin, and S.-W. Kim, “Absolute length measurement with the frequency comb of a femtosecond laser,” Meas. Sci. Technol. 20(9), 095302 (2009).
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Measurement (1)

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16(1), 1–6 (1995).
[Crossref]

Nat. Photonics (4)

S.-W. Kim, “Metrology: Combs rule,” Nat. Photonics 3(6), 313–314 (2009).
[Crossref]

N. R. Newbury, “Searching for applications with a fine-tooth comb,” Nat. Photonics 5(4), 186–188 (2011).
[Crossref]

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[Crossref]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010).
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I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34(1), 183–188 (1995).
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Opt. Lett. (5)

Opt. Rev. (1)

M. Tsai, H. Huang, M. Itoh, and T. Yatagai, “Fractional fringe order method using Fourier analysis for absolute measurement of block gauge thickness,” Opt. Rev. 6(5), 449–454 (1999).
[Crossref]

Phys. Rev. Lett. (2)

T. Udem, J. Reichert, R. Holzwarth, and T. W. Hänsch, “Absolute optical frequency measurement of the Cesium D1 line with a mode-locked laser,” Phys. Rev. Lett. 82(18), 3568–3571 (1999).
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R. J. Jones and J.-C. Diels, “Stabilization of femtosecond lasers for optical frequency metrology and direct optical to radio frequency synthesis,” Phys. Rev. Lett. 86(15), 3288–3291 (2001).
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Figures (7)

Fig. 1
Fig. 1

Frequency-comb-referenced scheme of multi-wavelength interferometry for fast measurement of largely stepped surface profiles. Four wavelengths in the 1.5 μm range are generated with reference to the Rb atomic clock and then frequency doubled using a PPLN crystal to the 0.75 μm range to fit in the detection wavelength range of the conventional CCD camera. A Twyman-Green interferometer is used to detect multiple interferograms by phase shifting at each wavelength. PLL: phase locked loop, PPLN: periodically poled lithium niobate, PZT: piezoelectric transducer, CCD: charge couple device, M: mirror, FBG: fiber Bragg grating, BS: beam splitter, OFG: optical frequency generator.

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Fig. 2
Fig. 2

Generation of four wavelengths referenced to the frequency comb: (a) four wavelengths generated in parallel (measured using an OSA with 0.07 nm resolution), (b) sequential transfer of the generated four wavelengths using a high-speed switch (monitored by a wavelength meter with 30 MHz accuracy), and (c) wavelength uncertainty evaluated as the Allan deviation (with the frequency counter). fr: pulse repetition rate, fo: carrier offset frequency, fb: beat frequency used for phase locking, and fOFG: frequency of the finally generated wavelengths.

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Fig. 3
Fig. 3

Measurement procedure of the absolute 3-D surface profile: (a) interferograms obtained for four selected wavelengths with six phase shifts for each wavelength, (b) extracted phase maps and (c) reconstructed surface 3-D profile.

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Fig. 4
Fig. 4

Measurement flow of multi-wavelength interferometry exploiting the A-bucket phase measuring algorithm together with the exact fraction method.

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Fig. 5
Fig. 5

Wavefront distortion measured at the exit aperture of the PPLN crystal (a) and after the single-mode fiber used for spatial mode filtering (b).

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Fig. 6
Fig. 6

Measured step heights of the standard step specimen: (a) 3-D surface profile and (b) its sectional view (along line a-a’) of the gauge blocks with heights of 0.5 mm and 1.8 mm; (c) 3-D surface profile and (d) its sectional view (along line b-b’) of the 70 μm standard specimen.

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Fig. 7
Fig. 7

Repeatability evaluation using 30 consecutive height measurements: (a) six sample points (a to f) on the two gauge blocks, (b) variation of the measured step-heights at three sample points on gauge block A (height: 0.5 mm), and (c) variation of the measured step-height at three sample points on gauge block B (height: 1.8 mm).

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Tables (2)

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Table 1 Wavefront aberration before and after spatial mode filtering

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Table 2 Uncertainty evaluation of step height measurement (h: meters)

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Equations (2)

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I( x,y )= I 0 ⋅[ 1+γ(x,y)⋅cos( 4π λ h( x,y )+Δ ϕ 0 ) ],
| h( x,y )− λ i 2 ⋅[ m i ( x,y )+ e i ( x,y ) ] |<α⋅( λ i 2 ),

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