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.

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2012

2011

2010

S. A. Diddams, “The evolving optical frequency comb [Invited],” J. Opt. Soc. Am. B27(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]

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[CrossRef]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics4(10), 716–720 (2010).
[CrossRef]

2009

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. Imaging28(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. Photonics3(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. Photonics3(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. Express17(13), 10939–10945 (2009).
[CrossRef] [PubMed]

2008

2006

2005

2004

2003

2002

J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express10(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. B74(6), 597–601 (2002).
[CrossRef]

2001

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

1999

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

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

1996

1995

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,” Measurement16(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

1988

1982

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus18, 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. Imaging28(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. B74(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. B74(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. Express17(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. Photonics3(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. Imaging28(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.

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. B74(6), 597–601 (2002).
[CrossRef]

J. D. Jost, J. L. Hall, and J. Ye, “Continuously tunable, precise, single frequency optical signal generator,” Opt. Express10(12), 515–520 (2002).
[CrossRef] [PubMed]

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,” Measurement16(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. B74(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 CIRP59(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. Express17(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. Express16(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. B74(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. Nanomanufacturing8(1/2), 31 (2012).
[CrossRef]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics4(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 CIRP59(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.-W. Kim, “Metrology: Combs rule,” Nat. Photonics3(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. Express17(13), 10939–10945 (2009).
[CrossRef] [PubMed]

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, 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. Express16(1), 258–264 (2008).
[CrossRef] [PubMed]

K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express14(13), 5954–5960 (2006).
[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. Express14(13), 5968–5974 (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 CIRP59(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]

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. Express17(13), 10939–10945 (2009).
[CrossRef] [PubMed]

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, 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. Express16(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. Express14(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. Nanomanufacturing8(1/2), 31 (2012).
[CrossRef]

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics4(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 CIRP59(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]

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. Express17(13), 10939–10945 (2009).
[CrossRef] [PubMed]

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, 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. Express16(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. Express14(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. Photonics4(10), 716–720 (2010).
[CrossRef]

Lee, K.

J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics4(10), 716–720 (2010).
[CrossRef]

Lee, S.

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and S. Lee, “Precision depth measurement of through silicon vias (TSVs) on 3D semiconductor packaging process,” Opt. Express20(5), 5011–5016 (2012).
[CrossRef] [PubMed]

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J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement16(1), 1–6 (1995).
[CrossRef]

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S.-W. Kim, “Metrology: Combs rule,” Nat. Photonics3(6), 313–314 (2009).
[CrossRef]

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[CrossRef]

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J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics4(10), 716–720 (2010).
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Opt. Lett.

Opt. Rev.

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]

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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]

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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.

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.

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.

Fig. 4
Fig. 4

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

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).

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.

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).

Tables (2)

Tables Icon

Table 1 Wavefront aberration before and after spatial mode filtering

Tables Icon

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

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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