Abstract

An interferometer based on the differential heterodyne configuration and wavelength-scanning interferometry for measuring large step heights is presented. The proposed interferometer is less sensitive to environmental disturbances than other interferometers and can accurately measure interference phases. A tunable diode laser is utilized to illuminate the interferometer and thus solve the phase ambiguity problem. Counting the interference fringes as the wavelength is scanned through a known change in wavelength directly determines the step height. Three gauge blocks of different lengths, 5, 10, and 50 mm, are individually wrung on a steel plate to simulate large step heights. Comparing the results measured by the proposed interferometer with those by the gauge block interferometer reveals that the accuracy is approximately 100 nm.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. J. Tiziani, A. Rothe, N. Maier, “Dual-wavelength heterodyne differential interferometer for high-precision measurements of reflective aspherical surfaces and step heights,” Appl. Opt. 35, 3525–3533 (1996).
    [CrossRef] [PubMed]
  2. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
    [CrossRef] [PubMed]
  3. J. Thiel, T. Pfeifer, M. Hartmann, “Interferometric measurement of absolute distance of up to 40 m,” Measurement 16, 1–6 (1995).
    [CrossRef]
  4. X. Dai, K. Seta, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
    [CrossRef]
  5. J. A. Stone, A. Stejskal, L. Howard, “Absolute interferometry with a 670-nm external cavity diode laser,” Appl. Opt. 38, 5981–5994 (1999).
    [CrossRef]
  6. P. Hariharan, Basics of Interferometry (Academic, Boston, 1992), Chap. 8, pp. 70–71.
  7. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Geneva, Switzerland, 1995).
  8. K. Liu, M. G. Littman, “Novel geometry for single-mode scanning of tunable lasers,” Opt. Lett. 6, 117–118 (1981).
    [CrossRef] [PubMed]
  9. K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
    [CrossRef]
  10. N. Khélifa, H. Fang, J. Xu, P. Juncar, M. Himbert, “Refractometer for tracking changes in the refractive index of air near 780 nm,” Appl. Opt. 37, 156–161 (1998).
    [CrossRef]
  11. C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
    [CrossRef]

1999 (1)

1998 (2)

N. Khélifa, H. Fang, J. Xu, P. Juncar, M. Himbert, “Refractometer for tracking changes in the refractive index of air near 780 nm,” Appl. Opt. 37, 156–161 (1998).
[CrossRef]

X. Dai, K. Seta, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

1996 (2)

1995 (1)

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

1994 (1)

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

1986 (1)

1981 (1)

Birch, K. P.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Dai, X.

X. Dai, K. Seta, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Downs, M. J.

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Fang, H.

Hariharan, P.

P. Hariharan, Basics of Interferometry (Academic, Boston, 1992), Chap. 8, pp. 70–71.

Hartmann, M.

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

Himbert, M.

Howard, L.

Iwata, K.

Juncar, P.

Khélifa, N.

Kikuta, H.

Littman, M. G.

Liu, K.

Maier, N.

Nagata, R.

Pfeifer, T.

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

Rothe, A.

Seta, K.

X. Dai, K. Seta, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Stejskal, A.

Stone, J. A.

Su, C. S.

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

Thiel, J.

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

Tiziani, H. J.

Wu, C. M.

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

Xu, J.

Appl. Opt. (4)

Meas. Sci. Technol. (2)

C. M. Wu, C. S. Su, “Nonlinearity in measurements of length by optical interferometry,” Meas. Sci. Technol. 7, 62–68 (1996).
[CrossRef]

X. Dai, K. Seta, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Measurement (1)

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

Metrologia (1)

K. P. Birch, M. J. Downs, “Correction to the updated Edlén equation for the refractive index of air,” Metrologia 31, 315–316 (1994).
[CrossRef]

Opt. Lett. (1)

Other (2)

P. Hariharan, Basics of Interferometry (Academic, Boston, 1992), Chap. 8, pp. 70–71.

International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement (International Organization for Standardization, Geneva, Switzerland, 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

DHI. BSP, beam separation plate; PBS, polarization beam splitter; Q, quarter-wave plate; M, mirror; P, polarizer; D, detector.

Fig. 2
Fig. 2

Experimental setup for measuring large step heights. ECDL, external cavity diode laser; APP, anamorphic prism pair; I, isolator; H, half-wave plate; AOM, acousto-optic modulator; BSP, beam separation plate; BS, beam splitter; PBS, polarization beam splitter; Q, quarter-wave plate; M, mirror; P, polarizer; D, detector; PM, phase meter.

Fig. 3
Fig. 3

Variation in the interference phase with time, determined experimentally when the test sample is a plane mirror and the wavelength is not scanned.

Fig. 4
Fig. 4

Wavelength variation against time, determined after a wavelength scan has just been completed.

Fig. 5
Fig. 5

Test sample measured at two positions to eliminate the additional OPD due to the inclination of the test sample.

Tables (1)

Tables Icon

Table 1 Comparison of Large Step-Height Measurements by the DWSHI and the GBI

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

IAcos2πfdt+ϕA,
IBcos2πfdt+ϕB,
ϕ=ϕB-ϕA=4πnh/λ.
h=λ/2nϕ/2π=λ/2nm+e,
h=λ1/2nϕ1/2π=λ1/2nm1+e1,
h=λ2/2nϕ2/2π=λ2/2nm2+e2.
h=λs/2nϕs/2π=λs/2nms+es
λs=λ1λ2/λ2-λ1,
ϕs=ϕ1-ϕ2,
ms+es=m1+e1-m2+e2.
u2h=hλs2u2λs+hϕs2u2ϕs=h2uλsλs2+λs2n2uϕs2π2,
uλsλs2=λsλ12u2λ1+λsλ22u2λ2λs2=λs2u2λ1λ14+u2λ2λ24,
uλ1/λ1uλ2/λ2uλ/λWM,
uλs/λs2λ/Δλuλ/λWM.
uhλ/Δλλ/2n×uϕs/2π.
dϕ=-4πnh/λ2dλ.
ϕs=ϕh+ϕa,
ϕs1=ϕh+ϕa,
ϕs2=-ϕh+ϕa.

Metrics