Abstract

In a modified Twyman–Green interferometer, the optical path variation is measured with the heterodyne central fringe identification technique, as the light beam is focused by a displaced microscopic objective on the front/rear surface of the test transparent plate. The optical path length variation is then measured similarly after the test plate is removed. The geometrical thickness of the test plate can be calculated under the consideration of dispersion effect. This method has a wide measurable range and a high accuracy in the measurable range.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Tsuruta and Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” Jpn. J. Appl. Phys. 14, 369–372 (1975).
  2. B. L. Danielson and C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2975–2979 (1991).
    [CrossRef] [PubMed]
  3. C. J. R. Sheppard, T. J. Connolly, J. Lee, and C. J. Cogswell, “Confocal imaging of a stratified medium,” Appl. Opt. 33, 631–640 (1994).
    [CrossRef] [PubMed]
  4. T. Fukano and I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the 5th Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, 1995), pp. 91–98.
  5. Z. C. Jian, C. C. Hsu, and D. C. Su, “Improved technique for measuring refractive index and thickness of a transparent plate,” Opt. Commun. 226, 135–140 (2003).
    [CrossRef]
  6. J. C. Brasunas and G. M. Cushman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
    [CrossRef]
  7. C. H. Liu, S. C. Yeh, and H. L. Huang, “Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups,” Appl. Opt. 49, 637–643 (2010).
    [CrossRef] [PubMed]
  8. J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48, 2461–2467 (2009).
    [CrossRef] [PubMed]
  9. T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
    [CrossRef]
  10. M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
    [CrossRef]
  11. J. Y. Lee, M. H. Chiu, and D. C. Su, “Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode,” Opt. Commun. 128, 193–196 (1996).
    [CrossRef]
  12. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), p. 118.
  13. J. H. Shia, Z. P. Wang, and C. Y. Guana, “Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase,” Opt. Laser Technol. 41, 351–355 (2009).
    [CrossRef]
  14. J. L. Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33, 1916–1929(1994).
    [CrossRef]
  15. W. T. Wu, Y. L. Chen, H. C. Hsieh, W. Y. Chang, and D. C. Su, “Method for gauge block measurement with the heterodyne central fringe identification technique,” Appl. Opt. 49, 3182–3186 (2010).
    [CrossRef] [PubMed]
  16. IEEE, “Standard for terminology and test methods for analog-to-digital converters,” IEEE Std. 1241-2000 (IEEE, 2000), pp. 25–29.
  17. M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
    [CrossRef]
  18. B. E. A. Saleh and M. C. Teich, “Wave optics,” in Fundamentals of Photonics (Wiley, 1991), pp. 49–60.
  19. A. Miks, J. Novak, and P. Novak, “Analysis of method for measuring thickness of plane-parallel plates and lenses using chromatic confocal sensor,” Appl. Opt. 49, 3259–3264 (2010).
    [CrossRef] [PubMed]
  20. 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, 5968–5974 (2006).
    [CrossRef] [PubMed]
  21. E. Ikonen and K. Riski, “Gauge-block interferometer based on one stabilized laser and a white-light source,” Metrologia 30, 95–104 (1993).
    [CrossRef]
  22. A. Lewis, “Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength,” Meas. Sci. Technol. 5, 694–703 (1994).
    [CrossRef]
  23. K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155–162(1993).
    [CrossRef]

2010 (3)

2009 (2)

J. H. Shia, Z. P. Wang, and C. Y. Guana, “Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase,” Opt. Laser Technol. 41, 351–355 (2009).
[CrossRef]

J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48, 2461–2467 (2009).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

2003 (1)

Z. C. Jian, C. C. Hsu, and D. C. Su, “Improved technique for measuring refractive index and thickness of a transparent plate,” Opt. Commun. 226, 135–140 (2003).
[CrossRef]

2002 (1)

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), p. 118.

2000 (1)

IEEE, “Standard for terminology and test methods for analog-to-digital converters,” IEEE Std. 1241-2000 (IEEE, 2000), pp. 25–29.

1999 (2)

1996 (1)

J. Y. Lee, M. H. Chiu, and D. C. Su, “Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode,” Opt. Commun. 128, 193–196 (1996).
[CrossRef]

1995 (2)

J. C. Brasunas and G. M. Cushman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

T. Fukano and I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the 5th Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, 1995), pp. 91–98.

1994 (3)

1993 (2)

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155–162(1993).
[CrossRef]

E. Ikonen and K. Riski, “Gauge-block interferometer based on one stabilized laser and a white-light source,” Metrologia 30, 95–104 (1993).
[CrossRef]

1991 (2)

B. E. A. Saleh and M. C. Teich, “Wave optics,” in Fundamentals of Photonics (Wiley, 1991), pp. 49–60.

B. L. Danielson and C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2975–2979 (1991).
[CrossRef] [PubMed]

1975 (1)

T. Tsuruta and Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” Jpn. J. Appl. Phys. 14, 369–372 (1975).

Birch, K. P.

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155–162(1993).
[CrossRef]

Boisrobert, C. Y.

Brasunas, J. C.

J. C. Brasunas and G. M. Cushman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Chang, W. Y.

Chen, Y. L.

Chipman, R. A.

Chiu, M. H.

M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
[CrossRef]

J. Y. Lee, M. H. Chiu, and D. C. Su, “Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode,” Opt. Commun. 128, 193–196 (1996).
[CrossRef]

Choi, E. S.

Choi, H. Y.

Cogswell, C. J.

Connolly, T. J.

Cushman, G. M.

J. C. Brasunas and G. M. Cushman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Danielson, B. L.

Downs, M. J.

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155–162(1993).
[CrossRef]

Fukano, T.

T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
[CrossRef]

T. Fukano and I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the 5th Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, 1995), pp. 91–98.

Guana, C. Y.

J. H. Shia, Z. P. Wang, and C. Y. Guana, “Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase,” Opt. Laser Technol. 41, 351–355 (2009).
[CrossRef]

Haruna, M.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), p. 118.

Hsieh, H. C.

Hsu, C. C.

Z. C. Jian, C. C. Hsu, and D. C. Su, “Improved technique for measuring refractive index and thickness of a transparent plate,” Opt. Commun. 226, 135–140 (2003).
[CrossRef]

Huang, H. L.

Ichihara, Y.

T. Tsuruta and Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” Jpn. J. Appl. Phys. 14, 369–372 (1975).

Ikonen, E.

E. Ikonen and K. Riski, “Gauge-block interferometer based on one stabilized laser and a white-light source,” Metrologia 30, 95–104 (1993).
[CrossRef]

Jian, Z. C.

Z. C. Jian, C. C. Hsu, and D. C. Su, “Improved technique for measuring refractive index and thickness of a transparent plate,” Opt. Commun. 226, 135–140 (2003).
[CrossRef]

Jin, J.

Kang, C. S.

Kim, S. W.

Kim, Y.

Kim, Y. J.

Konishi, Y.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

Lee, B. H.

Lee, C.

Lee, J.

Lee, J. Y.

M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
[CrossRef]

J. Y. Lee, M. H. Chiu, and D. C. Su, “Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode,” Opt. Commun. 128, 193–196 (1996).
[CrossRef]

Lewis, A.

A. Lewis, “Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength,” Meas. Sci. Technol. 5, 694–703 (1994).
[CrossRef]

Liu, C. H.

Miks, A.

Na, J.

Nishi, H.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

Novak, J.

Novak, P.

Ohmi, M.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

Pezzaniti, J. L.

Riski, K.

E. Ikonen and K. Riski, “Gauge-block interferometer based on one stabilized laser and a white-light source,” Metrologia 30, 95–104 (1993).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, “Wave optics,” in Fundamentals of Photonics (Wiley, 1991), pp. 49–60.

Sheppard, C. J. R.

Shia, J. H.

J. H. Shia, Z. P. Wang, and C. Y. Guana, “Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase,” Opt. Laser Technol. 41, 351–355 (2009).
[CrossRef]

Su, D. C.

W. T. Wu, Y. L. Chen, H. C. Hsieh, W. Y. Chang, and D. C. Su, “Method for gauge block measurement with the heterodyne central fringe identification technique,” Appl. Opt. 49, 3182–3186 (2010).
[CrossRef] [PubMed]

Z. C. Jian, C. C. Hsu, and D. C. Su, “Improved technique for measuring refractive index and thickness of a transparent plate,” Opt. Commun. 226, 135–140 (2003).
[CrossRef]

M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
[CrossRef]

J. Y. Lee, M. H. Chiu, and D. C. Su, “Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode,” Opt. Commun. 128, 193–196 (1996).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, “Wave optics,” in Fundamentals of Photonics (Wiley, 1991), pp. 49–60.

Tsuruta, T.

T. Tsuruta and Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” Jpn. J. Appl. Phys. 14, 369–372 (1975).

Wang, Z. P.

J. H. Shia, Z. P. Wang, and C. Y. Guana, “Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase,” Opt. Laser Technol. 41, 351–355 (2009).
[CrossRef]

Wu, W. T.

Yamada, Y.

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

Yamaguchi, I.

T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
[CrossRef]

T. Fukano and I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the 5th Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, 1995), pp. 91–98.

Yeh, S. C.

Appl. Opt. (9)

B. L. Danielson and C. Y. Boisrobert, “Absolute optical ranging using low coherence interferometry,” Appl. Opt. 30, 2975–2979 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard, T. J. Connolly, J. Lee, and C. J. Cogswell, “Confocal imaging of a stratified medium,” Appl. Opt. 33, 631–640 (1994).
[CrossRef] [PubMed]

C. H. Liu, S. C. Yeh, and H. L. Huang, “Thickness measurement system for transparent plates using dual digital versatile disc (DVD) pickups,” Appl. Opt. 49, 637–643 (2010).
[CrossRef] [PubMed]

J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48, 2461–2467 (2009).
[CrossRef] [PubMed]

T. Fukano and I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
[CrossRef]

J. L. Pezzaniti and R. A. Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33, 1916–1929(1994).
[CrossRef]

W. T. Wu, Y. L. Chen, H. C. Hsieh, W. Y. Chang, and D. C. Su, “Method for gauge block measurement with the heterodyne central fringe identification technique,” Appl. Opt. 49, 3182–3186 (2010).
[CrossRef] [PubMed]

M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel’s equations and the uses of heterodyne interferometry,” Appl. Opt. 38, 4047–4052 (1999).
[CrossRef]

A. Miks, J. Novak, and P. Novak, “Analysis of method for measuring thickness of plane-parallel plates and lenses using chromatic confocal sensor,” Appl. Opt. 49, 3259–3264 (2010).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys. (1)

T. Tsuruta and Y. Ichihara, “Accurate measurement of lens thickness by using white-light fringes,” Jpn. J. Appl. Phys. 14, 369–372 (1975).

Meas. Sci. Technol. (2)

M. Ohmi, H. Nishi, Y. Konishi, Y. Yamada, and M. Haruna, “High-speed simultaneous measurement of refractive index and thickness of transparent plates by low-coherence interferometry and confocal optics,” Meas. Sci. Technol. 15, 1531–1535 (2004).
[CrossRef]

A. Lewis, “Measurement of length, surface form and thermal expansion coefficient of length bars up to 1.5 m using multiple wavelength,” Meas. Sci. Technol. 5, 694–703 (1994).
[CrossRef]

Metrologia (2)

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30, 155–162(1993).
[CrossRef]

E. Ikonen and K. Riski, “Gauge-block interferometer based on one stabilized laser and a white-light source,” Metrologia 30, 95–104 (1993).
[CrossRef]

Opt. Commun. (2)

J. Y. Lee, M. H. Chiu, and D. C. Su, “Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode,” Opt. Commun. 128, 193–196 (1996).
[CrossRef]

Z. C. Jian, C. C. Hsu, and D. C. Su, “Improved technique for measuring refractive index and thickness of a transparent plate,” Opt. Commun. 226, 135–140 (2003).
[CrossRef]

Opt. Eng. (1)

J. C. Brasunas and G. M. Cushman, “Interferometric but nonspectroscopic technique for measuring the thickness of a transparent plate,” Opt. Eng. 34, 2126–2130 (1995).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

J. H. Shia, Z. P. Wang, and C. Y. Guana, “Theoretical analysis of non-polarizing beam splitters with appropriate amplitude and phase,” Opt. Laser Technol. 41, 351–355 (2009).
[CrossRef]

Other (4)

IEEE, “Standard for terminology and test methods for analog-to-digital converters,” IEEE Std. 1241-2000 (IEEE, 2000), pp. 25–29.

B. E. A. Saleh and M. C. Teich, “Wave optics,” in Fundamentals of Photonics (Wiley, 1991), pp. 49–60.

T. Fukano and I. Yamaguchi, “Measurement of layer thickness by a laser confocal microscope,” in Proceedings of the 5th Meeting on Lightwave Sensing Technology (Japanese Society of Lightwave Sensing Technology, Japan Society of Applied Physics, 1995), pp. 91–98.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), p. 118.

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

The schematic diagram of this method. TDL, tunable diode laser; EOM, electro-optic modulator; FG, function generator; BS, beam splitter; PBS, polarizing beam splitter; MO, microscopic objective; T, transparent plate; M, mirror; TS, translation stage; AN, analyzer; ID, iris diaphragm; PD, photodetector; PM, phase meter.

Fig. 2
Fig. 2

Four identification points in the interferometer.

Fig. 3
Fig. 3

The result of a data acquisition test of the phase meter.

Fig. 4
Fig. 4

The phase changes with the wavelength scanning from λ a to λ b in (a) a correct identification and (b) an incorrect identification with the phase wrapping condition.

Fig. 5
Fig. 5

The MO has a defocus error on the test plane.

Equations (19)

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

I = 1 2 [ 1 + cos ( ω t ϕ ( λ ) ) ] ,
ϕ ( λ ) = 4 π [ d p d s ( λ ) ] λ + ϕ 0 ( λ ) .
I r = 1 2 [ 1 + cos ( ω t ) ] .
Δ ϕ ϕ ( λ b ) ϕ ( λ a ) = 0.
d p = λ a d s ( λ b ) λ b d s ( λ a ) λ a λ b + ξ b a ,
ξ b a λ a λ b [ ϕ 0 ( λ b ) ϕ 0 ( λ a ) ] 4 π ( λ b λ a ) .
d p 1 = d s 1 + ξ b a .
d p 2 = d s 1 + ( n ( λ 0 ) n ( λ 0 ) λ 0 ) d + ξ b a .
d = D 21 n ( λ 0 ) n ( λ 0 ) λ 0 ,
d p 3 = d s 2 + ( n ( λ 0 ) n ( λ 0 ) λ 0 1 ) d + ξ b a .
d p 4 = d s 2 + ξ b a .
d = D 34 n ( λ 0 ) n ( λ 0 ) λ 0 1 ,
{ d = D 21 D 34 n ( λ 0 ) n ( λ 0 ) λ 0 = D 21 ( D 21 D 34 ) ,
δ d c = δ ( Δ ϕ ) λ 1 λ 2 4 π Δ λ .
I = | E s + E p | 2 = 1 2 { 1 + cos [ ω t ϕ ( λ ) + k ρ 2 2 ( 1 f + 2 δ z 1 f ) ] } ,
I D = 1 π ρ 0 2 0 2 π 0 ρ 0 I ρ d ρ d θ = 1 2 [ 1 + V cos ( ω t ϕ ( λ ) ) ] ,
V = sin ( 2 k δ d f ) 2 k δ d f ,
ϕ ( λ ) = 4 π [ d p d s ( λ ) δ d f ] λ + ϕ 0 ( λ ) ,
δ d f = ρ 0 2 8 ( 1 f + 2 δ z 1 f ) .

Metrics