Abstract

A fiber-coupled infrared laser heterodyne interferometer system based on optical scanning is proposed. In this system, the sample is scanned through the combined configuration of a micro-electro-mechanical system mirror and an F-theta lens set. The distortion index of the F-theta lens set is less than 0.01%. In order to enhance the sensitivity of the heterodyne detection system, the dual-balanced heterodyne detection is applied in the measurement of the intermediate frequency signal. The theoretical model and the signal-to-noise ratio expression of the dual-balanced heterodyne detection system are derived in this paper. The interferometer system has a vertical resolution of 0.43 nm and a lateral resolution of 0.95μm. The stability of this system is approximately 1.90 nm for 1 h. Furthermore, the system possesses 8 s measurement time, 94.18 MHz output frequency, and 1550 nm eye-safe operating wavelength. Application of the system may be realized for any sample that has higher transmittance for the eye-safe wavelength.

© 2010 Optical Society of America

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  1. T. J. Kim, T. H. Ghong, and Y. W. Jung, “Study on interface analysis by using spectroscopic ellipsometry,” J. Korean Phys. Soc. 6, 2625–2629 (2009).
  2. A. Bourgeois, Y. Turcant, and C. Walsh, “Ellipsometry porosimetry (EP): Thin film porosimetry by coupling an adsorption setting with an optical measurement, highlights on diffusion results,” Appl. Surf. Sci. 256, S26–S29 (2009).
    [CrossRef]
  3. E. V. Davydenko and A. L. Priorov, “Signal processing in an optical laser triangulation system with the minimum set of components,” Meas. Tech. 10, 1097–1103 (2008).
    [CrossRef]
  4. L. J. Zeng, T. Ohnuki, and H. Matsumoto, “A new method for measuring the thickness and shape of a thin film simultaneously by combining interferometry and laser triangulation,” Proc. SPIE 2861, 1097–1103(1996).
  5. D. Z. Reinstein, T. J. Archer, and M. Gobbe, “Stromal thickness in the normal cornea: Three-dimensional display with Artemis very high-frequency digital ultrasound,” J. Refract. Surg. 25, 776–786 (2009).
    [CrossRef] [PubMed]
  6. M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
    [CrossRef]
  7. B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
    [CrossRef] [PubMed]
  8. K. H. Kwon, B. Soo Kim, and K. M. Chol, “A new scanning heterodyne interferometer scheme for mapping both surface structure and effective local reflection coefficient,” Opt. Express 16, 13456–13454 (2008).
    [CrossRef] [PubMed]
  9. C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
    [CrossRef]
  10. F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Opt. 40, 3389–3396 (1969).
  11. H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in un-doped LiNbO3,” Appl. Phys. Lett. 22, 626–627 (1973).
    [CrossRef]
  12. H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
    [CrossRef]
  13. M. Tsukiji, “The effect of excitation methods on electrical characteristic of fully superconducting generator model,” IEEE Trans. Magnetics 30, 2030–2033 (1994).
    [CrossRef]
  14. J. W. You, D. Kim, and S. Y. Ryu, “Simultaneous measurement method of total and self-interference for the volumetric thickness profilometer,” Opt. Express 17, 1352–1360 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  18. M. A. Arain and N. A. Riza, “Fiber-coupled in-line heterodyne optical interferometer for minimally invasive sensing,” J. Lightwave Technol. 23, 2449–2454 (2005).
    [CrossRef]
  19. N. A. Riza, M. Sheikh, and F. Perez, “Optical substrate thickness measurement system using hybrid fiber-free space optics and selective wavelength interferometry,” Opt. Commun. 269, 24–29 (2007).
    [CrossRef]
  20. Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
    [CrossRef]
  21. Y. Q. Ji and W. M. Shen, “Design of F-Theta lens used in laser marking machine,” Proc. SPIE 6722, 1–5 (2007).

2009

T. J. Kim, T. H. Ghong, and Y. W. Jung, “Study on interface analysis by using spectroscopic ellipsometry,” J. Korean Phys. Soc. 6, 2625–2629 (2009).

A. Bourgeois, Y. Turcant, and C. Walsh, “Ellipsometry porosimetry (EP): Thin film porosimetry by coupling an adsorption setting with an optical measurement, highlights on diffusion results,” Appl. Surf. Sci. 256, S26–S29 (2009).
[CrossRef]

D. Z. Reinstein, T. J. Archer, and M. Gobbe, “Stromal thickness in the normal cornea: Three-dimensional display with Artemis very high-frequency digital ultrasound,” J. Refract. Surg. 25, 776–786 (2009).
[CrossRef] [PubMed]

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

J. W. You, D. Kim, and S. Y. Ryu, “Simultaneous measurement method of total and self-interference for the volumetric thickness profilometer,” Opt. Express 17, 1352–1360 (2009).
[CrossRef] [PubMed]

2008

2007

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry,” Opt. Eng. (Bellingham) 46, 095601 (2007).
[CrossRef]

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

N. A. Riza, M. Sheikh, and F. Perez, “Optical substrate thickness measurement system using hybrid fiber-free space optics and selective wavelength interferometry,” Opt. Commun. 269, 24–29 (2007).
[CrossRef]

Y. Q. Ji and W. M. Shen, “Design of F-Theta lens used in laser marking machine,” Proc. SPIE 6722, 1–5 (2007).

2005

M. A. Arain and N. A. Riza, “Fiber-coupled in-line heterodyne optical interferometer for minimally invasive sensing,” J. Lightwave Technol. 23, 2449–2454 (2005).
[CrossRef]

C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
[CrossRef]

2004

Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
[CrossRef]

1997

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

1996

L. J. Zeng, T. Ohnuki, and H. Matsumoto, “A new method for measuring the thickness and shape of a thin film simultaneously by combining interferometry and laser triangulation,” Proc. SPIE 2861, 1097–1103(1996).

1994

M. Tsukiji, “The effect of excitation methods on electrical characteristic of fully superconducting generator model,” IEEE Trans. Magnetics 30, 2030–2033 (1994).
[CrossRef]

1974

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

1973

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in un-doped LiNbO3,” Appl. Phys. Lett. 22, 626–627 (1973).
[CrossRef]

1969

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Opt. 40, 3389–3396 (1969).

Aguanno, M. V.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry,” Opt. Eng. (Bellingham) 46, 095601 (2007).
[CrossRef]

Arain, M. A.

Archer, T. J.

D. Z. Reinstein, T. J. Archer, and M. Gobbe, “Stromal thickness in the normal cornea: Three-dimensional display with Artemis very high-frequency digital ultrasound,” J. Refract. Surg. 25, 776–786 (2009).
[CrossRef] [PubMed]

Barros, D.

Bourgeois, A.

A. Bourgeois, Y. Turcant, and C. Walsh, “Ellipsometry porosimetry (EP): Thin film porosimetry by coupling an adsorption setting with an optical measurement, highlights on diffusion results,” Appl. Surf. Sci. 256, S26–S29 (2009).
[CrossRef]

Chen, B. Y.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

Chen, F. S.

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Opt. 40, 3389–3396 (1969).

Chen, K. H.

C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
[CrossRef]

Cheon, M. S.

Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
[CrossRef]

Cho, S. H.

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

Chol, K. M.

Connelly, M. J.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry,” Opt. Eng. (Bellingham) 46, 095601 (2007).
[CrossRef]

Davydenko, E. V.

E. V. Davydenko and A. L. Priorov, “Signal processing in an optical laser triangulation system with the minimum set of components,” Meas. Tech. 10, 1097–1103 (2008).
[CrossRef]

Feng, Q. B.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

Ghong, T. H.

T. J. Kim, T. H. Ghong, and Y. W. Jung, “Study on interface analysis by using spectroscopic ellipsometry,” J. Korean Phys. Soc. 6, 2625–2629 (2009).

Gobbe, M.

D. Z. Reinstein, T. J. Archer, and M. Gobbe, “Stromal thickness in the normal cornea: Three-dimensional display with Artemis very high-frequency digital ultrasound,” J. Refract. Surg. 25, 776–786 (2009).
[CrossRef] [PubMed]

Goldner, R. B.

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in un-doped LiNbO3,” Appl. Phys. Lett. 22, 626–627 (1973).
[CrossRef]

Ha, J. H.

Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
[CrossRef]

Haruna, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Hsu, C. V.

C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
[CrossRef]

Hwang, Y. S.

Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
[CrossRef]

Ip, E.

Ji, Y. Q.

Y. Q. Ji and W. M. Shen, “Design of F-Theta lens used in laser marking machine,” Proc. SPIE 6722, 1–5 (2007).

Jung, Y. W.

T. J. Kim, T. H. Ghong, and Y. W. Jung, “Study on interface analysis by using spectroscopic ellipsometry,” J. Korean Phys. Soc. 6, 2625–2629 (2009).

Kahn, J. M.

Kim, D.

Kim, H.

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

Kim, K. S.

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

Kim, T. J.

T. J. Kim, T. H. Ghong, and Y. W. Jung, “Study on interface analysis by using spectroscopic ellipsometry,” J. Korean Phys. Soc. 6, 2625–2629 (2009).

Kwon, K. H.

Lakestani, F.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry,” Opt. Eng. (Bellingham) 46, 095601 (2007).
[CrossRef]

Lee, S. W.

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

Li, C. R.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

Lin, J. Y.

C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
[CrossRef]

Matsumoto, H.

L. J. Zeng, T. Ohnuki, and H. Matsumoto, “A new method for measuring the thickness and shape of a thin film simultaneously by combining interferometry and laser triangulation,” Proc. SPIE 2861, 1097–1103(1996).

Nam, Y. U.

Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
[CrossRef]

Ohmi, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Ohnuki, T.

L. J. Zeng, T. Ohnuki, and H. Matsumoto, “A new method for measuring the thickness and shape of a thin film simultaneously by combining interferometry and laser triangulation,” Proc. SPIE 2861, 1097–1103(1996).

Pak, A.

Perez, F.

N. A. Riza, M. Sheikh, and F. Perez, “Optical substrate thickness measurement system using hybrid fiber-free space optics and selective wavelength interferometry,” Opt. Commun. 269, 24–29 (2007).
[CrossRef]

Priorov, A. L.

E. V. Davydenko and A. L. Priorov, “Signal processing in an optical laser triangulation system with the minimum set of components,” Meas. Tech. 10, 1097–1103 (2008).
[CrossRef]

Protopopov, V. D.

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

Reinstein, D. Z.

D. Z. Reinstein, T. J. Archer, and M. Gobbe, “Stromal thickness in the normal cornea: Three-dimensional display with Artemis very high-frequency digital ultrasound,” J. Refract. Surg. 25, 776–786 (2009).
[CrossRef] [PubMed]

Riza, N. A.

N. A. Riza, M. Sheikh, and F. Perez, “Optical substrate thickness measurement system using hybrid fiber-free space optics and selective wavelength interferometry,” Opt. Commun. 269, 24–29 (2007).
[CrossRef]

M. A. Arain and N. A. Riza, “Fiber-coupled in-line heterodyne optical interferometer for minimally invasive sensing,” J. Lightwave Technol. 23, 2449–2454 (2005).
[CrossRef]

Ryu, S. Y.

Serreze, H. B.

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in un-doped LiNbO3,” Appl. Phys. Lett. 22, 626–627 (1973).
[CrossRef]

Sheikh, M.

N. A. Riza, M. Sheikh, and F. Perez, “Optical substrate thickness measurement system using hybrid fiber-free space optics and selective wavelength interferometry,” Opt. Commun. 269, 24–29 (2007).
[CrossRef]

Shen, W. M.

Y. Q. Ji and W. M. Shen, “Design of F-Theta lens used in laser marking machine,” Proc. SPIE 6722, 1–5 (2007).

Shiraishi, T.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Soo Kim, B.

Su, D. C.

C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
[CrossRef]

Tajiri, H.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Tang, W. H.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

Tsukiji, M.

M. Tsukiji, “The effect of excitation methods on electrical characteristic of fully superconducting generator model,” IEEE Trans. Magnetics 30, 2030–2033 (1994).
[CrossRef]

Turcant, Y.

A. Bourgeois, Y. Turcant, and C. Walsh, “Ellipsometry porosimetry (EP): Thin film porosimetry by coupling an adsorption setting with an optical measurement, highlights on diffusion results,” Appl. Surf. Sci. 256, S26–S29 (2009).
[CrossRef]

Walsh, C.

A. Bourgeois, Y. Turcant, and C. Walsh, “Ellipsometry porosimetry (EP): Thin film porosimetry by coupling an adsorption setting with an optical measurement, highlights on diffusion results,” Appl. Surf. Sci. 256, S26–S29 (2009).
[CrossRef]

Whelan, M. P.

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry,” Opt. Eng. (Bellingham) 46, 095601 (2007).
[CrossRef]

Yan, L. P.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

You, J. W.

Zeng, L. J.

L. J. Zeng, T. Ohnuki, and H. Matsumoto, “A new method for measuring the thickness and shape of a thin film simultaneously by combining interferometry and laser triangulation,” Proc. SPIE 2861, 1097–1103(1996).

Zhang, E. Z.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

Appl. Phys. Lett.

H. B. Serreze and R. B. Goldner, “Study of the wavelength dependence of optically induced birefringence change in un-doped LiNbO3,” Appl. Phys. Lett. 22, 626–627 (1973).
[CrossRef]

Appl. Surf. Sci.

A. Bourgeois, Y. Turcant, and C. Walsh, “Ellipsometry porosimetry (EP): Thin film porosimetry by coupling an adsorption setting with an optical measurement, highlights on diffusion results,” Appl. Surf. Sci. 256, S26–S29 (2009).
[CrossRef]

IEEE Trans. Magnetics

M. Tsukiji, “The effect of excitation methods on electrical characteristic of fully superconducting generator model,” IEEE Trans. Magnetics 30, 2030–2033 (1994).
[CrossRef]

J. Appl. Opt.

F. S. Chen, “Optically induced change of refractive indices in LiNbO3 and LiTaO3,” J. Appl. Opt. 40, 3389–3396 (1969).

J. Korean Phys. Soc.

T. J. Kim, T. H. Ghong, and Y. W. Jung, “Study on interface analysis by using spectroscopic ellipsometry,” J. Korean Phys. Soc. 6, 2625–2629 (2009).

J. Lightwave Technol.

J. Refract. Surg.

D. Z. Reinstein, T. J. Archer, and M. Gobbe, “Stromal thickness in the normal cornea: Three-dimensional display with Artemis very high-frequency digital ultrasound,” J. Refract. Surg. 25, 776–786 (2009).
[CrossRef] [PubMed]

Meas. Tech.

E. V. Davydenko and A. L. Priorov, “Signal processing in an optical laser triangulation system with the minimum set of components,” Meas. Tech. 10, 1097–1103 (2008).
[CrossRef]

Opt. Commun.

N. A. Riza, M. Sheikh, and F. Perez, “Optical substrate thickness measurement system using hybrid fiber-free space optics and selective wavelength interferometry,” Opt. Commun. 269, 24–29 (2007).
[CrossRef]

Opt. Eng. (Bellingham)

M. V. Aguanno, F. Lakestani, M. P. Whelan, and M. J. Connelly, “Full-field heterodyne interferometry using a complementary metal-oxide semiconductor digital signal processor camera for high-resolution profilometry,” Opt. Eng. (Bellingham) 46, 095601 (2007).
[CrossRef]

C. V. Hsu, J. Y. Lin, K. H. Chen, and D. C. Su, “Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates,” Opt. Eng. (Bellingham) 44, 055801–055806 (2005).
[CrossRef]

Opt. Express

Opt. Rev.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4, 507–515 (1997).
[CrossRef]

Proc. SPIE

L. J. Zeng, T. Ohnuki, and H. Matsumoto, “A new method for measuring the thickness and shape of a thin film simultaneously by combining interferometry and laser triangulation,” Proc. SPIE 2861, 1097–1103(1996).

Y. Q. Ji and W. M. Shen, “Design of F-Theta lens used in laser marking machine,” Proc. SPIE 6722, 1–5 (2007).

Rev. Sci. Instrum.

B. Y. Chen, E. Z. Zhang, L. P. Yan, C. R. Li, W. H. Tang, and Q. B. Feng, “A laser interferometer for measuring straightness and its position based on heterodyne interferometry,” Rev. Sci. Instrum. 80, 115113–5 (2009).
[CrossRef] [PubMed]

H. B. Serreze and R. B. Goldner, “A phase-sensitive technique for measuring small birefringence changes,” Rev. Sci. Instrum. 45, 1613–1614 (1974).
[CrossRef]

V. D. Protopopov, S. H. Cho, K. S. Kim, S. W. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78, 076101–10 (2007).
[CrossRef] [PubMed]

Y. U. Nam, M. S. Cheon, J. H. Ha, and Y. S. Hwang, “Improved common-path Fast-scanning heterodyne interferometer system as potential dense-plasma diagnostics,” Rev. Sci. Instrum. 75, 3417–3419 (2004).
[CrossRef]

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Fig. 1
Fig. 1

Schematic of the heterodyne detection: S, source; A, amplifier; BS1–BS5, beam splitters; AOM, acoustic optical modulator; BC1 and BC2, beam collimators; 1/2 WP, 1/2 wave plate; PBS, polarization beam splitter; 1/4 WP, 1/4 wave plate; MEMS M: MEMS mirror; F-THETA, F-theta lens set; SA, sample; M, reflective mirror; I, iris; L, lens; IA1 and IA2, inline analyzers; BDS, balanced detection system; LA, lock-in amplifier.

Fig. 2
Fig. 2

Signal-to-noise ratio relation between balanced detection and traditional detection.

Fig. 3
Fig. 3

Distortion of the F-theta lens.

Fig. 4
Fig. 4

Relation between position and scanning angle.

Fig. 5
Fig. 5

RF signal of the measurement beam and the reference local beam.

Fig. 6
Fig. 6

Example of the thickness variation profile for the 100 mm wide glass.

Fig. 7
Fig. 7

Stability curve of the whole measurement system.

Equations (12)

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S beat ( x , y ) = η A s ( x , y ) A p   cos [ Δ ω t φ m ( x , y ) φ 0 ] ,
S lo = η P LO   cos [ Δ ω t φ LO ] ,
φ m ( x , y ) = Δ φ s + tan 1 [ S Q ( x , y ) S I ( x , y ) ] ,
A s ( x , y ) = S Q ( x , y ) 2 + S I ( x , y ) 2 η A P P LO ,
S Q ( x , y ) = η 2 A s ( x , y ) A p P lo   cos ( φ m ( x , y ) Δ φ s ) ,
S I ( x , y ) = η 2 A s ( x , y ) A p P lo   sin ( φ m ( x , y ) Δ φ s ) ,
φ m ( x + Δ x , y ) φ m ( x , y ) = 2 π n λ [ h ( x + Δ x , y ) h ( x , y ) ] ,
T = 16 n 2 [ ( 1 + n ) 4 + ( n 1 ) 4 2 ( n 1 ) 2 ( n + 1 ) 2 cos ( 2 ψ ) ] ,
T = E 1 2 r 1 2 + E 2 2 r 2 2 E 1 2 + E 2 2 .
SNR balanced = P system P noise = 2 η ε ( 1 ε ) P s h ν ( 1 2 ε ( 1 ε ) ) Δ f i f
SNR c = η P s h ν Δ f i f ,
q f θ = Y f θ f θ < 0.5 % ,

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