Abstract

We describe a laser interferometric system in which two objectives are used to measure surface profile on a connectorized fiber-end surface. By the use of the proposed illumination design a He-Ne laser as a point light source is transformed to an extended light source, which is beneficial to localize interference fringe pattern near the test surface. To obtain an optimal contrast of the interference fringe pattern, the flat mirror with an adjustable reflection ratio is used to suit different test surfaces. A piezoelectric transducer attached on the reference mirror can move precisely along the optical axis of the objective and permits implementation of four-step phase-shifting interferometry without changing the relative position between the CCD sensor and the test surface. Therefore, an absolutely constant optical magnification can be accurately kept to capture the interference fringe patterns resulting from a combination of light reflected from both the reference flat mirror and the test surface. The experimental result shows that surface profile on a fiber-end with surface features such as a small fiber diameter of 125 μm and a low reflection ratio of less than 4% are measurable. Measurements on a standard calibration ball show that the accuracy of the proposed setup is comparable with that of existing white-light interferometers and stylus profilometers.

© 2004 Optical Society of America

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  1. L. Li, A. K. Somani, “Blocking performance of fixed-paths least-congestion routing in multifibre WDM networks,” International Journal of Communications Systems 15(2–3), 143–159 (2002).
    [CrossRef]
  2. M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
    [CrossRef]
  3. B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
    [CrossRef]
  4. S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).
  5. Y. Z. Dai, F. P. Chiang, “Contouring by moiré method interferometry,” Exp. Mech. 31, 76–81 (1991).
    [CrossRef]
  6. C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
    [CrossRef]
  7. C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
    [CrossRef]
  8. X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
    [CrossRef]
  9. P. S. Huang, Y. Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
    [CrossRef]
  10. R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
    [CrossRef]
  11. C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
    [CrossRef]
  12. C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
    [CrossRef]
  13. S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Investigation of membrane deformation by a fringe projection method,” Appl. Opt. 41, 101–106 (2002).
    [CrossRef] [PubMed]
  14. J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 35–44 (1989).
    [CrossRef]
  15. A. Ghatak, Optics (McGraw-Hill, New York, 1992).
  16. P. Hariharan, Optical Interferometry (Academic, Sydney, 1985).
  17. J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
    [CrossRef]
  18. S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
    [CrossRef]
  19. I. Abdulhalim, “Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).
  20. P. Armitage, “How to optimise interferometer performance,” Laser Focus World 35, 257–260 (1999).
  21. M. Stedman, K. Lindsey, “Limits of surface measurement by stylus instruments,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 56–61 (1989).
    [CrossRef]
  22. C. Y. Poon, B. Bhushan, “Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler,” Wear 190, 76–88 (1995).
    [CrossRef]

2002 (2)

L. Li, A. K. Somani, “Blocking performance of fixed-paths least-congestion routing in multifibre WDM networks,” International Journal of Communications Systems 15(2–3), 143–159 (2002).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Investigation of membrane deformation by a fringe projection method,” Appl. Opt. 41, 101–106 (2002).
[CrossRef] [PubMed]

2001 (5)

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
[CrossRef]

I. Abdulhalim, “Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).

R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
[CrossRef]

C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
[CrossRef]

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

2000 (2)

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

1999 (2)

P. Armitage, “How to optimise interferometer performance,” Laser Focus World 35, 257–260 (1999).

P. S. Huang, Y. Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

1998 (2)

S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

1995 (2)

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
[CrossRef]

C. Y. Poon, B. Bhushan, “Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler,” Wear 190, 76–88 (1995).
[CrossRef]

1992 (1)

X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
[CrossRef]

1991 (1)

Y. Z. Dai, F. P. Chiang, “Contouring by moiré method interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

1990 (1)

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Abdulhalim, I.

I. Abdulhalim, “Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).

Armitage, P.

P. Armitage, “How to optimise interferometer performance,” Laser Focus World 35, 257–260 (1999).

Bhushan, B.

C. Y. Poon, B. Bhushan, “Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler,” Wear 190, 76–88 (1995).
[CrossRef]

Biegen, J. F.

J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 35–44 (1989).
[CrossRef]

Bille, J. F.

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Bohris, C.

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Bryanston-Cross, P. J.

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
[CrossRef]

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Chan, K. C.

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

Chiang, F. P.

P. S. Huang, Y. Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Y. Z. Dai, F. P. Chiang, “Contouring by moiré method interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Chung, W. H.

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

Dai, Y. Z.

Y. Z. Dai, F. P. Chiang, “Contouring by moiré method interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Dong, X. Y.

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

Echarri, R. M.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

Fleischer, M.

R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
[CrossRef]

Garea, M. T.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

Ghatak, A.

A. Ghatak, Optics (McGraw-Hill, New York, 1992).

Guan, B. O.

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Interferometry (Academic, Sydney, 1985).

Ho, S. L.

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

Honda, R.

S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).

Hu, Y. Q.

P. S. Huang, Y. Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Huang, P. S.

P. S. Huang, Y. Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Klingenberg, M.

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Komer, K.

R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
[CrossRef]

Kurek, R.

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Li, L.

L. Li, A. K. Somani, “Blocking performance of fixed-paths least-congestion routing in multifibre WDM networks,” International Journal of Communications Systems 15(2–3), 143–159 (2002).
[CrossRef]

Lindsey, K.

M. Stedman, K. Lindsey, “Limits of surface measurement by stylus instruments,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 56–61 (1989).
[CrossRef]

Mitachi, S.

S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).

Nagase, R.

S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).

Niemz, M. H.

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Poon, C. Y.

C. Y. Poon, B. Bhushan, “Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler,” Wear 190, 76–88 (1995).
[CrossRef]

Quan, C.

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Investigation of membrane deformation by a fringe projection method,” Appl. Opt. 41, 101–106 (2002).
[CrossRef] [PubMed]

C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
[CrossRef]

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
[CrossRef]

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
[CrossRef]

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Shang, H. M.

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Investigation of membrane deformation by a fringe projection method,” Appl. Opt. 41, 101–106 (2002).
[CrossRef] [PubMed]

C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
[CrossRef]

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
[CrossRef]

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
[CrossRef]

Simon, J. M.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

Simon, M. C.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

Smythe, R. A.

J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 35–44 (1989).
[CrossRef]

Somani, A. K.

L. Li, A. K. Somani, “Blocking performance of fixed-paths least-congestion routing in multifibre WDM networks,” International Journal of Communications Systems 15(2–3), 143–159 (2002).
[CrossRef]

Stedman, M.

M. Stedman, K. Lindsey, “Limits of surface measurement by stylus instruments,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 56–61 (1989).
[CrossRef]

Su, X. Y.

X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
[CrossRef]

Takeuchi, Y.

S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).

Tam, H. Y.

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

Tay, C. J.

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Investigation of membrane deformation by a fringe projection method,” Appl. Opt. 41, 101–106 (2002).
[CrossRef] [PubMed]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
[CrossRef]

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
[CrossRef]

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
[CrossRef]

Tiziani, H. J.

R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
[CrossRef]

von Bally, G.

X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
[CrossRef]

Vukicevic, D.

X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
[CrossRef]

Wallwiener, D.

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Wang, S. H.

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Investigation of membrane deformation by a fringe projection method,” Appl. Opt. 41, 101–106 (2002).
[CrossRef] [PubMed]

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
[CrossRef]

Windecker, R.

R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
[CrossRef]

Zhou, W. S.

X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (1)

B. O. Guan, H. Y. Tam, S. L. Ho, W. H. Chung, X. Y. Dong, “Simultaneous strain and temperature measurement using a single fibre Bragg grating,” Electron. Lett. 36, 1018–1019 (2000).
[CrossRef]

Exp. Mech. (1)

Y. Z. Dai, F. P. Chiang, “Contouring by moiré method interferometry,” Exp. Mech. 31, 76–81 (1991).
[CrossRef]

Glass Technology (1)

S. Mitachi, R. Nagase, Y. Takeuchi, R. Honda, “Durable glass ceramic ferrule for general telecommunication use,” Glass Technology 39(3), 98–99 (1998).

International Journal of Communications Systems (1)

L. Li, A. K. Somani, “Blocking performance of fixed-paths least-congestion routing in multifibre WDM networks,” International Journal of Communications Systems 15(2–3), 143–159 (2002).
[CrossRef]

J. Mod. Opt. (2)

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

I. Abdulhalim, “Theory for double beam interference microscopes with coherence effects and verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).

Laser Focus World (1)

P. Armitage, “How to optimise interferometer performance,” Laser Focus World 35, 257–260 (1999).

Lasers in Medical Science (1)

M. Klingenberg, C. Bohris, M. H. Niemz, J. F. Bille, R. Kurek, D. Wallwiener, “Multifibre application in laser-induced interstitial thermotherapy under on-line MR control,” Lasers in Medical Science 15, 6–14 (2000).
[CrossRef]

Meas. Sci. Technol. (1)

S. H. Wang, C. J. Tay, C. Quan, H. M. Shang, “Determination of deflection and Young’s modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279–1286 (2001).
[CrossRef]

Opt. Commun. (4)

C. J. Tay, C. Quan, S. H. Wang, H. M. Shang, “Determination of a micromirror angular rotation using laser interferometric method,” Opt. Commun. 195, 71–77 (2001).
[CrossRef]

C. Quan, C. J. Tay, S. H. Wang, H. M. Shang, K. C. Chan, “Study on deformation of a microphone membrane using multiple-wavelength interferometry,” Opt. Commun. 197, 279–287 (2001).
[CrossRef]

C. Quan, C. J. Tay, H. M. Shang, P. J. Bryanston-Cross, “Contour measurement by fibre optic fringe projection and Fourier transform analysis,” Opt. Commun. 118, 479–483 (1995).
[CrossRef]

X. Y. Su, W. S. Zhou, G. von Bally, D. Vukicevic, “Automated phase measuring profilometry using defocused projection of a Ronchi grating,” Opt. Commun. 94, 561–571 (1992).
[CrossRef]

Opt. Eng. (1)

P. S. Huang, Y. Q. Hu, F. P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Opt. Laser Technol. (1)

C. Quan, P. J. Bryanston-Cross, “Double-source holographic contouring using fibre optics,” Opt. Laser Technol. 22, 255–259 (1990).
[CrossRef]

Opt. Lasers Eng. (1)

R. Windecker, M. Fleischer, K. Komer, H. J. Tiziani, “Testing micro devices with fringe protection and white-light interferometry,” Opt. Lasers Eng. 36, 141–154 (2001).
[CrossRef]

Wear (1)

C. Y. Poon, B. Bhushan, “Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler,” Wear 190, 76–88 (1995).
[CrossRef]

Other (4)

M. Stedman, K. Lindsey, “Limits of surface measurement by stylus instruments,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 56–61 (1989).
[CrossRef]

J. F. Biegen, R. A. Smythe, “High resolution phase measuring laser interferometric microscope for engineering surface metrology,” in Surface Measurement and Characterization, J. M. Bennett, ed., Proc. SPIE1009, 35–44 (1989).
[CrossRef]

A. Ghatak, Optics (McGraw-Hill, New York, 1992).

P. Hariharan, Optical Interferometry (Academic, Sydney, 1985).

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Figures (10)

Fig. 1
Fig. 1

(a) Close-up of an optical cable connector. (b) Schematic diagram of the connector (not to scale) shown in (a).

Fig. 2
Fig. 2

Experimental arrangement of the proposed method.

Fig. 3
Fig. 3

Fiber-end surface image.

Fig. 4
Fig. 4

Fringe pattern with phase shifts corresponding to (a) 0°; (b) 90°; (c) 180°; (d) 270°.

Fig. 5
Fig. 5

(a) Wrapped phase map. (b) Unwrapped phase map. (c) Cross section of the unwrapped phase map.

Fig. 6
Fig. 6

(a) Plot (3D) of the fiber-end surface. (b) Plot (2D) along the X axis. (c) Plot (2D) along the Y aixs.

Fig. 7
Fig. 7

Another set of typical measured results. (a) Plot (3D) of a fiber-end surface. (b) Plot (2D) along the X axis. (c) Plot (2D) along the Y axis.

Fig. 8
Fig. 8

Two cross-sectional profiles on a flat mirror: (a) with and (b) without isolation measures to prevent vibration and air turbulence.

Fig. 9
Fig. 9

Results of a diamond-turned spherical surface: (a) a 3D plot and (b) a 2D plot across the center of the spherical surface along the X axis.

Fig. 10
Fig. 10

Profile (2D) of a diamond-turned spherical surface produced with (a) the proposed method, (b) a Veeco white-light interferometer, (c) a Stylus Talyform profilometer.

Equations (7)

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Ix, y=I1x, y+I2x, ycosϕx, y+δt),
Ax, y=I1x, y+I2x, ycos ϕx, y,
Bx, y=I1x, y-I2x, ysin ϕx, y,
Cx, y=I1x, y-I2x, ycos ϕx, y,
Dx, y=I1x, y+I2x, ysin ϕx, y.
ϕx, y=arctanDx, y-Bx, yAx, y-Cx, y.
hx, y=λ4π ϕx, y,

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