Abstract

We describe an improved design of fiber-optic interferometer intended to measure surface profiles with enhanced capability of vibration suppression. The reference wavefront is generated directly from the measurement wave using a multi-mode fiber that eliminates only the spatial wavefront distortion by means of bend loss. The temporal fluctuation caused by vibration is consequently cancelled out in the process of interference since it becomes to exist in both the measurement and reference waves. Further, an injection locking technique is incorporated to stabilize the reference wave intensity and hence make stable the interferometric fringe intensity. Experimental result proves that the proposed fiber-optic interferometer is capable of producing sub-wavelength measurement precision even in the presence of severe vibration with 100-μm amplitude.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
    [CrossRef]
  2. R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).
  3. O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9(2), 59–61 (1984).
    [CrossRef] [PubMed]
  4. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
    [CrossRef]
  5. C. Zhao and J. H. Burge, “Vibration-compensated interferometer for surface metrology,” Appl. Opt. 40(34), 6215–6222 (2001).
    [CrossRef]
  6. M. B. North-Morris, J. VanDelden, and J. C. Wyant, “Phase-shifting birefringent scatterplate interferometer,” Appl. Opt. 41(4), 668–677 (2002).
    [CrossRef] [PubMed]
  7. H. Elfström, A. Lehmuskero, T. Saastamoinen, M. Kuittinen, and P. Vahimaa, “Common-path interferometer with diffractive lens,” Opt. Express 14(9), 3847–3852 (2006).
    [CrossRef] [PubMed]
  8. R. N. Smartt and W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, 351–356 (1975).
  9. H. Kihm and S.-W. Kim, “Fiber-diffraction interferometer for vibration desensitization,” Opt. Lett. 30(16), 2059–2061 (2005).
    [CrossRef] [PubMed]
  10. O. Wallner, P. J. Winzer, and W. R. Leeb, “Alignment tolerances for plane-wave to single-mode fiber coupling and their mitigation by use of pigtailed collimators,” Appl. Opt. 41(4), 637–643 (2002).
    [CrossRef] [PubMed]
  11. J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25(7), 442–444 (2000).
    [CrossRef]
  12. J. M. Fini, “Bend-resistant design of conventional and microstructure fibers with very large mode area,” Opt. Express 14(1), 69–81 (2006).
    [CrossRef] [PubMed]
  13. R. T. Schermer, “Mode scalability in bent optical fibers,” Opt. Express 15(24), 15674–15701 (2007).
    [CrossRef] [PubMed]
  14. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66(3), 216–220 (1976).
    [CrossRef]
  15. G. R. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22(3), 419–426 (1986).
    [CrossRef]
  16. F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21(7), 784–793 (1985).
    [CrossRef]
  17. J. Jin, J. W. Kim, C.-S. Kang, and J.-A. Kim, “Visibility enhanced interferometer based on an injection-locking technique for low reflective materials,” Opt. Express 18(23), 23517–23522 (2010).
    [CrossRef] [PubMed]
  18. I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-square fitting,” Opt. Eng. 34(1), 183–188 (1995).
    [CrossRef]

2010 (1)

2007 (1)

2006 (2)

2005 (1)

2004 (1)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

2002 (2)

2001 (1)

2000 (1)

1995 (1)

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-square fitting,” Opt. Eng. 34(1), 183–188 (1995).
[CrossRef]

1986 (1)

G. R. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22(3), 419–426 (1986).
[CrossRef]

1985 (1)

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21(7), 784–793 (1985).
[CrossRef]

1984 (2)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

O. Y. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9(2), 59–61 (1984).
[CrossRef] [PubMed]

1982 (1)

1976 (1)

1975 (1)

R. N. Smartt and W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, 351–356 (1975).

Brock, N. J.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Burge, J. H.

Elfström, H.

Fini, J. M.

Goldberg, L.

Hadley, G. R.

G. R. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22(3), 419–426 (1986).
[CrossRef]

Hayes, J. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Ina, H.

Jacobsen, G.

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21(7), 784–793 (1985).
[CrossRef]

Jin, J.

Kang, C.-S.

Kihm, H.

Kim, J. W.

Kim, J.-A.

Kim, S.-W.

H. Kihm and S.-W. Kim, “Fiber-diffraction interferometer for vibration desensitization,” Opt. Lett. 30(16), 2059–2061 (2005).
[CrossRef] [PubMed]

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-square fitting,” Opt. Eng. 34(1), 183–188 (1995).
[CrossRef]

Kliner, D. A. V.

Kobayashi, S.

Kong, I.-B.

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-square fitting,” Opt. Eng. 34(1), 183–188 (1995).
[CrossRef]

Koplow, J. P.

Kuittinen, M.

Kwon, O. Y.

Leeb, W. R.

Lehmuskero, A.

Marcuse, D.

Millerd, J. E.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Mogensen, F.

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21(7), 784–793 (1985).
[CrossRef]

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

North-Morris, M. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, “Phase-shifting birefringent scatterplate interferometer,” Appl. Opt. 41(4), 668–677 (2002).
[CrossRef] [PubMed]

Novak, M.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Olesen, H.

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21(7), 784–793 (1985).
[CrossRef]

Saastamoinen, T.

Schermer, R. T.

Smartt, R. N.

R. N. Smartt and W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, 351–356 (1975).

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Steel, W. H.

R. N. Smartt and W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, 351–356 (1975).

Takeda, M.

Vahimaa, P.

VanDelden, J.

Wallner, O.

Winzer, P. J.

Wyant, J. C.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, “Phase-shifting birefringent scatterplate interferometer,” Appl. Opt. 41(4), 668–677 (2002).
[CrossRef] [PubMed]

Zhao, C.

Appl. Opt. (3)

IEEE J. Quantum Electron. (2)

G. R. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22(3), 419–426 (1986).
[CrossRef]

F. Mogensen, H. Olesen, and G. Jacobsen, “Locking conditions and stability properties for a semiconductor laser with external light injection,” IEEE J. Quantum Electron. 21(7), 784–793 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

Jpn. J. Appl. Phys. (1)

R. N. Smartt and W. H. Steel, “Theory and application of point-diffraction interferometers,” Jpn. J. Appl. Phys. 14, 351–356 (1975).

Opt. Eng. (2)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-square fitting,” Opt. Eng. 34(1), 183–188 (1995).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Proc. SPIE (1)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Supplementary Material (4)

» Media 1: MOV (1782 KB)     
» Media 2: MOV (2443 KB)     
» Media 3: MOV (2153 KB)     
» Media 4: MOV (4103 KB)     

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

Interferometer system designed for vibration suppression by incorporating a multi-mode fiber for spatial mode filtering and also a laser diode for injection locking. The measurement wave is depicted in red while the reference wave in blue. HWP: half-wave plate, QWP: quarter-wave plate, LP: linear polarizer, PBS: polarizing beam splitter, BS: beam splitter, SMF: single-mode fiber, MMF: multi-mode fiber, L: lens, LD: laser diode, LP: linear polarizer, CL: collimating lens, FR: Faraday rotator, M: mirror, T: temperature, and i: electric current.

Fig. 2
Fig. 2

Interferometer system built to test vibration suppression in measuring the surface profile of a concave mirror of 25.4 mm diameter.

Fig. 3
Fig. 3

Spectra of the laser diode before and after injection locking. The master laser (blue) indicates the reference wave and the slave laser represents the laser diode before (red) and after (black) injection locking.

Fig. 4
Fig. 4

Fiber output intensity fluctuation measured with target vibration. (a) Excitation amplitude of 30 μm. (b) Excitation amplitude of 100 μm.

Fig. 5
Fig. 5

Singe-frame excerpts obtained by video recording the interference fringe of the target mirror with the same experimental conditions of Fig. 4. (a) Excitation amplitude of 30 μm for the case of MMF + IL (Media 1). (b) Excitation amplitude of 30 μm for the case of SMF (Media 2). (c) Excitation amplitude of 100 μm for MMF + IL (Media 3). (d) Excitation amplitude of 100 μm for SMF (Media 4).

Tables (2)

Tables Icon

Table 1 Combinations of Design Parameters for Bend Loss

Tables Icon

Table 2 Measurement Data of Surface Profile in RMS Value

Equations (2)

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

Δ P P = π κ 2 exp [ 2 γ 3 3 β g 2 R ] e ν γ 3 / 2 V 2 R K ν 1 ( γ a ) K ν + 1 ( γ a ) where  V = k a ( n 1 2 n 2 2 ) 1 / 2 e v = { 2 , v = 0 1 , v = 0 ,   κ = ( n 1 2 k 2 β g 2 ) 1 / 2  and  γ = ( β g 2 n 2 2 k 2 ) 1 / 2
Δ φ = γ δ I Δ ν L 1 cos ( Δ ν / Δ ν L )

Metrics