Abstract

A demodulation algorithm based on absolute phase recovery of a selected monochromatic frequency is proposed for optical fiber Fabry-Perot pressure sensing system. The algorithm uses Fourier transform to get the relative phase and intercept of the unwrapped phase-frequency linear fit curve to identify its interference-order, which are then used to recover the absolute phase. A simplified mathematical model of the polarized low-coherence interference fringes was established to illustrate the principle of the proposed algorithm. Phase unwrapping and the selection of monochromatic frequency were discussed in detail. Pressure measurement experiment was carried out to verify the effectiveness of the proposed algorithm. Results showed that the demodulation precision by our algorithm could reach up to 0.15kPa, which has been improved by 13 times comparing with phase slope based algorithm.

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2010 (1)

2006 (1)

2002 (3)

2001 (1)

2000 (2)

J. G. Kim, “Absolute temperature measurement using white light interferometry,” J. Opt. Soc. Kor.4(2), 89–93 (2000).
[CrossRef]

A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt.39(13), 2107–2115 (2000).
[CrossRef] [PubMed]

1997 (3)

1996 (2)

P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt.43, 1545–1554 (1996).

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white-light interferometry,” J. Opt. Soc. Am.13(4), 832–843 (1996).
[CrossRef]

1995 (1)

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42(2), 389–401 (1995).
[CrossRef]

1992 (4)

1990 (1)

1989 (1)

Boccara, A. C.

Chen, S.

Chim, S. S. C.

Colonna de Lega, X.

Dändliker, R.

de Groot, P.

P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt.41(22), 4571–4578 (2002).
[CrossRef] [PubMed]

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42(2), 389–401 (1995).
[CrossRef]

Debnath, S. K.

Deck, L.

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42(2), 389–401 (1995).
[CrossRef]

Devillers, R.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt.44(3), 519–534 (1997).
[CrossRef]

Dobson, C. C.

Dresel, T.

Dubois, A.

Farrant, D. I.

Frosio, G.

Grattan, K. T. V.

Harasaki, A.

Häusler, G.

Hibino, K.

Hirabayashi, A.

Kim, J. G.

J. G. Kim, “Absolute temperature measurement using white light interferometry,” J. Opt. Soc. Kor.4(2), 89–93 (2000).
[CrossRef]

Kim, K. H.

Kim, S. H.

Kino, G. S.

Kitagawa, K.

Kothiyal, M. P.

Kramer, J.

Larkin, K. G.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts,” J. Opt. Soc. Am. A14(4), 918–930 (1997).
[CrossRef]

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white-light interferometry,” J. Opt. Soc. Am.13(4), 832–843 (1996).
[CrossRef]

Lee, S. H.

Lim, J. I.

Meggitt, B. T.

Ogawa, H.

Oreb, B. F.

Palmer, A. W.

Pf rtner, A.

Plata, A.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt.44(3), 519–534 (1997).
[CrossRef]

Sandoz, P.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt.44(3), 519–534 (1997).
[CrossRef]

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett.22(14), 1065–1067 (1997).
[CrossRef] [PubMed]

P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt.43, 1545–1554 (1996).

Schmit, J.

Schwider, J.

Smith, L. M.

Turzhitsky, M.

Vabre, L.

Venzke, H.

Wyant, J. C.

Zimmermann, E.

Appl. Opt. (11)

T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt.31(7), 919–925 (1992).
[CrossRef] [PubMed]

A. Hirabayashi, H. Ogawa, and K. Kitagawa, “Fast surface profiler by white-light interferometry by use of a new algorithm based on sampling theory,” Appl. Opt.41(23), 4876–4883 (2002).
[CrossRef] [PubMed]

L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt.28(16), 3339–3342 (1989).
[CrossRef] [PubMed]

S. H. Kim, S. H. Lee, J. I. Lim, and K. H. Kim, “Absolute refractive index measurement method over a broad wavelength region based on white-light interferometry,” Appl. Opt.49(5), 910–914 (2010).
[CrossRef] [PubMed]

G. S. Kino and S. S. C. Chim, “Miraucorrelation microscope,” Appl. Opt.29(26), 3775–3783 (1990).
[CrossRef] [PubMed]

S. S. C. Chim and G. S. Kino, “Three-dimensional image realization in interference microscopy,” Appl. Opt.31(14), 2550–2553 (1992).
[CrossRef] [PubMed]

S. Chen, A. W. Palmer, K. T. V. Grattan, and B. T. Meggitt, “Digital signal-processing techniques for electronically scanned optical-fiber white-light interferometry,” Appl. Opt.31(28), 6003–6010 (1992).
[CrossRef] [PubMed]

A. Pf rtner and J. Schwider, “Dispersion error in white-light linnik interferometers and its implications for evaluation procedures,” Appl. Opt.40(34), 6223–6228 (2001).
[CrossRef] [PubMed]

A. Harasaki, J. Schmit, and J. C. Wyant, “Improved vertical-scanning interferometry,” Appl. Opt.39(13), 2107–2115 (2000).
[CrossRef] [PubMed]

P. de Groot, X. Colonna de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt.41(22), 4571–4578 (2002).
[CrossRef] [PubMed]

S. K. Debnath and M. P. Kothiyal, “Improved optical profiling using the spectral phase in spectrally resolved white-light interferometry,” Appl. Opt.45(27), 6965–6972 (2006).
[CrossRef] [PubMed]

J. Mod. Opt. (3)

P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt.42(2), 389–401 (1995).
[CrossRef]

P. Sandoz, “An algorithm for profilometry by white-light phase-shifting interferometry,” J. Mod. Opt.43, 1545–1554 (1996).

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt.44(3), 519–534 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white-light interferometry,” J. Opt. Soc. Am.13(4), 832–843 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Kor. (1)

J. G. Kim, “Absolute temperature measurement using white light interferometry,” J. Opt. Soc. Kor.4(2), 89–93 (2000).
[CrossRef]

Opt. Lett. (3)

Other (1)

S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, 1989).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup of spatial polarized low-coherence interferometry used to measure air pressure with a Fabry-Pérot sensor.

Fig. 2
Fig. 2

Schematic diagram of the Fabry- Pérot sensor.

Fig. 3
Fig. 3

Spectrum of LED used in experiment and a typical interference signal acquired through a digital acquisition card. (a) LED spectrum. (b) Interference signal.

Fig. 4
Fig. 4

Conceptual illustration of amplitude-frequency and phase-frequency characteristics and the transforming relationship between the relative phase and absolute phase with pressure (xₒ) in theory.

Fig. 5
Fig. 5

Part amplitude-frequency characteristic curve obtained by DFT and phase-contrast curves before and after phase unwrapping. (a) Amplitude-frequency characteristic curve. (b) Wrapped phase-frequency curve. (c) Unwrapped phase-frequency curve.

Fig. 6
Fig. 6

Linearity comparison charts. (a) DFT serial number is 1548. (b) DFT serial number is 1555. (c) DFT serial number is 1558. (d) DFT serial number is 1567.

Fig. 7
Fig. 7

The slope and intercept curves obtained by least square fit of unwrapped-phase-frequency. (a) Characteristic curve between slope and pressure. (b) Characteristic curve between intercept and pressure.

Fig. 8
Fig. 8

Relative phase of the selected frequency Ω1558 obtained by DFT, identified interference-order and the recovered absolute phase using the proposed algorithm. (a) Relative phase. (b) Identified interference order. (c) Recovered absolute phase.

Fig. 9
Fig. 9

Demodulation error curves between the set pressure and demodulated pressure. (a) Phase-slope-based algorithm. (b) The proposed algorithm.

Tables (1)

Tables Icon

Table 1 Quantitative linearity comparison table

Equations (13)

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Δd= 3(1 υ 2 ) r 4 16E h 3 ΔP
I(x)=γexp{ [α(x x 0 )] 2 }cos[β(x x 0 )]
f(x)=γexp[ (αx) 2 ]
G(Ω)=1/2 F[(Ω+β)] e jΩ x 0 +1/2 F([Ωβ]) e jΩ x 0
M(Ω, x 0 )=1/2 F[(Ωβ)]
φ(Ω, x 0 )=Ω x 0
φ(Ω, x 0 )=Φ(Ω, x 0 )2mπ, Φ(Ω, x 0 )(π,π), Ω( Ω sf Ω, Ω sf +Ω)
Φ(Ω, x 0 )= x 0 Ω+2mπ
Φ'( Ω l , x 0 )= x 0 Ω l +2nπ, l(kp,k+q)
n=floor(T/ 2π )
φ( Ω k , x 0 )=Φ( Ω k , x 0 )2π×floor(T/ 2π )
{ Φ'( Ω k )=Φ( Ω k ) Φ'( Ω ki1 )=Φ( Ω ki1 )2π×floor{ [Φ( Ω ki1 )Φ'( Ω kl )] / 2π } (i=0,1,,p1)
{ Φ'( Ω k )=Φ( Ω k ) Φ'( Ω k+i+1 )=Φ( Ω k+i+1 )2π×[floor{[ Φ( Ω k+i+1 )Φ'( Ω k+i )] / 2π }+1 ] (i=0,1,,q1)

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