Abstract

A new method for the synthesis of wavenumber series before and after mode hopping is proposed for depth-resolved wavenumber scanning interferometry. The classical Fourier transform is not suitable for mode hopping; consequently, the wavenumber scanning range of diode lasers is rather narrow, reducing the depth resolution and measurement accuracy. We show that the discontinuity in wavenumber domain interferograms caused by mode hopping can be removed by introducing the phase compensation of the interference spectrum. Thus, the wavenumber series before and after mode hopping can be synthesized. Experiments and numerical simulations validate the proposed method, and the measurement error is within 5nm.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Improvement of depth resolution in depth-resolved wavenumber-scanning interferometry using wavenumber-domain least-squares algorithm: comparison and experiment

Yulei Bai, Quanjie Jia, Yun Zhang, Qiquan Huang, Qiyu Yang, Shuangli Ye, Zhaoshui He, Yanzhou Zhou, and Shengli Xie
Appl. Opt. 55(13) 3413-3419 (2016)

Super-resolution reconstruction of speckle phase in depth-resolved wavelength scanning interference using the total least-squares analysis

Ziliang Lyu, Yulei Bai, Zhaoshui He, Shengli Xie, Zongze Wu, and Bo Dong
J. Opt. Soc. Am. A 36(5) 869-876 (2019)

Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland
Appl. Opt. 51(5) 558-567 (2012)

References

  • View by:
  • |
  • |
  • |

  1. P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
    [Crossref]
  2. G. Moschetti, A. Forbes, R. K. Leach, X. Jiang, and D. O’Connor, “Phase and fringe order determination in wavelength scanning interferometry,” Opt. Express 24(8), 8997–9012 (2016).
    [Crossref] [PubMed]
  3. L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
    [Crossref] [PubMed]
  4. H. Muhamedsalih, F. Gao, and X. Jiang, “Comparison study of algorithms and accuracy in the wavelength scanning interferometry,” Appl. Opt. 51(36), 8854–8862 (2012).
    [Crossref] [PubMed]
  5. T. Zhang, F. Gao, and X. Jiang, “Surface topography acquisition method for double-sided near-right-angle structured surfaces based on dual-probe wavelength scanning interferometry,” Opt. Express 25(20), 24148–24156 (2017).
    [Crossref] [PubMed]
  6. S. Chakraborty and P. D. Ruiz, “Measurement of all orthogonal components of displacement in the volume of scattering materials using wavelength scanning interferometry,” J. Opt. Soc. Am. A 29(9), 1776–1785 (2012).
    [Crossref] [PubMed]
  7. Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
    [Crossref]
  8. A. Davila, J. M. Huntley, C. Pallikarakis, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50(8), 1089–1096 (2012).
    [Crossref]
  9. M. Medhat, M. Sobee, H. M. Hussein, and O. Terra, “Distance measurement using frequency scanning interferometry with mode-hoped laser,” Opt. Laser Technol. 80, 209–213 (2016).
    [Crossref]
  10. A. Dávila, “Wavelength scanning interferometry using multiple light sources,” Opt. Express 24(5), 5311–5322 (2016).
    [Crossref] [PubMed]
  11. J. Xu, Y. Liu, B. Dong, Y. Bai, L. Hu, C. Shi, Z. Xu, and Y. Zhou, “Improvement of the depth resolution in depth-resolved wavenumber-scanning interferometry using multiple uncorrelated wavenumber bands,” Appl. Opt. 52(20), 4890–4897 (2013).
    [Crossref] [PubMed]
  12. A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping,” Appl. Opt. 51(5), 558–567 (2012).
    [Crossref] [PubMed]
  13. K. Kitagawa, “Surface and thickness profile measurement of a transparent film by three-wavelength vertical scanning interferometry,” Opt. Lett. 39(14), 4172–4175 (2014).
    [Crossref] [PubMed]
  14. Y. Bai, Y. He, H. Bao, Y. Zhang, S. Ye, and Y. Zhou, “Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry,” J. Opt. Soc. Am. A 32(7), 1352–1356 (2015).
    [Crossref] [PubMed]

2017 (1)

2016 (3)

2015 (2)

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

Y. Bai, Y. He, H. Bao, Y. Zhang, S. Ye, and Y. Zhou, “Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry,” J. Opt. Soc. Am. A 32(7), 1352–1356 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (1)

2012 (4)

2004 (1)

P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
[Crossref]

2003 (1)

Bai, Y.

Bao, H.

Chakraborty, S.

Coupland, J. M.

A. Davila, J. M. Huntley, C. Pallikarakis, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50(8), 1089–1096 (2012).
[Crossref]

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping,” Appl. Opt. 51(5), 558–567 (2012).
[Crossref] [PubMed]

Davila, A.

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping,” Appl. Opt. 51(5), 558–567 (2012).
[Crossref] [PubMed]

A. Davila, J. M. Huntley, C. Pallikarakis, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50(8), 1089–1096 (2012).
[Crossref]

Dávila, A.

Deck, L. L.

Dong, B.

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

J. Xu, Y. Liu, B. Dong, Y. Bai, L. Hu, C. Shi, Z. Xu, and Y. Zhou, “Improvement of the depth resolution in depth-resolved wavenumber-scanning interferometry using multiple uncorrelated wavenumber bands,” Appl. Opt. 52(20), 4890–4897 (2013).
[Crossref] [PubMed]

Forbes, A.

Gao, F.

He, Y.

Hu, L.

Huntley, J.

P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
[Crossref]

Huntley, J. M.

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping,” Appl. Opt. 51(5), 558–567 (2012).
[Crossref] [PubMed]

A. Davila, J. M. Huntley, C. Pallikarakis, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50(8), 1089–1096 (2012).
[Crossref]

Hussein, H. M.

M. Medhat, M. Sobee, H. M. Hussein, and O. Terra, “Distance measurement using frequency scanning interferometry with mode-hoped laser,” Opt. Laser Technol. 80, 209–213 (2016).
[Crossref]

Jiang, X.

Kitagawa, K.

Leach, R. K.

Liu, Y.

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

J. Xu, Y. Liu, B. Dong, Y. Bai, L. Hu, C. Shi, Z. Xu, and Y. Zhou, “Improvement of the depth resolution in depth-resolved wavenumber-scanning interferometry using multiple uncorrelated wavenumber bands,” Appl. Opt. 52(20), 4890–4897 (2013).
[Crossref] [PubMed]

Medhat, M.

M. Medhat, M. Sobee, H. M. Hussein, and O. Terra, “Distance measurement using frequency scanning interferometry with mode-hoped laser,” Opt. Laser Technol. 80, 209–213 (2016).
[Crossref]

Moschetti, G.

Muhamedsalih, H.

O’Connor, D.

Pallikarakis, C.

A. Davila, J. M. Huntley, C. Pallikarakis, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50(8), 1089–1096 (2012).
[Crossref]

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Simultaneous wavenumber measurement and coherence detection using temporal phase unwrapping,” Appl. Opt. 51(5), 558–567 (2012).
[Crossref] [PubMed]

Ruiz, P.

P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
[Crossref]

Ruiz, P. D.

Shi, C.

Sobee, M.

M. Medhat, M. Sobee, H. M. Hussein, and O. Terra, “Distance measurement using frequency scanning interferometry with mode-hoped laser,” Opt. Laser Technol. 80, 209–213 (2016).
[Crossref]

Terra, O.

M. Medhat, M. Sobee, H. M. Hussein, and O. Terra, “Distance measurement using frequency scanning interferometry with mode-hoped laser,” Opt. Laser Technol. 80, 209–213 (2016).
[Crossref]

Wildman, R.

P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
[Crossref]

Xu, J.

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

J. Xu, Y. Liu, B. Dong, Y. Bai, L. Hu, C. Shi, Z. Xu, and Y. Zhou, “Improvement of the depth resolution in depth-resolved wavenumber-scanning interferometry using multiple uncorrelated wavenumber bands,” Appl. Opt. 52(20), 4890–4897 (2013).
[Crossref] [PubMed]

Xu, Z.

Ye, S.

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

Y. Bai, Y. He, H. Bao, Y. Zhang, S. Ye, and Y. Zhou, “Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry,” J. Opt. Soc. Am. A 32(7), 1352–1356 (2015).
[Crossref] [PubMed]

Zhang, T.

Zhang, Y.

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

Y. Bai, Y. He, H. Bao, Y. Zhang, S. Ye, and Y. Zhou, “Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry,” J. Opt. Soc. Am. A 32(7), 1352–1356 (2015).
[Crossref] [PubMed]

Zhou, Y.

Y. Bai, Y. He, H. Bao, Y. Zhang, S. Ye, and Y. Zhou, “Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry,” J. Opt. Soc. Am. A 32(7), 1352–1356 (2015).
[Crossref] [PubMed]

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

J. Xu, Y. Liu, B. Dong, Y. Bai, L. Hu, C. Shi, Z. Xu, and Y. Zhou, “Improvement of the depth resolution in depth-resolved wavenumber-scanning interferometry using multiple uncorrelated wavenumber bands,” Appl. Opt. 52(20), 4890–4897 (2013).
[Crossref] [PubMed]

P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
[Crossref]

Appl. Opt. (4)

J. Opt. A, Pure Appl. Opt. (1)

P. Ruiz, Y. Zhou, J. Huntley, and R. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” J. Opt. A, Pure Appl. Opt. 6(7), 679–683 (2004).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Express (3)

Opt. Laser Technol. (1)

M. Medhat, M. Sobee, H. M. Hussein, and O. Terra, “Distance measurement using frequency scanning interferometry with mode-hoped laser,” Opt. Laser Technol. 80, 209–213 (2016).
[Crossref]

Opt. Lasers Eng. (1)

A. Davila, J. M. Huntley, C. Pallikarakis, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50(8), 1089–1096 (2012).
[Crossref]

Opt. Lett. (1)

Strain (1)

Y. Liu, B. Dong, Y. Bai, J. Xu, Y. Zhang, S. Ye, and Y. Zhou, “Perspective measurement of the out-of-plane displacement and normal strain field distributions inside glass fibre-reinforced resin matrix composite,” Strain 51(3), 198–205 (2015).
[Crossref]

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 (11)

Fig. 1
Fig. 1 Schematic of depth-resolved interference.
Fig. 2
Fig. 2 Wavenumber series for the case of one mode hopping.
Fig. 3
Fig. 3 Synthesizing a single-frequency sinusoidal signal, and the discontinuity of time series. (a) The time series; (b) the sinusoidal signal; (c) the signal before discontinuity; (d) the shifted signal after discontinuity; (e) the synthesized signal; (f) the FT of (b); (g) the FT of (g).
Fig. 4
Fig. 4 Geometric illustration of OPD maps.
Fig. 5
Fig. 5 Simulated wavenumber series and interferometric signal. (a) Wavenumber series with a single mode hopping; (b) wavenumber-domain interferograms at the cross-section y = 100.
Fig. 6
Fig. 6 Interference spectra evaluated from the wavenumber-domain interferograms for one mode hopping, where the upper panel shows the cross-sections of the spectra at the line y = 180, and the lower panel shows the spectra at the point (x, y) = (100, 180). The spectra in (a)–(c) correspond to Δk1 + Δk2, (a) for the wavenumber series before synthesis and (c) for the wavenumber series after synthesis. In (b), the spectrum corresponds to Δk1.
Fig. 7
Fig. 7 Wrapped phase maps of Λ12(x, y) and Λ13(x, y), where (a)-(d) correspond to Λ12(x, y), while (e)-(h) correspond to Λ13(x, y). (a)(e) show the ideal phase maps. (b)(f), (c)(g), and (d)(h) show the evaluated phase maps from the peaks of the main lobes in Figs. 6(a)-6(c), respectively.
Fig. 8
Fig. 8 Error wrapped phase maps e12(x, y) and e13(x, y), where (a) and (b) correspond to Λ12(x, y) and Λ13(x, y), respectively.
Fig. 9
Fig. 9 Experimental wavenumber series and interferometric signal. (a) Wavenumber series with double mode hopping. (b) Wavenumber-domain interferograms at the cross-section line x = 1.25mm.
Fig. 10
Fig. 10 Experimental four-surface interference spectra. (a) Before synthesizing the wavenumber series; (b) After synthesizing the wavenumber series.
Fig. 11
Fig. 11 Experimentally obtained wrapped phase and error maps. (a), (b) Wrapped phase maps of Λ13(x, y), where (a) corresponds to the case of the wavenumber series before synthesis, and (b) corresponds to the case of the wavenumber series after synthesis. (c) Error OPD map ΔΛ(x, y).

Equations (12)

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

I(x,y,k)= p=1 M I p (x,y)+2 p=1 M1 q=p+1 M I p (x,y) I q (x,y) cos[2k Λ pq (x,y)] ,
{ I(x,y,n)=2 p=1 M1 q=p+1 M I p (x,y) I q (x,y) cos[2π f pq (x,y) ρ n + φ pq (x,y)] ρ n = n1 N1 Δk . f pq (x,y)= Λ pq (x,y) π φ pq (x,y)=2 k 0 Λ pq (x,y)
k(n)={ k 0 + Δ k 1 N 1 1 (n1), 1n N 1 k + 0 Δ k 1 +Δ k Jmp + Δ k 2 N 2 N 1 1 (n N 1 1), N 1 +1n N 2 ,
s(x,y,n)=I(x,y,n)+jH[I(x,y,n)] =2 p=1 M1 q=p+1 M I p (x,y) I q (x,y) exp{j[2πk(n) Λ pq (x,y)]},
s(x,y,n)= { 2 p=1 M1 q=p+1 M I p (x,y) I q (x,y) exp{j[2π f pq (x,y) ρ n + φ pq (x,y)]} 2 p=1 M1 q=p+1 M I p (x,y) I q (x,y) exp{j[2π f pq (x,y) ρ n + φ pq (x,y)+2Δ k Jmp Λ pq (x,y)]} , ρ n = Δ k 1 N 1 1 (n1), {nZ | 1n N 1 }, ρ n = Δ k 2 N 2 N 1 1 (n N 1 1), {nZ | N 1 +1n N 2 },
S ˜ (x,y,f)= n=1 N 1 s(x,y,n) W k(n) + n= N 1 +1 N 2 s(x,y,n) W k(n) ,
s (x,y, N 1 +1)=2 p=1 M1 q=p+1 M I p (x,y) I q (x,y) exp{j[ φ pq (x,y)+ ξ pq (x,y)+2Δ k Jmp Λ pq (x,y)]} ,
{ s (x,y,n)= p=1 M1 q=p+1 M s pq [x,y,n+ ξ pq (x,y) 2π f pq (x,y) ] s pq (x,y,n)=2 I p (x,y) I q (x,y) exp{j[2π f pq (x,y) ρ n + φ pq (x,y)+2Δ k Jmp Λ pq (x,y)]} .
{ S ˜ (x,y,f)= n=1 N 1 s(x,y,n) W k(n) + n= N 1 +1 N 2 s (x,y,n) W k(n) s (x,y,n)= p=1 M1 q=p+1 M 2 I p (x,y) I q (x,y) exp{j[2π f pq (x,y) ρ n + φ pq (x,y)]}exp[j πf Λ pq ξ pq (x,y)] .
S ˜ (x,y,f)= n=1 N 1 s(x,y,n) W k(n) + n= N 1 +1 N 2 s(x,y,n)exp[j(2πfΔ k Jmp )] W k(n) .
{ Λ 13 (x,y)= z 0 R 2 [ (x x 0 ) 2 + (y y 0 ) 2 ] Λ 12 (x,y)=- D C A C x B C y Λ 23 (x,y)= Λ 13 (x,y) Λ 12 (x,y) ,
S ˜ (x,y,f)= n=1 81 s(x,y,n) W k(n) + n=82 277 s(x,y,n)exp(j2πfΔ k Jmp1 ) W k(n) . + n=278 581 s(x,y,n)exp(j2πfΔ k Jmp2 ) W k(n)

Metrics