Abstract

In this article, we provide a method to improve the depth resolution of wide-field depth-resolved wavenumber-scanning interferometry (DRWSI), because its depth resolution is limited by the range of the wavenumber scanning and mode hopping of the light source. An optical wedge is put into the optical path to measure the series of the wavenumber on time using a 2D spatial Fourier transform (FT) of the interferograms. Those uncorrelated multiple bands of the wavenumbers due to mode hopping of the diode laser can be synthesized into one band, to enlarge the range of the wavenumber scanning. A random-sampling FT is put forward to evaluate the distribution of frequencies and phases of the multiple surfaces measured. The benefit is that the depth resolution of the DRWSI is enhanced significantly with a higher signal-to-noise ratio. Because of its simplicity and practicability, this method broadens the way to employing multiple different lasers or lasers with mode hopping as the light sources in the DRWSI.

© 2013 Optical Society of America

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References

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  1. M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
    [CrossRef]
  2. P. D. Ruiz, Y. Zhou, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement using wavelength scanning interferometry,” Pure Appl. Opt. 6, 679–683 (2004).
    [CrossRef]
  3. P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
    [CrossRef]
  4. 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, 558–567 (2012).
    [CrossRef]
  5. A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50, 1089–1096 (2012).
    [CrossRef]
  6. Y. Ishii, J. Chen, and K. Murata, “Digital phase-measuring interferometry with a tunable laser diode,” Opt. Lett. 12, 233–235 (1987).
    [CrossRef]
  7. L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42, 2354–2365 (2003).
    [CrossRef]
  8. 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, 1776–1785 (2012).
    [CrossRef]
  9. Y. J. Shen and J. M. Huntley, “Simple method to calibrate phase modulators for use in dynamic phase-shifting interferometry,” Opt. Eng. 43, 2998–3002 (2004).
    [CrossRef]
  10. D. C. Harris, Quantitive Chemical Analysis, 6th ed. (W. H. Freeman & Company, 2003).

2012 (3)

2007 (1)

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

2005 (1)

2004 (2)

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

Y. J. Shen and J. M. Huntley, “Simple method to calibrate phase modulators for use in dynamic phase-shifting interferometry,” Opt. Eng. 43, 2998–3002 (2004).
[CrossRef]

2003 (1)

1987 (1)

Boppart, S. A.

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Chakraborty, S.

Chen, J.

Coupland, J. M.

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50, 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, 558–567 (2012).
[CrossRef]

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, 558–567 (2012).
[CrossRef]

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

Deck, L. L.

Harris, D. C.

D. C. Harris, Quantitive Chemical Analysis, 6th ed. (W. H. Freeman & Company, 2003).

Huntley, J. M.

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50, 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, 558–567 (2012).
[CrossRef]

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef]

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

Y. J. Shen and J. M. Huntley, “Simple method to calibrate phase modulators for use in dynamic phase-shifting interferometry,” Opt. Eng. 43, 2998–3002 (2004).
[CrossRef]

Ishii, Y.

Marks, D. L.

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Murata, K.

Nguyen, F. T.

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Oldenburg, A. L.

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Pallikarakis, C.

A. Davila, J. M. Huntley, C. Pallikarakis, P. D. Ruiz, and J. M. Coupland, “Wavelength scanning interferometry using a Ti:Sapphire laser with wide tuning range,” Opt. Lasers Eng. 50, 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, 558–567 (2012).
[CrossRef]

Ruiz, P. D.

Shen, Y. J.

Y. J. Shen and J. M. Huntley, “Simple method to calibrate phase modulators for use in dynamic phase-shifting interferometry,” Opt. Eng. 43, 2998–3002 (2004).
[CrossRef]

Wildman, R. D.

P. D. Ruiz, J. M. Huntley, and R. D. Wildman, “Depth-resolved whole-field displacement measurement by wavelength-scanning electronic speckle pattern interferometry,” Appl. Opt. 44, 3945–3953 (2005).
[CrossRef]

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

Zhou, Y.

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

Zysk, M.

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

Appl. Opt. (3)

J. Biomed. Opt. (1)

M. Zysk, F. T. Nguyen, A. L. Oldenburg, D. L. Marks, and S. A. Boppart, “Tomography: a review of clinical development from bench to bedside,” J. Biomed. Opt. 12, 051403 (2007).
[CrossRef]

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

Opt. Eng. (1)

Y. J. Shen and J. M. Huntley, “Simple method to calibrate phase modulators for use in dynamic phase-shifting interferometry,” Opt. Eng. 43, 2998–3002 (2004).
[CrossRef]

Opt. Lasers Eng. (1)

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

Opt. Lett. (1)

Pure Appl. Opt. (1)

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

Other (1)

D. C. Harris, Quantitive Chemical Analysis, 6th ed. (W. H. Freeman & Company, 2003).

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Figures (8)

Fig. 1.
Fig. 1.

Principle of DRWSI. (a) System of DRWSI. (b) Schematic of wavenumber scanning.

Fig. 2.
Fig. 2.

Interferometry from the two smooth surfaces of the optical wedge: (a) fringe pattern, (b) map of the amplitude, where ① and ③ are the peaks of the spatial carrier frequency of the straight fringes, and ② is the DC component, and (c) map of the wrapped phase.

Fig. 3.
Fig. 3.

Series of spatial frequencies, spatial phases, and wavenumbers. (a), (b) Series of spatial frequencies and wrapped spatial phases at the peak①, respectively. (c) Series of unwrapped spatial phases and actual spatial phases at the peak①. (d) Series of wavenumbers.

Fig. 4.
Fig. 4.

Simulation of the depth range of the DRWSI. (a) Series of the wavenumber scanning where there is mode hopping. (b) Corresponding series of interferometric intensities. (c) The OPD measured is less than the range of the depth resolution. (d) The OPD measured is more than the range of the depth resolution.

Fig. 5.
Fig. 5.

RSFT in the DRWSI. (a) Series of wavenumbers measured from the optical wedge frame by frame, as the diode laser is scanned without mode hopping. (b) Series of interferometric intensities in (x=0mm, y=0.0865mm). (c) Its amplitude spectrum using the RSFT with a rectangular window, the FT with a rectangular window, and the hanning window, respectively, where all the amplitudes are normalized by their own peaks at OPD=Λ12.

Fig. 6.
Fig. 6.

Series of the wavenumbers, as the diode laser is modulated by the temperature and the current, respectively; (a) 1: the temperature from 41°C to 32°C, the driving current 135 mA; 2: the temperature from 28°C to 38°C, the driving current 135 mA; 3: the temperature from 40°C to 31°C, the driving current 115 mA; 4: the temperature from 26°C to 36°C, the driving current 115 mA and (b) the synthesis series of the multiple uncorrelated bands of the wavenumbers.

Fig. 7.
Fig. 7.

Single-band and synthesis-band DRWSI. (a), (b) Fringe pattern and its zoom. (c)–(e) Maps of the amplitudes and the phases of the single-band DRWSI; the series of wavenumbers is 1 in Fig. 6(a). (f)–(h) Maps of the amplitudes and the phases of the synthesis-band DRWSI.

Fig. 8.
Fig. 8.

Unwrapped phase maps of the smooth surfaces measured, evaluated by the synthesis-band DRWSI: (a) Λ23, (b) Λ12, (c) Λ13, (d) Λ34, (e) Λ24, and (f) Λ14.

Equations (15)

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

I(x,y,k)=p=1Mq=1MIp(x,y)·Iq(x,y)cos[2π·Λpq(x,y)π·k+ϕpq0(x,y)],
I(x,y,n)=I1+I2+2I1·I2·cos[2π·Λ12(x,y)π·k(n)+ϕ120(x,y)],
Λ12(x,y)=Λ120+ΔΛ12x·(x1)+ΔΛ·12y(y1),
F(u,v,n)=(I1+I2)·δ(u,v)+I1·I2×δ[u±Ω12u(n),v±Ω12v(n)]·exp[j·Ψ12(n)],
Ω12u(n)=ΔΛ12xπ·k(n)Ω12v(n)=ΔΛ12yπ·k(n)Ψ12(n)=2Λ120·k(n)+ϕ120,
Γ=ΔΨ12(a,b)ΔΩ12(a,b)=2π·Λ120ΔΛ12x2+ΔΛ12y2.
k(n)=π·Ω12(n)ΔΛ12x2+ΔΛ12y2,
k(n)=Ψ12(n)2·Λ120ϕ1202·Λ120.
I˜(x,y,f)=F[I(x,y,k)]F[w(k)]F[n=1Nδ(kk(n))]=+I(x,y,k)·w(k)·n=1Nδ(kk(n))·exp(j·2π·f·k)·dk,
I˜(x,y,f)=n=1N+δ[kk(n)]·I(x,y,k)·w(k)·exp(j·2π·f·k)·dk.
abδ(kk0)·f(k)·dk=f(k0)(a<k0<b),
I˜(x,y,f)=n=1NI(x,y,k(n))·w(k(n))·exp(j·2π·f·k(n)).
I˜(x,y,f)=n=1NI(x,y,k(n))·w(k(n))·exp[j·2πf·(Ψ12(n)2·Λ120ϕ1202·Λ120)].
δΛ=γ·4π·Λ120ΔΨ12(1,N),
ΔΛ=N·π2·(Δks=1SΔks),

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