Abstract

Several methods were developed in the past to analyze interferograms produced by optical coherence tomography, and successfully applied to simulated or animated samples. However, these techniques do not cope with noisy and distorted interferograms from biological tissues. In this paper, known techniques, including the fast Fourier transform and several variations of the continuous wavelet transform, were employed to analyze the interferogram data. However, to cope with the difficulties in biological data, pre- and post-processing procedures and adaptive thresholding were developed to provide stability and robustness. Additionally, three-dimensional structural models of the biological samples were constructed, and revealed information like the number and locations of interfaces, the layer thickness and pattern, and abnormalities.

© 2012 Optical Society of America

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    [CrossRef]

2011

2010

R. Sharon, R. Friedmann, and I. Abdulhalim, “Multilayered scattering reference mirror for full field optical coherence tomography with application to cell profiling,” Opt. Commun. 283, 4122–4125 (2010).
[CrossRef]

2007

I. Abdulhalim, R. Friedman, L. Liraz, and R. Dadon, “Full field frequency domain common path optical coherence tomography with annular aperture,” Proc. SPIE 6627, 662719 (2007).
[CrossRef]

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

C. J. Tay, C. Quan, and C. Li, “Investigation of a dual layer structure using vertical scanning interferometry,” Opt. Lasers Eng. 45, 907–913 (2007).
[CrossRef]

2006

I. Abdulhalim, “Competence between spatial and temporal coherence in full field optical coherence tomography and interference microscopy,” J. Opt. Pure Appl. Opt. 8, 952–958 (2006).
[CrossRef]

2005

Z. Sarac, A. Dursun, S. Yerdelen, and F. N. Ecevit, “Wavelet phase evaluation of white light interferograms,” Meas. Sci. Technol. 16, 1878–1882 (2005).
[CrossRef]

P. H. Tomlins and R. K. Wang, “Theory, development and applications of optical coherence tomography,” J. Phys. D 38, 2519–2535 (2005).
[CrossRef]

2004

I. De Moortel, S. A. Munday, and A. W. Hood, “Wavelet analysis: the effect of varying basic wavelet,” Sol. Phys. 222, 203–228 (2004).
[CrossRef]

2001

I. Abdulhalim, “Theory for double beam interferometric microscopes and experimental verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).
[CrossRef]

2000

M. C. Park and S. W. Kim, “Direct quadratic polynominal fitting for fringe peak detection of white light scanning interferogram,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

1998

R. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

1997

1996

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

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

1995

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

1993

1992

1990

Abdulhalim, I.

A. Safrani and I. Abdulhalim, “Spatial coherence effect on layers thickness determination in narrowband full field optical coherence tomography,” Appl. Opt. 50, 3021–3027 (2011).
[CrossRef]

R. Sharon, R. Friedmann, and I. Abdulhalim, “Multilayered scattering reference mirror for full field optical coherence tomography with application to cell profiling,” Opt. Commun. 283, 4122–4125 (2010).
[CrossRef]

I. Abdulhalim, R. Friedman, L. Liraz, and R. Dadon, “Full field frequency domain common path optical coherence tomography with annular aperture,” Proc. SPIE 6627, 662719 (2007).
[CrossRef]

I. Abdulhalim, “Competence between spatial and temporal coherence in full field optical coherence tomography and interference microscopy,” J. Opt. Pure Appl. Opt. 8, 952–958 (2006).
[CrossRef]

I. Abdulhalim, “Theory for double beam interferometric microscopes and experimental verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).
[CrossRef]

Bui, A. T.

A. T. Bui and R. K. Taira, Medical Imaging Informatics (Springer, 2010).

Caber, P. J.

Chim, S. C.

Dadon, R.

I. Abdulhalim, R. Friedman, L. Liraz, and R. Dadon, “Full field frequency domain common path optical coherence tomography with annular aperture,” Proc. SPIE 6627, 662719 (2007).
[CrossRef]

De Groot, P.

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

De Moortel, I.

I. De Moortel, S. A. Munday, and A. W. Hood, “Wavelet analysis: the effect of varying basic wavelet,” Sol. Phys. 222, 203–228 (2004).
[CrossRef]

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, 389–401 (1995).
[CrossRef]

Dursun, A.

Z. Sarac, A. Dursun, S. Yerdelen, and F. N. Ecevit, “Wavelet phase evaluation of white light interferograms,” Meas. Sci. Technol. 16, 1878–1882 (2005).
[CrossRef]

Ecevit, F. N.

Z. Sarac, A. Dursun, S. Yerdelen, and F. N. Ecevit, “Wavelet phase evaluation of white light interferograms,” Meas. Sci. Technol. 16, 1878–1882 (2005).
[CrossRef]

Friedman, R.

I. Abdulhalim, R. Friedman, L. Liraz, and R. Dadon, “Full field frequency domain common path optical coherence tomography with annular aperture,” Proc. SPIE 6627, 662719 (2007).
[CrossRef]

Friedmann, R.

R. Sharon, R. Friedmann, and I. Abdulhalim, “Multilayered scattering reference mirror for full field optical coherence tomography with application to cell profiling,” Opt. Commun. 283, 4122–4125 (2010).
[CrossRef]

Hood, A. W.

I. De Moortel, S. A. Munday, and A. W. Hood, “Wavelet analysis: the effect of varying basic wavelet,” Sol. Phys. 222, 203–228 (2004).
[CrossRef]

Kazakevich, Y.

Y. Kazakevich and R. Lobrutto, HPLC for Pharmaceutical Scientists (Wiley, 2010).

Kim, S. W.

M. C. Park and S. W. Kim, “Direct quadratic polynominal fitting for fringe peak detection of white light scanning interferogram,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

Kino, G. S.

Larkin, K. G.

Li, C.

C. J. Tay, C. Quan, and C. Li, “Investigation of a dual layer structure using vertical scanning interferometry,” Opt. Lasers Eng. 45, 907–913 (2007).
[CrossRef]

Liraz, L.

I. Abdulhalim, R. Friedman, L. Liraz, and R. Dadon, “Full field frequency domain common path optical coherence tomography with annular aperture,” Proc. SPIE 6627, 662719 (2007).
[CrossRef]

Lobrutto, R.

Y. Kazakevich and R. Lobrutto, HPLC for Pharmaceutical Scientists (Wiley, 2010).

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Munday, S. A.

I. De Moortel, S. A. Munday, and A. W. Hood, “Wavelet analysis: the effect of varying basic wavelet,” Sol. Phys. 222, 203–228 (2004).
[CrossRef]

Notni, G.

R. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Park, M. C.

M. C. Park and S. W. Kim, “Direct quadratic polynominal fitting for fringe peak detection of white light scanning interferogram,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

Quan, C.

C. J. Tay, C. Quan, and C. Li, “Investigation of a dual layer structure using vertical scanning interferometry,” Opt. Lasers Eng. 45, 907–913 (2007).
[CrossRef]

Recknagel, R.

R. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Safrani, A.

Sandoz, P.

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

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

Sarac, Z.

Z. Sarac, A. Dursun, S. Yerdelen, and F. N. Ecevit, “Wavelet phase evaluation of white light interferograms,” Meas. Sci. Technol. 16, 1878–1882 (2005).
[CrossRef]

Sharon, R.

R. Sharon, R. Friedmann, and I. Abdulhalim, “Multilayered scattering reference mirror for full field optical coherence tomography with application to cell profiling,” Opt. Commun. 283, 4122–4125 (2010).
[CrossRef]

Stifter, D.

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

Taira, R. K.

A. T. Bui and R. K. Taira, Medical Imaging Informatics (Springer, 2010).

Tay, C. J.

C. J. Tay, C. Quan, and C. Li, “Investigation of a dual layer structure using vertical scanning interferometry,” Opt. Lasers Eng. 45, 907–913 (2007).
[CrossRef]

Teolis, A.

A. Teolis, Computational Signal Processing with Wavelets (Birkhauser, 1998).

Tomlins, P. H.

P. H. Tomlins and R. K. Wang, “Theory, development and applications of optical coherence tomography,” J. Phys. D 38, 2519–2535 (2005).
[CrossRef]

Wang, R. K.

P. H. Tomlins and R. K. Wang, “Theory, development and applications of optical coherence tomography,” J. Phys. D 38, 2519–2535 (2005).
[CrossRef]

Yerdelen, S.

Z. Sarac, A. Dursun, S. Yerdelen, and F. N. Ecevit, “Wavelet phase evaluation of white light interferograms,” Meas. Sci. Technol. 16, 1878–1882 (2005).
[CrossRef]

Appl. Opt.

Appl. Phys. B

D. Stifter, “Beyond biomedicine: a review of alternative applications and developments for optical coherence tomography,” Appl. Phys. B 88, 337–357 (2007).
[CrossRef]

J. Mod. Opt.

I. Abdulhalim, “Theory for double beam interferometric microscopes and experimental verification using the Linnik microscope,” J. Mod. Opt. 48, 279–302 (2001).
[CrossRef]

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

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

J. Opt. Pure Appl. Opt.

I. Abdulhalim, “Competence between spatial and temporal coherence in full field optical coherence tomography and interference microscopy,” J. Opt. Pure Appl. Opt. 8, 952–958 (2006).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

P. H. Tomlins and R. K. Wang, “Theory, development and applications of optical coherence tomography,” J. Phys. D 38, 2519–2535 (2005).
[CrossRef]

Meas. Sci. Technol.

Z. Sarac, A. Dursun, S. Yerdelen, and F. N. Ecevit, “Wavelet phase evaluation of white light interferograms,” Meas. Sci. Technol. 16, 1878–1882 (2005).
[CrossRef]

Opt. Commun.

R. Sharon, R. Friedmann, and I. Abdulhalim, “Multilayered scattering reference mirror for full field optical coherence tomography with application to cell profiling,” Opt. Commun. 283, 4122–4125 (2010).
[CrossRef]

R. Recknagel and G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Opt. Eng.

M. C. Park and S. W. Kim, “Direct quadratic polynominal fitting for fringe peak detection of white light scanning interferogram,” Opt. Eng. 39, 952–959 (2000).
[CrossRef]

Opt. Lasers Eng.

C. J. Tay, C. Quan, and C. Li, “Investigation of a dual layer structure using vertical scanning interferometry,” Opt. Lasers Eng. 45, 907–913 (2007).
[CrossRef]

Opt. Lett.

Proc. SPIE

I. Abdulhalim, R. Friedman, L. Liraz, and R. Dadon, “Full field frequency domain common path optical coherence tomography with annular aperture,” Proc. SPIE 6627, 662719 (2007).
[CrossRef]

Sol. Phys.

I. De Moortel, S. A. Munday, and A. W. Hood, “Wavelet analysis: the effect of varying basic wavelet,” Sol. Phys. 222, 203–228 (2004).
[CrossRef]

Other

E. Billauer, “Peakdet: peak detection using MATLAB,” http://billauer.co.il/peakdet.html .

Y. Kazakevich and R. Lobrutto, HPLC for Pharmaceutical Scientists (Wiley, 2010).

A. T. Bui and R. K. Taira, Medical Imaging Informatics (Springer, 2010).

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

A. Teolis, Computational Signal Processing with Wavelets (Birkhauser, 1998).

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Figures (15)

Fig. 1.
Fig. 1.

Comparison of ridges extracted by the Morlet and complex Morlet wavelets.

Fig. 2.
Fig. 2.

Original interferogram from biological sample.

Fig. 3.
Fig. 3.

(a) Interferogram before pre-processing: blue dashed curve, interferogram; red curve, baseline. (b) Interferogram after pre-processing.

Fig. 4.
Fig. 4.

Comparison between two adjacent pixels from garlic epidermis specimen: (a) intensity of the pixel at location (1,34), (b) intensity of the pixel at location (1,33), (c) the two signals after pre-processing, (d) the two obtained envelopes.

Fig. 5.
Fig. 5.

Cumulative histograms of (a) pixel at location (1,34) and (b) pixel at location (1,33). The pink lines define the value of Δy for each pixel according to a criterion of 90% of histogram.

Fig. 6.
Fig. 6.

Extracted envelope by FFT method with and without post-processing. Insert, magnified image of the first peak.

Fig. 7.
Fig. 7.

Simulated interferogram with two theoretical layer interfaces. The inset emphasizes that there might be miss sampling (the blue circles) of the layer interface location.

Fig. 8.
Fig. 8.

Ridge of Paul 4 versus Paul 12 wavelet.

Fig. 9.
Fig. 9.

Ridge of complex Morlet versus Paul 12.

Fig. 10.
Fig. 10.

(a) Scalogram of CWT with complex Morlet wavelet. (b) Scalogram of CWT with Paul wavelet. (c) Comparison of extracted ridges using Paul and complex Morlet wavelets. (d) Difference between the two ridges.

Fig. 11.
Fig. 11.

Y-cross section of the garlic sample. The white lines show the areas of the two interference patterns. It provides a rough estimation of each interface location. The first pattern is relatively weak and appears in depth of about 20 μm, while the second is very clear in depth of about 80 μm.

Fig. 12.
Fig. 12.

Histogram of the detected peaks from entire garlic sample.

Fig. 13.
Fig. 13.

3D model of the garlic specimen. The dots are the outliers. (a) Obtained by CWT ridge based method. (b) Missing data filled by a spatial 3×3 median filter.

Fig. 14.
Fig. 14.

3D models of the onion specimen (left column) and their corresponding histograms (right column) obtained by proposed modified methods: (a), (b) CWT ridge; (c), (d) CWT phase correction; (e), (f) CWT Gaussian fit (g), (h) CWT phase; (i), (j) FFT.

Fig. 15.
Fig. 15.

Onion epidermis (a) 3D structural model obtained by the improved FFT method, (b) Y-cross section of the onion epidermis, showing the interface location at 8 μm, (c) XY-cross-section of the onion epidermis (100×100 pixels).

Tables (4)

Tables Icon

Table 1. Structure Parameters for Simulated Interferogram

Tables Icon

Table 2. Summary of the Results from all the Methods Applied to the Simulated Signala

Tables Icon

Table 3. Scanning Setup and Parameters for Garlic and Onion Epidermises

Tables Icon

Table 4. Computation Time for Each Method Is the Sum of the Peak Detection Time and the Duration of the Distinguishing Algorithm (at the right column)

Equations (3)

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

I(z)=I0(1+V(z)cos(ϕ(z))).
ψ(x)=1πfbexp(i2πfcx)exp(x2fb),
ψ(x)=2nn!(1ix)(n+1)2π(2n)!/2,

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