Abstract

The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations. The values of the scaling exponent observed for these tissues indicate the differences in the self-similarity for dysplastic tissues and their normal counterparts. The strong dependence of the elastic light scattering on the size distribution of the scatterers manifests in the angular variation of the scaling exponent. Interestingly, the spectral fluctuations in both these tissues showed multi-fractality (non-stationarity in fluctuations), the degree of multi-fractality being marginally higher in the case of dysplastic tissues. These findings using the multi-resolution analysis capability of the discrete wavelet transform can contribute to the recent surge in the exploration for non-invasive optical tools for pre-cancer detection.

©2011 Optical Society of America

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2011 (3)

N. Ghosh, A. Banerjee, and J. Soni, “Turbid medium polarimetry in biomedical imaging and diagnosis,” Eur. Phys. J. Appl. Phys. 54, 30001 (2011).
[Crossref]

A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
[Crossref] [PubMed]

S. Ghosh, P. Manimaran, and P. K. Panigrahi, “Characterizing multi-scale self-similar behavior and non-statistical properties of financial time series,” Physica A 390, 4304–4316 (2011).
[Crossref]

2010 (3)

A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron. 16, 893–899 (2010).
[Crossref]

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010).
[Crossref] [PubMed]

W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt. 15, 030502 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (3)

2007 (3)

2006 (4)

N. Ghosh, P. Buddhiwant, A. Uppal, S. K. Majumder, H. S. Patel, and P. K. Gupta, “Simultaneous determination of size and refractive index of red blood cells by light scattering measurements,” Appl. Phys. Lett. 88, 084101 (2006).
[Crossref]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006).
[Crossref] [PubMed]

Y. L. Kim, V. M. Turzhitsky, Y. Liu, H. Subramanian, and P. Pradhan, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11, 041125 (2006).
[Crossref] [PubMed]

L. Perelman, “Optical diagnostic technology based on light scattering spectroscopy for early cancer detection,” Expert Rev. Med. Devices 3, 787–803 (2006).
[Crossref]

2005 (6)

M. Xu and R. R. Alfano, “Fractal mechanisms of light scattering in biological tissue and cells,” Opt. Lett. 30, 3051–3053 (2005).
[Crossref] [PubMed]

R. Graf and A. Wax, “Nuclear morphology measurements using Fourier domain low coherence interferometry,” Opt. Express 13, 4693–4698 (2005).
[Crossref]

A. S. Haka, K. E. Shafer-Peltier, M. Fitzmaurice, J. Crowe, R. R. Dasari, and M. S. Feld, “Diagnosing breast cancer by using Raman spectroscopy,” Proc. Natl. Acad. Sci. (USA) 102, 12371–12376 (2005).
[Crossref]

N. Ghosh, S. K. Majumder, H. S. Patel, and P. K. Gupta, “Depth-resolved fluorescence measurement in a layered turbid mediumby polarized fluorescence spectroscopy,” Opt. Lett. 30, 162–164 (2005).
[Crossref] [PubMed]

P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Phys. Rev. E 72, 046120 (2005).
[Crossref]

S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt. 10, 054012 (2005).
[Crossref] [PubMed]

2003 (6)

N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003).
[Crossref]

J. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivo imaging,” Nat. Biotechnol. 21, 1361–1367 (2003).
[Crossref] [PubMed]

N. Biswal, S. Gupta, N. Ghosh, and A. Pradhan, “Recovery of turbidity free fluorescence from measured fluorescence: an experimental approach,” Opt. Express 11, 3320–3331 (2003).
[Crossref] [PubMed]

A. Wax, C. Yang, and J. A. Izatt, “Fourier-domain low-coherence interferometry for light-scattering spectroscopy,” Opt. Lett. 28, 1230–1232 (2003).
[Crossref] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[Crossref] [PubMed]

A. Wax, C. Yang, M. G. Mller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, and M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
[PubMed]

2002 (4)

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, “Multifractal detrended fluctuation analysis of nonstationary time series,” Physica A 316, 87–114 (2002).
[Crossref]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[Crossref] [PubMed]

N. Ghosh, S. K. Majumder, and P. K. Gupta, “Polarized fluorescence spectroscopy of human tissues,” Opt. Lett. 27, 2007–2009 (2002).
[Crossref]

A. Eke, P. Herman, L. Kocsis, and L. R. Kozak, “Fractal characterization of complexity in temporal physiological signals,” Physiol. Meas. 23, R1–R38 (2002).
[Crossref] [PubMed]

2001 (2)

N. Ghosh, S. K. Mohanty, S. K. Majumder, and P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissue,” Appl. Opt. 40, 176–184 (2001).
[Crossref]

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[Crossref] [PubMed]

2000 (1)

N. Ramanujam, “Fluorescence spectroscopy of neoplastic and non-neoplastic tissues,” Neoplasia 2, 89–117 (2000).
[Crossref] [PubMed]

1999 (1)

J. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5, 1205–1215 (1999).
[Crossref]

1998 (2)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[Crossref]

C. Torrence and G. Compo, “A practical guide to wavelet analysis,” Bull. Am. Meteorol. Soc. 79, 61–78 (1998).
[Crossref]

1997 (1)

J. C. Hebden, S. R. Arridge, and D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[Crossref] [PubMed]

1996 (2)

R. Richards-Kortum and E. Sevick-Muraca, “Quantitative optical spectroscopy for tissue diagnosis,” Annu. Rev. Phys. Chem. 47, 555–606 (1996).
[Crossref] [PubMed]

J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996).
[Crossref] [PubMed]

1992 (1)

M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech. 24, 395–458 (1992).
[Crossref]

1988 (1)

H. E. Stanley and P. Meakin, “Multifractal phenomena in physics and chemistry,” Nature 335, 405–409 (1988).
[Crossref]

1987 (1)

R. Alfano, G. Tang, A. Pradhan, W. Lam, D. Choy, and E. Opher, “Fluorescence spectra from cancerous and normal human breast and lung tissues,” IEEE J. Quantum Electron. 23, 1806–1811 (1987).
[Crossref]

1981 (1)

P. Šeba, “Random matrix analysis of human EEG data,” Phys. Rev. Lett. 91, 198104 (2003).

1951 (1)

H. Hurst, “Long-term storage capacity of reservoirs,” Trans. Am. Soc. Civ. Eng. 116, 770–808 (1951).

Agarwal, A.

S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt. 10, 054012 (2005).
[Crossref] [PubMed]

Agarwal, N.

S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt. 10, 054012 (2005).
[Crossref] [PubMed]

N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003).
[Crossref]

Alfano, R.

R. Alfano, G. Tang, A. Pradhan, W. Lam, D. Choy, and E. Opher, “Fluorescence spectra from cancerous and normal human breast and lung tissues,” IEEE J. Quantum Electron. 23, 1806–1811 (1987).
[Crossref]

Alfano, R. R.

Arora, S.

A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
[Crossref] [PubMed]

A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron. 16, 893–899 (2010).
[Crossref]

A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt. 13, 054063 (2008).
[Crossref] [PubMed]

Arridge, S. R.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[Crossref] [PubMed]

Backman, V.

N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010).
[Crossref] [PubMed]

İ. R. Çapoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett. 34, 2679–2681 (2009).
[Crossref] [PubMed]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006).
[Crossref] [PubMed]

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001).
[Crossref] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
[Crossref]

Badizadegan, K.

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P. Manimaran, P. Panigrahi, and J. Parikh, “Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets,” Physica A 388, 2306–2314 (2009).
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P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Phys. Rev. E 72, 046120 (2005).
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L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
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A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt. 13, 054063 (2008).
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McGee, S.

Meakin, P.

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Mller, M. G.

A. Wax, C. Yang, M. G. Mller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, and M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
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Nair, M.

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A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
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Panigrahi, P.

A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron. 16, 893–899 (2010).
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N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003).
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Panigrahi, P. K.

A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
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S. Ghosh, P. Manimaran, and P. K. Panigrahi, “Characterizing multi-scale self-similar behavior and non-statistical properties of financial time series,” Physica A 390, 4304–4316 (2011).
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P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Phys. Rev. E 72, 046120 (2005).
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Parikh, J.

P. Manimaran, P. Panigrahi, and J. Parikh, “Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets,” Physica A 388, 2306–2314 (2009).
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P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Phys. Rev. E 72, 046120 (2005).
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A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
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A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron. 16, 893–899 (2010).
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A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt. 13, 054063 (2008).
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S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt. 10, 054012 (2005).
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N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003).
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R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. Macaulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
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A. Wax, C. Yang, M. G. Mller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, and M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
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Sureshkumar, M.

A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt. 13, 054063 (2008).
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A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
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N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003).
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Wallace, M.

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N. Ghosh, M. Wood, and A. Vitkin, “Polarized light assessment of complex turbid media such as biological tissues using mueller matrix decomposition,” in Handbook of Photonics for Biomedical Science, V. V. Tuchin, ed. (CRC Press, 2010), Medical Physics and Biomedical Engineering, pp. 253–282.
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Xu, M.

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L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998).
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Annu. Rev. Biomed. Eng. (1)

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Appl. Opt. (1)

Appl. Phys. Lett. (1)

N. Ghosh, P. Buddhiwant, A. Uppal, S. K. Majumder, H. S. Patel, and P. K. Gupta, “Simultaneous determination of size and refractive index of red blood cells by light scattering measurements,” Appl. Phys. Lett. 88, 084101 (2006).
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Cancer Res. (1)

A. Wax, C. Yang, M. G. Mller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, and M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003).
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N. Ghosh, A. Banerjee, and J. Soni, “Turbid medium polarimetry in biomedical imaging and diagnosis,” Eur. Phys. J. Appl. Phys. 54, 30001 (2011).
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Expert Rev. Med. Devices (1)

L. Perelman, “Optical diagnostic technology based on light scattering spectroscopy for early cancer detection,” Expert Rev. Med. Devices 3, 787–803 (2006).
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IEEE J. Quantum Electron. (1)

R. Alfano, G. Tang, A. Pradhan, W. Lam, D. Choy, and E. Opher, “Fluorescence spectra from cancerous and normal human breast and lung tissues,” IEEE J. Quantum Electron. 23, 1806–1811 (1987).
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IEEE J. Sel. Top. Quantum Electron. (3)

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[Crossref]

N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003).
[Crossref]

A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron. 16, 893–899 (2010).
[Crossref]

J. Biomed. Opt. (7)

A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011).
[Crossref] [PubMed]

A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt. 13, 054063 (2008).
[Crossref] [PubMed]

S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt. 10, 054012 (2005).
[Crossref] [PubMed]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
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W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt. 15, 030502 (2010).
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Y. L. Kim, V. M. Turzhitsky, Y. Liu, H. Subramanian, and P. Pradhan, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11, 041125 (2006).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Schematic representation of the fluctuation extraction algorithm (adapted from [51]).

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Fig. 2
Fig. 2 (Color Online) Schematic representation of the experimental set-up for the light scattering measurement. The sample mounted on a goniometer is illuminated by a white light collimated from a Xe-source and the scattered light is then collimated using two lenses (L 2 and L 3) and recorded using a Fiber-Optic Spectrometer. The θf represents the forward scattering angle, while θb is the backward scattering angle. The forward and backward scattering process are represented by red and blue lines respectively while the Fiber-Optic Spectrometer set-up is shown in green. 0 ≤ θ ≤ 180° is the scattering angle at which the spectra were recorded. Note that the rectangular shape of the glass slides prevented acquiring spectra in the angular range 80° – 110°.

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Fig. 3
Fig. 3 Typical peak normalized elastic light scattering spectra recorded from normal and dysplastic tissues at scattering angles (a) θ = 10° and (b) θ = 150°.

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Fig. 4
Fig. 4 The variation of the mean values of the scaling exponent α(θ) as a function of scattering angle θ for normal and dysplastic tissues, as determined from Fourier analysis. The error bars represent standard deviations.

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Fig. 5
Fig. 5 The variation of the mean values of the power law exponent α with the wavelet scale s at representative forward and backward scattering angles θ for (a) normal and (b) dysplastic tissues. The error bars represent standard deviations.

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Fig. 6
Fig. 6 The variation of the mean values for the Hurst parameter, H = h(q = 2) as a function of the scattering angle θ for normal and dysplastic tissues, as determined from WB-MFDFA analysis. The error bars represent standard deviations.

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Fig. 8
Fig. 8 The singularity spectrum f(β) plotted against β at all scattering angles θ for (a) typical normal tissue and (b) typical dysplastic tissue.

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Fig. 7
Fig. 7 The scaling function h(q) at different forward and backward scattering angles for (a) typical normal tissue and (b) typical dysplastic tissue. The weaker q dependence of h(q) for normal samples in the forward scattering angles (50° – 70°) is indicative of a trend towards mono-fractality, while the stronger dependence of the scaling function on the order of moments for dysplastic sample is indicative of a multi-fractal trend.

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Fig. 9
Fig. 9 (Color Online) The correlation matrices in the wavelength domain for (a) typical normal tissue and (b) typical dysplastic tissue. The results are shown for the same tissues whose results were presented in Figs. 7 and 8.

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Equations (9)

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x ( k ) = ∑ n = 0 N − 1 x ( n ) exp ( − 2 π ι N kn ) ,   k ∈ [ 0 , N − 1 ]
P ( k ) = | ∑ n = 0 N − 1 x ( n ) exp ( − 2 π ι N kn ) | 2
P ( k ) ≈ k α .
ψ s , m ( n ) = 2 s / 2 ψ ( 2 s n − m ) , m ∈ ℝ , s ∈ ℤ + ,
f ( t ) = ∑ m = − ∞ ∞ a m ϕ m ( t ) + ∑ m = − ∞ ∞ ∑ s ≥ 0 l d s , m ψ s , m ( t ) ,
F q ( s ) = [ 1 M s ∑ m = 1 2 M s { F 2 ( m , s ) } q 2 ] 1 q , q ≠ 0
and ,   F q = 0 ( s ) = exp [ 1 M s ∑ m = 1 2 M s log { F 2 ( m , s ) } q 2 ] 1 q , q = 0 .
f ( β ) = q [ β − h ( q ) ] + 1 .
C i j = 〈 x i y j 〉 − 〈 x i 〉 〈 y j 〉 ( 〈 x i 2 〉 − 〈 x i 〉 2 ) ( 〈 y j 2 〉 − 〈 y j 〉 2 )

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