Abstract

This research was conducted to estimate the optical absorption and reduced scattering coefficients of two-layer turbid media using a stepwise method from the spatial-frequency domain reflectance generated by Monte Carlo (MC) simulation. The stepwise method’s feasibility for optical property estimations was first investigated by comparing the reflectance generated by the diffusion model and MC simulation for one-layer and two-layer turbid media. The results showed that, with proper frequency selection, the one-layer model could be used for estimating the optical properties of the first layer of the two-layer turbid media. A sample-based calibration method was proposed for calibrating discrepancies of the reflectance between the diffusion model and MC simulation. This significantly improved the parameter estimation accuracy. Results showed that the stepwise method’s parameter estimation efficacy and accuracy were much better than that for the one-step method. This was especially true when estimating the absorption coefficient. Absolute error contour maps were generated in order to determine the constraining conditions for the first-layer thickness. It was found that, when each layer’s optical properties are within the range of 0.005 mm−1μa ≤ 0.04 mm−1 and 0.69 mm−1μs≤ 2.2 mm−1, the first-layer’s minimum thickness—for which the first layer’s optical properties could be accurately estimated—could be as small as 0.2 mm. Further, the first layer’s maximum thickness could not exceed 2.0 mm, in order to have acceptable estimations of the optical properties of the second layer.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

D. Hu, R. Lu, and Y. Ying, “A two-step parameter optimization algorithm for improving estimation of optical properties using spatial frequency domain imaging,” J. Quant. Spectrosc. Ra. 207, 32–40 (2018).
[Crossref]

2017 (1)

2016 (4)

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
[Crossref]

A. Wang, R. Lu, and L. Xie, “A sequential method for measuring the optical properties of two-layer media with spatially-resolved diffuse reflectance: simulation study,” SPIE Commercial+ Scientific. Sens. Imaging,  986498640Q (2016).

Y. Lu, R. Li, and R. Lu, “Structured-illumination reflectance imaging (SIRI) for enhanced detection of fresh bruises in apples,” Postharvest Biol. Technol. 117, 89–93 (2016).
[Crossref]

D. Hu, X. Fu, X. He, and Y. Ying, “Noncontact and wide-field characterization of the absorption and scattering properties of apple fruit using spatial-frequency domain imaging,” Sci. Rep. 6(1), 37920 (2016).
[Crossref] [PubMed]

2015 (1)

D. Hu, X. Fu, A. Wang, and Y. Ying, “Measurement methods for optical absorption and scattering properties of fruits and vegetables,” Trans. ASABE 58, 1387–1401 (2015).

2014 (1)

W. Wang, C. Li, and R. D. Gitaitis, “Optical properties of healthy and diseased onion tissues in the visible and near-infrared spectral region,” Trans. ASABE 57, 1771–1782 (2014).

2012 (2)

A. Liemert and A. Kienle, “Analytical approach for solving the radiative transfer equation in two-dimensional layered media,” J. Quant. Spectrosc. Ra. 113(7), 559–564 (2012).
[Crossref]

D. Yudovsky, J. Q. M. Nguyen, and A. J. Durkin, “In vivo spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 17(10), 107006 (2012).
[Crossref] [PubMed]

2011 (2)

R. B. Saager, A. Truong, D. J. Cuccia, and A. J. Durkin, “Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy,” J. Biomed. Opt. 16(7), 077002 (2011).
[Crossref] [PubMed]

D. Yudovsky and A. J. Durkin, “Spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 16(10), 107005 (2011).
[Crossref] [PubMed]

2010 (2)

H. Cen, R. Lu, and K. Dolan, “Optimization of inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance,” Inverse Probl. Sci. Eng. 18(6), 853–872 (2010).
[Crossref]

H. Cen and R. Lu, “Optimization of the hyperspectral imaging-based spatially-resolved system for measuring the optical properties of biological materials,” Opt. Express 18(16), 17412–17432 (2010).
[Crossref] [PubMed]

2009 (3)

H. Cen and R. Lu, “Quantification of the optical properties of two-layer turbid materials using a hyperspectral imaging-based spatially-resolved technique,” Appl. Opt. 48(29), 5612–5623 (2009).
[Crossref] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
[Crossref] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. 105(10), 102028 (2009).
[Crossref]

2008 (2)

2007 (1)

2006 (1)

2005 (1)

2001 (1)

2000 (1)

1999 (1)

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves,” Phys. Med. Biol. 44, 801–813 (1999).

1998 (1)

1997 (1)

1995 (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

1994 (1)

1990 (1)

Aernouts, B.

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
[Crossref]

Arazuri, S.

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
[Crossref]

Ayers, F. R.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
[Crossref] [PubMed]

Bays, R.

Berns, M. W.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves,” Phys. Med. Biol. 44, 801–813 (1999).

Bevilacqua, F.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
[Crossref] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30(11), 1354–1356 (2005).
[Crossref] [PubMed]

Cen, H.

Cuccia, D. J.

R. B. Saager, A. Truong, D. J. Cuccia, and A. J. Durkin, “Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy,” J. Biomed. Opt. 16(7), 077002 (2011).
[Crossref] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. 105(10), 102028 (2009).
[Crossref]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
[Crossref] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30(11), 1354–1356 (2005).
[Crossref] [PubMed]

Culver, J. P.

De Baerdemaeker, J.

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
[Crossref]

Dögnitz, N.

Dolan, K.

H. Cen, R. Lu, and K. Dolan, “Optimization of inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance,” Inverse Probl. Sci. Eng. 18(6), 853–872 (2010).
[Crossref]

Durkin, A. J.

D. Yudovsky, J. Q. M. Nguyen, and A. J. Durkin, “In vivo spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 17(10), 107006 (2012).
[Crossref] [PubMed]

D. Yudovsky and A. J. Durkin, “Spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 16(10), 107005 (2011).
[Crossref] [PubMed]

R. B. Saager, A. Truong, D. J. Cuccia, and A. J. Durkin, “Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy,” J. Biomed. Opt. 16(7), 077002 (2011).
[Crossref] [PubMed]

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. 105(10), 102028 (2009).
[Crossref]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
[Crossref] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30(11), 1354–1356 (2005).
[Crossref] [PubMed]

Feng, T.-C.

Fishkin, J. B.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves,” Phys. Med. Biol. 44, 801–813 (1999).

Fu, X.

D. Hu, X. Fu, X. He, and Y. Ying, “Noncontact and wide-field characterization of the absorption and scattering properties of apple fruit using spatial-frequency domain imaging,” Sci. Rep. 6(1), 37920 (2016).
[Crossref] [PubMed]

D. Hu, X. Fu, A. Wang, and Y. Ying, “Measurement methods for optical absorption and scattering properties of fruits and vegetables,” Trans. ASABE 58, 1387–1401 (2015).

Gitaitis, R. D.

W. Wang, C. Li, and R. D. Gitaitis, “Optical properties of healthy and diseased onion tissues in the visible and near-infrared spectral region,” Trans. ASABE 57, 1771–1782 (2014).

Haskell, R. C.

He, X.

D. Hu, X. Fu, X. He, and Y. Ying, “Noncontact and wide-field characterization of the absorption and scattering properties of apple fruit using spatial-frequency domain imaging,” Sci. Rep. 6(1), 37920 (2016).
[Crossref] [PubMed]

Hollmann, J. L.

Hu, D.

D. Hu, R. Lu, and Y. Ying, “A two-step parameter optimization algorithm for improving estimation of optical properties using spatial frequency domain imaging,” J. Quant. Spectrosc. Ra. 207, 32–40 (2018).
[Crossref]

D. Hu, R. Lu, and Y. Ying, “Finite element simulation of light transfer in turbid media under structured illumination,” Appl. Opt. 56(21), 6035–6042 (2017).
[Crossref] [PubMed]

D. Hu, X. Fu, X. He, and Y. Ying, “Noncontact and wide-field characterization of the absorption and scattering properties of apple fruit using spatial-frequency domain imaging,” Sci. Rep. 6(1), 37920 (2016).
[Crossref] [PubMed]

D. Hu, X. Fu, A. Wang, and Y. Ying, “Measurement methods for optical absorption and scattering properties of fruits and vegetables,” Trans. ASABE 58, 1387–1401 (2015).

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Jarén, C.

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
[Crossref]

Kienle, A.

Li, C.

W. Wang, C. Li, and R. D. Gitaitis, “Optical properties of healthy and diseased onion tissues in the visible and near-infrared spectral region,” Trans. ASABE 57, 1771–1782 (2014).

Li, R.

Y. Lu, R. Li, and R. Lu, “Structured-illumination reflectance imaging (SIRI) for enhanced detection of fresh bruises in apples,” Postharvest Biol. Technol. 117, 89–93 (2016).
[Crossref]

Liemert, A.

A. Liemert and A. Kienle, “Analytical approach for solving the radiative transfer equation in two-dimensional layered media,” J. Quant. Spectrosc. Ra. 113(7), 559–564 (2012).
[Crossref]

Liu, Q.

López-Maestresalas, A.

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
[Crossref]

Lu, R.

D. Hu, R. Lu, and Y. Ying, “A two-step parameter optimization algorithm for improving estimation of optical properties using spatial frequency domain imaging,” J. Quant. Spectrosc. Ra. 207, 32–40 (2018).
[Crossref]

D. Hu, R. Lu, and Y. Ying, “Finite element simulation of light transfer in turbid media under structured illumination,” Appl. Opt. 56(21), 6035–6042 (2017).
[Crossref] [PubMed]

Y. Lu, R. Li, and R. Lu, “Structured-illumination reflectance imaging (SIRI) for enhanced detection of fresh bruises in apples,” Postharvest Biol. Technol. 117, 89–93 (2016).
[Crossref]

A. Wang, R. Lu, and L. Xie, “A sequential method for measuring the optical properties of two-layer media with spatially-resolved diffuse reflectance: simulation study,” SPIE Commercial+ Scientific. Sens. Imaging,  986498640Q (2016).

H. Cen, R. Lu, and K. Dolan, “Optimization of inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance,” Inverse Probl. Sci. Eng. 18(6), 853–872 (2010).
[Crossref]

H. Cen and R. Lu, “Optimization of the hyperspectral imaging-based spatially-resolved system for measuring the optical properties of biological materials,” Opt. Express 18(16), 17412–17432 (2010).
[Crossref] [PubMed]

H. Cen and R. Lu, “Quantification of the optical properties of two-layer turbid materials using a hyperspectral imaging-based spatially-resolved technique,” Appl. Opt. 48(29), 5612–5623 (2009).
[Crossref] [PubMed]

Lu, Y.

Y. Lu, R. Li, and R. Lu, “Structured-illumination reflectance imaging (SIRI) for enhanced detection of fresh bruises in apples,” Postharvest Biol. Technol. 117, 89–93 (2016).
[Crossref]

McAdams, M. S.

Nguyen, J. Q. M.

D. Yudovsky, J. Q. M. Nguyen, and A. J. Durkin, “In vivo spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 17(10), 107006 (2012).
[Crossref] [PubMed]

Nicolaï, B. M.

Nieto-Vesperinas, M.

Ntziachristos, V.

Pattanayak, D. N.

Patterson, M. S.

Pham, T.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves,” Phys. Med. Biol. 44, 801–813 (1999).

Ramanujam, N.

Ramon, H.

Ripoll, J.

Saager, R. B.

R. B. Saager, A. Truong, D. J. Cuccia, and A. J. Durkin, “Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy,” J. Biomed. Opt. 16(7), 077002 (2011).
[Crossref] [PubMed]

Saeys, W.

Schmitt, J. M.

Spott, T.

T. Spott and L. O. Svaasand, “Collimated light sources in the diffusion approximation,” Appl. Opt. 39(34), 6453–6465 (2000).
[Crossref] [PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves,” Phys. Med. Biol. 44, 801–813 (1999).

Svaasand, L. O.

Thennadil, S. N.

Tromberg, B. J.

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. 105(10), 102028 (2009).
[Crossref]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
[Crossref] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30(11), 1354–1356 (2005).
[Crossref] [PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves,” Phys. Med. Biol. 44, 801–813 (1999).

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, B. J. Tromberg, and M. S. McAdams, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11(10), 2727–2741 (1994).
[Crossref] [PubMed]

Truong, A.

R. B. Saager, A. Truong, D. J. Cuccia, and A. J. Durkin, “Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy,” J. Biomed. Opt. 16(7), 077002 (2011).
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A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
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A. Wang, R. Lu, and L. Xie, “A sequential method for measuring the optical properties of two-layer media with spatially-resolved diffuse reflectance: simulation study,” SPIE Commercial+ Scientific. Sens. Imaging,  986498640Q (2016).

D. Hu, X. Fu, A. Wang, and Y. Ying, “Measurement methods for optical absorption and scattering properties of fruits and vegetables,” Trans. ASABE 58, 1387–1401 (2015).

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L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
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W. Wang, C. Li, and R. D. Gitaitis, “Optical properties of healthy and diseased onion tissues in the visible and near-infrared spectral region,” Trans. ASABE 57, 1771–1782 (2014).

Weber, J. R.

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. 105(10), 102028 (2009).
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A. Wang, R. Lu, and L. Xie, “A sequential method for measuring the optical properties of two-layer media with spatially-resolved diffuse reflectance: simulation study,” SPIE Commercial+ Scientific. Sens. Imaging,  986498640Q (2016).

Ying, Y.

D. Hu, R. Lu, and Y. Ying, “A two-step parameter optimization algorithm for improving estimation of optical properties using spatial frequency domain imaging,” J. Quant. Spectrosc. Ra. 207, 32–40 (2018).
[Crossref]

D. Hu, R. Lu, and Y. Ying, “Finite element simulation of light transfer in turbid media under structured illumination,” Appl. Opt. 56(21), 6035–6042 (2017).
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D. Hu, X. Fu, X. He, and Y. Ying, “Noncontact and wide-field characterization of the absorption and scattering properties of apple fruit using spatial-frequency domain imaging,” Sci. Rep. 6(1), 37920 (2016).
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D. Hu, X. Fu, A. Wang, and Y. Ying, “Measurement methods for optical absorption and scattering properties of fruits and vegetables,” Trans. ASABE 58, 1387–1401 (2015).

Yodh, A. G.

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D. Yudovsky, J. Q. M. Nguyen, and A. J. Durkin, “In vivo spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 17(10), 107006 (2012).
[Crossref] [PubMed]

D. Yudovsky and A. J. Durkin, “Spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 16(10), 107005 (2011).
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Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
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W. Saeys, M. A. Velazco-Roa, S. N. Thennadil, H. Ramon, and B. M. Nicolaï, “Optical properties of apple skin and flesh in the wavelength range from 350 to 2200 nm,” Appl. Opt. 47(7), 908–919 (2008).
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H. Cen and R. Lu, “Quantification of the optical properties of two-layer turbid materials using a hyperspectral imaging-based spatially-resolved technique,” Appl. Opt. 48(29), 5612–5623 (2009).
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Q. Liu and N. Ramanujam, “Sequential estimation of optical properties of a two-layered epithelial tissue model from depth-resolved ultraviolet-visible diffuse reflectance spectra,” Appl. Opt. 45(19), 4776–4790 (2006).
[Crossref] [PubMed]

D. Hu, R. Lu, and Y. Ying, “Finite element simulation of light transfer in turbid media under structured illumination,” Appl. Opt. 56(21), 6035–6042 (2017).
[Crossref] [PubMed]

W. Saeys, M. A. Velazco-Roa, S. N. Thennadil, H. Ramon, and B. M. Nicolaï, “Optical properties of apple skin and flesh in the wavelength range from 350 to 2200 nm,” Appl. Opt. 47(7), 908–919 (2008).
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Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Food Bioprocess Technol. (1)

A. López-Maestresalas, B. Aernouts, R. Van Beers, S. Arazuri, C. Jarén, J. De Baerdemaeker, and W. Saeys, “Bulk optical properties of potato flesh in the 500-1900 nm range,” Food Bioprocess Technol. 9(3), 463–470 (2016).
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H. Cen, R. Lu, and K. Dolan, “Optimization of inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance,” Inverse Probl. Sci. Eng. 18(6), 853–872 (2010).
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J. Appl. Phys. (1)

J. R. Weber, D. J. Cuccia, A. J. Durkin, and B. J. Tromberg, “Noncontact imaging of absorption and scattering in layered tissue using spatially modulated structured light,” J. Appl. Phys. 105(10), 102028 (2009).
[Crossref]

J. Biomed. Opt. (4)

R. B. Saager, A. Truong, D. J. Cuccia, and A. J. Durkin, “Method for depth-resolved quantitation of optical properties in layered media using spatially modulated quantitative spectroscopy,” J. Biomed. Opt. 16(7), 077002 (2011).
[Crossref] [PubMed]

D. Yudovsky and A. J. Durkin, “Spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 16(10), 107005 (2011).
[Crossref] [PubMed]

D. Yudovsky, J. Q. M. Nguyen, and A. J. Durkin, “In vivo spatial frequency domain spectroscopy of two layer media,” J. Biomed. Opt. 17(10), 107006 (2012).
[Crossref] [PubMed]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14(2), 024012 (2009).
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D. Hu, R. Lu, and Y. Ying, “A two-step parameter optimization algorithm for improving estimation of optical properties using spatial frequency domain imaging,” J. Quant. Spectrosc. Ra. 207, 32–40 (2018).
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Opt. Express (1)

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Phys. Med. Biol. (1)

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Sci. Rep. (1)

D. Hu, X. Fu, X. He, and Y. Ying, “Noncontact and wide-field characterization of the absorption and scattering properties of apple fruit using spatial-frequency domain imaging,” Sci. Rep. 6(1), 37920 (2016).
[Crossref] [PubMed]

SPIE Commercial+ Scientific. Sens. Imaging (1)

A. Wang, R. Lu, and L. Xie, “A sequential method for measuring the optical properties of two-layer media with spatially-resolved diffuse reflectance: simulation study,” SPIE Commercial+ Scientific. Sens. Imaging,  986498640Q (2016).

Trans. ASABE (2)

D. Hu, X. Fu, A. Wang, and Y. Ying, “Measurement methods for optical absorption and scattering properties of fruits and vegetables,” Trans. ASABE 58, 1387–1401 (2015).

W. Wang, C. Li, and R. D. Gitaitis, “Optical properties of healthy and diseased onion tissues in the visible and near-infrared spectral region,” Trans. ASABE 57, 1771–1782 (2014).

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R. C. Aster, B. Borchers, and C. H. Thurber, Parameter estimation and inverse problems (Academic, 2011).

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Figures (8)

Fig. 1
Fig. 1 Flow chart of the stepwise method for inversely estimating absorption (μa) and reduced scattering (μs) coefficients of two-layer turbid media from Monte Carlo-generated reflectance, where MC and DM stand for Monte Carlo and diffusion model, respectively.
Fig. 2
Fig. 2 Sensitivity coefficients as a function of spatial frequency for the two combinations of optical properties: (a) μa1/μa2 = 0.5 and μs1/μs2 = 2.0 (0.01, 2, 0.02, 1, 2); and (b) μa1/μa2 = 1.5 and μs1/μs2 = 0.7 (0.03, 2, 0.02, 3, 2). The values in the brackets are μa1, μs1, μa2, μs2 and d with the unit of mm−1 for optical properties and mm for the first-layer thickness.
Fig. 3
Fig. 3 Sensitivity coefficients as a function of spatial frequency for μa1 = 0.03 mm−1, μs1 = 2 mm−1, μa2 = 0.02 mm−1, μs2 = 1 mm−1, and the first-layer thickness: (a) d = 0.5 mm, (b) d = 1.0 mm, (c) d = 2.0 mm, and (d) d = 4.0 mm.
Fig. 4
Fig. 4 Comparison of spatial-frequency domain reflectance obtained from (a) the two-layer model, MC simulation and calibrated MC simulation for different mfp1 values, and (b) the diffusion model and MC simulation for one-layer and two-layer turbid media (μa1 = 0.03 mm−1, μs1 = 3 mm−1, μa2 = 0.02 mm−1, μs2 = 1 mm−1 and d = 2 mm). mfp1 denotes mean free path of the first-layer tissue.
Fig. 5
Fig. 5 Relative errors (absolute values) for estimating the optical properties of all 35 two-layer samples with the first-layer thickness of 2.0 mm, by using the stepwise and the one-step methods from the calibrated Monte Carlo-generated reflectance.
Fig. 6
Fig. 6 Reflectance predicted by the two-layer model versus spatial frequency for different thicknesses of the first layer, compared with two semi-infinite homogeneous samples, denoted as ‘Homogeneous-1’ and ‘Homogeneous-2’, which had the same optical properties as that of the first layer and the second layer, respectively. μa1 = 0.03 mm−1, μs1 = 2 mm−1, μa2 = 0.02 mm−1, μs2 = 1 mm−1 and the first-layer thickness was varied from 0.1 mm to 4.0 mm.
Fig. 7
Fig. 7 Absolute error contour maps for estimating μa1 (left panel) and μs1 (right panel) of a two-layer sample (μa1 = 0.04 mm−1, μs1 = 1.6 mm−1, μa2 = 0.015 mm−1 and μs2 = 1.25 mm−1) when using different start and end spatial frequencies. The first-layer thicknesses are 0.1 mm, 0.2 mm, 0.5 mm and 1.0 mm for (a), (b), (c) and (d), respectively. The one-layer model was used here. Note that the absolute errors of μa1 and μs1 larger than 60% and 30% were clipped to be 60% and 30% for better visual effect.
Fig. 8
Fig. 8 Absolute error contour maps for estimating μa2 (left panel) and μs2 (right panel) of a two-layer sample (μa1 = 0.04 mm−1, μs1 = 1.6 mm−1, μa2 = 0.015 mm−1 and μs2 = 1.25 mm−1) when using different start and end spatial frequencies. The first-layer thicknesses are 1.0 mm, 1.5 mm, 2.0 mm and 2.5 mm for (a), (b), (c) and (d), respectively. The two-layer model was used here assuming that μa1, μs1 and the first-layer thickness were known. Note that the absolute errors of μa2 and μs2 larger than 60% and 30% were clipped to be 60% and 30% for better visual effect.

Tables (4)

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Table 1 Five two-layer simulation samples with different combinations of μa and μs and their corresponding mean free paths of the first layer (mfp1) for determining the constraining conditions for the first-layer thickness

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Table 2 Selection of calibration samples based on the initial estimation of reduced scattering coefficient (μs1) for the first layer of two-layer samples for calibrating Monte Carlo-generated or experimentally measured spatial-frequency domain reflectance

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Table 3 Summary of different frequency ranges for optical property estimations

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Table 4 Mean absolute errors for estimating μa1 and μs1 of all 35 samples with different first-layer thicknesses by using stepwise and one-step methods from Monte Carlo-generated reflectance before and after the calibration

Equations (15)

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

2 ϕ( x,z ) μ eff '2 ϕ( x,z )=3 μ tr S,
S= 1 2 S 0 [ 1+cos( 2π f x +α ) ],
R 1 ( f x )= 3A a ' ( μ eff ' / μ tr +1 )( μ eff ' / μ tr +3A ) ,
S 1 = P 0 μ s1 ' exp( μ tr1 z ), 0<zd
S 2 = P 0 μ s2 ' exp( μ tr1 d )exp[ μ tr2 ( zd ) ], z>d
ϕ 1 = 3 P 0 μ tr1 μ s1 ' μ eff1 '2 μ tr1 2 exp( μ tr1 z )+ A 1 exp( μ eff1 ' z )+ A 2 exp( μ eff1 ' z ), 0<zd
ϕ 2 = 3 P 0 μ tr2 μ s2 ' μ eff2 '2 μ tr2 2 exp[ ( μ tr1 μ tr2 )d ]exp( μ tr2 z )+ A 3 exp( μ eff2 ' z )+ A 4 exp( μ eff2 ' z ), z>d
ϕ 1 | z= d = ϕ 2 | z= d + ,
j 1 | z= d = j 2 | z= d + ,
j 1 | z= 0 + = R eff 1 2( R eff +1 ) ϕ 1 | z= 0 + ,
ϕ 2 | z+ =0,
R 2 ( f x )= j| z=0 P 0 =A μ s1 ' μ eff1 ' A 1 + A 2 A 3 ,
R μ ai =| μ ai R μ ai |,
R μ si ' =| μ si ' R μ si ' |,
R MC_C ( f x )= R DA_R ( f x ) R MC_R ( f x ) R MC_O ( f x ),

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