Abstract

Estimation of the bulk optical properties of turbid samples from spatially resolved reflectance measurements remains challenging, as the relation between the bulk optical properties and the acquired spatially resolved reflectance profiles is influenced by wavelength-dependent properties of the measurement system. The resulting measurement noise is apparent in the estimation of the bulk optical properties. In this study, a constrained inverse metamodeling approach is proposed to overcome these problems. First, a metamodel has been trained on a set of intralipid phantoms covering a wide range of optical properties to link the acquired spatially resolved reflectance profiles to the respective combinations of bulk optical properties (absorption coefficient and reduced scattering coefficient). In this metamodel, the wavelength (500 – 1700 nm) is considered as a third input parameter for the model to account for the wavelength dependent effects introduced by the measurement system. Secondly, a smoothness constraint on the reduced scattering coefficient spectra was implemented in the iterative inverse estimation procedure to robustify it against measurement noise and increase the reliability of the obtained bulk absorption and reduced scattering coefficient spectra. As the estimated values in some regions may be more reliable than others, the difference between simulated and measured values as a function of the evaluated absorption and scattering coefficients was combined in a 2D cost function. This cost function was used as a weight in the fitting procedure to find the parameters of the µs’ function giving the lowest cost over all the wavelengths together. In accordance with previous research, an exponential function was considered to represent the µs’ spectra of intralipid phantoms. The fitting procedure also provides an absorption coefficient spectrum which is in accordance with the measurements and the estimated parameters of the exponential function. This robust inverse estimation algorithm was validated on an independent set of intralipid® phantoms and its performance was also compared to that of a classical single-wavelength inverse estimation algorithm. While its performance in estimating µa was comparable (R2 of 0.844 vs. 0.862), it resulted in a large improvement in the estimation of µs’ (R2 of 0.987 vs. 0.681). The change in performance is more apparent in the improvement of RMSE of µs’, which decreases from 10.36 cm−1 to 2.10 cm−1. The SRS profiles change more sensitively as a function of µa. As a result, there is a large range of µs’ and a small range of µa resulting in a good fit between measurement and simulation. The robust inverse estimator incorporates information over the different wavelengths, to increase the accuracy of µs’estimations and robustify the estimation process.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]

2015 (1)

B. Aernouts, R. Van Beers, R. Watté, T. Huybrechts, J. Lammertyn, and W. Saeys, “Visible and near-infrared bulk optical properties of raw milk,” J. Dairy Sci. 98(10), 6727–6738 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (4)

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

2012 (1)

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

2010 (3)

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (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]

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

2009 (2)

2008 (1)

W. Saeys, B. De Ketelaere, and P. Darius, “Potential applications of functional data analysis in chemometrics,” J. Chemometr. 22(5), 335–344 (2008).
[Crossref]

2007 (1)

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

2006 (3)

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11(6), 064027 (2006).
[Crossref] [PubMed]

D. Sharma, A. Agrawal, L. S. Matchette, and T. J. Pfefer, “Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media,” Biomed. Eng. Online 5(1), 49 (2006).
[Crossref] [PubMed]

C. D’Andrea, L. Spinelli, A. Bassi, A. Giusto, D. Contini, J. Swartling, A. Torricelli, and R. Cubeddu, “Time-resolved spectrally constrained method for the quantification of chromophore concentrations and scattering parameters in diffusing media,” Opt. Express 14(5), 1888–1898 (2006).
[Crossref] [PubMed]

2005 (3)

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, “Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction,” Appl. Opt. 44(10), 1858–1869 (2005).
[Crossref] [PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).
[Crossref] [PubMed]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

2004 (2)

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29(3), 256–258 (2004).
[Crossref] [PubMed]

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

2003 (3)

2001 (3)

D. G. Fraser, V. A. McGlone, R. B. Jordan, and R. Künnemeyer, “NIR (Near Infra-Red) light penetration into an apple,” Postharvest Biol. Technol. 22, 191–194 (2001).
[Crossref]

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

T. W. Simpson, J. D. Poplinsky, P. N. Koch, and J. K. Allen, “Meta-models for computer-based engineering design: survey and recommendations,” Eng. Comput. 17(2), 129–150 (2001).
[Crossref]

2000 (2)

J. Y. Le Pommellec and J. P. L’Huillier, “Determination of the optical properties of breast tissues using frequency-resolved transillumination: basic theory and preliminary results,” Proc. SPIE 4161, 202–215 (2000).
[Crossref]

J. Lammertyn, A. Peirs, J. De Baerdemaeker, and B. Nicolaï, “Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment,” Postharvest Biol. Technol. 18(2), 121–132 (2000).
[Crossref]

1999 (2)

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

1998 (1)

B. Guan, Y. Zhang, S. Huang, and B. Chance, “Determination of optical properties using improved frequency-resolved spectroscopy,” Proc. SPIE 3548, 17–26 (1998).
[Crossref]

1990 (1)

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Aalders, M. C.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

Aernouts, B.

B. Aernouts, R. Van Beers, R. Watté, T. Huybrechts, J. Lammertyn, and W. Saeys, “Visible and near-infrared bulk optical properties of raw milk,” J. Dairy Sci. 98(10), 6727–6738 (2015).
[Crossref] [PubMed]

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

B. Aernouts, R. Van Beers, R. Watté, J. Lammertyn, and W. Saeys, “Dependent scattering in Intralipid® phantoms in the 600-1850 nm range,” Opt. Express 22(5), 6086–6098 (2014).
[Crossref] [PubMed]

B. Aernouts, R. Watté, R. Van Beers, F. Delport, M. Merchiers, J. De Block, J. Lammertyn, and W. Saeys, “Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation,” Opt. Express 22(17), 20223–20238 (2014).
[Crossref] [PubMed]

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Agrawal, A.

D. Sharma, A. Agrawal, L. S. Matchette, and T. J. Pfefer, “Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media,” Biomed. Eng. Online 5(1), 49 (2006).
[Crossref] [PubMed]

Aladangady, N.

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

Allen, J. K.

T. W. Simpson, J. D. Poplinsky, P. N. Koch, and J. K. Allen, “Meta-models for computer-based engineering design: survey and recommendations,” Eng. Comput. 17(2), 129–150 (2001).
[Crossref]

Andersson-Engels, S.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Arifler, D.

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11(6), 064027 (2006).
[Crossref] [PubMed]

Arridge, S. R.

Avrillier, S.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Bassi, A.

Beullens, K.

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

Boas, D. A.

Bobelyn, E.

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

Cen, H.

Chance, B.

B. Guan, Y. Zhang, S. Huang, and B. Chance, “Determination of optical properties using improved frequency-resolved spectroscopy,” Proc. SPIE 3548, 17–26 (1998).
[Crossref]

Chang, T.-H.

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

Cheong, W.-F.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Choe, R.

Contini, D.

Corlu, A.

Costeloe, K.

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

Couckuyt, I.

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (2010).
[Crossref]

Cross, F. W.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

Cubeddu, R.

C. D’Andrea, L. Spinelli, A. Bassi, A. Giusto, D. Contini, J. Swartling, A. Torricelli, and R. Cubeddu, “Time-resolved spectrally constrained method for the quantification of chromophore concentrations and scattering parameters in diffusing media,” Opt. Express 14(5), 1888–1898 (2006).
[Crossref] [PubMed]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11(8), 853–867 (2003).
[Crossref] [PubMed]

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

Cucchiara, B. L.

Culver, J. P.

D’Andrea, C.

Danesini, G.

Darius, P.

W. Saeys, B. De Ketelaere, and P. Darius, “Potential applications of functional data analysis in chemometrics,” J. Chemometr. 22(5), 335–344 (2008).
[Crossref]

De Baerdemaeker, J.

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

J. Lammertyn, A. Peirs, J. De Baerdemaeker, and B. Nicolaï, “Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment,” Postharvest Biol. Technol. 18(2), 121–132 (2000).
[Crossref]

De Block, J.

De Ketelaere, B.

W. Saeys, B. De Ketelaere, and P. Darius, “Potential applications of functional data analysis in chemometrics,” J. Chemometr. 22(5), 335–344 (2008).
[Crossref]

De Turck, F.

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

Declerq, F.

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (2010).
[Crossref]

Dehghani, H.

Delport, F.

Delpy, D. T.

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

Detre, J. A.

Dhaene, T.

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (2010).
[Crossref]

Do Trong, N. N.

Doornbos, R. M. P.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

Durduran, T.

Duvic, M.

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

Edlow, B. L.

Elwell, C. E.

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

Erkinbaev, C.

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Follen, M.

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11(6), 064027 (2006).
[Crossref] [PubMed]

Forrester, A.

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

Fraser, D. G.

D. G. Fraser, R. B. Jordan, R. Künnemeyer, and V. A. McGlone, “Light distribution inside mandarin fruit during internal quality assessment by NIR spectroscopy,” Postharvest Biol. Technol. 27(2), 185–196 (2003).
[Crossref]

D. G. Fraser, V. A. McGlone, R. B. Jordan, and R. Künnemeyer, “NIR (Near Infra-Red) light penetration into an apple,” Postharvest Biol. Technol. 22, 191–194 (2001).
[Crossref]

Garcia-Uribe, A.

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

Garrido-Varo, A.

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

Giambattistelli, E.

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

Giusto, A.

Gorissen, D.

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

Greenberg, J. H.

Grosenick, D.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Guan, B.

B. Guan, Y. Zhang, S. Huang, and B. Chance, “Determination of optical properties using improved frequency-resolved spectroscopy,” Proc. SPIE 3548, 17–26 (1998).
[Crossref]

Guerrero-Ginel, J.

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

Guerrero-Ginel, J. É.

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

Hillman, E. M.

Hillman, E. M. C.

Huang, S.

B. Guan, Y. Zhang, S. Huang, and B. Chance, “Determination of optical properties using improved frequency-resolved spectroscopy,” Proc. SPIE 3548, 17–26 (1998).
[Crossref]

Huybrechts, T.

B. Aernouts, R. Van Beers, R. Watté, T. Huybrechts, J. Lammertyn, and W. Saeys, “Visible and near-infrared bulk optical properties of raw milk,” J. Dairy Sci. 98(10), 6727–6738 (2015).
[Crossref] [PubMed]

Jiang, S.

Jordan, R. B.

D. G. Fraser, R. B. Jordan, R. Künnemeyer, and V. A. McGlone, “Light distribution inside mandarin fruit during internal quality assessment by NIR spectroscopy,” Postharvest Biol. Technol. 27(2), 185–196 (2003).
[Crossref]

D. G. Fraser, V. A. McGlone, R. B. Jordan, and R. Künnemeyer, “NIR (Near Infra-Red) light penetration into an apple,” Postharvest Biol. Technol. 22, 191–194 (2001).
[Crossref]

Kasner, S. E.

Kim, M. N.

Knockaert, L.

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (2010).
[Crossref]

Koch, P. N.

T. W. Simpson, J. D. Poplinsky, P. N. Koch, and J. K. Allen, “Meta-models for computer-based engineering design: survey and recommendations,” Eng. Comput. 17(2), 129–150 (2001).
[Crossref]

Künnemeyer, R.

D. G. Fraser, R. B. Jordan, R. Künnemeyer, and V. A. McGlone, “Light distribution inside mandarin fruit during internal quality assessment by NIR spectroscopy,” Postharvest Biol. Technol. 27(2), 185–196 (2003).
[Crossref]

D. G. Fraser, V. A. McGlone, R. B. Jordan, and R. Künnemeyer, “NIR (Near Infra-Red) light penetration into an apple,” Postharvest Biol. Technol. 22, 191–194 (2001).
[Crossref]

L’Huillier, J. P.

J. Y. Le Pommellec and J. P. L’Huillier, “Determination of the optical properties of breast tissues using frequency-resolved transillumination: basic theory and preliminary results,” Proc. SPIE 4161, 202–215 (2000).
[Crossref]

Lammertyn, J.

B. Aernouts, R. Van Beers, R. Watté, T. Huybrechts, J. Lammertyn, and W. Saeys, “Visible and near-infrared bulk optical properties of raw milk,” J. Dairy Sci. 98(10), 6727–6738 (2015).
[Crossref] [PubMed]

B. Aernouts, R. Van Beers, R. Watté, J. Lammertyn, and W. Saeys, “Dependent scattering in Intralipid® phantoms in the 600-1850 nm range,” Opt. Express 22(5), 6086–6098 (2014).
[Crossref] [PubMed]

B. Aernouts, R. Watté, R. Van Beers, F. Delport, M. Merchiers, J. De Block, J. Lammertyn, and W. Saeys, “Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation,” Opt. Express 22(17), 20223–20238 (2014).
[Crossref] [PubMed]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

J. Lammertyn, A. Peirs, J. De Baerdemaeker, and B. Nicolaï, “Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment,” Postharvest Biol. Technol. 18(2), 121–132 (2000).
[Crossref]

Lang, R.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

Le Pommellec, J. Y.

J. Y. Le Pommellec and J. P. L’Huillier, “Determination of the optical properties of breast tissues using frequency-resolved transillumination: basic theory and preliminary results,” Proc. SPIE 4161, 202–215 (2000).
[Crossref]

Lee, K.

León Gutiérrez, L.

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Leung, T. S.

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

Li, A.

Lu, R.

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]

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agric. 68(1), 44–51 (2009).
[Crossref]

MacAulay, C.

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11(6), 064027 (2006).
[Crossref] [PubMed]

Macdonald, R.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Matchette, L. S.

D. Sharma, A. Agrawal, L. S. Matchette, and T. J. Pfefer, “Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media,” Biomed. Eng. Online 5(1), 49 (2006).
[Crossref] [PubMed]

McGlone, V. A.

D. G. Fraser, R. B. Jordan, R. Künnemeyer, and V. A. McGlone, “Light distribution inside mandarin fruit during internal quality assessment by NIR spectroscopy,” Postharvest Biol. Technol. 27(2), 185–196 (2003).
[Crossref]

D. G. Fraser, V. A. McGlone, R. B. Jordan, and R. Künnemeyer, “NIR (Near Infra-Red) light penetration into an apple,” Postharvest Biol. Technol. 22, 191–194 (2001).
[Crossref]

Merchiers, M.

Miller, E. L.

Möller, M.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Nghiem, H.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Nicolai, B.

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Nicolaï, B.

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

J. Lammertyn, A. Peirs, J. De Baerdemaeker, and B. Nicolaï, “Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment,” Postharvest Biol. Technol. 18(2), 121–132 (2000).
[Crossref]

Paulsen, K. D.

Peirs, A.

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

J. Lammertyn, A. Peirs, J. De Baerdemaeker, and B. Nicolaï, “Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment,” Postharvest Biol. Technol. 18(2), 121–132 (2000).
[Crossref]

Pérez-Marin, D.

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

Pfefer, T. J.

D. Sharma, A. Agrawal, L. S. Matchette, and T. J. Pfefer, “Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media,” Biomed. Eng. Online 5(1), 49 (2006).
[Crossref] [PubMed]

Pifferi, A.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11(8), 853–867 (2003).
[Crossref] [PubMed]

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

Pogue, B. W.

Poplinsky, J. D.

T. W. Simpson, J. D. Poplinsky, P. N. Koch, and J. K. Allen, “Meta-models for computer-based engineering design: survey and recommendations,” Eng. Comput. 17(2), 129–150 (2001).
[Crossref]

Prahl, S. A.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Prieto, V.

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

Putt, M. E.

Qin, J.

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agric. 68(1), 44–51 (2009).
[Crossref]

Richards-Kortum, R.

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11(6), 064027 (2006).
[Crossref] [PubMed]

Rogier, H.

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (2010).
[Crossref]

Rutten, K.

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Saeys, W.

B. Aernouts, R. Van Beers, R. Watté, T. Huybrechts, J. Lammertyn, and W. Saeys, “Visible and near-infrared bulk optical properties of raw milk,” J. Dairy Sci. 98(10), 6727–6738 (2015).
[Crossref] [PubMed]

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

B. Aernouts, R. Van Beers, R. Watté, J. Lammertyn, and W. Saeys, “Dependent scattering in Intralipid® phantoms in the 600-1850 nm range,” Opt. Express 22(5), 6086–6098 (2014).
[Crossref] [PubMed]

B. Aernouts, R. Watté, R. Van Beers, F. Delport, M. Merchiers, J. De Block, J. Lammertyn, and W. Saeys, “Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation,” Opt. Express 22(17), 20223–20238 (2014).
[Crossref] [PubMed]

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

W. Saeys, B. De Ketelaere, and P. Darius, “Potential applications of functional data analysis in chemometrics,” J. Chemometr. 22(5), 335–344 (2008).
[Crossref]

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Schenk, A.

R. Van Beers, B. Aernouts, L. León Gutiérrez, C. Erkinbaev, K. Rutten, A. Schenk, B. Nicolai, and W. Saeys, “Optimal illumination-detection distance and detector size for predicting Braeburn apple maturity from Vis/NIR laser reflectance measurements,” Food Bioprocess Tech.submitted.

Schweiger, M.

Shah, Q.

Sharma, D.

D. Sharma, A. Agrawal, L. S. Matchette, and T. J. Pfefer, “Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media,” Biomed. Eng. Online 5(1), 49 (2006).
[Crossref] [PubMed]

Simpson, T. W.

T. W. Simpson, J. D. Poplinsky, P. N. Koch, and J. K. Allen, “Meta-models for computer-based engineering design: survey and recommendations,” Eng. Comput. 17(2), 129–150 (2001).
[Crossref]

Spinelli, L.

Srinivasan, S.

Stamm, H.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Sterenborg, H.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Sterenborg, H. J. C. M.

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

Svensson, T.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Swartling, J.

C. D’Andrea, L. Spinelli, A. Bassi, A. Giusto, D. Contini, J. Swartling, A. Torricelli, and R. Cubeddu, “Time-resolved spectrally constrained method for the quantification of chromophore concentrations and scattering parameters in diffusing media,” Opt. Express 14(5), 1888–1898 (2006).
[Crossref] [PubMed]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Taroni, P.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11(8), 853–867 (2003).
[Crossref] [PubMed]

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

Theron, K.

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

Torricelli, A.

C. D’Andrea, L. Spinelli, A. Bassi, A. Giusto, D. Contini, J. Swartling, A. Torricelli, and R. Cubeddu, “Time-resolved spectrally constrained method for the quantification of chromophore concentrations and scattering parameters in diffusing media,” Opt. Express 14(5), 1888–1898 (2006).
[Crossref] [PubMed]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11(8), 853–867 (2003).
[Crossref] [PubMed]

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

Tsuta, M.

Tualle, J.-M.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Valentini, G.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

Van Beers, R.

van Veen, R.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Wabnitz, H.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Wang, L.

Wang, L. V.

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

Watté, R.

Welch, A. J.

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Whelan, M.

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

Yodh, A. G.

Yu, G.

Zamora-Rojas, E.

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

Zhang, Q.

Zhang, Y.

B. Guan, Y. Zhang, S. Huang, and B. Chance, “Determination of optical properties using improved frequency-resolved spectroscopy,” Proc. SPIE 3548, 17–26 (1998).
[Crossref]

Zhou, C.

Zou, J.

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

Adv. Eng. Soft. (1)

I. Couckuyt, A. Forrester, D. Gorissen, F. De Turck, and T. Dhaene, “Blind Kriging: Implementation and performance analysis,” Adv. Eng. Soft. 49, 1–13 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of human breast,” Appl. Phys. Lett. 74(6), 874–876 (1999).
[Crossref]

Biomed. Eng. Online (1)

D. Sharma, A. Agrawal, L. S. Matchette, and T. J. Pfefer, “Evaluation of a fiberoptic-based system for measurement of optical properties in highly attenuating turbid media,” Biomed. Eng. Online 5(1), 49 (2006).
[Crossref] [PubMed]

Comput. Electron. Agric. (1)

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agric. 68(1), 44–51 (2009).
[Crossref]

Eng. Comput. (1)

T. W. Simpson, J. D. Poplinsky, P. N. Koch, and J. K. Allen, “Meta-models for computer-based engineering design: survey and recommendations,” Eng. Comput. 17(2), 129–150 (2001).
[Crossref]

IEEE J. Quantum Electron. (1)

W.-F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical Properties of Biological Tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Innov. Food Sci. Emerg. Technol. (3)

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, D. Pérez-Marin, J. Guerrero-Ginel, and W. Saeys, “Double integrating sphere measurements for estimating optical properties of pig subcutaneous adipose tissue,” Innov. Food Sci. Emerg. Technol. 19, 218–226 (2013).
[Crossref]

E. Zamora-Rojas, B. Aernouts, A. Garrido-Varo, W. Saeys, D. Pérez-Marin, and J. Guerrero-Ginel, “Optical properties of pig skin epidermis and dermis estimated with double integrating spheres measurements,” Innov. Food Sci. Emerg. Technol. 20, 343–349 (2013).
[Crossref]

E. Zamora-Rojas, A. Garrido-Varo, B. Aernouts, D. Pérez-Marin, W. Saeys, and J. É. Guerrero-Ginel, “Understanding near infrared radiation propagation in pig skin reflectance measurements,” Innov. Food Sci. Emerg. Technol. 22, 137–146 (2014).
[Crossref]

Int. J. RF Microw. C. E. (1)

I. Couckuyt, F. Declerq, T. Dhaene, H. Rogier, and L. Knockaert, “Surrogate-Based Infill Optimization Applied to Electromagnetic Problems,” Int. J. RF Microw. C. E. 20(5), 492–501 (2010).
[Crossref]

J. Biomed. Opt. (2)

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11(6), 064027 (2006).
[Crossref] [PubMed]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. van Veen, H. Sterenborg, J.-M. Tualle, H. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assesment of photon migration instruments: the MEDPHOT protocol,” J. Biomed. Opt. 9, 2104–2114 (2005).

J. Chemometr. (1)

W. Saeys, B. De Ketelaere, and P. Darius, “Potential applications of functional data analysis in chemometrics,” J. Chemometr. 22(5), 335–344 (2008).
[Crossref]

J. Dairy Sci. (1)

B. Aernouts, R. Van Beers, R. Watté, T. Huybrechts, J. Lammertyn, and W. Saeys, “Visible and near-infrared bulk optical properties of raw milk,” J. Dairy Sci. 98(10), 6727–6738 (2015).
[Crossref] [PubMed]

Opt. Express (8)

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acite stroke patients,” Opt. Express 17, 3884–3902 (2009).

C. D’Andrea, L. Spinelli, A. Bassi, A. Giusto, D. Contini, J. Swartling, A. Torricelli, and R. Cubeddu, “Time-resolved spectrally constrained method for the quantification of chromophore concentrations and scattering parameters in diffusing media,” Opt. Express 14(5), 1888–1898 (2006).
[Crossref] [PubMed]

B. Aernouts, R. Watté, R. Van Beers, F. Delport, M. Merchiers, J. De Block, J. Lammertyn, and W. Saeys, “Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation,” Opt. Express 22(17), 20223–20238 (2014).
[Crossref] [PubMed]

B. Aernouts, R. Van Beers, R. Watté, J. Lammertyn, and W. Saeys, “Dependent scattering in Intralipid® phantoms in the 600-1850 nm range,” Opt. Express 22(5), 6086–6098 (2014).
[Crossref] [PubMed]

R. Watté, N. N. Do Trong, B. Aernouts, C. Erkinbaev, J. De Baerdemaeker, B. Nicolaï, and W. Saeys, “Metamodeling approach for efficient estimation of optical properties of turbid media from spatially resolved diffuse reflectance measurements,” Opt. Express 21(26), 32630–32642 (2013).
[Crossref] [PubMed]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11(8), 853–867 (2003).
[Crossref] [PubMed]

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]

Opt. Lett. (2)

Pediatr. Res. (1)

T. S. Leung, N. Aladangady, C. E. Elwell, D. T. Delpy, and K. Costeloe, “A new method for the measurement of cerebral blood volume and total circulating blood volume using Near Infrared spatially resolved spectroscopy and indocyanine green: application and validation in neonates,” Pediatr. Res. 55(1), 134–141 (2004).
[Crossref] [PubMed]

Phys. Med. Biol. (2)

A. Torricelli, A. Pifferi, P. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46(8), 2227–2237 (2001).
[Crossref] [PubMed]

R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and H. J. C. M. Sterenborg, “The determination of in vivo human tissue optical properties and absolute chromophore concentrations using spatially resolved steady-state diffuse reflectance spectroscopy,” Phys. Med. Biol. 44(4), 967–981 (1999).
[Crossref] [PubMed]

Postharvest Biol. Technol. (4)

B. Nicolaï, K. Beullens, E. Bobelyn, A. Peirs, W. Saeys, K. Theron, and J. Lammertyn, “Nondestructive measurement of fruit and vegetable quality by means of NIR spectroscopy: q review,” Postharvest Biol. Technol. 46(2), 99–118 (2007).
[Crossref]

J. Lammertyn, A. Peirs, J. De Baerdemaeker, and B. Nicolaï, “Light penetration properties of NIR radiation in fruit with respect to non-destructive quality assessment,” Postharvest Biol. Technol. 18(2), 121–132 (2000).
[Crossref]

D. G. Fraser, R. B. Jordan, R. Künnemeyer, and V. A. McGlone, “Light distribution inside mandarin fruit during internal quality assessment by NIR spectroscopy,” Postharvest Biol. Technol. 27(2), 185–196 (2003).
[Crossref]

D. G. Fraser, V. A. McGlone, R. B. Jordan, and R. Künnemeyer, “NIR (Near Infra-Red) light penetration into an apple,” Postharvest Biol. Technol. 22, 191–194 (2001).
[Crossref]

Proc. SPIE (3)

A. Garcia-Uribe, J. Zou, T.-H. Chang, M. Duvic, V. Prieto, and L. V. Wang, “Oblique-incidence spatially resolved diffuse reflectance spectroscopic diagnosis of skin cancer,” Proc. SPIE 7572, 75720L (2010).
[Crossref]

B. Guan, Y. Zhang, S. Huang, and B. Chance, “Determination of optical properties using improved frequency-resolved spectroscopy,” Proc. SPIE 3548, 17–26 (1998).
[Crossref]

J. Y. Le Pommellec and J. P. L’Huillier, “Determination of the optical properties of breast tissues using frequency-resolved transillumination: basic theory and preliminary results,” Proc. SPIE 4161, 202–215 (2000).
[Crossref]

Other (5)

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V. V. Tuchin, Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues (Chemical Rubber Company, 2008).

V. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE, 2007), Chap. 2.

I. Couckuyt, K. Crombecq, D. Gorissen, and T. Dhaene, “Automated response surface model generation with sequential design,” in Proceedings of First International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering, Funchal, Portugal, ed. (Civil-Comp. Press, 2009), 52.

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Figures (12)

Fig. 1
Fig. 1 Estimated µs spectrum, using a point-by-point approach, resulting in a noisy profile.
Fig. 2
Fig. 2 Generating the initial cost function: for a large number of µs – 721 intervals – and a gradually increasing number of µa values. The value of the cost function is illustrated on a logarithmic scale on the colorbar.
Fig. 3
Fig. 3 Mechanism of the inverse estimator: at each wavelength, a as’) combination is found which provides the best match between measurement and simulation (top). In the bottom figure these are all superposed to one single matrix. The unconstrained scattering profile connecting the best matches per wavelength (red line) is very jumpy, while the exponential function minizing the global cost function (black line) seems to be more realistic. The colorbars represent the local cost on a logarithmic scale.
Fig. 4
Fig. 4 (a) original µs and µa of the optical phantoms used for calibration (b) trimmed µs and µa of the optical phantoms used for calibration (c) µs and µa of the optical phantoms used for validation.
Fig. 5
Fig. 5 Boundaries of µs’-and µa: limits of the phantom calibration set (500 nm–1700 nm).
Fig. 6
Fig. 6 (a) Scatter plots of estimated versus reference µs (b) Scatter plots of estimated versus reference µa values, both for the validation set, using the robust inverse estimator. The red line represents the 1:1 line.
Fig. 7
Fig. 7 (a) Scatter plots of estimated versus reference µs’ (b) Scatter plots of estimated versus reference µa, both for the validation set, using the point-by-point inverse estimator. The red line represents the 1:1 line.
Fig. 8
Fig. 8 (a) Overlay of the estimated and reference µs profile (b) Overlay of the estimated and reference µa profile, both for phantom 33 of the calibration set.
Fig. 9
Fig. 9 (a) Inverse estimation of the µs profile (b) Inverse estimation of the µa (profile, both of phantom 32, using the robust inverse estimator.
Fig. 10
Fig. 10 Average BOP spectra estimated from DIS measurements for phantom 32 with error bars indicating the variation in the estimated values obtained from the 3 replicate measurements.
Fig. 11
Fig. 11 (a) Inverse estimation of the µs profile (b) Inverse estimation of the µa (profile, both for the virtual phantoms, using the robust inverse estimator.
Fig. 12
Fig. 12 (a) Inverse estimation of the µs profile (b) Inverse estimation of the µa (profile, both for the virtual phantomsof the wavelength dependency test, using the point-by-point inverse estimator.

Tables (2)

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Table 1 Composition of the Calibration Optical Phantoms

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Table 2 Statistics of Inverse Estimation of Calibration and Validation Set Using both the Robust Estimator and the Point-by-point Inverse Estimator

Equations (4)

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min F = min ( log ( i = 1 N ( I i , m e a s I i , s i m I i , m e a s ) 2 ) ) .
µ s ' ( λ ) = p 1 exp ( p 2 λ ) + p 3 .
min F g l o b a l = min i = 1 N λ F W L i [ λ i , µ s ' ( p 1 , p 2 , p 3 , λ i ) ] .
µ s ' ( λ ) = p 1 exp ( p 2 λ ) + p 3 + p 4 λ + p 5 λ 2 + p 6 λ 3 .

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