Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method

Jean-Pierre Bouchard; Israël Veilleux; Rym Jedidi; Isabelle Noiseux; Michel Fortin; Ozzy Mermut

doi:10.1364/OE.18.011495

Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method

Jean-Pierre Bouchard, Israël Veilleux, Rym Jedidi, Isabelle Noiseux, Michel Fortin, and Ozzy Mermut

Optics Express
Vol. 18,
Issue 11,
pp. 11495-11507
(2010)
•https://doi.org/10.1364/OE.18.011495

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Jean-Pierre Bouchard, Israël Veilleux, Rym Jedidi, Isabelle Noiseux, Michel Fortin, and Ozzy Mermut, "Reference optical phantoms for diffuse optical spectroscopy. Part 1 – Error analysis of a time resolved transmittance characterization method," Opt. Express 18, 11495-11507 (2010)

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Related Topics
Table of Contents Category
- Medical Optics and Biotechnology
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Medical optics instrumentation (120.3890)
- Spectroscopy, tissue diagnostics (170.6510)

About this Article
History
- Original Manuscript: March 10, 2010
- Revised Manuscript: April 22, 2010
- Manuscript Accepted: May 6, 2010
- Published: May 14, 2010
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 5, Iss. 10

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Abstract

Development, production quality control and calibration of optical tissue-mimicking phantoms require a convenient and robust characterization method with known absolute accuracy. We present a solid phantom characterization technique based on time resolved transmittance measurement of light through a relatively small phantom sample. The small size of the sample enables characterization of every material batch produced in a routine phantoms production. Time resolved transmittance data are pre-processed to correct for dark noise, sample thickness and instrument response function. Pre-processed data are then compared to a forward model based on the radiative transfer equation solved through Monte Carlo simulations accurately taking into account the finite geometry of the sample. The computational burden of the Monte-Carlo technique was alleviated by building a lookup table of pre-computed results and using interpolation to obtain modeled transmittance traces at intermediate values of the optical properties. Near perfect fit residuals are obtained with a fit window using all data above 1% of the maximum value of the time resolved transmittance trace. Absolute accuracy of the method is estimated through a thorough error analysis which takes into account the following contributions: measurement noise, system repeatability, instrument response function stability, sample thickness variation refractive index inaccuracy, time correlated single photon counting system time based inaccuracy and forward model inaccuracy. Two sigma absolute error estimates of 0.01 cm⁻¹ (11.3%) and 0.67 cm⁻¹ (6.8%) are obtained for the absorption coefficient and reduced scattering coefficient respectively.

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References

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|
Year
|
Author
|
Publication

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]
F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36(19), 4600–4612 (1997).
[Crossref] [PubMed]
S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, “Determining the optical properties of turbid media by using the adding-doubling method,” Appl. Opt. 32(4), 559–568 (1993).
[Crossref] [PubMed]
J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek, H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-integrating sphere system for measuring the optical properties of tissue,” Appl. Opt. 32(4), 399–410 (1993).
[Crossref] [PubMed]
M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989).
[Crossref] [PubMed]
J. B. Fishkin, P. T. C. So, A. E. Cerissi, S. Fantini, M. A. Franceschini, and E. Gratton, “Frequency-domain method for measuring spectral properties in multiple-scattering media: methemoglobin absorption spectrum in a tissuelike phantom,” Appl. Opt. 34(7), 1143–1155 (1995).
[Crossref] [PubMed]
D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36(19), 4587–4599 (1997).
[Crossref] [PubMed]
E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 15, 10434–10448 (2007).
A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[Crossref] [PubMed]
C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X.-H. Hu, “A primary method for determination of optical parameters of turbid samples and application to intralipid between 550 and 1630 nm,” Opt. Express 14(16), 7420–7435 (2006).
[Crossref] [PubMed]
L. Spinelli, F. Martelli, A. Farina, A. Pifferi, A. Torricelli, R. Cubeddu, and G. Zaccanti, “Accuracy of the nonlinear fitting procedure for time-resolved measurements on diffusive phantoms at NIR wavelength,” Proc. SPIE 717424, 1–10 (2009).
L. Spinelli, F. Martelli, A. Farina, A. Pifferi, A. Torricelli, R. Cubeddu, and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method,” Opt. Express 15(11), 6589–6604 (2007).
[Crossref] [PubMed]
A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. 44(11), 2104–2114 (2005).
[Crossref] [PubMed]
F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express 15(2), 486–500 (2007).
[Crossref] [PubMed]
E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved reflectance spectroscopy,” Opt. Express 16(14), 10440–10448 (2008).
[Crossref] [PubMed]
T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11(4), 041103 (2006).
[Crossref] [PubMed]
M. L. Vernon, J. Freàchette, Y. Painchaud, S. Caron, and P. Beaudry, “Fabrication and characterization of a solid polyurethane phantom for optical imaging through scattering media,” Appl. Opt. 38(19), 4247–4251 (1999).
[Crossref]
A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]
J.-P. Bouchard, National Optics Institute, 2740 Einstein, Québec, Qc, G1P 4S4 are preparing a manuscript to be called “Reference optical phantoms for diffuse optical spectroscopy. Part 2 - Fabrication”.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77, (Cambridge, 1992), Chap. 15.
W. Becker, The bh TCSPC Handbook, Third Edition (Becker & Hickl GmbH, 2008)
L. V. Wang, Biomedical Optocs, Principles and Imaging (Wiley, 2007), Chap. 5.
“(MCML) Monte Carlo for Multi-Layered media, ” http://omlc.ogi.edu/software/mc/
F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45(5), 1359–1373 (2000).
[Crossref] [PubMed]
W. Becker, Becker & Hickl, Nahmitzer Damm 30, 12277 Berlin, (personal communication, 2008).

2009 (1)

L. Spinelli, F. Martelli, A. Farina, A. Pifferi, A. Torricelli, R. Cubeddu, and G. Zaccanti, “Accuracy of the nonlinear fitting procedure for time-resolved measurements on diffusive phantoms at NIR wavelength,” Proc. SPIE 717424, 1–10 (2009).

2008 (1)

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved reflectance spectroscopy,” Opt. Express 16(14), 10440–10448 (2008).
[Crossref] [PubMed]

2007 (3)

L. Spinelli, F. Martelli, A. Farina, A. Pifferi, A. Torricelli, R. Cubeddu, and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method,” Opt. Express 15(11), 6589–6604 (2007).
[Crossref] [PubMed]

F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express 15(2), 486–500 (2007).
[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 15, 10434–10448 (2007).

2006 (4)

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

C. Chen, J. Q. Lu, H. Ding, K. M. Jacobs, Y. Du, and X.-H. Hu, “A primary method for determination of optical parameters of turbid samples and application to intralipid between 550 and 1630 nm,” Opt. Express 14(16), 7420–7435 (2006).
[Crossref] [PubMed]

T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11(4), 041103 (2006).
[Crossref] [PubMed]

A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]

2005 (1)

A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. 44(11), 2104–2114 (2005).
[Crossref] [PubMed]

2000 (1)

F. Martelli, M. Bassani, L. Alianelli, L. Zangheri, and G. Zaccanti, “Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation,” Phys. Med. Biol. 45(5), 1359–1373 (2000).
[Crossref] [PubMed]

1999 (1)

M. L. Vernon, J. Freàchette, Y. Painchaud, S. Caron, and P. Beaudry, “Fabrication and characterization of a solid polyurethane phantom for optical imaging through scattering media,” Appl. Opt. 38(19), 4247–4251 (1999).
[Crossref]

1997 (2)

F. Martelli, D. Contini, A. Taddeucci, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36(19), 4600–4612 (1997).
[Crossref] [PubMed]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36(19), 4587–4599 (1997).
[Crossref] [PubMed]

1996 (1)

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 15, 10434–10448 (2007).

Alianelli, L.

Andersson-Engels, S.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved reflectance spectroscopy,” Opt. Express 16(14), 10440–10448 (2008).
[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 15, 10434–10448 (2007).

Arridge, S. R.

A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]

Avrillier, S.

Barrett, H.

A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]

Bassani, M.

Bassi, A.

Beaudry, P.

Beek, J. F.

Caron, S.

Cerissi, A. E.

Chance, B.

Chen, C.

Chen, Y.-C.

T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11(4), 041103 (2006).
[Crossref] [PubMed]

Contini, D.

Cubeddu, R.

Ding, H.

Du, Y.

Fantini, S.

Farina, A.

Fishkin, J. B.

Franceschini, M. A.

Freàchette, J.

Gratton, E.

Grosenick, D.

Hu, X.-H.

Jacobs, K. M.

Kienle, A.

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[Crossref] [PubMed]

Lu, J. Q.

Macdonald, R.

Martelli, F.

Moffitt, T.

T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11(4), 041103 (2006).
[Crossref] [PubMed]

Möller, M.

Nghiem, H. L.

Painchaud, Y.

Patterson, M. S.

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[Crossref] [PubMed]

Pickering, J. W.

Pifferi, A.

Pineda, A. R.

A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]

Pogue, B. W.

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

Prahl, S. A.

T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11(4), 041103 (2006).
[Crossref] [PubMed]

Schweiger, M.

A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]

So, P. T. C.

Spinelli, L.

Stamm, H.

Sterenborg, H. J. C. M.

Svensson, T.

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved reflectance spectroscopy,” Opt. Express 16(14), 10440–10448 (2008).
[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 15, 10434–10448 (2007).

Swartling, J.

Taddeucci, A.

Taroni, P.

Torricelli, A.

Tualle, J.-M.

van Gemert, M. J. C.

van Veen, R. L. P.

van Wieringen, N.

Vernon, M. L.

Wabnitz, H.

Welch, A. J.

Whelan, M.

Wilson, B. C.

Zaccanti, G.

Zangheri, L.

Appl. Opt. (8)

J. Biomed. Opt. (2)

B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11(4), 041102 (2006).
[Crossref] [PubMed]

T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. 11(4), 041103 (2006).
[Crossref] [PubMed]

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

A. R. Pineda, M. Schweiger, S. R. Arridge, and H. Barrett, “Information content of data types in time-domain optical tomography,” J. Opt. Soc. Am. A 23(12), 2989–2996 (2006).
[Crossref]

Opt. Express (5)

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved reflectance spectroscopy,” Opt. Express 16(14), 10440–10448 (2008).
[Crossref] [PubMed]

E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express 15, 10434–10448 (2007).

Phys. Med. Biol. (2)

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[Crossref] [PubMed]

Proc. SPIE (1)

Other (6)

J.-P. Bouchard, National Optics Institute, 2740 Einstein, Québec, Qc, G1P 4S4 are preparing a manuscript to be called “Reference optical phantoms for diffuse optical spectroscopy. Part 2 - Fabrication”.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN 77, (Cambridge, 1992), Chap. 15.

W. Becker, The bh TCSPC Handbook, Third Edition (Becker & Hickl GmbH, 2008)

L. V. Wang, Biomedical Optocs, Principles and Imaging (Wiley, 2007), Chap. 5.

“(MCML) Monte Carlo for Multi-Layered media, ” http://omlc.ogi.edu/software/mc/

W. Becker, Becker & Hickl, Nahmitzer Damm 30, 12277 Berlin, (personal communication, 2008).

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Fig. 1 Sensitivity of a transmittance TPSF trace of a 2 cm thick slab to a perturbation of 1% in the optical properties.

Y_{0}

(blue) is the reference TPSF.

Y_{δ μ_{a}}

and

Y_{δ μ_{s}^{'}}

refers to the perturbed TPSF traces. Difference between the perturbed TPSF and the reference TPSF are plotted in red and green for a

μ_{a}

and a

μ_{s}^{'}

perturbations respectively.

Download Full Size | PPT Slide | PDF

Fig. 2 Experimental setup for time resolved transmittance measurements.

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Fig. 3 TPSF database for a 20 mm thick cylindrical sample (D = 55 mm).

Download Full Size | PPT Slide | PDF

Fig. 4 Fit results for cylindrical samples coming from 4 separate batches B0052, B0053, B0054 and B0055 of our phantom production samples collection [19]. Note that the residuals have been magnified by a factor of 10.

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Fig. 5 Instrument response functions acquired over a 4 hr time period

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Fig. 6 Phantom set fabricated from a single batch to evaluate the model limitations

Download Full Size | PPT Slide | PDF

Fig. 7 μ _a and μ _s’ dependence on the sample’s lateral dimension and thickness

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Tables (2)

Table 1 Characterization results for all phantoms

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Table 2 Contribution of errors

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Equations (4)

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

\begin{array}{l} C y l i n d r i c a l {(x + s u_{x})}^{2} + {(y + s u_{y})}^{2} > R^{2}, \\ Re c \tan g u l a r | x + s u_{x} | > X or | y + s u_{y} | > Y, \end{array}

L_{μ_{a}} (\hat{r}, \hat{u}, t) = L_{μ_{a} = 0} (\hat{r}, \hat{u}, t) \exp (- μ_{a} v t),

M (t) = \int_{ω} \int_{A} L [\hat{r} = (ρ, θ, z = d), \hat{u}, t] d A d Ω,

{m |}_{μ_{a}, μ_{s}^{'}} = G \cdot M ([0, Δ t, 2 Δ t, \dots]) * I R F .

			Low absorption batch		High absorption batch
Geometry	Size	Thickness	$μ_{a}$	$μ_{s}^{'}$	$μ_{a}$	$μ_{s}^{'}$
	mm	mm	cm⁻¹	cm⁻¹	cm⁻¹	cm⁻¹
Cyl	55	10	0.060	9.08	0.146	8.82
Cyl	55	20	0.069	9.28	0.161	9.15
Cyl	55	30	0.071	9.49	0.164	9.32
Rec	30	20	0.072	9.50	0.162	9.33
Rec	50	20	0.070	9.45	0.162	9.35
Rec	80	20	0.070	9.46	0.160	9.20
		Mean	0.069	9.38	0.159	9.20
		Std. dev.	0.0042	0.17	0.0064	0.20
		% variation	6.2%	1.8%	4.0%	2.2%

Error source	Absolute error (cm⁻¹)		Relative error (%)*
Error source	$μ_{a}$	$μ_{s}^{'}$	$μ_{a}$	$μ_{s}^{'}$
Random error sources
Measurement noise	0.0006	0.027	0.71%	0.27%
System repeatability	0.0017	0.12	1.8%	1.2%
IRF instabilities	0.0005	0.04	0.59%	0.4%
Systematic error sources
Sample thickness	0.001	0.25	1.18%	2.5%
Refractive index	0.001	0.035	1.18%	0.35%
Anisotropy factor	0.0001	0.003	0.1%	0.03%
Time base inaccuracies	0.0015	0.07	1.76%	0.7%
Monte-Carlo model	0.004**	0.20	4.71%	2.2%
Total error (RSS, 1σ)	0.005	0.34	5.7%	3.4%
Total error (RSS, 2σ)	0.010	0.67	11.3%	6.8%

			Low absorption batch		High absorption batch
Geometry	Size	Thickness	$μ_{a}$	$μ_{s}^{'}$	$μ_{a}$	$μ_{s}^{'}$
	mm	mm	cm⁻¹	cm⁻¹	cm⁻¹	cm⁻¹
Cyl	55	10	0.060	9.08	0.146	8.82
Cyl	55	20	0.069	9.28	0.161	9.15
Cyl	55	30	0.071	9.49	0.164	9.32
Rec	30	20	0.072	9.50	0.162	9.33
Rec	50	20	0.070	9.45	0.162	9.35
Rec	80	20	0.070	9.46	0.160	9.20
		Mean	0.069	9.38	0.159	9.20
		Std. dev.	0.0042	0.17	0.0064	0.20
		% variation	6.2%	1.8%	4.0%	2.2%

Error source	Absolute error (cm⁻¹)		Relative error (%)*
Error source	$μ_{a}$	$μ_{s}^{'}$	$μ_{a}$	$μ_{s}^{'}$
Random error sources
Measurement noise	0.0006	0.027	0.71%	0.27%
System repeatability	0.0017	0.12	1.8%	1.2%
IRF instabilities	0.0005	0.04	0.59%	0.4%
Systematic error sources
Sample thickness	0.001	0.25	1.18%	2.5%
Refractive index	0.001	0.035	1.18%	0.35%
Anisotropy factor	0.0001	0.003	0.1%	0.03%
Time base inaccuracies	0.0015	0.07	1.76%	0.7%
Monte-Carlo model	0.004**	0.20	4.71%	2.2%
Total error (RSS, 1σ)	0.005	0.34	5.7%	3.4%
Total error (RSS, 2σ)	0.010	0.67	11.3%	6.8%

Abstract

References

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1997 (2)

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1995 (1)

1993 (2)

1989 (1)

Alerstam, E.

Alianelli, L.

Andersson-Engels, S.

Arridge, S. R.

Avrillier, S.

Barrett, H.

Bassani, M.

Bassi, A.

Beaudry, P.

Beek, J. F.

Caron, S.

Cerissi, A. E.

Chance, B.

Chen, C.

Chen, Y.-C.

Contini, D.

Cubeddu, R.

Ding, H.

Du, Y.

Fantini, S.

Farina, A.

Fishkin, J. B.

Franceschini, M. A.

Freàchette, J.

Gratton, E.

Grosenick, D.

Hu, X.-H.

Jacobs, K. M.

Kienle, A.

Lu, J. Q.

Macdonald, R.

Martelli, F.

Moffitt, T.

Möller, M.

Nghiem, H. L.

Painchaud, Y.

Patterson, M. S.

Pickering, J. W.

Pifferi, A.

Pineda, A. R.

Pogue, B. W.

Prahl, S. A.

Schweiger, M.

So, P. T. C.

Spinelli, L.

Stamm, H.

Sterenborg, H. J. C. M.

Svensson, T.

Swartling, J.

Taddeucci, A.

Taroni, P.

Torricelli, A.

Tualle, J.-M.

van Gemert, M. J. C.

van Veen, R. L. P.

van Wieringen, N.

Vernon, M. L.

Wabnitz, H.

Welch, A. J.

Whelan, M.

Wilson, B. C.

Zaccanti, G.

Zangheri, L.

Appl. Opt. (8)

J. Biomed. Opt. (2)

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