## Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method

Optics Express, Vol. 15, Issue 11, pp. 6589-6604 (2007)

http://dx.doi.org/10.1364/OE.15.006589

Acrobat PDF (925 KB)

### Abstract

In this paper, a general method to calibrate the absorption coefficient of an absorber and the reduced scattering coefficient of a liquid diffusive medium, based on time-resolved measurements, is reported. An exhaustive analysis of the error sources affecting the estimation is also performed. The method has been applied with a state-of-the-art time-resolved instrumentation to determine the intrinsic absorption coefficient of Indian ink and the reduced scattering coefficient of Intralipid-20%, with a standard error smaller than 1% and 2%, respectively. Finally, the results have been compared to those retrieved for the same compounds by applying a continuous wave method recently published, obtaining an agreement within the error bars. This fact represents a cross validation of the two independent calibration methods.

© 2007 Optical Society of America

## 1 Introduction

*μ*′

_{s}and

*μ*coefficients, and many tissue-like phantoms have been proposed to assess the performance of NIR instrumentation [1

_{a}1. B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. **11**, 041102 (2006). [CrossRef] [PubMed]

2. H. Xu and M. S. Patterson, “Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference,” Opt. Express **14**, 6485 (2006). [CrossRef] [PubMed]

3. 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**, 7420 (2006). [CrossRef] [PubMed]

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

5. Y. Hasegawa*et al*., “Monte Carlo simulation of light transmission through living tissues,” Appl. Opt. **30**, 4515 (1991). [CrossRef] [PubMed]

6. Y. Nomura, O. Hazeki, and M. Tamura, “Relationship between time-resolved and non-time-resolved Beer-Lambert law in turbid media,” Phys. Med. Biol. **42**, 1009 (1997). [CrossRef] [PubMed]

7. F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Method for measuring the diffusion coefficient of homogeneous and layered media,” Opt. Lett. **25**, 1508 (2000). [CrossRef]

8. R. K. Wang and Y. A. Wickramasinghe, “Fast algorithm to determine optical properties of a turbid medium from time-resolved measurements,” Appl. Opt. **37**, 7342 (1998). [CrossRef]

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

## 2. The method

### 2.1 The absorber

9. 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**, 4587 (1997). [CrossRef] [PubMed]

*I*(

*x*⃗,

*t*,

*s*̑) is the radiance in the direction

*s*̑ ;

*v*is the speed of light in the medium;

*μ*and

_{s}*μ*are the scattering and absorption coefficient of the medium, respectively;

_{a}*p*(

*s*̑,

*s*̑′) is the scattering function representing the probability for a photon traveling in the direction

*s*̑′ to be scattered in the direction

*s*̑ ;

*q*(

*x*⃗,

*t*,

*s*̑) is the source term, representing the light power per unit of volume and solid angle.

*I*

_{0}(

*x*⃗,

*t*,

*s*̑) is the solution corresponding to a non-absorbing medium (

*μ*=0),

_{a}*I*(

*x*⃗,

*t*,

*s*̑) =

*I*

_{0}(

*x*⃗,

*t*,

*s*̑)exp(-

*μ*) is the solution when a uniform absorption coefficient

_{a}vt*μ*is present, that is the absorption coefficient appears only in the exponential factor. This fact can be exploited to calibrate an absorber.

_{a}*μ*and

_{s}*μ*

_{a0}; the detected power in a defined point

*x*⃗

_{d}of the medium can be written as:

*A*

_{0}accounts for the source power and the detection efficiency, while in the term

*S*are gathered all the geometry factors, the boundary conditions and the scattering properties of the medium. Now, if we add to the medium a defined quantity of the absorber to be calibrated, the new power detected at the same position is:

*μ*. We have also allowed that the source power and/or the detection efficiency can change from the previous measure.

_{a}*S*simplifies and, by taking the natural logarithm of both sides, we recover a linear relation between the measured power and time:

*μ*=

_{a}*μ*-

_{a}*μ*

_{a0}is the increase of the absorption coefficient due to the added absorber. Now, we can extract the value of Δ

*μ*from the slope of the linear regression between the independent variables

_{a}*X*=

*t*and

*Y*≡ ln(

*M*

_{0}/

*M*).

*ε*, that is the absorption coefficient

_{a}*per*unit of absorber concentration

*ρ*, expressed as the volume of the absorber over the volume of the diffusing mudium:

_{a}### 2.2 The scattering compound

*μ*in the RTE, as we did for the absorption coefficient. However, it is well known that, if some simplifying assumptions are considered in Eq. (1) [9

_{s}9. 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**, 4587 (1997). [CrossRef] [PubMed]

*U*(

*x*⃗,

*t*):

*D*= 1/(3

*μ*′

_{s}) is the diffusion coefficient,

*μ*′

_{s}=

*μ*

_{s}(1-

*g*) being the reduced scattering coefficient and

*g*the anisotropy factor, and

*Q*(

*x*⃗,

*t*) is the isotropic source term.

*Q*(

*x*⃗,

*t*) = 1/4

*π*

*δ*(

*x*⃗-

*x*⃗

_{s})

*δ*(

*t*), representing a point-like isotropic source located at

*x*⃗

_{s}, and consider an infinite slab of diffusing medium with optical properties

*μ*and

_{a}*μ*′

_{s}, according to Eq. (6), the measured power in both the reflectance and the transmittance geometry is given by [7

7. F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Method for measuring the diffusion coefficient of homogeneous and layered media,” Opt. Lett. **25**, 1508 (2000). [CrossRef]

8. R. K. Wang and Y. A. Wickramasinghe, “Fast algorithm to determine optical properties of a turbid medium from time-resolved measurements,” Appl. Opt. **37**, 7342 (1998). [CrossRef]

*A*accomplishes for the source power and the detection efficiency, while the factor

*S*accounts for the boundary conditions and depends on only the slab thickness

*d*and the scattering properties of the medium. Finally,

*r*is the distance in the slab plane between the injection and detection points.

*r*appears only in the exponential factor, if we perform two measurements at two different source-detector lateral distances (

*r*

_{0}and

*r*) and take the natural logarithm of the ratio of the measured power in the two conditions

*M*

_{0}and

*M*, respectively, we get a linear relation between such logarithm and the inverse of time:

*X*= 1/

*t*and

*Y*≡ ln(

*M*

_{0}/

*M*) one can determine the reduced scattering coefficient

*μ*′

_{s}. We note that expression (7) and, then, (8) are strictly valid only for point-like source and detector, located at

*x*⃗

_{s}and

*x*⃗

_{d}, respectively. For finite dimensions of source and/or detector some distortions of the linear dependence foreseen in (8) can be expected.

*ε*′

_{s}, that is the reduced scattering coefficient

*per*unit of the scatterer concentration

*ρ*. In a linear regime, one has simply:

_{s}*ρ*is expressed as the volume of the scatterer over the volume of the diffusing suspension.

_{s}## 3 Error analysis

### 3.1 Time scale

*t*

_{0}can fluctuate from one measure to another; ii) the time scale can be expanded or shrunk by a factor

*α*.

*t*

_{0}and

*t*′

_{0}for the measurements

*M*

_{0}and

*M*, respectively, the expression of these two quantities becomes:

*X*≡

*t*and

*Y*≡ ln(

*M*

_{0}/

*M*) is not affected by the two time shifts

*t*

_{0}and

*t*′

_{0}.

*t*

_{0}and

*t*′

_{0}for the measurements

*M*

_{0}and

*M*, respectively, the Eq. (8) becomes:

*t*

_{0}/

*t*and

*t*′

_{0}/

*t*. This assumption is reasonable because one expects only small fluctuations in time. From Eq. (12), it is possible to foresee a quadratic deviation from the linear dependence of

*Y*≡ ln(

*M*

_{0}/

*M*) on

*X*≡ 1/

*t*. This deviation is of the order of |

*t*

_{0}|/

*t*(or |

*t*′

_{0}|/

*t*) and obviously depends on the time range where the linear regression is performed. Then, one simple way for reducing the uncertainty due to a systematic time shift

*t*

_{0}is to avoid in the retrieval procedure the use of the first part of the temporal range. As an example, we consider a slab 20 mm thick,

*μ*′

_{s}=1.5 mm

^{-1}and source-detector lateral distances

*r*

_{0}= 0 and

*r*

_{1}= 25 mm: for a

*t*

_{0}= ±20 ps, we obtain a systematic error on the retrieved

*μ*′

_{s}that, assuming a time range for the linear regression with a lowest time of 1000 ps and a maximum time always greater than 3000 ps, is less than 3%, while for a

*t*

_{0}= ±10 ps the error is less than 1.5%.

*e*.

*g*. with 0.1% error, a time interval of 2 ns could results in a measure of 2.002 ns). We took into account this fact by putting such a kind of uncertainty into a scale factor

*α*so that the time

*t*of the measurements can be expressed as

*t*=

*α*

*t*̃, where

*t*̃ is the real time. Then, because in the proposed method we are interested to the slope of a linear regression where the independent variable is proportional to time (

*X*≡

*t*and

*X*≡ 1/

*t*for absorption and scattering, respectively),

*α*enters this slope as a factor and then its eventual relative error must be added to the relative error of the slope.

### 3.2 Instrument Response Function

*T*(

*r*,

*t*;

*μ*,

_{a}*μ*′

_{s}) considering the theoretical time-resolved curve, solution of the DE for a slab in transmission geometry with extrapolated boundary conditions, convolved with a given IRF.

*t*, in the estimation of Δ

*μ*by applying the method described in Sect. 1.1. Due to the fact that we have the same amplitude factor

_{a}*A*for all curves, the estimated absorption increment (Δ

*μ*)

_{a}^{est}(

*t*) results:

*r*

_{0}= 0 and

*r*

_{1}= 25 mm. Two examples of simulated curves for such lateral distances are reported in Fig. 1(d). From Eq. (8), considering that the amplitude factor is the same, we can calculate the estimated reduced scattering coefficient (

*μ*′

_{s})

^{est}as a function of time as follows:

### 3.3 Model adopted for light propagation

*μ*

_{a}as long as the RTE gives an accurate description of the stream of photons flowing inside the medium.

*μ*

_{a}=0 and

*μ*′

_{s}= 1.5mm

^{-1}has been considered. Moreover, the source and receiver have been assumed with a dimension of 3 mm. The method described in Section 2.2 has been used for retrieving the

*μ*′

_{s}of the medium, considering the two distances

*r*

_{0}= 0 and

*r*

_{1}= 25 mm. Provided that all the times with

*t*< 2.5

*t*

_{B}(

*t*

_{B}being the ballistic time between source and receiver) were disregarded from the retrieval procedure, the systematic error due to the intrinsic approximations of the DE shows to be always less than 0.2%. By changing some of the parameters, also the error changes. In particular, if the source-detector lateral distance is decreased, the error increases: for instance, with

*r*

_{1}= 10 mm we have an error always less than 1.2%. On the other hand, increasing

*μ*′

_{s}and keeping all the others parameters unchanged the error decreases.

### 3.4 Source-detector lateral distance

*r*(see Eq. (8)). Then, errors in the determination of such distances contribute straightforwardly to the indetermination of the scattering coefficient. More precisely, from Eq. (8) we have:

*s*is the slope of the linear relation appearing in the equation. Then, if we call σ

_{r}the standard deviation for

*r*, by using the formulas for the propagation of stochastic errors, the contribution to the relative error of the scattering coefficient

*ε*

_{μ′s}due to the uncertainty of

*r*is given by:

### 3.5 Preparation of the liquid diffusive media

*ρ*and

_{a}*ρ*contribute accordingly to the relative errors of

_{s}*ε*and

_{a}*ε*′

_{s}, respectively.

### 3.6 Concluding remarks on error analysis

*ε*

_{Δμa}affecting the increase in the absorption coefficient Δ

*μ*

_{a}due to all the possible stochastic error sources can be estimated as (see Sec. 3.1):

*ε*and

_{s}*ε*are the relative fluctuations of the slope

_{α}*s*of the linear relationship present in Eq. (4) and of the time-stretching factor

*α*introduced in Sec. 3.1, respectively. Moreover, to this value we have to add the systematic error due to the IRF of the measurement system (see Sec. 3.2).

*ε*

_{μ′s}due to all the possible stochastic error sources can be estimated as (see Sec. 3.1, Eqs. (15) and (16)):

*ε*

_{t0}is the relative error due to the stochastic shift of the time origin

*t*

_{0}. As before, to expression (18) we have to add the systematic errors introduced by the IRF and the diffusion model approximation (see Secs. 3.2 and 3.3).

*ε*and the reduced scattering coefficient

_{a}*ε*′

_{s}of the absorber and the scatterer compounds, respectively, can be smaller than those of Δ

*μ*and

_{a}*μ*′

_{s}calculated in Eqs. (17) and (18), if they are retrieved from a series of measurements by varying the compound concentrations, according to Eqs. (5) and (9).

## 4 Experimental results

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

### 4.1 System set-up

*α*, considered in Sec. 3.2, for our system consists in the indetermination of the conversion factor from MCA channel to picoseconds. For integrated systems this factor is usually calibrated by the factory: for our system,

*ε*can be assumed to be a fraction of a percent [12

_{α}12. W. Becker, *Advanced Time-Correlated Single Photon Counting Techniques* (Spinger-Verlag, Berlin Heidelberg, 2005). [CrossRef]

**15**, 486–500 (2007). [CrossRef] [PubMed]

*ρ*

_{sil}is of the order of 2 ∙ 10

^{-4}. On the other hand, we pre-diluted in distilled water the Indian ink, in order to reduce the uncertainty affecting its concentration

*ρ*

_{aink}in the diffusive suspensions. In this way, the relative error of

*ρ*

_{aink}can be estimated as 2 ∙ 10

^{-3}.

### 4.2 Calibration of the absorber

**15**, 486–500 (2007). [CrossRef] [PubMed]

*μ*′

_{s}= 0.64 mm

^{-1}. This will be our starting diffusive medium to which we will add different quantities of the pre-diluted absorber. We put this diffusing suspension in a tank of thickness

*d*= 40.8 mm and measure the transmitted on-axis time-resolved curve. In Fig. 2 is reported such a curve together with the IRF.

*μ*. The linear fitting method described in Sec. 2.1 was applied for different time ranges. We decided to fix the time ranges considering, for each curve, temporal points where the counts are a fixed percentage of the counts of the curve peak. In this way the time ranges adapt themselves to different curve shapes. From what we concluded in Sec. 3.2, we have to consider both extremes of the time ranges on the tail of the curves. For the ending time we chose the time corresponding to 0.5% of the curve peak. In this way we are reasonably away from the noise of the final part of the curve (see Fig. 2). Moreover, we varied the initial time taking the time corresponding to different percentages (namely, from 10% to 1%) of the counts of the curve peak. In Fig. 3 we report the relative error of the absorption coefficient, calculated for different values of the absorption increment, as a function of the initial time. It results that a reasonable choice for the percentage corresponding to the initial time is 5%: indeed, for this choice, if we limit to absorption increase of about 0.006 mm

_{a}^{-1}, we keep the relative error introduced by the convolution well below 1%.

*μ*. In Fig. 4 we have reported the value of Δ

_{a}*μ*as a function of the absorber concentration. Furthermore, we have evaluated the relative error of the slope of the linear regression expressed in Eq. (4), resulting of the order of 1%. For what we stated about the error due to the convolution and the time-scale factor, this is the major source of error for the first five addings, corresponding to a maximum absorption increase Δ

_{a}*μ*= 0.0061

_{a}*mm*

^{-1}. Then, by considering that independent relative errors have to be summed squared (see Eq. (17)), for these first five measurements the relative error affecting the estimated value of Δ

*μ*can be assumed to be 1%. For the higher values of absorber concentrations, corresponding to larger values of absorption, the systematic error introduced by IRF becomes prevalent, resulting in an underestimation of the absorption coefficient (compare Fig. 3).

_{a}*ε*

_{aink}of Indian ink:

### 4.3 Calibration of the scatterer

**15**, 486–500 (2007). [CrossRef] [PubMed]

*d*= 20.4 mm and performed transmittance measurements for 6 different off-axis values

*r*: 0 (on-axis), 5, 10, 15, 20, 25 mm. Indeed the method for the scatterer calibration relies on measurements at different source-detector lateral distances. Then, we prepared four diffusing suspensions corresponding to the following values for reduced scattering coefficient: 0.97, 1.4, 1.8, 2.2 mm

^{-1}, as one can establish adopting the calibration reported in [4

**15**, 486–500 (2007). [CrossRef] [PubMed]

*r*= 5, 10, 15, 20, 25 mm with that measured on-axis (

*i*.

*e*. we assumed

*r*

_{0}= 0). We note that we reduced the thickness of the tank (see Sec. 4.2), in order to enhance the differences between the on-axis and off-axis measurements. Then, by applying the linear regression reported in Eq. (8), we get 5 estimations for the reduced scattering coefficient

*μ*′

_{s}.

*r*: we can assume that in centering the 3 mm diameter transparent window with an about 2 mm wide beam, we make a maximum error of σ

_{r}=0.5 mm. According to Eq. (16), this means that the contribution to the relative error of

*μ*′

_{s}ranges from 20%, for

*r*= 5 mm, to 4%, for

*r*= 25 mm. As for the other sources of errors, the contribution

*ε*due to the indetermination of the slope of the linear regression is always lower than 1%. Furthermore, the error due to the convolution with the IRF can be evaluated by means of simulations. To this aim, we considered different time ranges for the linear regression in Eq. (8), expressed in percentage of the curve peak, considering for the raising edge the curve at

_{s}*r*> 0 and for the tail the curve at

*r*= 0, and calculated the relative error of the estimated reduced scattering coefficient. In Fig. 5 are reported the plots resulting from such a calculation as a function of the source-detector lateral distance

*r*, for the values of reduced scattering coefficients used in the measurements. By inspecting this figure, we decided to use as linear fitting range the time interval from 10% in the rising edge of the curve to 1% in the tail: with this choice, we have a relative error less that 2%, at least for the three largest lateral distances (compare Fig. 5(b)). As for the time shift affecting our measurements, we monitored it by recording the IRF after every set of about 5 measures taken over a period of about 10 minutes. The resulting indeterminacy on the time origin for each independent acquisition was about ±2 ps. Since the time range we consider for the linear regression has an initial time of some hundreds of picoseconds, also the

*ε*

_{t0}contribution to the total error can be assumed well lower than 1%. Finally, considering the time ranges adopted, the optical and geometrical properties of the measured suspensions and the simulations reported in Sec. 3.3, the error due to the diffusion approximation is estimable on the order of a fraction of percent.

*μ*′

_{s}emerging from the largest lateral distances:

*r*= 15, 20, 25 mm. Only for these measurements, in fact, the error can be assumed lower than 10%. In order to calculate the errors affecting these three estimations of

*μ*′

_{s}, we summed up all the relative errors squared, as reported in Eq. (18), noting that the only relevant contributions come from the lateral distances

*r*and the convolution. Finally, we ended up with the best value for

*μ*′

_{s}, by performing a weighted average of the three estimations of

*μ*′

_{s}for each source-detector lateral distance [13]. The resulting relative error affecting the best value is of 3%.

*r*

_{0}= 0 and

*r*= 25mm,

*Y*= ln(

*M*

_{0}/

*M*), as function of

*X*≡ 1/

*t*and resulting linear best fits (line) according to Eq. (8), are reported as examples for four values of Intralipid-20% concentration. Furthermore, in Fig. 6(b) the four best estimations of

*μ*′

_{s}are plotted as a function of the Intralipid concentration. Also the error bars for each reduced scattering coefficient are reported. Finally, we calculated the intrinsic reduced scattering coefficient

*ε*′

_{sil}of the Intralipid-20%, by performing the best linear fit of these data, as stated in Eq. (9):

*ε*′

_{sil}is 1.5%. In comparison, the uncertainty due to preparation of the suspension (see Sec. 4.1) can be neglected. Then, this is the accuracy that would characterize a diffusive sample prepared with this calibrated batch of Intralipid-20%. On the contrary, with a single multi-distance measurement the reduced scattering coefficient can be measured with a relative error of 3%, as stated above.

### 4.4 Comparison with CW results

*ε*

_{aink}and

*ε*′

_{sil}, respectively, obtained by applying the calibration methods in the two experimental approaches. In table 1 the results obtained with the two independent procedures are summarized. The best estimations of the uncertainty affecting the results are also reported. As one can see from the table, the results obtained with the two calibration methods are in agreement within the error bars. A discussion on how these values compare with similar results reported in literature is reported in [4

**15**, 486–500 (2007). [CrossRef] [PubMed]

## 5. Conclusions

**15**, 486–500 (2007). [CrossRef] [PubMed]

**15**, 486–500 (2007). [CrossRef] [PubMed]

14. 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, E. Tinet, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. **44**, 2104 (2005). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | B. W. Pogue and M. S. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. |

2. | H. Xu and M. S. Patterson, “Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference,” Opt. Express |

3. | 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 |

4. | F. Martelli and G. Zaccanti, “Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. CW method,” Opt. Express |

5. | Y. Hasegawa |

6. | Y. Nomura, O. Hazeki, and M. Tamura, “Relationship between time-resolved and non-time-resolved Beer-Lambert law in turbid media,” Phys. Med. Biol. |

7. | F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Method for measuring the diffusion coefficient of homogeneous and layered media,” Opt. Lett. |

8. | R. K. Wang and Y. A. Wickramasinghe, “Fast algorithm to determine optical properties of a turbid medium from time-resolved measurements,” Appl. Opt. |

9. | 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. |

10. | D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near infrared spectroscopy,” Opt. Express |

11. | 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. |

12. | W. Becker, |

13. | J. R. Taylor, |

14. | 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, E. Tinet, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. |

**OCIS Codes**

(170.3890) Medical optics and biotechnology : Medical optics instrumentation

(170.5280) Medical optics and biotechnology : Photon migration

(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics

(170.7050) Medical optics and biotechnology : Turbid media

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: March 7, 2007

Revised Manuscript: April 20, 2007

Manuscript Accepted: May 3, 2007

Published: May 14, 2007

**Virtual Issues**

Vol. 2, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Lorenzo Spinelli, Fabrizio Martelli, Andrea Farina, Antonio Pifferi, Alessandro Torricelli, Rinaldo Cubeddu, and Giovanni Zaccanti, "Calibration of scattering and absorption properties of a liquid diffusive medium at NIR wavelengths. Time-resolved method," Opt. Express **15**, 6589-6604 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-11-6589

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### References

- B. W. Pogue and M. S. Patterson, "Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry," J. Biomed. Opt. 11, 041102 (2006). [CrossRef] [PubMed]
- H. Xu and M. S. Patterson, "Determination of the optical properties of tissue-simulating phantoms from interstitial frequency domain measurements of relative fluence and phase difference," Opt. Express 14, 6485 (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, 7420 (2006). [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, 486-500 (2007). [CrossRef] [PubMed]
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