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

Optics Express, Vol. 18, Issue 11, pp. 11495-11507 (2010)

http://dx.doi.org/10.1364/OE.18.011495

Acrobat PDF (1187 KB)

### 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.

© 2010 OSA

## 1. Introduction

1. 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]

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]

7. 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]

10. 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]

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

13. 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]

12. 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]

14. 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]

16. 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]

17. 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]

1. 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]

## 2. Time resolved transmittance characterization method

18. 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]

### 2.1 Sample size

### 2.2 Experimental setup

### 2.3 Numerical modeling of light transport through the sample

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]

24. 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]

### 2.4 Monte Carlo solution of the RTE

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

*s*, boundary crossing event are detected when the following condition is met:where

*R*,

*X*and

*Y*represents the position of the boundary in cylindrical or rectangular coordinates (radius or half-length of the phantom). If the conditions are such that a photon packet would cross the boundary, the intersection position and an updated direction vector are computed. The photon packet is then reduced in weight according to Fresnel formulas and propagated with the updated direction.

### 2.5 Speeding up Monte Carlo simulations

9. 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]

*g*was fixed at the constant value of 0.62 [19] leaving

9. 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]

*v*, at any given time

*t*they all have travelled the same distance

^{−1}to 74 cm

^{−1}and tabulated into a reference database. The diffusion approximation was used to determine the required step size between successive

### 2.6 Data pre-treatment and analysis

*ω*denote the acceptance solid angle of the detector and

*A*is the exposed output surface of the sample.

*d*to be located on the output surface of the sample and to measure the experimental trace

**m**to extract optical properties. The model vector was obtained by the following expression:Convolution with the IRF introduces the effect of the finite response time of the TCSPC system and also translates the modeled TPSF to the correct position on the TCSPC system time axis. Convolution with the IRF also has the added benefit of smoothing out the statistical variations of the Monte-Carlo model. A gain factor

*G*is introduced to account for the measured arbitrary amplitude output by the system. Fitting of

**m**to the measurement vector

## 3. Error analysis: Sources of random errors

### 3.1 Measurement noise

### 3.2 System repeatability

- a) power up the system and wait five minutes for warm-up,
- b) measure the IRF,
- c) insert the sample in the sample holder,
- d) measure the sample TPSF,
- e) repeat step c) and d) three times randomly rotating the sample each time,
- f) shut down the system.

### 3.3Instrument response function (IRF) instability

## 4. Error analysis: Sources of systematic errors

### 4.1 Sample thickness inaccuracy

7. 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]

### 4.2 Refractive index inaccuracy

### 4.3 Anisotropy factor inaccuracy

*g*may also impact the recovered optical properties. The

*g*factor used in the Monte-Carlo model was determined experimentally as described in [19]. In brief, phantom batches with TiO

_{2}particles but no absorber were prepared and machined into thin wedges in addition to our standard characterization cylinders. The thickness of the wedged samples was selected to insure single scattering regime in transmission. The anisotropy factor was calculated using

*g*value of 0.59. The mean value of the anisotropy factor obtained for the various TiO

_{2}concentration was

*g*was calculated using the

*g*values excursion of 0.015. These traces were then treated like experimental input vectors to recover the optical properties using our reference database (which assumes a

*g*value of 0.62). The dependence on the

*g*value was found to be relatively weak. The average of the bias values are of

### 4.3 Time base inaccuracy

### 4.4 Forward model inaccuracy

^{−1}) but different absorption coefficients (approximately 0.07 cm

^{−1}and 0.16 cm

^{−1}) were casted into molds and machined into cylinder and rectangular blocks for a total of six different geometries (Fig. 6 .). More details about our phantom fabrication process including scatterer and absorber calibrations can be found in [19,17

17. 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]

## 5. Error analysis budget

## 6. Conclusion

## 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. | 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. |

3. | 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. |

4. | 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. |

5. | 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. |

6. | 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. |

7. | 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. |

8. | E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved diffuse reflectance spectroscopy,” Opt. Express |

9. | A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. |

10. | 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 |

11. | 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 |

12. | 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 |

13. | 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. |

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

15. | E. Alerstam, S. Andersson-Engels, and T. Svensson, “Improved accuracy in time-resolved reflectance spectroscopy,” Opt. Express |

16. | T. Moffitt, Y.-C. Chen, and S. A. Prahl, “Preparation and characterization of polyurethane optical phantoms,” J. Biomed. Opt. |

17. | 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. |

18. | 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 |

19. | 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”. |

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

21. | W. Becker, |

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

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

24. | 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. |

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

**OCIS Codes**

(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation

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

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: March 10, 2010

Revised Manuscript: April 22, 2010

Manuscript Accepted: May 6, 2010

Published: May 14, 2010

**Virtual Issues**

Vol. 5, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

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)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-11-11495

Sort: Year | Journal | Reset

### References

- 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).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.