Abstract

Noncontact optical imaging has attracted increasing attention in recent years due to its significant advantages on detection sensitivity, spatial resolution, image quality and system simplicity compared with contact measurement. However, photon transport simulation in free-space is still an extremely challenging topic for the complexity of the optical system. For this purpose, this paper proposes an analytical model for photon propagation in free-space based on hybrid radiosity-radiance theorem (HRRT). It combines Lambert’s cosine law and the radiance theorem to handle the influence of the complicated lens and to simplify the photon transport process in the optical system. The performance of the proposed model is evaluated and validated with numerical simulations and physical experiments. Qualitative comparison results of flux distribution at the detector are presented. In particular, error analysis demonstrates the feasibility and potential of the proposed model for simulating photon propagation in free-space.

© 2009 Optical Society of America

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2008

2007

2006

R. B. Schultz, J. Peter, and W. Semmler, "Comparison of noncontact and fiber-based fluorescence-mediated tomography," Opt. Lett. 31, 769-771 (2006).
[CrossRef]

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 631801 (2006).

2005

2004

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

J. H. Lee, S. Kim, and Y. T. Kim, "Finite element method for diffusive light propagation in index-mismatched media," Opt. Express 12,1727-1740 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1727.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

J. Ripoll, and V. Ntziachristos, "Imaging scattering media from a distance: theory and applications of noncontact optical tomography," Mod. Phys. Lett. B 18, 1-29 (2004).
[CrossRef]

2003

R. Weissleder, and V. Ntziachristos, "Shedding light onto live molecular targets," Nat. Med. 9, 123-128 (2003).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Noncontact optical tomography of turbid media," Opt. Lett. 28, 1701-1703 (2003).
[CrossRef] [PubMed]

2002

2001

R. Weissleder, and U. Mahmood, "Molecular imaging," Radiology 219, 316-333 (2001).
[PubMed]

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light-emitting probes," J. Biomed. Opt. 6, 432-440 (2001).
[CrossRef] [PubMed]

2000

1996

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

1995

L. V. Wang, S. L. Jacques, L. Q. Zheng, "MCML-Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Met. Prog. Biomed. 47, 131-146 (1995).
[CrossRef]

Aggarwal, M.

M. Aggarwal, and N. Ahuja, "A pupil-centric model of image formation," Int. J. Comput. Vis. 48, 195-214 (2002).
[CrossRef]

Ahuja, N.

M. Aggarwal, and N. Ahuja, "A pupil-centric model of image formation," Int. J. Comput. Vis. 48, 195-214 (2002).
[CrossRef]

Arridge, S. R.

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, "Optical tomography in the presence of void regions," J. Opt. Soc. Am. A 17, 1659-1670 (2000).
[CrossRef]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

Arridge, S.R.

Bai, J.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Bao, S.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Boas, D.

Cable, M. D.

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light-emitting probes," J. Biomed. Opt. 6, 432-440 (2001).
[CrossRef] [PubMed]

Cong, A.

Cong, W.

Cong, W. X.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Culver, J.

Dehghani, H.

Deliolanis, N.

Delpy, D. T.

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, "Optical tomography in the presence of void regions," J. Opt. Soc. Am. A 17, 1659-1670 (2000).
[CrossRef]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

Dunn, A.

Economou, E. N.

Feng, J.

Firbank, M.

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

French, P. J.

Gao, F.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Garofalakis, A.

Hoffman, E. A.

Hyde, D.

Jacques, S. L.

L. V. Wang, S. L. Jacques, L. Q. Zheng, "MCML-Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Met. Prog. Biomed. 47, 131-146 (1995).
[CrossRef]

Jiang, M.

Kim, S.

Kim, Y. T.

Kioussis, D.

Kumar, D.

Lasser, T.

Lee, J. H.

Li, H.

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 631801 (2006).

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Li, Y.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Liang, W.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Liu, K.

Liu, Y.

Luo, J.

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 631801 (2006).

Lv, Y.

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, "Galerkin-based meshless methods for photon transport in the biological tissue," Opt. Express 16, 20317-20333 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 631801 (2006).

Mahmood, U.

R. Weissleder, and U. Mahmood, "Molecular imaging," Radiology 219, 316-333 (2001).
[PubMed]

Mamalaki, C.

Margallo-Balbas, E.

McCray, P. B.

McLennan, G.

Meyer, H.

Nelson, M. B.

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light-emitting probes," J. Biomed. Opt. 6, 432-440 (2001).
[CrossRef] [PubMed]

Nieto-vesperinas, M.

Ntziachristos, V.

N. Deliolanis, T. Lasser, D. Hyde, A. Soubert, J. Ripoll, and V. Ntziachristos, "Free-space fluorescence molecular tomography utilizing 360° geometry projections," Opt. Lett. 32, 382-384 (2007).
[CrossRef] [PubMed]

H. Meyer, A. Garofalakis, G. Zacharakis, S. Psycharakis, C. Mamalaki, D. Kioussis, E. N. Economou, V. Ntziachristos, and J. Ripoll, "Noncontact optical imaging in mice with full angular coverage and automatic surface extraction," Appl. Opt. 46,3617-3627 (2007).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

J. Ripoll, and V. Ntziachristos, "Imaging scattering media from a distance: theory and applications of noncontact optical tomography," Mod. Phys. Lett. B 18, 1-29 (2004).
[CrossRef]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Noncontact optical tomography of turbid media," Opt. Lett. 28, 1701-1703 (2003).
[CrossRef] [PubMed]

R. Weissleder, and V. Ntziachristos, "Shedding light onto live molecular targets," Nat. Med. 9, 123-128 (2003).
[CrossRef] [PubMed]

Peter, J.

Piley, J.

Psycharakis, S.

Qin, C.

Qin, D.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Rice, B. W.

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light-emitting probes," J. Biomed. Opt. 6, 432-440 (2001).
[CrossRef] [PubMed]

Ripoll, J.

N. Deliolanis, T. Lasser, D. Hyde, A. Soubert, J. Ripoll, and V. Ntziachristos, "Free-space fluorescence molecular tomography utilizing 360° geometry projections," Opt. Lett. 32, 382-384 (2007).
[CrossRef] [PubMed]

H. Meyer, A. Garofalakis, G. Zacharakis, S. Psycharakis, C. Mamalaki, D. Kioussis, E. N. Economou, V. Ntziachristos, and J. Ripoll, "Noncontact optical imaging in mice with full angular coverage and automatic surface extraction," Appl. Opt. 46,3617-3627 (2007).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

J. Ripoll, and V. Ntziachristos, "Imaging scattering media from a distance: theory and applications of noncontact optical tomography," Mod. Phys. Lett. B 18, 1-29 (2004).
[CrossRef]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Noncontact optical tomography of turbid media," Opt. Lett. 28, 1701-1703 (2003).
[CrossRef] [PubMed]

J. Piley, H. Dehghani, M. Schweiger, S.R. Arridge, J. Ripoll, and M. Nieto-vesperinas, "3D optical tomography in the presence of void regions," Opt. Express 7, 462-467 (2000), http://www.opticsinfobase.org/abstract.cfm?URI=oe-7-13-462.
[CrossRef]

Schultz, R. B.

Schulz, R. B.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Noncontact optical tomography of turbid media," Opt. Lett. 28, 1701-1703 (2003).
[CrossRef] [PubMed]

Schweiger, M.

Semmler, W.

Soubert, A.

Stott, J.

Tanikawa, Y.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Tian, J.

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, "Galerkin-based meshless methods for photon transport in the biological tissue," Opt. Express 16, 20317-20333 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 631801 (2006).

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Wang, G.

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 631801 (2006).

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6756-6771 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Wang, L. V.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6756-6771 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

L. V. Wang, S. L. Jacques, L. Q. Zheng, "MCML-Monte Carlo modeling of photon transport in multi-layered tissues," Comput. Met. Prog. Biomed. 47, 131-146 (1995).
[CrossRef]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

R. Weissleder, and V. Ntziachristos, "Shedding light onto live molecular targets," Nat. Med. 9, 123-128 (2003).
[CrossRef] [PubMed]

R. Weissleder, and U. Mahmood, "Molecular imaging," Radiology 219, 316-333 (2001).
[PubMed]

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[CrossRef] [PubMed]

Appl. Opt.

Comput. Met. Prog. Biomed.

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J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging

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Figures (12)

Fig. 1.
Fig. 1.

Schematic diagram for the radiance theorem.

Fig. 2.
Fig. 2.

Schematic diagram for simplification of the Gaussian thick-lens model to a thin-lens model. (a) Gaussian thick-lens model; (b) Thin-lens model.

Fig. 3.
Fig. 3.

Schematic diagram for noncontact experimental configuration.

Fig. 4.
Fig. 4.

Numerical simulation experiment for the flat surface. (a) Phantom configuration; (b) and (c) Photon flux density at the detector obtained by HRRT and TracePro.

Fig. 5.
Fig. 5.

Comparison between the calculated results using HRRT model and the experimental data obtained from TracePro at the position yd =0.0mm at the detector. (a) Original curves; (b) Filtered curves based on (a).

Fig. 6.
Fig. 6.

Numerical simulation experiment for the curved surface. (a) Phantom configuration; (b) and (c) Photon flux density at the detector obtained by HRRT and TracePro.

Fig. 7.
Fig. 7.

Comparison between the calculated results using HRRT model and the experimental data obtained from TracePro at the position zd =5.2mm at the detector. (a) Original curves; (b) Filtered curves based on (a).

Fig. 8.
Fig. 8.

Physical experiment for cubic phantom. (a) Physical phantom with one light source; (b) Schematic diagram of four different perspectives; (c) Schematic diagram of numerical calculation phantom.

Fig. 9.
Fig. 9.

Photon flux distribution measured using CCD camera or solved by HRRT. (a)–(d) experimental data, (e)–(h) calculated results; (a) and (e) 0°, (b) and (f) 90°, (c) and (g) 180°, (d) and (h) 270°.

Fig. 10.
Fig. 10.

Comparison between the calculated and experimental photon flux at height 0, 1.6875 and 3.375mm from the center of the detector. (a) 0°, (b) 90°, (c) 180° and (d) 270°.

Fig. 11.
Fig. 11.

Physical experiment for cylinder phantom. (a) Physical phantom with one light source; (b) Schematic diagram of numerical calculation phantom.

Fig. 12.
Fig. 12.

Comparison between the calculated and experimental results at the detector positions: zd =0.0, 2.0, 4.0mm. (a) Comparison between HRRT and experimental results; (b) Comparison between the published method and experimental results

Tables (2)

Tables Icon

Table 1. Error comparisons between the calculated and experimental results of four perspectives

Tables Icon

Table 2. Error comparisons between calculated results and experimental data

Equations (17)

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

dP (rd)=1πsJn(r)ξ(r,rd)cosθscosθdrdr2dAdS
L = L
E = L Acos2θr2
E = L Acos2θr2
E = Et2
r' = tr
dS = t2 dS
P = EdS
P = E dS
P = P
1u + 1νh = 1f
dP (rvd)=1π SJn(r)ξ(r,rvd)cosθscosθvdrvdr2dAvddS
rd = rvd + d s
rvd = rd tu2fcosθ s
P (rd)=1πSJn(r)ξ(r,rd;f)cosθscosθdrdrtu2fcosθs2dAdt2dS
P (rd)=1πSJn(r)T(r,rd)dS
T (r,rd)=ξ(r,rd;f)1rdrtu2fcosθs2cosθscosθddAdt2,rS

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