Abstract

A novel method is presented for accurately reconstructing a spatially resolved map of diffuse light flux on a surface using images of the surface and a model of the imaging system. This is achieved by applying a model-based reconstruction algorithm with an existing forward model of light propagation through free space that accounts for the effects of perspective, focus, and imaging geometry. It is shown that flux can be mapped reliably and quantitatively accurately with very low error, <3% with modest signal-to-noise ratio. Simulation shows that the method is generalizable to the case in which mirrors are used in the system and therefore multiple views can be combined in reconstruction. Validation experiments show that physical diffuse phantom surface fluxes can also be reconstructed accurately with variability <3% for a range of object positions, variable states of focus, and different orientations. The method provides a new way of making quantitatively accurate noncontact measurements of the amount of light leaving a diffusive medium, such as a small animal containing fluorescent or bioluminescent markers, that is independent of the imaging system configuration and surface position.

© 2013 Optical Society of America

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2013 (1)

2012 (2)

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

X. Chen, J. Liang, X. Qu, Y. Hou, S. Zhu, D. Chen, X. Gao, and J. Tian, “Mapping of bioluminescent images onto ct volume surface for dual-modality blt and ct imaging,” J. X-ray Sci. Technol. 20, 31–44 (2012).

2011 (3)

2010 (3)

2009 (3)

2008 (1)

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

2006 (2)

A. X. Cong and G. Wang, “Multispectral bioluminescence tomography: methodology and simulation,” Int. J. Biomed. Imag. 2006, 57614 (2006).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

2005 (2)

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

S. Gross and D. Piwnica-Worms, “Spying on cancer: molecular imaging in vivo with genetically encoded reporters,” Cancer Cell 7, 5–15 (2005).

2004 (2)

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, “Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models,” Mol. Imaging 3, 9–23 (2004).
[CrossRef]

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of noncontact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

2003 (3)

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef]

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

2002 (2)

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

R. Weissleder, “Scaling down imaging: molecular mapping of cancer in mice,” Nat. Rev. Cancer 2, 11–18 (2002).
[CrossRef]

2001 (1)

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

2000 (1)

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

1993 (2)

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

N. Fortier, G. Demoment, and Y. Goussard, “GCV and ML methods of determining parameters in image restoration by regularization: fast computation in the spatial domain and experimental comparison,” J. Vis. Commun. Image Represent. 4, 157–170 (1993).
[CrossRef]

1966 (1)

Aguirre, J.

Ahn, S.

Bachmann, M. H.

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Basevi, H.

J. A. Guggenheim, H. Dehghani, H. Basevi, I. B. Styles, and J. Frampton, “Development of a multi-view multi-spectral bioluminescence tomography small animal imaging system,” in European Conferences on Biomedical Optics (International Society for Optics and Photonics, 2011), p. 80881K.

Basevi, H. R.

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Multi-view, multi-spectral bioluminescence tomography,” in Biomedical Optics (Optical Society of America, 2012), p. BW4A.7

Basevi, H. R. A.

Blifford, I. H.

Cardozo, S. J.

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Chamorro-Servent, J.

Chaudhari, A. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Chen, D.

X. Chen, J. Liang, X. Qu, Y. Hou, S. Zhu, D. Chen, X. Gao, and J. Tian, “Mapping of bioluminescent images onto ct volume surface for dual-modality blt and ct imaging,” J. X-ray Sci. Technol. 20, 31–44 (2012).

X. Chen, X. Gao, X. Qu, D. Chen, X. Ma, J. Liang, and J. Tian, “Generalized free-space diffuse photon transport model based on the influence analysis of a camera lens diaphragm,” Appl. Opt. 49, 5654–5664 (2010).
[CrossRef]

X. Chen, X. Gao, X. Qu, D. Chen, B. Ma, L. Wang, K. Peng, J. Liang, and J. Tian, “Qualitative simulation of photon transport in free space based on monte carlo method and its parallel implementation,” Int. J. Biomed. Imag. 2010, 650298 (2010).
[CrossRef]

X. Chen, X. Gao, D. Chen, X. Ma, X. Zhao, M. Shen, X. Li, X. Qu, J. Liang, J. Ripoll, and J. Tian, “3d reconstruction of light flux distribution on arbitrary surfaces from 2d multi-photographic images,” Opt. Express 18, 19876–19893 (2010).
[CrossRef]

Chen, D.-F.

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Chen, X.

Chen, X.-L.

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Cherry, S. R.

C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. M. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17, 7571–7585 (2009).
[CrossRef]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Chudakov, D. M.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Cong, A. X.

A. X. Cong and G. Wang, “Multispectral bioluminescence tomography: methodology and simulation,” Int. J. Biomed. Imag. 2006, 57614 (2006).
[CrossRef]

Contag, C. H.

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Contag, P. R.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Crooks, G. M.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Darvas, F.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

Dehghani, H.

H. R. A. Basevi, J. A. Guggenheim, H. Dehghani, and I. B. Styles, “Simultaneous multiple view high resolution surface geometry acquisition using structured light and mirrors,” Opt. Express 21, 7222–7239 (2013).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Multi-view, multi-spectral bioluminescence tomography,” in Biomedical Optics (Optical Society of America, 2012), p. BW4A.7

J. A. Guggenheim, H. Dehghani, H. Basevi, I. B. Styles, and J. Frampton, “Development of a multi-view multi-spectral bioluminescence tomography small animal imaging system,” in European Conferences on Biomedical Optics (International Society for Optics and Photonics, 2011), p. 80881K.

Demoment, G.

N. Fortier, G. Demoment, and Y. Goussard, “GCV and ML methods of determining parameters in image restoration by regularization: fast computation in the spatial domain and experimental comparison,” J. Vis. Commun. Image Represent. 4, 157–170 (1993).
[CrossRef]

Desco, M.

Dusich, J.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Dutta, J.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Edinger, M.

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

Fathman, C. G.

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

Fortier, N.

N. Fortier, G. Demoment, and Y. Goussard, “GCV and ML methods of determining parameters in image restoration by regularization: fast computation in the spatial domain and experimental comparison,” J. Vis. Commun. Image Represent. 4, 157–170 (1993).
[CrossRef]

Frampton, J.

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Multi-view, multi-spectral bioluminescence tomography,” in Biomedical Optics (Optical Society of America, 2012), p. BW4A.7

J. A. Guggenheim, H. Dehghani, H. Basevi, I. B. Styles, and J. Frampton, “Development of a multi-view multi-spectral bioluminescence tomography small animal imaging system,” in European Conferences on Biomedical Optics (International Society for Optics and Photonics, 2011), p. 80881K.

Gao, X.

Garofalakis, A.

Ge, S.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Geng, J.

Goussard, Y.

N. Fortier, G. Demoment, and Y. Goussard, “GCV and ML methods of determining parameters in image restoration by regularization: fast computation in the spatial domain and experimental comparison,” J. Vis. Commun. Image Represent. 4, 157–170 (1993).
[CrossRef]

Gross, S.

S. Gross and D. Piwnica-Worms, “Spying on cancer: molecular imaging in vivo with genetically encoded reporters,” Cancer Cell 7, 5–15 (2005).

Guggenheim, J. A.

H. R. A. Basevi, J. A. Guggenheim, H. Dehghani, and I. B. Styles, “Simultaneous multiple view high resolution surface geometry acquisition using structured light and mirrors,” Opt. Express 21, 7222–7239 (2013).
[CrossRef]

J. A. Guggenheim, H. Dehghani, H. Basevi, I. B. Styles, and J. Frampton, “Development of a multi-view multi-spectral bioluminescence tomography small animal imaging system,” in European Conferences on Biomedical Optics (International Society for Optics and Photonics, 2011), p. 80881K.

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Multi-view, multi-spectral bioluminescence tomography,” in Biomedical Optics (Optical Society of America, 2012), p. BW4A.7

Gupta, S.

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Hall, D. E.

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Hansen, P. C.

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Hardy, J.

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

Hornig, Y. S.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Hou, Y.

X. Chen, J. Liang, X. Qu, Y. Hou, S. Zhu, D. Chen, X. Gao, and J. Tian, “Mapping of bioluminescent images onto ct volume surface for dual-modality blt and ct imaging,” J. X-ray Sci. Technol. 20, 31–44 (2012).

Jekic-McMullen, D.

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, “Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models,” Mol. Imaging 3, 9–23 (2004).
[CrossRef]

Jenkins, D. E.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Jiang, S.

Kanade, T.

M. Kimura, M. Mochimaru, and T. Kanade, “Projector calibration using arbitrary planes and calibrated camera,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–2.

Kimura, M.

M. Kimura, M. Mochimaru, and T. Kanade, “Projector calibration using arbitrary planes and calibrated camera,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–2.

Kohn, D. B.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Leahy, R. M.

C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. M. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17, 7571–7585 (2009).
[CrossRef]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Lewin, S. A.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Li, C.

Li, X.

Liang, J.

Liang, J.-M.

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Luker, G. D.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Luker, K. E.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Ma, B.

X. Chen, X. Gao, X. Qu, D. Chen, B. Ma, L. Wang, K. Peng, J. Liang, and J. Tian, “Qualitative simulation of photon transport in free space based on monte carlo method and its parallel implementation,” Int. J. Biomed. Imag. 2010, 650298 (2010).
[CrossRef]

Ma, X.

Mandl, S.

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

McNamara, G.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Mihalko, L. A.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Mitchell, G. S.

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Mochimaru, M.

M. Kimura, M. Mochimaru, and T. Kanade, “Projector calibration using arbitrary planes and calibrated camera,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–2.

Negrin, R. S.

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

Nelson, M. D.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Ntziachristos, V.

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of noncontact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef]

O’Leary, D. P.

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Oei, Y.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Patterson, M. S.

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

Peng, K.

X. Chen, X. Gao, X. Qu, D. Chen, B. Ma, L. Wang, K. Peng, J. Liang, and J. Tian, “Qualitative simulation of photon transport in free space based on monte carlo method and its parallel implementation,” Int. J. Biomed. Imag. 2010, 650298 (2010).
[CrossRef]

Peterson, D.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Piwnica-Worms, D.

S. Gross and D. Piwnica-Worms, “Spying on cancer: molecular imaging in vivo with genetically encoded reporters,” Cancer Cell 7, 5–15 (2005).

Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

Pollack, H.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Purchio, T.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Qu, X.

Qu, X.-C.

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Ray, P.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Rehemtulla, A.

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Rice, B.

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, “Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models,” Mol. Imaging 3, 9–23 (2004).
[CrossRef]

Ripoll, J.

Rosol, M.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Ross, B. D.

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Sambucetti, L.

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, “Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models,” Mol. Imaging 3, 9–23 (2004).
[CrossRef]

Schimmelpfennig, C.

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

Schmidt, B. T.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Schulz, R. B.

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef]

Shcherbo, D.

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Shen, M.

Smith, D. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Stegman, L. D.

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Styles, I. B.

H. R. A. Basevi, J. A. Guggenheim, H. Dehghani, and I. B. Styles, “Simultaneous multiple view high resolution surface geometry acquisition using structured light and mirrors,” Opt. Express 21, 7222–7239 (2013).
[CrossRef]

J. A. Guggenheim, H. Dehghani, H. Basevi, I. B. Styles, and J. Frampton, “Development of a multi-view multi-spectral bioluminescence tomography small animal imaging system,” in European Conferences on Biomedical Optics (International Society for Optics and Photonics, 2011), p. 80881K.

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Multi-view, multi-spectral bioluminescence tomography,” in Biomedical Optics (Optical Society of America, 2012), p. BW4A.7

Tian, J.

Troy, T.

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, “Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models,” Mol. Imaging 3, 9–23 (2004).
[CrossRef]

Vaquero, J. J.

Wang, G.

A. X. Cong and G. Wang, “Multispectral bioluminescence tomography: methodology and simulation,” Int. J. Biomed. Imag. 2006, 57614 (2006).
[CrossRef]

Wang, L.

X. Chen, X. Gao, X. Qu, D. Chen, B. Ma, L. Wang, K. Peng, J. Liang, and J. Tian, “Qualitative simulation of photon transport in free space based on monte carlo method and its parallel implementation,” Int. J. Biomed. Imag. 2010, 650298 (2010).
[CrossRef]

X. Chen, X. Gao, X. Qu, J. Liang, L. Wang, D. Yang, A. Garofalakis, J. Ripoll, and J. Tian, “A study of photon propagation in free-space based on hybrid radiosity-radiance theorem,” Opt. Express 17, 16266–16280 (2009).
[CrossRef]

Wang, X.

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Wang, X.-R.

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Weissleder, R.

R. Weissleder, “Scaling down imaging: molecular mapping of cancer in mice,” Nat. Rev. Cancer 2, 11–18 (2002).
[CrossRef]

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Yang, D.

Yu, S.-F.

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Zhang, Z.

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (IEEE, 1999), pp. 666–673.

Zhao, H.

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Zhao, X.

Zhu, S.

X. Chen, J. Liang, X. Qu, Y. Hou, S. Zhu, D. Chen, X. Gao, and J. Tian, “Mapping of bioluminescent images onto ct volume surface for dual-modality blt and ct imaging,” J. X-ray Sci. Technol. 20, 31–44 (2012).

Adv. Opt. Photon. (1)

Appl. Opt. (2)

Blood (1)

X. Wang, M. Rosol, S. Ge, D. Peterson, G. McNamara, H. Pollack, D. B. Kohn, M. D. Nelson, and G. M. Crooks, “Dynamic tracking of human hematopoietic stem cell engraftment using in vivo bioluminescence imaging,” Blood 102, 3478–3482 (2003).
[CrossRef]

Cancer Cell (1)

S. Gross and D. Piwnica-Worms, “Spying on cancer: molecular imaging in vivo with genetically encoded reporters,” Cancer Cell 7, 5–15 (2005).

Clin. Exp. Metastasis (1)

D. E. Jenkins, Y. Oei, Y. S. Hornig, S.-F. Yu, J. Dusich, T. Purchio, and P. R. Contag, “Bioluminescent imaging (bli) to improve and refine traditional murine models of tumor growth and metastasis,” Clin. Exp. Metastasis 20, 733–744 (2003).
[CrossRef]

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using nirfast: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Exp. Hematol. (1)

J. Hardy, M. Edinger, M. H. Bachmann, R. S. Negrin, C. G. Fathman, and C. H. Contag, “Bioluminescence imaging of lymphocyte trafficking in vivo,” Exp. Hematol. 29, 1353–1360 (2001).
[CrossRef]

Int. J. Autom. Comput. (1)

X.-L. Chen, H. Zhao, X.-C. Qu, D.-F. Chen, X.-R. Wang, and J.-M. Liang, “All-optical quantitative framework for bioluminescence tomography with non-contact measurement,” Int. J. Autom. Comput. 9, 72–80 (2012).
[CrossRef]

Int. J. Biomed. Imag. (2)

A. X. Cong and G. Wang, “Multispectral bioluminescence tomography: methodology and simulation,” Int. J. Biomed. Imag. 2006, 57614 (2006).
[CrossRef]

X. Chen, X. Gao, X. Qu, D. Chen, B. Ma, L. Wang, K. Peng, J. Liang, and J. Tian, “Qualitative simulation of photon transport in free space based on monte carlo method and its parallel implementation,” Int. J. Biomed. Imag. 2010, 650298 (2010).
[CrossRef]

J. Cell. Biochem. (1)

S. Mandl, C. Schimmelpfennig, M. Edinger, R. S. Negrin, and C. H. Contag, “Understanding immune cell trafficking patterns via in vivo bioluminescence imaging,” J. Cell. Biochem. 87, 239–248 (2002).
[CrossRef]

J. Vis. Commun. Image Represent. (1)

N. Fortier, G. Demoment, and Y. Goussard, “GCV and ML methods of determining parameters in image restoration by regularization: fast computation in the spatial domain and experimental comparison,” J. Vis. Commun. Image Represent. 4, 157–170 (1993).
[CrossRef]

J. X-ray Sci. Technol. (1)

X. Chen, J. Liang, X. Qu, Y. Hou, S. Zhu, D. Chen, X. Gao, and J. Tian, “Mapping of bioluminescent images onto ct volume surface for dual-modality blt and ct imaging,” J. X-ray Sci. Technol. 20, 31–44 (2012).

Med. Phys. (1)

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

Mod. Phys. Lett. B (1)

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of noncontact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

Mol. Imaging (1)

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, “Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models,” Mol. Imaging 3, 9–23 (2004).
[CrossRef]

Nat. Med. (1)

K. E. Luker, L. A. Mihalko, B. T. Schmidt, S. A. Lewin, P. Ray, D. Shcherbo, D. M. Chudakov, and G. D. Luker, “In vivo imaging of ligand receptor binding with Gaussia luciferase complementation,” Nat. Med. 18, 172–177 (2011).
[CrossRef]

Nat. Rev. Cancer (1)

R. Weissleder, “Scaling down imaging: molecular mapping of cancer in mice,” Nat. Rev. Cancer 2, 11–18 (2002).
[CrossRef]

Neoplasia (1)

A. Rehemtulla, L. D. Stegman, S. J. Cardozo, S. Gupta, D. E. Hall, C. H. Contag, and B. D. Ross, “Rapid and quantitative assessment of cancer treatment response using in vivo bioluminescence imaging,” Neoplasia 2, 491–495 (2000).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Med. Biol. (1)

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef]

SIAM J. Sci. Comput. (1)

P. C. Hansen and D. P. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Other (4)

J. A. Guggenheim, H. R. Basevi, I. B. Styles, J. Frampton, and H. Dehghani, “Multi-view, multi-spectral bioluminescence tomography,” in Biomedical Optics (Optical Society of America, 2012), p. BW4A.7

J. A. Guggenheim, H. Dehghani, H. Basevi, I. B. Styles, and J. Frampton, “Development of a multi-view multi-spectral bioluminescence tomography small animal imaging system,” in European Conferences on Biomedical Optics (International Society for Optics and Photonics, 2011), p. 80881K.

Z. Zhang, “Flexible camera calibration by viewing a plane from unknown orientations,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (IEEE, 1999), pp. 666–673.

M. Kimura, M. Mochimaru, and T. Kanade, “Projector calibration using arbitrary planes and calibrated camera,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–2.

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Figures (18)

Fig. 1.
Fig. 1.

(a) Cross-sectional schematic, and (b), (c) surface images (counts/s) of a diffuse light-emitting phantom taken from two viewing angles separated by 60°.

Fig. 2.
Fig. 2.

Schematic of imaging system model in which the position and behavior of the lens, detector, and focal plane adhere to the thin-lens equation. Emission points on the surface are either visible or invisible to detection points on the CCD dependant upon whether or not the ray passing through the corresponding virtual detection (focal plane) point location intersects the lens plane within the bounds of the lens or aperture and is not obscured by any part of the surface. In the example shown, the surface point is visible at the detection point.

Fig. 3.
Fig. 3.

Illustration of the improved visibility factor α^.

Fig. 4.
Fig. 4.

Imaging system diagram.

Fig. 5.
Fig. 5.

Luminescence phantom photograph and schematic of two experimental configurations with different source locations.

Fig. 6.
Fig. 6.

Diagram of first 2D simulation setup.

Fig. 7.
Fig. 7.

(a) Diagram showing all surface points used in the simulation along with the normals. (b) Plot of total system sensitivity to the surface for different stage heights, h.

Fig. 8.
Fig. 8.

(a) Simulated surface flux (ground truth) and (b) measurement on line detector simulated in each height-resolved setup.

Fig. 9.
Fig. 9.

Sample reconstructed fluxes overlaid on ground truth values for h=40mm and 50 million photons: (a), (b) backprojection approach with absolute or normalized comparison; (c), (d) proposed approach with absolute and normalized comparisons. Note particularly the 8.5× factor indicated in (a).

Fig. 10.
Fig. 10.

Errors in total flux reconstructed on the surface across 50 repeats for a range of stage heights affecting imaging geometry and for a range of signal strengths affecting signal-to-noise ratio (SNR). Note that only one data set is plotted for the backprojection method because the quantitative error was practically 100% in all cases.

Fig. 11.
Fig. 11.

Plot showing the position of the cylindrical phantom, mirrors, and focal planes (the direct focal plane of the lens-camera system and the two focal planes of the virtual systems through the mirrors).

Fig. 12.
Fig. 12.

Simulated forward images with the phantom at different orientations. Approximate phantom outlines shown for reference in direct and mirror views (recall the mirror positions in the simulated imaging system; Fig. 4). Some empty space has been cropped.

Fig. 13.
Fig. 13.

(a) Target and (b) reconstructed fluxes for set 3 in the simulation study. (c) Illustration of the axial plane at which cross-sectional data were extracted (i.e., flux values around the circumference) and plotted for this set (d) and others (see Fig. 14).

Fig. 14.
Fig. 14.

Slices through reconstruction and target.

Fig. 15.
Fig. 15.

(a)–(g) Images acquired in the practical imaging experiment shown in units of electrons per second on each pixel of the CCD, overlaid on a backlit image. (h) Maximum signal visible in the direct view (nonmirror) in each case.

Fig. 16.
Fig. 16.

Reconstructed fluxes from real data in arbitrary but consistent units, in a common orientation.

Fig. 17.
Fig. 17.

Slices through reconstructions using real data with (a)–(g) individual data sets and (h) sets 1–5 shown overlaid together.

Fig. 18.
Fig. 18.

Estimates of total source as a function of rotation and height of imaged surfaces.

Tables (1)

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Table 1. Maximum SNR in Simulated Noisy Measurements Used for Reconstructions

Equations (15)

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P(rd)=1πSJ(r)T(r,rd)dS,
T(r,rd)=α(r,rvd)β(r,rvd;ΩD)cosθscosθd|rvdr|2dAvd.
α(r,rvd)={1If(rvdΩE)AND(srrvdS={r})0Otherwise
β(r,rvd;ΩD)={1If(srrvdΩD)0If(srrvdΩD=),
α^(r,rvd;ΩE)={1If(rvdΩE)AND(srrlS={r})0Otherwise,
P(rd)=1πSJ(r)Γ(r,rvd;ΩD)dS
Γ(r,rvd;ΩD)=α^(r,rvd;ΩE)β(r,rvd;ΩD)cosθscosθd|rvdr|2dAvd.
a=Tb,
{ai=P(rdi)Tij=1πΓ(rj,rvdi;ΩD)bj=J(rj)dSj.
J(r)=1πAP(rd)α(rvd,r)β(rd,r;ΩD)cosθscosθd|rrvd|dA.
b˜=TTa.
b˜=T1a.
b˜=minbTba22,
b˜=(TTT+λ˜I)1TTa,
error(b,b)=j=1n|bjbj|j=1nbj,

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