Abstract

Optode geometry plays an important role in achieving both good spatial resolution and spatial uniformity of detection in diffuse-optical-imaging-based brain activation studies. The quality of reconstructed images for six optode geometries were studied and compared using a laboratory tissue phantom model that contained an embedded object at two separate locations. The number of overlapping measurements per pixel (i.e., the measurement density) and their spatial distributions were quantified for all six geometries and were correlated with the quality of the resulting reconstructed images. The latter were expressed by the area ratio (AR) and contrast-to-noise ratio (CNR) between reconstructed and actual objects. Our results revealed clearly that AR and CNR depended on the measurement density asymptotically, having an optimal point for measurement density beyond which more overlapping measurements would not significantly improve the quality of reconstructed images. Optimization of probe geometry based on our method demonstrated that a practical compromise can be attained between DOI spatial resolution and measurement density.

© 2009 Optical Society of America

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2007 (1)

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotoptic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (2007).
[CrossRef] [PubMed]

2006 (3)

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef] [PubMed]

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

D. K. Joseph, T. J. Huppert, M. A. Franceschini, and D. A. Boas, “Diffuse optical tomography system to image brain activation with improved spatial resolution and validation with functional magnetic resonance imaging,” Appl. Opt. 45, 8142-8151 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (3)

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

D. A. Boas, K. Chen, D. Grebert, and M. A. Franceschini, “Improving the diffuse optical imaging spatial resolution of the cerebral hemodynamic response to brain activation in humans,” Opt. Lett. 29, 1506-1509 (2004).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275-S288 (2004).
[CrossRef] [PubMed]

2003 (1)

L. Wu, “A parameter choice method for Tikhonov regularization,” Electron. Trans. Numer. Anal. 16, 107-128(2003).

2002 (3)

D. A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10, 159-170 (2002).
[PubMed]

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

2001 (1)

1999 (1)

R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

1997 (1)

A. Villringer and B. Chance, “Noninvasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

1995 (1)

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

1993 (2)

P. C. Hansen and D. 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]

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

Alter, C.

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

Arridge, R.

R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

Barbieri, B. B.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

Barbour, R. L.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

Boas, D. A.

Bunce, S.

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

Chance, B.

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

A. Villringer and B. Chance, “Noninvasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

Chen, K.

Culver, J. P.

Dale, A. M.

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275-S288 (2004).
[CrossRef] [PubMed]

Dehghani, H.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotoptic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (2007).
[CrossRef] [PubMed]

Diamond, S. G.

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef] [PubMed]

Dunn, A. K.

Engl, H. W.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).
[CrossRef]

Fantini, S.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

Franceschini, M. A.

Franceschini, M.-A.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

Frostig, R. D.

D. A. Boas and R. D. Frostig, “Optics in neuroscience,” J Biomed. Opt. 10, 011001 (2005).
[CrossRef]

Gratton, E.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

Grebert, D.

Hanke, M.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).
[CrossRef]

Hansen, P. C.

P. C. Hansen and D. 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]

Hielscher, A. H.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

Holboke, M. J.

Hsieh, J.

Huppert, T. J.

Izzetoglu, K.

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

Ji, L.

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

Jiang, C.

Jiang, T.

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

Joseph, D. K.

Kadoya, T.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Koizumi, H.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Lasker, J. M.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

Lee, C.

Lee, H.

Lee, P.

Lipton, L.

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

Liu, H.

F. Tian, S. Prajapati, and H. Liu, “A location-adaptive, frequency-specific cancellation algorithm to improve optical brain functional imaging,” in Spring Optics and Photonics Congress, Biomedical Optics (BIOMED), 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper BMD29.

Löcker, M.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

Maier, J. S.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

Maki, A.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Neubauer, A.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).
[CrossRef]

Ntziachristos, V.

Okada, E.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

O'Leary, D.

P. C. Hansen and D. 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]

Onaral, B.

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

Pourrezaei, K.

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

Prahl, S.

S. Prahl, “Tabulated molar extinction coefficient for hemoglobin in water,” http://omlc.ogi.edu/spectra/hemoglobin/summary.html.

Prajapati, S.

F. Tian, S. Prajapati, and H. Liu, “A location-adaptive, frequency-specific cancellation algorithm to improve optical brain functional imaging,” in Spring Optics and Photonics Congress, Biomedical Optics (BIOMED), 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper BMD29.

Schlaggar, B. L.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotoptic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (2007).
[CrossRef] [PubMed]

Schmitz, C. H.

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

Stott, J. J.

Sun, C.

Tanikawa, Y.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Tian, F.

F. Tian, S. Prajapati, and H. Liu, “A location-adaptive, frequency-specific cancellation algorithm to improve optical brain functional imaging,” in Spring Optics and Photonics Congress, Biomedical Optics (BIOMED), 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper BMD29.

Tong, Y.

UnAh, C.

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

Villringer, A.

A. Villringer and B. Chance, “Noninvasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

Walker, S. A.

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

White, B. R.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotoptic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (2007).
[CrossRef] [PubMed]

Wu, L.

L. Wu, “A parameter choice method for Tikhonov regularization,” Electron. Trans. Numer. Anal. 16, 107-128(2003).

Yamada, Y.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Yamamoto, T.

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Yang, C.

Yeh, T.

Yodh, A. G.

Zeff, B. W.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotoptic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (2007).
[CrossRef] [PubMed]

Zhao, Q.

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

Zhuang, Z.

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

Appl. Opt. (1)

Electron. Trans. Numer. Anal. (1)

L. Wu, “A parameter choice method for Tikhonov regularization,” Electron. Trans. Numer. Anal. 16, 107-128(2003).

Int. J. Human-Comp. Int. (1)

K. Izzetoglu, S. Bunce, B. Onaral, K. Pourrezaei, and B. Chance, “Functional optical brain imaging using near-infrared during cognitive tasks,” Int. J. Human-Comp. Int. 17, 211-231 (2004).

Inverse Probl. (1)

R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

J Biomed. Opt. (1)

D. A. Boas and R. D. Frostig, “Optics in neuroscience,” J Biomed. Opt. 10, 011001 (2005).
[CrossRef]

J. Biomed. Opt. (2)

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef] [PubMed]

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

NeuroImage (1)

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275-S288 (2004).
[CrossRef] [PubMed]

Opt. Eng. (1)

S. Fantini, M.-A. Franceschini, J. S. Maier, S. A. Walker, B. B. Barbieri, and E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32-42 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Med. Biol. (1)

T. Yamamoto, A. Maki, T. Kadoya, Y. Tanikawa, Y. Yamada, E. Okada, and H. Koizumi, “Arranging optical fibers for the spatial resolution improvement of topographical images,” Phys. Med. Biol. 47, 3429-3440 (2002).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

B. Chance, Z. Zhuang, C. UnAh, C. Alter, and L. Lipton, “Cognition-activated low-frequency modulation of light absorption in human brain,” Proc. Natl. Acad. Sci. USA 90, 3770-3774 (1993).
[CrossRef] [PubMed]

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotoptic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

C. H. Schmitz, M. Löcker, J. M. Lasker, A. H. Hielscher, and R. L. Barbour, “Instrumentation for fast functional optical tomography,” Rev. Sci. Instrum. 73, 429-439 (2002).
[CrossRef]

SIAM J. Sci. Comput. (1)

P. C. Hansen and D. 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]

Trends Neurosci. (1)

A. Villringer and B. Chance, “Noninvasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

Other (5)

S. Prahl, “Tabulated molar extinction coefficient for hemoglobin in water,” http://omlc.ogi.edu/spectra/hemoglobin/summary.html.

ISS Inc., http://www.iss.com/Products/oxiplex.html.

NIRx Medical Technologies, LLC, http://www.nirx.net/products_instrument.html.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer, 1996).
[CrossRef]

F. Tian, S. Prajapati, and H. Liu, “A location-adaptive, frequency-specific cancellation algorithm to improve optical brain functional imaging,” in Spring Optics and Photonics Congress, Biomedical Optics (BIOMED), 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper BMD29.

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Figures (7)

Fig. 1
Fig. 1

Six optode geometries investigated in this study (×, source fibers; ∘, detector fibers; ⊗, bifurcated fibers for both source and detector). (a) to (f) correspond to G-I to G-VI. The optodes in each geometry were placed over 1 cm rectangular grids (dotted line) within a constant FOV of 4 cm × 4 cm ; they were utilized in the phantom experiments.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup. A 5 × 5 square optode array was placed on the top surface of an Intralipid phantom. The separation of neighboring optodes was 1.0 cm . A thin cylindrical absorbing object ( ϕ = 1.1 cm ) was placed into the phantom during the measurements with one circular side facing up. The depth of the object in the phantom was 1.5 cm below the surface. Two object positions were measured separately; one was at the center (P1) and the other one was one grid ( = 1 cm ) shifted along the y direction (P2).

Fig. 3
Fig. 3

Spatial distributions of overlapping measurements in six geometries. (a) to (f) correspond to G-I to G-VI. The locations of sources and detectors in each geometry (×, source fibers; ∘, detector fibers; ⊗, bifurcated fibers for sources/detectors) are superimposed in the corresponding map. The black circles (P1, solid circle; P2, dotted circle) indicate the two object locations that were placed and measured separately.

Fig. 4
Fig. 4

Reconstructed images of the absorbing object at P1. (a) to (f) correspond to the reconstructed images from G-I to G-VI. The dotted circle indicates the true object region. The locations of sources and detectors in each geometry (×, sources; ∘, detectors; ⊗, bifurcated for sources/detectors) are superimposed in the corresponding images.

Fig. 5
Fig. 5

Reconstructed images of the absorbing object at P2. (a) to (f) correspond to the reconstructed images from G-I to G-VI. The dotted circle indicates the true object region. The locations of sources and detectors in each geometry (×, sources; ∘, detectors; ⊗, bifurcated for sources/detectors) are superimposed in the corresponding images.

Fig. 6
Fig. 6

Correlation between the reconstructed image quality and the mean measurement density in the object region: (a) AR versus mean measurement density and (b) CNR versus mean measurement density. In each graph, two sets of data, one each from the P1 (circle) and P2 (plus) positions, were combined.

Fig. 7
Fig. 7

Schematic diagram to demonstrate an insensitive region of an optode. The ROI is right under detector D1. In this case, little portion of the light received by D1 passes through the ROI and, thus, D1 is not sensitive to the absorption perturbation in this region. Some neighboring detecting optodes, i.e., D2 and D3, are needed to detect the absorption perturbation in this region.

Tables (3)

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Table 1 Available S–D Separations (r, cm) and the Number of Measurements at Each Separation Obtained from G-I to G-VI

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Table 2 Reconstruction Results of the Absorbing Object at P1 from G-I to G-VI a

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Table 3 Reconstruction Results of the Absorbing Object at P2 from G-I to G-VI a

Equations (5)

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Δ OD = ln ( I I 0 ) ,
y i = j A i j x j .
x ^ = A T ( AA T + α s max I ) 1 y ,
AR = A r A o ,
CNR = μ ROI μ ROB [ w ROI σ ROI 2 + w ROB σ ROB 2 ] 1 / 2 ,

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