Abstract

An experimental study of the detectability of an object embedded in optically tissue-equivalent media by frequency-domain image reconstruction is presented. The experiments were performed in an 86-mm-diameter cylindrical phantom containing an optically homogeneous cylindrical target whose absorption and scattering properties presented a 2:1 contrast with the background medium. The parameter space explored during experimentation involved object size (15-, 8-, and 4-mm targets) and location (centered, 20-mm off-centered, and 35-mm off-centered) variations. Image reconstruction was achieved with a previously reported regularized least-squares approach that incorporates finite-element solutions of the diffusion equation and Newton’s method solutions of the nonlinear minimization problem. Also included during image formation were image enhancement schemes—(1) total variation minimization, (2) dual meshing, and (3) spatial low-pass filtering—which have recently been added. Quantitative measures of image quality including the size, location, and shape of the heterogeneity along with errors in its recovered optical property values are used to quantify the image reconstructions. The results show that a near 22:1 ratio of tissue thickness relative to detectable object size has been achieved with this approach in the laboratory conditions and parameter space that have been investigated.

© 1997 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1996 (2)

K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 19, 3447–3458 (1996).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

1995 (8)

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, J. M. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithm,” IEEE Trans. Med. Imag. 14, 504–514 (1995).
[CrossRef]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
[CrossRef]

1994 (5)

1993 (4)

1992 (2)

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Alfano, R. R.

Anderson, E. R.

Aronson, R.

Arridge, S. R.

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweijer, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–308 (1993).
[CrossRef] [PubMed]

Boas, D. A.

Bonner, R. F.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Burch, C. L.

Chance, B.

Das, B. B.

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

J. C. Hebden, D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311–313 (1994).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweijer, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–308 (1993).
[CrossRef] [PubMed]

Duncan, M. D.

Egan, R. L.

R. L. Egan, Breast Imaging: Diagnosis and Morphology of Breast Diseases (Saunders, Philadelphia, Pa., 1988).

Farrell, T.

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Farrell, T. J.

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3D frequency-domain diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

Fatemi, E.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Fishkin, J. B.

Frisoli, J. J.

Gandjbakhche, A. H.

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Gratton, E.

Haskell, R. C.

Hebden, J. C.

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

J. C. Hebden, D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311–313 (1994).
[CrossRef] [PubMed]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweijer, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–308 (1993).
[CrossRef] [PubMed]

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 19, 3447–3458 (1996).
[CrossRef]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He-Ne laser for breast cancer detection,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 615–620 (1995).
[CrossRef]

Lakowicz, J. R.

Madsen, S. J.

Mahon, R.

Meaney, P. M.

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, J. M. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithm,” IEEE Trans. Med. Imag. 14, 504–514 (1995).
[CrossRef]

Moon, J. A.

Moskowitz, M. J.

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, J. M. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithm,” IEEE Trans. Med. Imag. 14, 504–514 (1995).
[CrossRef]

Nossal, R.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

O’Leary, M. A.

Osher, S.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Osterberg, U. L.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He-Ne laser for breast cancer detection,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 615–620 (1995).
[CrossRef]

Patterson, M. S.

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3D frequency-domain diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

Paulsen, K. D.

K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 19, 3447–3458 (1996).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, J. M. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithm,” IEEE Trans. Med. Imag. 14, 504–514 (1995).
[CrossRef]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He-Ne laser for breast cancer detection,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 615–620 (1995).
[CrossRef]

Pogue, B. W.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3D frequency-domain diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

Reintjes, J.

Rudin, L. I.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

Schweijer, M.

S. R. Arridge, M. Schweijer, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–308 (1993).
[CrossRef] [PubMed]

Sevick, E. M.

Sullivan, J. M.

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, J. M. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithm,” IEEE Trans. Med. Imag. 14, 504–514 (1995).
[CrossRef]

Tromberg, B. J.

Wilson, B. C.

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Yodh, A. G.

Yoo, K. M.

Appl. Opt. (2)

K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 19, 3447–3458 (1996).
[CrossRef]

E. M. Sevick, J. J. Frisoli, C. L. Burch, J. R. Lakowicz, “Localization of absorbers in scattering media by use of frequency-domain measurements of time-dependent photon migration,” Appl. Opt. 33, 3562–3570 (1994).
[CrossRef] [PubMed]

IEEE Trans. Med. Imag. (1)

K. D. Paulsen, P. M. Meaney, M. J. Moskowitz, J. M. Sullivan, “A dual mesh scheme for finite element based reconstruction algorithm,” IEEE Trans. Med. Imag. 14, 504–514 (1995).
[CrossRef]

J. Opt. Soc. Am. A (3)

Med. Phys. (6)

S. R. Arridge, M. Schweijer, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–308 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

J. C. Hebden, A. H. Gandjbakhche, “Experimental validation of an elementary formula for estimating spatial resolution for optical transillumination imaging,” Med. Phys. 22, 1271–1272 (1995).
[CrossRef] [PubMed]

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

Opt. Lett. (7)

Phys. Med. Biol. (1)

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Physica D (1)

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Other (10)

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3D frequency-domain diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

G. Muller, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).

Y. Yamishita, M. Kaneko, “Infrared diaphanoscopy for medical diagnosis,” in Ref. 1, pp. 283–316.

S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Ref. 1, pp. 35–64.

H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: derivation and evaluation of imaging operators,” in Ref. 1, pp. 121–143.

R. L. Egan, Breast Imaging: Diagnosis and Morphology of Breast Diseases (Saunders, Philadelphia, Pa., 1988).

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He-Ne laser for breast cancer detection,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 615–620 (1995).
[CrossRef]

R. Berg, S. Andersson-Engels, S. Svanberg, “Time-resolved transillumination imaging,” in Ref. 1, pp. 397–424.

M. S. Patterson, B. W. Pogue, B. C. Wilson, “Computer simulation and experimental studies of optical imaging with photon density waves,” in Ref. 1, pp. 513–533.

R. L. Barbour, H. Graber, Y. Wang, J. Chang, R. Aronson, “Perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Ref. 1, pp. 87–120.

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Figures (10)

Fig. 1
Fig. 1

Sketch of phantom geometry illustrating important dimensions and target locations for a single-sized object. Transects (AB, CD, EF, GH) used to quantify imaging performance are also shown.

Fig. 2
Fig. 2

Simultaneous reconstruction of both diffusion and absorption coefficients with 2:1 contrast for the 4-mm-diameter target at three different locations: (a) D image, centered target; (b) μa image, centered target; (c) D image, 20-mm offset target; (d) μa image, 20-mm offset target; (e) D image, 35-mm offset target; (f) μa image, 35-mm offset target.

Fig. 3
Fig. 3

Simultaneous reconstruction of both diffusion and absorption coefficients with 2:1 contrast for the 8-mm-diameter target at three different locations: (a) D image, centered target; (b) μa image, centered target; (c) D image, 20-mm offset target; (d) μa image, 20-mm offset target; (e) D image, 35-mm offset target; (f) μa image, 35-mm offset target.

Fig. 4
Fig. 4

Simultaneous reconstruction of both diffusion and absorption coefficients with 2:1 contrast for the 15-mm-diameter target at three different locations: (a) D image, centered target; (b) μa image, centered target; (c) D image, 20-mm offset target; (d) μa image, 20-mm offset target; (e) D image, 35-mm offset target; (f) μa image, 35-mm offset target.

Fig. 5
Fig. 5

Comparison of the exact (solid line) and reconstructed (circles) optical properties along a transect (AB in Fig. 1) through the center of both the target and the background for the images appearing in Fig. 2: (a) D profile, centered target; (b) μa profile, centered target; (c) D profile, 20-mm offset target; (d) μa profile, 20-mm offset target; (e) D profile, 35-mm offset target; (f) μa profile, 35-mm offset target. The horizontal axes indicate distance along the transect in millimeters.

Fig. 6
Fig. 6

Comparison of the exact (solid line) and reconstructed (circles) optical properties along a transect through the center of the target only (CD in Fig. 1 or equivalent, depending on actual target location) for the images appearing in Fig. 2: (a) D profile, centered target; (b) μa profile, centered target; (c) D profile, 20-mm offset target; (d) μa profile, 20-mm offset target; (e) D profile, 35-mm offset target; (f) μa profile, 35-mm offset target. The horizontal axes indicate distance along the transect in millimeters. Note that the transect becomes shorter as the target progresses off center.

Fig. 7
Fig. 7

Comparison of the exact (solid line) and reconstructed (circles) optical properties along a transect (AB in Fig. 1) through the center of both the target and the background for the images appearing in Fig. 3: (a) D profile, centered target; (b) μa profile, centered target; (c) D profile, 20-mm offset target; (d) μa profile, 20-mm offset target; (e) D profile, 35-mm offset target; (f) μa profile, 35-mm offset target. The horizontal axes indicate distance along the transect in millimeters.

Fig. 8
Fig. 8

Comparison of the exact (solid line) and reconstructed (circles) optical properties along a transect through the center of the target only (CD in Fig. 1 or equivalent, depending on actual target location) for the images appearing in Fig. 3: (a) D profile, centered target; (b) μa profile, centered target; (c) D profile, 20-mm offset target; (d) μa profile, 20-mm offset target; (e) D profile, 35-mm offset target; (f) μa profile, 35-mm offset target. The horizontal axes indicate distance along the transect in millimeters. Note that the transect becomes shorter as the target progresses off center.

Fig. 9
Fig. 9

Comparison of the exact (solid line) and reconstructed (circles) optical properties along a transect (AB in Fig. 1) through the center of both the target and the background for the images appearing in Fig. 4: (a) D profile, centered target; (b) μa profile, centered target; (c) D profile, 20-mm offset target; (d) μa profile, 20-mm offset target; (e) D profile, 35-mm offset target; (f) μa profile, 35-mm offset target. The horizontal axes indicate distance along the transect in millimeters.

Fig. 10
Fig. 10

Comparison of the exact (solid line) and reconstructed (circles) optical properties along a transect through the center of the target only (CD in Fig. 1 or equivalent, depending on actual target location) for the images appearing in Fig. 4: (a) D profile, centered target; (b) μa profile, centered target; (c) D profile, 20-mm offset target; (d) μa profile, 20-mm offset target; (e) D profile, 35-mm offset target; (f) μa profile, 35-mm offset target. The horizontal axes indicate distance along the transect in millimeters. Note that the transect becomes shorter as the target progresses off center.

Tables (2)

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Table 1 Image rms Errorsa for Reconstructed Phantom Optical Properties with Various Sizes and Different Locations of Targetsb

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Table 2 Geometric Information Derived from the Reconstructed Images with Various Sizes and Different Locations of Targeta

Equations (2)

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χnewi=1-θχoldi+θM*j=1M* χoldj  for i=1, 2, , M,
1Ni=1Nχexact-χreconstructedχexact21/2,

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