Abstract

An approach for the fast localization and detection of an absorbing inhomogeneity in a tissuelike scattering medium is presented. The probability of detection as a function of the size, location, and absorptive properties of the inhomogeneity is investigated. The detection sensitivity in relation to the source and detector location serves as a basis for instrument design.

© 2007 Optical Society of America

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References

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2005 (2)

2003 (2)

2002 (1)

1997 (1)

M. G. Erickson, J. S. Reynolds, and K. J. Webb, J. Opt. Soc. Am. A 14, 3080 (1997).
[CrossRef]

1992 (1)

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, Phys. Rev. Lett. 69, 2658 (1992).
[CrossRef] [PubMed]

1991 (1)

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Figures (4)

Fig. 1
Fig. 1

Measurement geometry for localization. A spherical absorber at depth d is assumed in the simulation. The background optical parameters are μ a 0 = 0.02 cm 1 , D 0 = 0.03 cm , and the modulation frequency is ω = 2 π × 10 8 rad s .

Fig. 2
Fig. 2

Localization versus reconstruction: (a) Negative log likelihood: 엯 denotes the true inhomogeneity location and × the estimated location. (b) Optical diffusion tomography reconstruction of μ a . Parameters: five sources and five detectors and background parameters as in Fig. 1; inhomogeneity μ a = 0.12 cm 1 , D = 0.03 cm ; average SNR is 40 dB ; spherical inhomogeneity diameter of 0.625 cm .

Fig. 3
Fig. 3

Influence of inhomogeneity depth, size, and optical contrast ( Δ μ a ) on P D for the geometry and parameters shown in Fig. 1, with P F = 0.03 and an average SNR of 40 dB . (a) P D as a function of depth, for an inhomogeneity having diameter 0.625 cm , μ a = 0.12 cm 1 , and D = 0.03 cm . (b) P D as a function of size and Δ μ a , with d = 1.5 cm . (c) P D as a function of depth and Δ μ a , with a 0.625 cm diameter inhomogeneity. (d) P D as a function of depth and size, with Δ μ a = 0.1 cm 1 .

Fig. 4
Fig. 4

Detection sensitivity as a function of SD distance for two inhomogeneity depths. The background optical parameters are μ a 0 = 0.1 cm 1 and D 0 = 0.03 cm , which give k = 0.9 cm 1 . The sensitivity for inhomogeneity depth of 3 cm is magnified 20 times. The points are the approximate solution from Eq. (9).

Equations (9)

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[ D ( r ) μ a ( r ) + j ω c ] ϕ ( r , ω ) = β δ ( r r s ) ,
C ( r , δ u ( r ) ) = arg min r y y 0 f ( r ) δ u ( r ) Λ 2 ,
δ u ̂ ( r ) = arg min δ u C ( r , δ u ( r ) ) = Re [ ( y y 0 ) H Λ f ( r ) ] f ( r ) Λ 2 ,
r ̂ = arg min r y y 0 f ( r ) δ u ̂ ( r ) Λ 2 .
p ( y H 1 , r ) = Λ ( 2 π ) M exp ( 1 2 y f ( r ) Λ 2 ) ,
p ( y H 0 ) = Λ ( 2 π ) M exp ( 1 2 y y 0 Λ 2 ) .
L ( y , r ) = log p ( y H 1 , r ) p ( y H 0 ) = Re [ h ( r ) H ( y y 0 ) ] c ( r ) ,
P D = k P F p ( q H 1 , r ) d q = 1 Φ ( k P F q ¯ σ q ) .
S A γ 2 exp [ 4 k ( γ 2 4 + d 2 ) 1 2 ] ( γ 2 4 + d 2 ) 4 exp ( k γ ) ,

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