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Diffuse optical reflection tomography with continuous-wave illumination

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Abstract

Diffuse optical reflection tomography is used to reconstruct absorption images from continuous-wave measurements of diffuse light re-emitted from a “semi-infinite” medium. The imaging algorithm is simple and fast and permits psuedo-3D images to be reconstructed from measurements made with a single source of light. Truly quantitative three-dimensional images will require modifications to the algorithm, such as incorporating measurements from multiple sources.

©1998 Optical Society of America

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Figures (5)

Fig. 1.
Fig. 1. Schematic illustration of the set-up for diffuse optical reflectance tomography. The phantom is 30 × 30 × 20 cm with μs ′ = 10.0 cm-1 and μa = 0.05 cm-1. The properties of the objects are given in the text.
Fig. 2
Fig. 2 Difference of the images obtained by the CCD camera without and with the absorbing objects. The absorbing objects cause the measured diffuse reflectance to decrease. The color scale is linear where red corresponds to maximum change and blue corresponds to zero change. The peak attenuation for the first (second) object corresponds to a 24% (8%) change in the signal.
Fig.3.
Fig.3. Images reconstruction at different depths from the raw data presented in fig. 2. The objects can be localized in depth by minimizing the size of the object in the X and Y directions. The color scale is linear. Reconstruct absorption coefficients are given in the text.
Fig. 4.
Fig. 4. Measured reflectance versus radial position from the source. Experimental data with the absorbing objects present given by symbols. Theoretical fit for a semi-infinite homogeneous medium is given by the solid line. The object is to the left resulting in the difference between theory and experiment.
Fig. 5. A)
Fig. 5. A) Reconstruction of the upper left object by subtracting a theoretical background from the experimental data. B) Reconstruction of the lower center object by subtracting the theoretical background from the experimental data.

Equations (9)

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ϕ sc ( r d ) = dr ϕ inc r s r νδ μ a ( r ) D G r r d .
ϕ ˜ sc ω x ω y = G ˜ ω x ω y z A ω x ω y z dz ,
A ω x ω y z = ∫∫ d x d y ϕ inc r s x y z νδ μ a x y z D exp ( x x + y y )
G r r d = exp k ( ( x x d ) 2 + ( y y d ) 2 + z 2 ) 1 / 2 4 πD ( ( x x d ) 2 + ( y y d ) 2 + z 2 ) 1 / 2
exp [ k ( ( x x d ) 2 + ( y y d ) 2 + ( z + 2 z e ) 2 ) 1 / 2 ] 4 πD ( ( x x d ) 2 + ( y y d ) 2 + ( z + 2 z e ) 2 ) 1 / 2
z e = 2 3 μ s ' 1 + R eff 1 R eff
G ˜ ω x ω y = 1 2 D ω x 2 + ω y 2 + k 2
{ exp ( z ω x 2 + ω y 2 + k 2 ) exp [ ( z + z e ) ω x 2 + ω y 2 + k 2 ] } .
δμ a x y z = D vhϕ inc x y z FT 1 [ ϕ ˜ sc ω x ω y z G ˜ ω x ω y z ]
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