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Systematic diffuse optical image errors resulting from uncertainty in the background optical properties

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Abstract

We investigated the diffuse optical image errors resulting from systematic errors in the background scattering and absorption coefficients, Gaussian noise in the measurements, and the depth at which the image is reconstructed when using a 2D linear reconstruction algorithm for a 3D object. The fourth Born perturbation approach was used to generate reflectance measurements and k-space tomography was used for the reconstruction. Our simulations using both single and dual wavelengths show large systematic errors in the absolute reconstructed absorption coefficients and corresponding hemoglobin concentrations, while the errors in the relative oxy- and deoxy- hemoglobin concentrations are acceptable. The greatest difference arises from a systematic error in the depth at which an image is reconstructed. While an absolute reconstruction of the hemoglobin concentrations can deviate by 100% for a depth error of ±1 mm, the error in the relative concentrations is less than 5%. These results demonstrate that while quantitative diffuse optical tomography is difficult, images of the relative concentrations of oxy- and deoxy-hemoglobin are accurate and robust. Other results, not presented, confirm that these findings hold for other linear reconstruction techniques (i.e. SVD and SIRT) as well as for transmission through slab geometries.

©1999 Optical Society of America

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Figures (6)

Figure 1.
Figure 1. Images reconstructed at various depths. Each image is 6 × 6 cm.
Figure 2.
Figure 2. Absorption coefficients of hemoglobin (50 μmole/liter) and H2O.
Figure 3.
Figure 3. Systematic errors in the reconstructed image values of the object resulting from the errors in the depth at which the image is reconstructed.
Figure 4.
Figure 4. Systematic errors in the reconstructed image values of the object resulting from the errors in the background absorption (red line) and scattering coefficient (black line).
Figure 5.
Figure 5. Uncertainties in the image value caused by Gaussian measurement noise. In (a) the depth of the object is 2 cm and the noise is varied. In (b) the depth is varied while the noise is held constant at 3×10-5 percent.
Figure 6.
Figure 6. Systematic errors in the reconstructed Δ[Hb], Δ[HbO], and Δ[Hb]/Δ[HbO] resulting from errors in the depth of the image reconstruction.

Tables (2)

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Table 1. Errors and uncertainties in the images values resulting from the systematic errors of background optical properties, the depth position of the image and random system noise in one-wavelength simulation.

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Table 2. Image errors in the absolute and ratio reconstruction resulting from the systematic errors of background optical properties, the depth position of the image in two-wavelength simulation

Equations (9)

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ϕ sc 1 ( r d ) = d r ϕ inc ( r s , r ) v δ μ a ( r ) D G ( r , r d ) .
ϕ sc 2 ( r d ) = d r ( ϕ inc ( r s , r ) + ϕ sc 1 ( r ) ) v δ μ a ( r ) D G ( r , r d )
ϕ sc n ( r d ) = d r ( ϕ inc ( r s , r ) + ϕ sc n 1 ( r ) ) v δ μ a ( r ) D G ( r , r d ) .
ϕ ˜ sc n ( 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 ) v δ μ a ( x , y , z ) D exp ( i ω x x + i ω y y )
δ μ a ( x , y , z ) = D h ϕ inc ( x , y , z ) FT 1 [ ϕ ˜ sc n ( ω x , ω y ) G ˜ ( ω x , ω y , z ) ]
μ a ( λ ) = ε Hbo ( λ ) [ HbO ] + ε Hb ( λ ) [ Hb ]
Δ [ Hb ] = ε Hbo λ 2 δ μ a λ 1 ε Hbo λ 1 δ μ a λ 2 ε Hb λ 1 ε Hbo λ 2 ε Hb λ 2 ε Hbo λ 1
Δ [ HbO ] = ε Hbo λ 1 δ μ a λ 2 ε Hbo λ 2 δ μ a λ 1 ε Hb λ 1 ε Hbo λ 2 ε Hb λ 2 ε Hbo λ 1
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