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Simultaneous imaging and optode calibration with diffuse optical tomography

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Abstract

In order for diffuse optical tomography to realize its potential of obtaining quantitative images of spatially varying optical properties within random media, several potential experimental systematic errors must be overcome. One of these errors is the calibration of the emitter strength and detector efficiency/gain. While in principle these parameters can be determined accurately prior to an imaging experiment, slight fluctuations will cause significant image artifacts. For this reason, it is necessary to consider including their calibration as part of the inverse problem for image reconstruction. In this paper, we show that this can be done successfully in a linear reconstruction model with simulated continuous-wave data. The technique is general for frequency and time domain data.

©2001 Optical Society of America

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Figures (2)

Fig. 1.
Fig. 1. Illustration of experimental geometry with the absorbing object.
Fig. 2.
Fig. 2. Absorption image reconstructions from simulated data with uncertainty in the source and detector strengths of 0%, 40%, and 80% in a/d, b/e, and c/f respectively. The images span X and Y from -3 to 3 cm and Z-slices are indicated from 0.5 to 5.5 cm. Reconstructions without consideration for the uncertainty in the optode coupling strengths are shown in a-c. d-f show the results when simultaneously reconstructing the optode strengths.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

· ( D ( r ) Φ ( r , t ) ) + v μ a ( r ) Φ ( r , t ) + Φ ( r , t ) t = vS ( r , t ) .
Φ = Φ ο + Φ pert
Φ = Φ o exp ( Φ pert ) .
Φ pert ( r s , r d ) = 1 Φ o ( r s , r d ) Φ o ( r s , r ) v δ μ a ( r ) D o G ( r , r d ) d r .
Φ o ( r s , r d ) = sd G ( r s , r d ) .
F ( x ) = i = 1 N meas [ ln Φ Theory, i ( x ) ln Φ Meas, i ] 2
x ̂ = A T ( AA T + λI ) 1 y ,
y i = ln [ Φ ( r s , i , r d , i ) Φ o ( r s , i , r d , i ) ] = ln [ s k ( i ) ] + ln [ d l ( i ) ] + j A i , j δμ a , j .
ξ = [ δμ a , 1 μ ao δμ a , N v μ ao ln s 1 ln s N s ln d 1 ln d N d ] .
[ S D ] = [ 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 ] .
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