]> Fitting Source/Detector Coupling Coefficients

Fit Source and Detector Amplitudes

fitSD() and its cousins estimate the source and detector amplitudes and/or phases by minimizing the difference between the experimental data and a theoretical prediction. If a theory curve is not supplied as a function argument, then one is calculated from the given SD and Medium structures.

Function Summary

Syntax:	[sa, da, pa] = fitSD(SD, Medium, MeasList, data[, Phi0]);
	[sa, da, pa] = fitSDAmp(SD, Medium, MeasList, data[, Phi0]);
	[sa, da, pa] = fitSDPhs(SD, Medium, MeasList, data[, Phi0]);
Inputs:	SD	SD structure
	Medium	Medium structure
	MeasList	Measurement List that corresponds to experimental data
	data	Experimental data to be fit against
	Phi0	Theory results (optional). If missing, the theory result will be re-calculated from SD, Medium, and MeasList.
Outputs:	sa	Source amplitude coefficients (can use as new SD.SrcAmp)
	da	Detector amplitude coefficients (can use as new SD.DetAmp)
	pa	Scaling factors to rescale previous Phi0 to data amplitudes

Detailed Descriptions

For every source-detector pair, the value calculated by the toolbox for the measured fluence is

Φ_{i}^{0} = S_{j (i)} D_{k (i)} φ^{0}

where $S_{j (i)}$ is the source amplitude SD.SrcAmp used to make the $i$ -th measurement, $D_{k (i)}$ is the detector amplitude SD.DetAmp used to make the $i$ -th measurement, and $φ^{0}$ is the theoretic calculation with all the amplitudes set to $1.0$ .

In the Rytov approximation, the source and detector amplitudes that minimize the difference between the data and the theory reduce to a system of linear equations (in the Born approximation, the equations are non-linear). The matrix that represents this system of equations is rank-deficient, but can be made well-posed by arbitrarily assigning one of the amplitudes (either a source or a detector) to have a value of $1.0$ . Phase terms are handled the same way (the real part of the logarithm give the amplitude fits, the imaginary part is the phase fits).

For more information see:

David A. Boas, Thomas Gaudette, and Simon R. Arridge, "Simultaneous imaging and optode calibration with diffuse optical tomography," Optics Express, 8(5), pg. 263, 2001.