]> Generate Jacobian for unknown positions

Generate Jacobian for Unknown Positions

Calculate the Jacobian matrix for variations in optode position from the nominal values in the SD structure

J_{i j} = \frac{\partial φ_{i} (r)}{\partial r_{j}}

where $r_{j}$ refers to a single coordinate axis of the vector $r$ .

Function Summary

Syntax:	J = genPosJacobian(SD, Medium, MeasList, Method, posFlags);
Inputs:	SD	SD structure
	Medium	Medium structure
	MeasList	Measurement List that corresponds to experimental data
	Method	How the Jacobian should be calculated, "Born" or "Rytov"
	posFlags	Six element vector of 1/0 flags, to calculate perturbations for $[s_{x}, s_{y}, s_{z}, d_{x}, d_{y}, d_{z}]$
Outputs:	J	The Jacobian

Detailed Descriptions

The matrix $J$ is normally used as part of a non-linear iterative solver. All derivatives are calculated using finite difference and assume a homogeneous medium. For more information on positional calibration see:

Jonathan J. Stott, Joseph P. Culver, Simon R. Arridge, David A. Boas "Optode positional calibration in diffuse optical tomography," Applied Optics, 42(16), pp. 3154–3162, 2003.