]> Generate Jacobian for unknown background optical properties

Generate Jacobian for Unknown Background Optical Properties

genMuJacobian() calculates the Jacobian matrix

J_{i j} = \frac{\partial φ_{i} (μ_{a}, μ_{s}^{'})}{\partial μ (λ_{j})}

where $μ = μ_{a}$ or $μ_{s}^{'},$ depending on the argument muvec. The Jacobian matrix can then be used as part of a non-linear iterative scheme to determine the background optical properties.

Function Summary

Syntax:	J = genMuJacobian(SD, Medium, MeasList, Method, dMu, muvec);
Inputs:	SD	SD structure
	Medium	Medium structure
	MeasList	Measurement List that corresponds to experimental data
	Method	Method to use in generating the Jacobian, either "Born" or "Rytov"
	muvec	mu flags: calculate absorption, scattering, or both
	dMu	Increments to use calculating finite difference estimates
Outputs:	J	The Jacobian

Detailed Descriptions

The Jacobian is calculated using a finite difference approximation for the derivatives. The size of the step is controlled by dMu. In other words,

J \propto \frac{J (μ + Δμ) - J (μ)}{Δμ} .