k-Wave Toolbox

fitPowerLawParams

Fit power law absorption parameters for highly absorbing media.

Syntax

[a0_fit, y_fit] = fitAbsorptionValues(a0, y, c0, f_min, f_max)
[a0_fit, y_fit] = fitAbsorptionValues(a0, y, c0, f_min, f_max, plot_fit)

Description

fitPowerLawParams calculates the absorption parameters that should be defined in the simulation functions given the desired power law absorption behaviour defined by a0 and y. This takes into account the actual absorption behaviour exhibited by the fractional Laplacian wave equation.

This fitting is required when using large absorption values or high frequencies, as the fractional Laplacian wave equation solved in kspaceFirstOrder1D, kspaceFirstOrder2D, kspaceFirstOrder3D, and kspaceSecondOrder no longer encapsulates absorption of the form a = a0*f^y.

The returned values should be used to define the medium.alpha_coeff and medium.alpha_power within the simulation functions. The absorption behaviour over the frequency range f_min:f_max will then follow the power law defined by a0 and y.

Inputs

a0 desired power law absorption prefactor [dB/(MHz^y cm)]
y desired power law exponent
c0 medium sound speed [m/s]
f_min minimum frequency of interest [Hz]
f_max maximum frequency of interest [Hz]

Optional Inputs

plot_fit Boolean controlling whether the final fit is displayed (default = false)

Outputs

a0_fit power law absorption prefactor that should be used to define medium.alpha_coeff in the simulation functions
y_fit power law exponent that should be used to define medium.alpha_power in the simulation functions

See Also

kspaceFirstOrder1D, kspaceFirstOrder2D, kspaceFirstOrder3D