solve

The input IFTSolver object specifies the 2-D inverse Fourier transform method and defines the spatial (x,y) and spatial-frequency (u,v) arguments.

Data Type: IFTSolver

The 3D Fourier-domain surface temperature—T0hat or \(\hat{T}_0(u,v,f)\)—is obtained by applying a 2D spatial Fourier transform over \(x\) and \(y\) and a temporal Fourier transform over \(t\), as follows.

\( \hat{T}_0 \left( u,v,f \right) = \left. \mathcal{F}_{x,y,t} \left\{ T \left( x,y,z,t \right) \right\} \right|_{z=0} \)

If solver.method = "integral2", then T0hat must be a symbolic expression of u and v (the value(s) of f must be baked into T0hat).

If solver.method = "ifft2", then T0hat must be an \(N_x \times N_y \times N_T \times N_\mathrm{pump} \times N_f\) matrix or compatible in size.

Data Types: double | single | sym

X_probe specifies the \(x,y\)-coordinates at which to evaluate T0tilde

Data Types: double | single

The phasor surface temperature—T0tilde or \(\tilde{T}_0(x,y,f)\)—is the temporal Fourier-transformed temperature evaluated at \(z=0\). It is obtained by performing a 2D inverse Fourier transform on \(\hat{T}_0\) over parameters \(u\) and \(v\), as follows.

\( \tilde{T}_0 \left( x,y,f \right) = \left. \mathcal{F}_t \left\{ T \left( x,y,z,t \right) \right\} \right|_{z=0} = \mathcal{F}^{-1}_{u,v} \left( \hat{T}_0(u,v,f) \right) \)

• If X_probe is not provided, and
  • solver.method = "ifft2"; then, T0tilde is an \(N_x \times N_y \times N_T \times N_\mathrm{pump} \times N_f\) matrix and is the exact output of fftshift(ifft2(ifftshift(T0hat))).
  • solver.method = "integral2"; then, T0tilde is a function handle of arguments x_probe and y_probe (the two columns of X_probe).
• If X_probe is provided, T0tilde is an \(N_T \times N_\mathrm{pump} \times N_f \times N_\mathrm{probe}\) matrix, obtained either directly (if solver.method = "integral2") or via interpolation of the ifft2 result.

Data Type: double