ForwardModel

The film arguments is a Layer object that specifies how thermal conductivity is represented for the thin film layer of the sample.

Data Types: Layer

The substrate arguments is a Layer object that specifies how thermal conductivity is represented for the substrate layer of the sample.

Data Types: Layer

The ift_solver arguments is an IFTSolver object containing specifications for solving the inverse Fourier transform.

Data Types: IFTSolver

The input scale factor defines the units of certain forward model inputs by scaling their base SI units as follows:

• \( {\left[ h_f \right]} = {\left[ h_s \right]} = {\left[ s_x \right]} = {\left[ s_y \right]} = {\left[ x_\mathrm{probe} \right]} = {\mathrm{scale} \cdot \mathrm{m}} \)
• \( {\left[ \alpha_f \right]} = {\left[ \alpha_s \right]} = {\left[ u \right]} = {\left[ v \right]} = {\left[\frac{1}{ x_\mathrm{probe}} \right]} = {\frac{1}{\mathrm{scale} \cdot \mathrm{m}}} \)
• \( {\left[C_f\right]} = {\left[C_s\right]} = {\frac{\mathrm{W}}{\mathrm{scale} \cdot \mathrm{m}^3 \cdot \mathrm{K}}} \)
• \( {\left[ P \right]} = {\mathrm{scale} \cdot \mathrm{W}} \)
• \( {\left[ f_0 \right]} = {\frac{\mathrm{Hz}}{\mathrm{scale}}} \)

Example: If scale = 1e-6 forward model inputs are considered to be in the following units:

• \( {\left[ h_f \right]} = {\left[ h_s \right]} = {\left[ s_x \right]} = {\left[ s_y \right]} = {\left[ x_\mathrm{probe} \right]} = {\mathrm{scale} \cdot \mathrm{m}} = {10^{-6} \cdot \mathrm{m}} = {\mathrm{\upmu m}} \)
• \( {\left[ \alpha_f \right]} = {\left[ \alpha_s \right]} = {\left[ u \right]} = {\left[ v \right]} = {\left[\frac{1}{ x_\mathrm{probe}} \right]} = {\frac{1}{\mathrm{scale} \cdot \mathrm{m}}} = {\frac{1}{10^{-6} \cdot \mathrm{m}}} = {\frac{1}{\mathrm{\upmu m}}} \)
• \( {\left[C_f\right]} = {\left[C_s\right]} = {\frac{\mathrm{W}}{\mathrm{scale} \cdot \mathrm{m}^3 \cdot \mathrm{K}}} = {\frac{\mathrm{W}}{10^{-6} \cdot \mathrm{m}^3 \cdot \mathrm{K}}} = {\frac{\mathrm{W}}{\mathrm{cm}^3 \cdot \mathrm{K}}} \)
• \( {\left[ P \right]} = {\mathrm{scale} \cdot \mathrm{W}} = {10^{-6} \cdot \mathrm{W}} = {\mathrm{\upmu W}} \)
• \( {\left[ f_0 \right]} = {\frac{\mathrm{Hz}}{\mathrm{scale}}} = {\frac{\mathrm{Hz}}{10^{-6}}} = {10^6 \cdot \mathrm{Hz}} = {\mathrm{MHz}} \)

Data Types: double | single

When set to true, approximates the thickness of the substrate as infinite in the z-direction, which is more numerically stable than using a finite substrate thickness.

Data Types: logical

When set to true, tells the solver that the user is only interested in phase; not amplitude nor DC temperature change.

Data Types: logical

When set to true, the solver expects the natural log of thermal conductivity, volumetric heat capacity, optical absorption coefficient, z-direction thickness, pump laser deviation, and power as inputs.

Data Types: logical

When set to true, forces the reexecution of the symbolic solutions even if the files already exist.

Data Types: logical

c_args is a struct of validated constructor arguments (input and default) populated by validate_c_args, a private ForwardModel method.

Struct of format specifications for method inputs M, O, chi, f0, and X_probe (used in ForwardModel.plot and ForwardModel.solve).

Each field value is another struct with the following fields:

• ncols: Number of columns
• cols: 1-by-ncols string array; Specifies the variable name associated with each column of M.
• units: 1-by-ncols string array; Specifies the units of each column of M. If c_args.log_args is true, these units refer to the values before log-transformation, since the transformation implicitly normalizes by the base unit, yielding a unitless quantity.
• msg: A formatted string message for displaying the values of ncols, cols, and units to the screen.
• vld: Input validation function handle.

fun_inputs is populated by get_input_structure, a private ForwardModel method.

Function Inputs Nomenclature

• M: Material parameters.
• kf, ks: Isotropic thermal conductivity of the film and substrate.
• kf⊥, ks⊥: Transverse (radial) thermal conductivity of the film and substrate (simple anisotropy).
• kf∥, ks∥: Axial (longitudinal) thermal conductivity of the film and substrate (simple anisotropy).
• kpfi, kpsi: \(i\)-th principal thermal conductivity of the film and substrate (complex anisotropy), with \(i \in \{1,2,3\}\).
• kfij, ksij: \((i,j)\)-th component of the thermal conductivity tensor of the film and substrate, with \(i,j \in \{1,2,3\}\).
• Cf, Cs: Volumetric heat capacity of the film and substrate.
• αf, αs: Optical absorption coefficient of the film and substrate.
• Rf, Rs: Optical reflectivity of the film and substrate.
• hf, hs: Thickness of the film and substrate in the \(z\)-direction.
• Rth: Thermal contact resistance between film and substrate.
• O: Orientation parameters.
• θf_az, θs_az: Azimuthal angle of the thermal conductivity axis of rotation for the film and substrate (simple anisotropy).
• θf_pol, θs_pol: Polar angle of the thermal conductivity axis of rotation for the film and substrate (simple anisotropy).
• θfai, θsai: \(i\)-th Euler rotation angle about the \(a\)-axis, defining the orientation of the principal thermal condcutivity axes of the film and substrate, with \(i \in \{1,2,3\}\), \(a \in \{X,Y,Z\}\).
• vfi, vsi: \(i\)-th component of the unit vector along the thermal conductivity axis of rotation for the film and substrate (simple anisotropy), with \(i \in \{1,2,3\}\).
• qfi, qsi: \(i\)-th component of the unit quaternion defining the orientation of the principal thermal condcutivity axes of the film and substrate, with \(i \in \{1,2,3,4\}\).
• Rfij, Rsij: \((i,j)\)-th component of the rotation matrix defining the orientation of the principal thermal condcutivity axes of the film and substrate, with \(i,j \in \{1,2,3\}\).
• chi: Experimental parameters.
• sx, sy: Standard deviations of the pump laser's distribution in the \(x\)- and \(y\)-directions.
• P: Pump laser power.
• f0: Pump laser temporal frequency.
• X_probe: Probe laser offsets, with each row being the \(x,y\)-coordinate of the probe wrt. the pump.

2-column matrix where the 1st column is the descretized spatial vector, and the 2nd column is the descretized spatial-frequency vector referenced when ift_method="ifft2".