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Tt_ADE.m
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Tt_ADE.m
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function Tt = Tt_ADE(t, L, n_in, n_ext, lx, ly, lz, mua)
% TT_ADE time-resolved transmittance from a turbid slab
%
% Brief: this function returns the total time-resolved transmittance T(t)
% from an anisotropic slab of thickness L [μm].
% xy is the slab plane, while z is the direction of incidence of the pencil beam.
% If a refractive index contrast is set, the effect of Fresnel
% reflections at the boundaries is considered. Absorption is assumed to be
% uniform, mua [1/μm].
% t is an array of times [ps], while lx, ly and lz are scalars [μm].
%
% Inputs:
% t - array of times [ps]
% L - slab thickness [μm]
% n_in - refractive index of the diffusive medium
% n_ext - refractive index of the external medium
% lx - scattering mean free path along x [μm]
% ly - scattering mean free path along y [μm]
% lz - scattering mean free path along z [μm]
% mua - absorption rate [1/μm]
%
% Outputs:
% Tt - array of total time-resolved transmittance T(t)
%
% See also: Test_function.m
% Author: Ernesto Pini
% Affiliation: Department of Physics and Astronomy, Università di Firenze
% Email: pinie@lens.unifi.it
[Dx, Dy, Dz] = D_Tensor_ADE(n_in, lx, ly, lz);
ze = Ze_ADE(n_in, n_ext, lx, ly, lz);
v = 299.7924589/n_in;
D = (Dx*Dy*Dz)^(1/3);
z0 = lz;
T = zeros(size(t));
M = 10000; % number of virtual sources considered in the expansion
for m = -M:M
z1 = L*(1-2*m) - 4*m*ze - z0;
z2 = L*(1-2*m) - (4*m - 2)*ze + z0;
T = T + (z1*exp(-(z1)^2./(4*Dz*t)) - z2*exp(-(z2)^2./(4*Dz*t)));
end
Tt = (1/4)*((pi.*Dz.*(t).^3).^(-1/2)).*T.*exp(-v*t*mua);
end