You are fitting multivariate data (function dependent on x and y) but your data only has one coordinate logged (either x or y). so either add the respective x and y values to your data or just generate the full data range for x and y.
Both are equally valid in this case.
Dif = 0.00000013; K0 = 0.5; z = 0; linf\[Alpha] = 0.0;
T1[x_, y_, t_, b_, l_, d_, m_, Intens_] /;
NumberQ[x] && NumberQ[y] && NumberQ[b] && NumberQ[l] && NumberQ[d] &&
NumberQ[m] && NumberQ[Intens] :=
Intens/(2*\[Pi]*K0)*
NIntegrate[
Sqrt[1 + m^2]*
Erfc[Sqrt[(x - \[Alpha])^2 + (y - \[Beta])^2 + (z - (m*\[Alpha] -
d))^2]/Sqrt[
Dif*4*t]]/(Sqrt[(x - \[Alpha])^2 + (y - \[Beta])^2 + (z - (m*\
\[Alpha] - d))^2]), {\[Beta], -b/2, b/2}, {\[Alpha], linf\[Alpha],
l*(1/(1 + m^2))}]
t = 1;
b = 0.001;
l = 0.001;
d = 0.0001;
m = -Tan[45*Pi/180];
Intens = 25000;
step = 0.00006;
datax = Table[{x, 0,
T1[x, 0, t, b, l, d, m, Intens] +
Random[NormalDistribution[0, 0.1]]}, {x, -0.002, 0.002, step}];
datay = Table[{0, y,
T1[0, y, t, b, l, d, m, Intens] +
Random[NormalDistribution[0, 0.1]]}, {y, -0.002, 0.002, step}];
alldata = Join[datax, datay];
dataxy = Flatten[
Table[{x, y,
T1[x, y, t, b, l, d, m, Intens] +
Random[NormalDistribution[0, 0.1]]}, {x, -0.002, 0.002,
4 step}, {y, -0.002, 0.002, 4 step}], 1];
Show[
Plot[{T1[x, 0, t, b, l, d, m, Intens],
T1[0, x, t, b, l, d, m, Intens]}, {x, -0.002, 0.002},
PlotStyle -> Red],
ListPlot[{datax[[All, {1, 3}]], datay[[All, {2, 3}]]},
PlotStyle -> {Black, Gray}]
]
Show[
Plot3D[
T1[x, y, t, b, l, d, m, Intens], {x, -0.002, 0.002}, {y, -0.002,
0.002},
PlotRange -> Full, Mesh -> False, PlotStyle -> Gray,
Lighting -> "Neutral"],
ListPointPlot3D[dataxy, PlotRange -> Full, PlotStyle -> Black],
Graphics3D[{Thick, Red, Line[datax], Line[datay]}]
]
(*only lines*)
fitL = FindFit[alldata,
T1[x, y, 1, bf, lf, d, m, Intens], {{bf, 0.005}, {lf, 0.005}(*,d,m,
Intens*)}, {x, y}, Method -> "LevenbergMarquardt"]
(*full surface*)
fitS = FindFit[dataxy,
T1[x, y, 1, bf, lf, d, m, Intens], {{bf, 0.005}, {lf, 0.005}(*d,m,
Intens*)}, {x, y}, Method -> "LevenbergMarquardt"]