Surface Fitting with Custom Equations

Hi, I want to fit a surface through data points that I got from a simulation. I calculated a curvature (k) for several combinations of wavelengths (l) and numerical apertures (NA). I know the relation between the curvature and wavelength for constant NA, also between curvature and NA for constant wavelength. The one dimensional fit functions are:

k = a1*NA^(-2) (for one wavelength)

k = b1*l^4 + b2*l^3 + b3*l^2 + b4*l (for one NA)

Now I want to use the Curve Fitting Tool with a custom equation to fit a surface through my data points. Probably a simple question but how can I combine my two fit functions into one function describig the surface? Just combining them like

z=f(x,y)=a1*NA^(-2) + b1*l^4 + b2*l^3 + b3*l^2 + b4*l

didn't work as planned. Thanks!

[Torsten]

Did you make a surface plot for your data using "ScatteredInterpolant", e.g. ?

Knowing possible fitting functions in the coordinate directions in general doesn't help for a useful surface equation.

In your case, a1 will be a function of l and b1,b2,b3 and b4 will be functions of NA - and the behaviour of these functions is not known.

[Lucas Weissmann]

Thanks for your advise. I had some success with "griddedInterpolant".

[Torsten]

Thanks for your advise. I had some success with "griddedInterpolant".

It's just to get an impression how a surface might look and if your data are not too noisy to be fitted. Maybe by looking at the surface you have an idea how a possible surface equation might look.