4D fit with matlab

Hi everyone, I have a particular problem with matlab and after fruitless researches, I finally post here. I have datas from a simulation, looking like :

Xfield Yfield Xpsf Ypsf

-0.3843 0.5215 83.0432 68.1101

-0.3843 0.5715 82.9743 57.2404

-0.3843 0.6215 82.9117 46.3871

-0.3843 0.6715 82.8554 35.5475

-0.3843 0.7215 82.8054 24.7194

-0.3843 0.7715 82.7616 13.9002

-0.3843 0.8215 82.7240 3.0877

... ... ... ...

The firt two columns are (X,Y) coordinates in the field of view of an optical instrument, and the two last columns are the (X,Y) coordinates of the associated image at the focal plane of the instrument. I want to find a function which links the coordinates in the field of view to the coordinates at the focal plane of the detector. The thing is, I don't even know what such a function look like, even mathematically.

I did something of the form :

F1(Xfield, Yfield) = Xpsf

F2(Xfield, Yfield) = Ypsf

So I have two fits for one problem, with a chi-squared for each fit. I would like to know if Matlab can do a global fit looking like :

F(Xfield, Yfield) = (Xpsf, Ypsf) with a global chi-squared.

I wanted to simply sum the two chi-squared from the two fits to have a global chi-squared but if Xpsf and Ypsf are correlated, a correlation term has to be added to the sum which will not simply be Chi-squared1 + Chi-squared2.

Well I hope i've been clear enough.

Thanks a lot.

Maxime