Creating and storing non uniform data/grid using interp2

Hi I have tried construct a non uniform data set based upon uniform data. The idea is I want a finer mesh in the middle as can be seen in the attached image. I used interp2 to create the finer mesh, the code I have used is below.

if true
  % code
end
[X,Y] = meshgrid(-0.00005:0.0000025:0.00005); %Coarse mesh%
h=sqrt((((dh.^2+rp.^2)/(2*dh)).^2)-(X.^2+Y.^2))-((rp.^2-dh.^2)/(2*dh));
h(:,(1:41))=(h(:,(1:41))> 0).* h(:,(1:41));
[Xq,Yq] = meshgrid(-0.000030:0.0000005:0.000030); %Fine mesh%
Vq = interp2(X,Y,h,Xq,Yq);
figure
mesh(X,Y,h), hold, mesh(Xq,Yq,Vq)

The problem is that I want to be able to (a) name the non uniform data and (b) keep the non uniform grid for further calculations. Is this possible or have I gone about this the wrong way.

Help would be greatly appreciated.