Problem in fitting when unit circle is used instead of sqaure array of pixels

Hi,

I have following strange situation:

(1) Suppose I have array 13x13 pixels; I superimpose (x,y) co-ordinate system on it. Then I define some function phi(x,y) on it; where phi is obtained from some linear combination of basis functions. I am using zernike polynomials as basis functions.

I know that zernikes are defined on unit circle (they are orthogonal on unit circle).

But I am using square array of 13x13 zernike values to build phi.

Then I find x,y slopes (using gradient function) of phi. Next, (using procedure described in Tyson's book on AO), I retrieve fitted coefficients. They match with input coefficients.

(2) Now, I restrict my phi over unit circle. Basically, phi matrix is still 13x13, but now all values are zeros which are outside the boundary of circle; i.e. using this line of code:

                    if(sqrt(x^2+y^2)<=1.0)

Then every fitted coefficient is half the input coefficient.

I would like to know why this happens.

Any help will be highly appreciated.|