Derivation of Chi-Squared Value for 2-Band Merged Positions
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      ChiSq = (observed deviation)^2 / (expected error)^2

There are 2 degrees of freedom, X and Y.

                ( X(nuv) - X(fuv) )^2         ( Y(nuv) - Y(fuv) )^2
      ChiSq = --------------------------  +  -------------------------  .
               ErrX(nuv)^2 + ErrX(fuv)^2      ErrY(nuv)^2 + ErrY(fuv)^2

Assume that ErrX() = ErrY() = ErrAve():

                ( X(nuv) - X(fuv) )^2   +     ( Y(nuv) - Y(fuv) )^2
      ChiSq = --------------------------------------------------------  .
                           ErrAve(nuv)^2 + ErrAve(fuv)^2

Note that the numerator is just the separation squared:

      ChiSq = ( angular separation ) ^2 /  ( ErrAve(nuv)^2 + ErrAve(fuv)^2 )
or:
      ChiSq = ( angular separation ) ^2 /  ( AvePoissonError(nuv)^2 + AvePoissonError(fuv)^2 + TOT_IBF_ERR^2 )
or:
      ChiSq = ( angular separation ) ^2 /  ( AvePoissonError(nuv)^2 + AvePoissonError(fuv)^2 + IBF_ERR^2 + IBF_ERR^2 )

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In terms of SExtractor columns and header cards in the -xd-mcat.fits file:  

      AvePoissonError(nuv) = (  (sqrt(NUV_ERRX2_IMAGE) * NSXPIXS) + (sqrt(NUV_ERRY2_IMAGE) * NSXPIXS) ) / 2.

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