signal        noise 
   angle θ        I(θ)    sqrt[I(θ)]      noise in mag
---------------------------------------------------------------------------

    0              1.0        1.0            0.0

    0.5 FWHM       0.5        0.71           0.38

    1.0 FWHM       6.3E-2     0.25           1.5

    2.0 FWHM       1.6E-5     4.0E-3         6.0

    3.0 FWHM       1.6E-11    4.0E-6        13.5         

    4.0 FWHM       6.5E-20    2.5E-10       24.0

    5.0 FWHM       1.0E-30    1.0E-15       37.5

---------------------------------------------------------------------------