At each location (x0,y0) in the output image, the variance of the confusion noise is given by the product of 2 integrals
var(x0,y0) = I1 * I2(x0,y0)
where I1 is the source integral defined by
- Smax I1 = | N(S) S**2 dS - Smin
and I2 is the beam integral defined by
-- I2(x0,y0) = || [SB(x-x0,y-y0) * PB(x,y)]**2 dx dy --
Thus, at the desired output location (x0,y0), the synthesized beam is shifted to the location (x0,y0), and then the product of the shifted beam and the primary beam is formed, and then that product squared is summed over the size of the synthesized beam image.
The user is told what the source integral value is. Thus, you can in fact rescale the output image to other flux density ranges just by knowing the square root of the flux integral.
The program can run without an input beam or output image whereupon just the source integral is done. This can be useful because the computation of the beam integral is very slow, as for each output pixel, a sum over an image the size of the synthesized beam must be done.
The user inputs the differential and normalized source count function N(S)/N0(S) where S is the flux density. The units of N(S) are counts/Jy/steradian. The user also specifies N0, which is a cosmological normalization, usually a power law of S. This function is input via a power law and/or polynomial. A break flux density is given below which the power law is used and above which the polynomial is used.
In the help file, examples are given for keyword values for the 20cm number counts. These results come from Windhorst et al 1993, ApJ, 405, 409
For the 20cm counts, the break point is flux(3) = 1E-4 Jy The polynomial coefficients are good from flux(3) to flux(2) = 10 Jy. The power law is good from flux(1) = 1E-5 Jy to flux(3) = 1E-4 Jy. Below 1E-5 Jy the function is unknown, but must turn over and converge so as not to distort the CMB spectrum.
For the 20cm number counts, the polynomial coefficients are 2.519192, -0.139680, -0.302235, 0.067539, 0.046945, 0.005320 See the flux keyword for the acceptable range.
For the 20cm number counts, the power law is a = 195 and p = 0.45 See the flux keyword for the acceptable range.
For the 20cm number counts, f = 1.0 and b = -2.5