Documentation on imcfn

Task: imcfn
Purpose: Compute confusion noise for an interferometer image
Categories: image analysis

        IMCFN computes confusion noise in an interferometer image
        owing to the presence of unresolved background sources.

        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

Key: beam
        Synthesised dirty beam image (must be power of 2). No default.

Key: out
        Confusion noise (sigma) image (1/2 size of beam image) in Jy 

Key: flux
        3 numbers (Jy).  flux(1) and flux(2) define the range of flux 
        densities for which the confusion noise is calculated.  
        flux(3) is the break point below which the power law is
        used, and above which the polynomial is used.  Set flux(3)
        above flux(2) if you wish to use only the power law. Set
        flux(3) below flux(1) if you wish to use only the polynomial.
        No defaults.

        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.

Key: poly
        N(S)/N0(S) specified as a polynomial of up to 5th order fit to 
        log10(N/N0 counts/Jy/sr) vs log10(S Jy)  You input up to 6
        polynomial coefficients (low to high order).

        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.

Key: power
        N(S)/N0(S) (counts/Jy/sr) specified as a power law  
        a * S**p where S is in Jy and you give a and p.

        For the 20cm number counts, the power law is a = 195
        and p = 0.45   See the flux keyword for the acceptable range.

Key: n0
        The normalization factor N0 = f * S**b  where S is in Jy
        You give f and b.

        For the 20cm number counts, f = 1.0 and b = -2.5

Key: device
        Plot device on which to plot the differential normalized
        and un-normalized source count functions.  You can specify 
        a plot device but not an output or beam image if you just 
        want to see the plots but don't want to spend ages computing
        the beam integral.