Filter Function

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The ATCA Cosmic Microwave Background Radiation Anisotropy Experiment

ATCA Telescope Filter Function

The ATCA telescope filter function is given in the figure below.

ATCA telescope filter function

You can download the ATCA telescope filter function as an ascii file. The two columns are, respectively, the multipole order l and values of the filter function Fl.

The expected variance in the ATCA image, in units of flux density per beam (Jy/beam), is given by

equation 1

where Cl are the spherical harmonic expansion coefficients at multipole orders l and Fl are the filter function values. The summation has to be made over all l=1,2,3,4....

The filter function that you can download as an ascii file (above) is tabulated at intervals of 200 and so each may be multiplied by 200 if the summation is done only over the values tabulated.

If the CMB spectrum is adopted to have flat l(l+1)Cl that is normalized by a quadrupole term Qflat, the expected variance in the ATCA images is given by

Equation 2.

A summation over the ATCA filter function yields

Equation 3.

As an example, adopting a Qflat=18 microK implies that the ATCA image would be expected to have an image variance of 248 (micro Jy/beam)2.