5 Estimating T_sys

For an unresolved source of known brightness I, in the limit T_a ≪ T_sys, ρ_ij^∘ = I and Eq. 1 can be written as

(11)

where η_i = A_e∕2k_b, A_e is the effective area of the dish, k_b is the Boltzman’s constant and

(12)

Hence, knowing η_i, T_sysi can be estimated from the amplitude of the antenna dependent complex gains.

All contributions to ρ_ij^Obs, which cannot be factored into antenna dependent gains, will result in the reduction of |g|. η remaining constant, this will be indistinguishable from an increase in the effective system temperature. Since majority of later processing of interferometry data for mapping (primary calibration, bandpass calibration, SelfCal, etc.) is done by treating the visibility as a product of two antenna based numbers, this is the effective system temperature that will determine the noise in the final map (though, as a final step in the mapping process, baseline based calibration can possibly improve the noise in the map).

In the normal case of no significant baseline based terms (ϵ_ij) in X_ij, the system temperature as measured by the above method will be equivalent to any other determination of T_sysi.

T_sys can also be determined by recording interferometric data for a strong point source with and without an independent noise source of known temperature at each antenna. In this case

(13)

where g_i^ON and g _i^OFF are the antenna dependent gains with and without the noise source of temperature T_n. Note that η_i does not enter this equation. Also, T_n should be such that ≥ 0.2 to ensure that the correlated signal is measured with sufficient signal-to-noise ratio (in this case, ≥ 0.04).