Image sensitivity of a heterogenous array
Here we provide a recipe to determine the imaging sensitivity (natural weight) of a heterogeneous array. We will make use of the SEFD of the individual antennas and weight accordingly to the number of baselines.
The following information is needed:
Observing time [s]: T_obs
Number of polarisation: N_pol
Bandwidth [Hz]: BW
Number of polarisation: N_pol
Number of MK antennas in the array: N_MK
Number of SKAMID antennas in the array: N_MKplus
SEFD_MK
SEFD_SKA = 0.7332 * SEFD_MK
Array efficiency (assume 100%): array_eff_mkplus = 1
Step 1: Determine the number of baselines N_tot = N_MK + N_MKplus N_bsl_tot = N_tot * (N_tot -1) / 2 # total number of baselines N_bsl_MK = N_MK * (N_MK -1) / 2 # pure MK Antenna baselines N_bsl_MKplus = N_MKplus * (N_MKplus -1) / 2 # pure SKAMID antenna baselines N_bsl_MK_MKplus = N_bsl_tot - N_bsl_MK - N_bsl_MKplus # intermixed baselines
Step 2: Calculate image sensitivity
image_sensitivity_MKplus = 1/array_eff_mkplus * sqrt( 1 / (N_pol * N_tot * (N_tot - 1) * BW * T_obs) * (SEFD_MK**2 * N_bsl_MK + SEFD_SKA**2 * N_bsl_MKplus + SEFD_SKA * SEFD_MK * N_bsl_MK_MKplus) / N_bsl_tot )
print('MeerKATplus image seensitivity: ',image_sensitivity_MKplus,'[Jy]')
Example for L-Band: N_MK = 60 N_MKplus = 13 T_obs = 3600 [s] BW = 875E6 [Hz] N_pol = 2 SEFD_MK = 426 [Jy] SEFD_SKA = 0.7332 * SEFD_MK array_eff_mkplus = 1 MeerKATplus image sensitivity: 2.229632808322377e-06 [Jy]