Firstly, we find the temperature of the noise diode through an observation of a known calibrator source. For frequencies between 1 GHz and 10 GHz, 1934-638 is the preferred flux calibrator; its cm model is described in A revised flux scale for the AT Compact Array (AT Memo 39.3/040):
def flux1934(f):
""" Return 1934-638 model flux over freq
frequency in MHz
"""
log10 = np.log10
x = -30.7667 + 26.4908*log10(f) - 7.0977*(log10(f))**2 + 0.605334*(log10(f))**3
flux = 10**x
return flux
We then find the system temperature through on and off source measurements (essentially a Y-factor method, see “Microwave Engineering”, Pozar 2004).
T_sys = T_1934 / (P_1934 / P_blank -1)
Once we know the system temperature, we can use a Y-factor measurement again, but this time turning the noise diode on and off:
T_diode = T_sys * (P_diode_on/P_diode_off - 1)
In subsequent observations, we assume the noise diode temperature, and solve for T_sys
T_sys = T_diode / (P_diode_on/P_diode_off -1)
Data are converted from arbitrary backend units to Jy by normalizing the data then multiplying through by the system temperature:
xx = xx / average(xx) * T_sys_x
yy = yy / average(yy) * T_sys_y
re_xy = re_xy / average(re_xy) * sqrt(T_sys_x * T_sys_y)
im_xy = im_xy / average(im_xy) * sqrt(T_sys_x * T_sys_y)
Note the use of geometric mean to compute cross-pol Tsys. To convert this into Stokes I, Q, U and V, we use the definition that Stokes I is the average of XX and YY (this is consisten with past methods):
ii = (xx + yy) / 2
qq = (xx - yy) / 2
uu = re_xy
vv = im_xy
This calibration is done by the sdfits conversion program. The sdfits program either stores (XX, YY), or (I,Q,U,V). It does not store (XX, YY, re(XY), im(XY)) as there is no fits stokes parameter code designated to real/imaginary cross terms.