.. _calibration-chapter:
Flux calibration method
=======================
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):
.. code:: python
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).
.. code:: python
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:
.. code:: python
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
.. code:: python
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:
.. code:: python
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):
.. code:: python
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.
.. _`A revised flux scale for the AT Compact Array` : http://www.atnf.csiro.au/observers/memos/d96783~1.pdf