.. _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