SARG: Modelling Kutunse Primary Beams from Simulations I

[philusnarh]

Sim 1: Using OSKAR

1. Geometrical model of Kutunse dish

• Consider the dish as a collection of dipoles;
• Assume the radial distribution of the dipoles to be a Super-Gaussian; (Note: This will mimic an aperture illumination of the dish)
• Introduce errors in the dipole orientations to distort the main reflector
• Introduce phase error to also distort the beam (this will introduce feed displacement)
• remove the supporting structures (i.e. the struts and secondary reflector)
• vary the size of the secondary reflector

2. Produce Complex beams

• Refer to Jones matrix

3. Produce Complete beams

   • Refer to Mueller matrix

4. Measure the Intrinsic Polarisation Leakage (IXR)

5. Estimate the FWHM across all frequencies (5 - 6.7 GHz)

6. Reconstruct the simulated beam models

• Apply Zernike Moments Using the strongest Coefficients
• Apply SVD using fewer eigenvalues for reconstruction.

[philusnarh]

Consider the Kutunse dish as a collection of dipoles such that the dipoles are randomly drawn from a Uniform distribution with the orientation defined within a circular medium:

horizontal representation

vertical representation

The following algorithm describes the ITM used to draw random values from a cumulative distribution function (CDF), of a known density :

(i) Find the quantile function . (ii) Generate a uniform random number u. (iii) Return the random number .

Consider::

For an aperture illumination behaviour we use Inverse transform approach to describe the radial distribution of the dish::

Fig 1: the distribution of the dipoles across the radius

Fig 2: Station setup for using 10,000 dipoles

Fig 3: Station setup for using 50,000 dipoles

Fig 4: Station setup for using 80,000 dipoles

[philusnarh]

Refer to Jones & Mueller matrix

What the instrument actually measures is a set of pairwise correlations between two voltages induced by the EM field in two orthogonal mode feeds, and . The Jones formalism assumes that these are linearly related to the EM field (i.e. that all signal propagation effects are linear). This can be written as , where is a column vector of the two voltages, and the Jones matrix describes signal propagation. The measured coherency can then be written as:

----->>> (1)

and the measured Stokes parameter vector s0 relates to the original Stokes vector via the so-called Mueller matrix M:

----->>> (2)

----->>> (3)

For the Mueller matrix:

----->>> (4)

Therefore, to determine the measured Stokes; ----->>> (4)

Script Update 1 http://nbviewer.jupyter.org/urls/dl.dropbox.com/s/97lotj2lfv61pnm/kutunse-PB-model.ipynb

[philusnarh]

Intrinsic Cross-Polarisation (IXR)

The term “intrinsic” in IXR indicates that the parameter is independent of the choice of coordinate systems. For Stokes polarimeters, IXR can be easily converted to a Mueller IXR, which, in turn, is directly related to the fractional polarisation leakage:

[philusnarh]

scripts used for the simulations

1. https://github.com/philusnarh/PROJECT/tree/master/COProject-scripts

Beam modelling & Zernike fits

2. http://nbviewer.jupyter.org/urls/dl.dropbox.com/s/lcko9z05vpmn2de/kutunse-PB-model.ipynb

Reconstructing Kutunse Beams with SVD

3. http://nbviewer.jupyter.org/urls/dl.dropbox.com/s/1w4xzhg7brvheca/svd_decompos.ipynb

[akotodanso]

Are the quadripod legs that huge. Can we also look at from the angle where some of the signals hitting the legs bounces back into the dish, and what. Say let's consider 5 percent of the signals bouncing back to add to the signals and the effect it will have.

[Proven-Adzri]

Thanks

[philusnarh]

Yeah!, it works!!!!