===== Data Processing School :: Exercise 45 =====

^ Source directory | /data/lofarschool/data/exercise 45 |
^ Contact person | Casey Law/Michael Wise |

==== Context ====

This exercise will demonstrate how some simple Python commands can help visualize how a single polarization of the LOFAR low band antennae responds to electromagnetic radiation.

=== Prerequisite ===

Basic python.

==== Description ====

This exercise describes two functions you can use in this exercise to
visualize the LOFAR LBA beam.  The beam model is an analytic solution to how a single polarization of the LBA (e.g., "x") sees electromagnetic radiation from the sky.  This model only applies to a single polarization that is rotated 45 degrees relative to local north.  For the x+y sensitivity, imagine rotating the sensitivity pattern of x by 90 degrees and adding it to the original pattern.

The exercise consists of two functions that can plot either one or a set of slices through the beam.  

  - "show_azimuth" requires as input the observing frequency and an azimuth value.  It then plots a slice through the beam at that frequency and azimuth (from horizon to zenith).  Azimuth=0deg is due north and increases to the east.
  - "show_elevation" is the same, but plots a slice through the beam at a given elevation, starting from azimuth zero through 360 degrees.

Both functions can take one input value of azimuth or elevation.  They can also take lists of multiple azimuths and elevations.  A list in python is defined with square brackets, e.g., "[10., 50.]".

==== Files & Directories ====

The following files are found in the exercise directory:

  - ''coordinates_mod.py'' -- A Python script the does coordinate conversion.  Not used directly.
  - ''exercise.py'' -- A Python script that defines a few functions for plotting the beam amplitude.
  - ''inputs'' -- A directory for associated files and libraries.  Not used directly.
  - ''inputs_old''  -- An old inputs directory.  Not used directly.
  - ''lofar_beams.py'' -- A Python script that reads in the LOFAR LBA beam model.  Not used directly in the exercise, but could be fun for experimentation.
  - ''README.txt'' -- File that introduces the exercise and problems.

==== Step-by-step instructions ====

Use these functions to answer the following questions.

  - Imagine a cell phone tower that is 50m tall and located 50km away to the east.  How much will the x-dipole signal be reduced by the beam sensitivity at 30. and 80. MHz?
  - What is the elevation of the x-dipole half-power point for frequency = 30 MHz and azimuth = 0., pi/8, pi/4, 3pi/8, pi/2, pi?
  - How is the x-dipole beam pattern is symmetric in azimuth?  How often does it repeat itself in a full 360 degrees?  How often would the x+y dipole pattern repeat in 360 degrees?
  - Estimate the most that the x+y beam amplitude changes with azimuth at 30 and at 80 MHz?
  - At what frequency between 30-80 MHz does the x+y beam have the least structure (most smooth)?

==== Example outputs ====

Here is are quick exapmles of how you can run the two functions:

    # first, run python interactively and import the script.
    > ipython -pylab
    >>> import exercise

    # this shows an azimuth slice through the beam at 30 MHz toward the east.
    >>> exercise.show_azimuth(30e6,90.)      

    # this shows three elevation slices through the beam at 80 MHz.
    >>> exercise.show_elevation(80e6,[10.,30.,50.])