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This is the website for the 2016 NASSP masters Fundamentals of Radio Interferometry course. The course is based on the ipython-based book of the same name. This site will be updated regularly.

Course Schedule

Lectures run from March 15 to May 20, 2016 from 2:00 - 4:00 (check the outline below for dates) at UCT in lecture theatre 2A in the RW James Building. Practical session are in the NASSP computing lab, Maths Building, Room 408. See the Upper Campus Map.

  1. March 15: Introduction to Radio Interferometry
    1. Course Details - G. Foster (pdf, odp)
    2. An Introduction - O. Smirnov (pdf, odp)
    3. Limitations of Single Dish Astronomy - G. Foster (pdf, odp)
    4. Modern Interferometric Arrays - G. Foster (pdf, odp)
  2. March 17: Radio Science and Positional Astronomy
    1. Radio Science - G. Jozsa (pdf, odp)
    2. Positional Astronomy - T. Grobler (pdf, odp)
  3. April 5: Fourier Theory and Discrete Fourier Transforms - G. Jozsa (pdf, odp)
  4. April 7: Fourier Tutorial and Visibility Space (part 1)
    1. Discrete Fourier Transforms and Sampling Practical (see sections 2.8 and 2.9) - L. Bester
    2. Visibility Space: The van Cittert-Zernike Theorem - G. Foster (pdf, odp)
  5. April 12: Visibility Space - J. Girard (pdf)
  6. April 14: Practical Session - S. Makhathini (notebook, data)
  7. April 19: Imaging: Spatial Frequencies, Sampling Functions, and Point Spread Functions - G. Foster (pdf, odp)
  8. April 21: Imaging: Gridding, Weight Functions, the W-term - G. Foster (pdf, odp)
  9. April 26: Deconvolution - G. Foster (pdf, odp)
  10. April 28: Practical Session - S. Makhathini
  11. May 3: The Radio Interferometric Measurement Equation (RIME) - O. Smirnov (pdf, odp)
  12. May 6: Practical Session - S. Makhathini, S. Sirothia
  13. May 10: Instrumentation - G. Foster (pdf, odp)
  14. May 13: Calibration - T. Grobler (pdf, odp)
  15. May 17: Practical Session - S. Sirothia
  16. May 20: Exam Talks and Questions

Book Outline

  1. Radio Science using Interferometric Arrays
    1. Basic remarks on astrophysics
    2. Electromagnetic radiation and astronomical quantities
    3. Radiation transport
    4. Radio regime
    5. Black body radiation
    6. Synchrotron emission
    7. Line emission
    8. Astronomical radio sources
    9. A brief introduction to interferometry
    10. Limits of single dishes
    11. Modern interferometric arrays
    12. Further reading and references
  2. Mathematical Groundwork
    1. Complex Numbers
    2. Important functions
    3. Fourier Series
    4. The Fourier Transform
    5. Convolution
    6. Auto-correlation and cross-correlation
    7. Fourier Theorems
    8. The Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
    9. Sampling Theory
    10. Linear Algrebra
    11. Least-squares Minimization
    12. Solid Angle
    13. Spherical Trigonometry
    14. Further Reading and References
  3. Positional Astronomy
    1. Equatorial Coordinates (RA, Dec)
    2. Hour Angle (HA) and Local Sidereal Time (LST)
    3. Horizontal Coordinates (ALT,AZ)
    4. Direction Cosine Coordinates (l,m,n)
    5. Further Reading and References
  4. Visibility Space
    1. The Baseline and its representations in space
    2. The 2-element Interferometer: a spatial filter
    3. The Visibility Function
    4. UV Coverage
      1. UV Tracks
      2. Improving Coverage
    5. The Fourier Approximation & Van Cittert-Zernike Theorem
    6. Further Reading and References
  5. Imaging
    1. Spatial Frequencies
    2. Sampling and Point Spread Functions
    3. Gridding and Degridding for using the FFT
    4. The Dirty Image and Visibility Weightings
    5. The Break Down of the Small Angle Approximation and the W-Term
    6. Further Reading and References
  6. Deconvolution in Imaging
    1. Sky Models
    2. Interative Deconvolution with Point Sources (CLEAN)
    3. CLEAN Implementations
      1. Hogbom's Method
    4. Residuals and Image Quality
    5. Source Finding and Detection
    6. Further Reading and References
  7. Observing Systems
    1. Jones Notation
    2. The Measurement Equation (RIME)
    3. Analogue Electronics
    4. Digital Electronics
    5. Primary Beam
    6. Polarization and Antenna Feeds
    7. Propagation Effects
    8. Radio Frequency Interference (RFI)
    9. Further Reading and References
  8. Calibration
    1. Calibration as a Least Squares Problem
    2. 1GC calibration
    3. 2GC calibration
    4. 3GC calibration
    5. Further Reading and References

Assignments

There are three assignments, only two are required.

Exam

The exam is a project to reduce a real measurement set from a KAT-7 observation, and write up the steps and results in a report. Each student will present their results in a 5-10 minute presentation on the final day. Students will be given the opportunity to revise their report in the week after the talks.

Notebook Setup

To setup the ipython notebook environment to interactively use the book follow the virtualenv setup guide.

Data

There are additional large files (> 1MB), mainly FITS images, which are needed for some of the sections, these can be downloaded here, the original simulated KAT-7 measurement sets can be downloaded here. To place them in the correct paths do the following:

$ cd [fundamentals root]/data/
$ mv [location of download]/fundamentals_fits.tar.gz .
$ tar xvzf fundamentals_fits.tar.gz
$ cd simulated_kat_7_vis/
$ mv [location of download]/simulated_KAT-7_ms.tar.gz .
$ tar xvzf simulated_KAT-7_ms.tar.gz

Practical 1 Data Sets:

External Software

For data reduction we will be using NRAO's CASA software package.

Contributors