1. Interferometry Discuss Group & Python Tutorial Adam Leroy & Scott Schnee (NRAO) February 28, 2014

2. What to Expect A series of discussions about interferometry and practical Python usage Audience of beginners, with “experts” leading the discussion topics – If you are an expert, please volunteer to lead a discussion For Python and CASA portions of IDG, please bring your laptop and install CASA – http://casa.nrao.edu/

3. Example Interferometry Topics Fourier transforms and the importance of “uv coverage” What happens between waves hitting antennas and writing a raw data file Hands-on data reduction using CASA Methods of imaging and deconvolution Please send us requests! – sschnee@nrao.edu and aleroy@nrao.edu sschnee@nrao.edualeroy@nrao.edu

4. Logistics Weekly meetings in ER230, Fridays @10:30 – Switching between interferometry and Python Check the IDG wiki for syllabus – https://safe.nrao.edu/wiki/bin/view/Main/Interfer ometryDiscussionGroup2014 https://safe.nrao.edu/wiki/bin/view/Main/Interfer ometryDiscussionGroup2014 http://casaguides.nrao.edu/index.php?title=P ythonOverview http://casaguides.nrao.edu/index.php?title=P ythonOverview http://casaguides.nrao.edu/index.php?title=A LMA_SIS14 http://casaguides.nrao.edu/index.php?title=A LMA_SIS14

5. 1.An interferometer measures the interference pattern produced by two apertures. 2.The interference pattern is directly related to the source brightness. In particular, for small fields of view the complex visibility, V(u,v), is the 2D Fourier transform of the brightness on the sky, T(x,y) (van Cittert-Zernike theorem) T(x,y) x y uv plane Fourier space/domain Image space/domain image plane From Sky Brightness to Visibility

6. |V | b (meters) 0 0.5 1 b 1  = /b b1b1 b2b2 b 2 phase Visibility and Sky Brightness The visibility is a complex quantity: - amplitude tells “how much” of a certain frequency component - phase tells “where” this component is located Andrea Isella :: ALMA community day :: Caltech, March 16, 2011

7. V b (meters) 0 0.5 1 b1b1 b1b1 Visibility and Sky Brightness b2b2 b3b3 Andrea Isella :: ALMA community day :: Caltech, March 16, 2011 The visibility is a complex quantity: - amplitude tells “how much” of a certain frequency component - phase tells “where” this component is located

8. 2 Antennas

9. 3 Antennas

10. 4 Antennas

11. 8 Antennas

12. 16 Antennas - Compact

13. 16 Antennas - Extended

14. 32 Antennas – C32-3

15. 32 Antennas – C32-3 – 8 hours

16. T(x,y)|V(u,v)| Gaussian  Function Constant Gaussian 2D Fourier Transform Pairs

17. T(x,y)|V(u,v)| elliptical Gaussian sharp edges result in many high spatial frequencies elliptical Gaussian DiskBessel 2D Fourier Transform Pairs

18. Fourier Transforms of Images From http://carmilumban-ap186.blogspot.com

19. Model ImageConvolved Model“Observed” Image 2 hour observation Model: Early Science Compact Configuration

20. Model: Full Science Main Array - Compact Model ImageConvolved Model“Observed” Image 2 hour observation Large scale emission: Observe with ACA and possibly TPA

21. Model: Full Science Main Array - Extended Model ImageConvolved Model“Observed” Image 2 hour observation

22.  Angular resolution  ~ λ/B max, where B max is the longest baseline  Maximum angular scale  the source is resolved if θ>λ/B min, where B min is the minimum separation between apertures.  Field of view of the single aperture  ~ λ/D, where D is the diameter of the telescope. Source more extended than the field of view can be observed using multiple pointing centers in a mosaic. Characteristic Angular Scales An interferometer is sensitive to a range of angular sizes λ/B max < θ < λ/B min Since B min > D, an interferometer is not sensitive to the large angular scales and cannot recover the total flux of resolved sources (you need a single dish, e.g., CSO, APEX, IRAM 30 m, ALMA total power array, CCAT).