Interferometry Discuss Group & Python Tutorial

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

4. Logistics • Weekly meetings in ER230, Fridays @10:30 • Switching between interferometryand Python • Check the IDG wiki for syllabus • https://safe.nrao.edu/wiki/bin/view/Main/InterferometryDiscussionGroup2014 • http://casaguides.nrao.edu/index.php?title=PythonOverview • http://casaguides.nrao.edu/index.php?title=ALMA_SIS14

5. From Sky Brightness to Visibility An interferometer measures the interference pattern produced by two apertures. 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) y x T(x,y) image plane (van Cittert-Zernike theorem) Fourier space/domain Image space/domain uv plane

6. Visibility and Sky Brightness 1 |V| 0.5 b1 b2 b2 0 b (meters) b1 =/b =/b phase • 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. Visibility and Sky Brightness 1 V 0.5 b1 b3 b2 0 b (meters) b1 • 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

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

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

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

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

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

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

22. Characteristic Angular Scales • Angular resolution • ~ λ/Bmax, where Bmax is the longest baseline • Maximum angular scale • the source is resolved if θ>λ/Bmin, where Bminis 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. An interferometer is sensitive to a range of angular sizes λ/Bmax< θ <λ/Bmin Since Bmin> 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).