Interferometry Discuss Group & Python Tutorial

Adam Leroy & Scott Schnee (NRAO)February 28, 2014

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/

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

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/Interfero

metryDiscussionGroup2014

• http://casaguides.nrao.edu/index.php?title=PythonOverview

• http://casaguides.nrao.edu/index.php?title=ALMA_SIS14

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

| V|

b (meters)0

0.5

1

b1

=/bb1b2

=/b

b2

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

Vb (meters)

0

0.5

1

b1

b1

Visibility and Sky Brightness

b2b3

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

2 Antennas

3 Antennas

4 Antennas

8 Antennas

16 Antennas - Compact

16 Antennas - Extended

32 Antennas – C32-3

32 Antennas – C32-3 – 8 hours

T(x,y) |V(u,v)|

Gaussian

Function Constant

Gaussian

2D Fourier Transform Pairs

T(x,y) |V(u,v)|

ellipticalGaussian

sharp edges result in many high spatial frequencies

ellipticalGaussian

Disk Bessel

2D Fourier Transform Pairs

Fourier Transforms of Images

From http://carmilumban-ap186.blogspot.com

Model Image Convolved Model “Observed” Image

2 hour observation

Model: Early Science Compact Configuration

Model: Full Science Main Array - CompactModel Image Convolved Model “Observed” Image

2 hour observation Large scale emission: Observe with ACA and possibly TPA

Model: Full Science Main Array - ExtendedModel Image Convolved Model “Observed” Image

2 hour observation

Angular resolution ~ λ/Bmax , where Bmax is the longest baseline

Maximum angular scale the source is resolved if θ>λ/Bmin, where Bmin 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/Bmax < θ < λ/Bmin

Since Bmin> D, an interferometer is not sensitive to the large angular scalesand cannot recover the total flux of resolved sources (you need a singledish, e.g., CSO, APEX, IRAM 30 m, ALMA total power array, CCAT).