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Interferometry Discuss Group & Python TutorialPowerPoint Presentation

Interferometry Discuss Group & Python Tutorial

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Interferometry Discuss Group & Python Tutorial

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Interferometry Discuss Group & Python Tutorial

Adam Leroy & Scott Schnee (NRAO)

February 28, 2014

- 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/

- 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

- 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

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

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

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

2D Fourier Transform Pairs

- T(x,y)

- |V(u,v)|

Function

Constant

Gaussian

Gaussian

2D Fourier Transform Pairs

- T(x,y)

- |V(u,v)|

elliptical

Gaussian

elliptical

Gaussian

Disk

Bessel

sharp edges result in many high spatial frequencies

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

Convolved Model

Model Image

“Observed” Image

2 hour observation

Model Image

Convolved Model

“Observed” Image

Large scale emission: Observe with ACA and possibly TPA

2 hour observation

Model Image

Convolved Model

“Observed” Image

2 hour observation

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).