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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

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Interferometry discuss group python tutorial

Interferometry Discuss Group & Python Tutorial

Adam Leroy & Scott Schnee (NRAO)

February 28, 2014


What to expect

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

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!

    • [email protected] and [email protected]


Logistics

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


From sky brightness to visibility

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


Interferometry discuss group python tutorial

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


Interferometry discuss group python tutorial

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


2 antennas

2 Antennas


3 antennas

3 Antennas


4 antennas

4 Antennas


8 antennas

8 Antennas


16 antennas compact

16 Antennas - Compact


16 antennas extended

16 Antennas - Extended


32 antennas c32 3

32 Antennas – C32-3


32 antennas c32 3 8 hours

32 Antennas – C32-3 – 8 hours


Interferometry discuss group python tutorial

2D Fourier Transform Pairs

  • T(x,y)

  • |V(u,v)|

 Function

Constant

Gaussian

Gaussian


Interferometry discuss group python tutorial

2D Fourier Transform Pairs

  • T(x,y)

  • |V(u,v)|

elliptical

Gaussian

elliptical

Gaussian

Disk

Bessel

sharp edges result in many high spatial frequencies


Fourier transforms of images

Fourier Transforms of Images

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


Model early science compact configuration

Model: Early Science Compact Configuration

Convolved Model

Model Image

“Observed” Image

2 hour observation


Model full science main array compact

Model: Full Science Main Array - Compact

Model Image

Convolved Model

“Observed” Image

Large scale emission: Observe with ACA and possibly TPA

2 hour observation


Model full science main array extended

Model: Full Science Main Array - Extended

Model Image

Convolved Model

“Observed” Image

2 hour observation


Interferometry discuss group python tutorial

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).


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