imaging_mar23

# imaging_mar23 - 1 Imaging Greg Taylor University of New...

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1 Imaging Greg Taylor University of New Mexico Spring 2011

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2 Plan for the lecture-I How do we go from the measurement of the coherence function (the Visibilities) to the images of the sky? First half of the lecture: Imaging Measured Visibilities Dirty Image
3 Plan for the lecture-II Second part of the lecture: Deconvolution Dirty image Model of the sky

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4 Imaging Interferometers are indirect imaging devices For small w (small max. baseline) or small field of view (l 2 + m 2 << 1) I(l,m) is 2D Fourier transform of V (u,v)
5 Imaging: Ideal 2D Fourier relationship Ideal visibilities( V ) True image( I ) FT  This is true ONLY if V is measured for all (u,v) !

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6 Imaging: UV-plane sampling With limited number of antennas, the uv-plane is sampled at descrete points: = X V M S V o
7 Convolution with the PSF Effect of sampling the uv-plane: Using the Convolution Theorem: The Dirty Image ( I d ) is the convolution of the True Image ( I o ) and the Dirty Beam/Point Spread Function ( B ) B = FT -1 ( S ) In practice I d = B*I o + B*I N where I N = FT -1 (Vis. Noise) To recover I o , we must deconvolve B from I d . The algorithm must also separate B*I o from B*I N .

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8 The Dirty Image FT The PSF  UV-coverage * The Dirty Image
9 Making of the Dirty Image Fast Fourier Transform (FFT) is used for efficient Fourier transformation. It however requires regularly spaced grid of data. Measured visibilities are irregularly sampled (along uv-tracks). Convolutional gridding is used to effectively interpolate the visibilities everywhere and then re- sample them on a regular grid (the Gridding operation)

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10 Dirty Beam: Interesting properties
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## This note was uploaded on 12/13/2011 for the course ASTRO 423 taught by Professor Gregtaylor during the Fall '11 term at New Mexico.

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imaging_mar23 - 1 Imaging Greg Taylor University of New...

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