1 VariableStep Frequency Integration in the DecadeCenturyBand Imaging 2010 Nov 45 SKA Japan Workshop Mitaka Tomoharu Kurayama Kagoshima Univ Abstract In decadecenturyband imaging we have a problem in the frequency integration ID: 657217
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Slide1
2010/11/04-05
SKA Japan Workshop
1
Variable-Step Frequency Integration in the Decade/Century-Band Imaging
2010 Nov 4-5
SKA Japan Workshop @
Mitaka
Tomoharu Kurayama
(Kagoshima Univ.)Slide2
Abstract
In decade/century-band
imaging, we have a problem in the frequency integration.We propose the variable-step frequency integration in order to minimize this problem.From the simple
simulation, synthesized beams and images become more sharp in the variable-step frequency integration.
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2Slide3
Synthesis Imaging
Synthesized images are Fourier transforms of visibilities on (u, v) planes.
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Fourier Transform
Image
Visibilities
(Observables)
RA
l
m
dec
u
v
(Taylor,
Carilli
&
Perley
ed
. 1999
)
I(
l,m
)
V(
u,v
)Slide4
Integration for Weak Sources
We can detect low-flux sources by integrating frequency points.
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Integration
of images
Integration
of visibilities
RA
l
m
dec
I
1
(
l,m
)
I
3
(
l,m
)
I
2
(
l,m
)
sensitivity
u
v
V
1
(
u,v
)
V
2
(
u,v
)
V
3
(
u,v
)
frequency
frequencySlide5
Current Data Analysis
Integrating frequency points of visibilities
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Making images with Fourier transform
frequency
Frequency-integrated visibilities
Images
RA
l
m
dec
I(
l,m
)
u
v
V(
u,v
)
u
v
V
1
(
u,v
)
V
2
(
u,v
)
V
3
(
u,v
)Slide6
What is (u, v)?
(u, v) : Projected baseline lengths in the unit of
wavelengths
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(u, v)s depend on
frequencie
s!
earth
u-direction
v-direction
w-direction
L
x
L
y
observing sourceSlide7
Problem in Decade/Century Bands
e.g.) VERA
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Decade band
22 GHz
Bandwidth ~ 0.25 GHz
1 GHz
10 GHz
We can NOT ignore
the effect of bandwidth in the case of decade/century band.
integrating areaSlide8
Visibility Gridding
Requirement of FFT :
Data points are on rectangular gridsWe need ‘gridding’ before Fourier transform
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gridding
When
the point distribution is more uniform,
We can get more points in the process of gridding, and
The quality
of image becomes more sharp.Slide9
(u, v) Loci and Frequency Step
(u, v) change with the earth’s spin.
The loci are ellipse if we can observe 24 hours.
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length
area
Frequency :
Frequency :
The numbers of points are same for
both loci
.
The point distribution is more uniform when
:
: Slide10
Simple Simulation
Considering SKA…
Band : 1 – 10 GHz10-hour observationTime step : 48 s
48 stations2010/11/04-05
SKA Japan Workshop
10
~ 5 km
~ 180 km
12 stations
~ 500 km
12 stations
24
stations
30
o
S
north
uv
loci of one baseline, one frequency pointSlide11
(u, v) Loci of One Baseline
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(u, v) Loci of All Baselines
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Sampled Grids
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462382 grids
1024 grids
1024 grids
Total : 1048576 grids
758383 gridsSlide14
Synthesized Beam
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0.109
0.122
0.235
0.371
Width of main beam is smaller.
First
sidelobe
is slightly higher.
~ 14 pixels
~ 14 pixelsSlide15
Imaging Simulation : Method
Making model visibilities with Fourier transform
Picking up the grids covered by (u, v) lociGetting simulated images with inverse transform
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model image
model visibilities
FT
inverse Fourier transform
observed image
0
0
0
0
0
0
0
0
0
0
0
0
0
0Slide16
Imaging Simulation : Result (1)
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model image
1024 pixels
1024 pixels
1024 pixelsSlide17
Imaging Simulation : Result (2)
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model image
100 pixelsSlide18
Imaging Simulation : Result (3)
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model image
25
pixelsSlide19
Summary
We have proposed a new type of frequency integration for decade/century-band imaging.
Setting the frequency step asFrom a simple simulation, we have found
The sampled points distribute more uniformly on (u, v) planeSynthesized beams and images become more sharp
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Thank you!
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