SKA Japan Workshop 12010/11/04-05

Variable-Step Frequency Integration in the

Decade/Century-Band Imaging

2010 Nov 4-5SKA Japan Workshop @ Mitaka

Tomoharu Kurayama(Kagoshima Univ.)

SKA Japan Workshop 2

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.2010/11/04-05

SKA Japan Workshop 3

Synthesis Imaging►Synthesized images are Fourier

transforms of visibilities on (u, v) planes.

2010/11/04-05

Fourier Transform

ImageVisibilities

(Observables)

RA

lmdec

uv

(Taylor, Carilli & Perley ed. 1999)

I(l,m) V(u,v)

)(2),(),( vmulievuVdvdumlI

SKA Japan Workshop 4

Integration for Weak Sources►We can detect low-flux sources by

integrating frequency points.

2010/11/04-05

Integration of images

Integration of visibilities

)(221

)(22

)(21 )( mulimulimuli eVVddueVddueVddu

N11

RA lmdec I1(l,m)

I3(l,m)I2(l,m)

sensitivity

uv

V1(u,v)V2(u,v)

V3(u,v)

frequency frequen

cy

SKA Japan Workshop 5

Current Data AnalysisIntegrating frequency points of visibilities

2010/11/04-05

Making images with Fourier transform

frequency

Frequency-integrated visibilities

Images

RAlm

dec I(l,m)

uv

V(u,v)

uv

V1(u,v)V2(u,v)

V3(u,v)

SKA Japan Workshop 6

What is (u, v)?►(u, v) : Projected baseline lengths in

the unit of wavelengths

2010/11/04-05

►(u, v)s depend on frequencies!

earthu-direction

v-direction

w-direction

Lx

Ly

cLLcLLu

yy

xx

observing source

SKA Japan Workshop 7

Problem in Decade/Century Bands

►e.g.) VERA

2010/11/04-05

►Decade band

cLL yy

cLLu xx

cLL yy

cLLu xx

22 GHz Bandwidt

h ~ 0.25 GHz

1 GHz

10 GHz

► We can NOT ignore the effect of bandwidth in the case of decade/century band.

integrating area

SKA Japan Workshop 8

Visibility Gridding► Requirement of FFT :

Data points are on rectangular grids► We need ‘gridding’ before Fourier transform

2010/11/04-05

cLL yy

cLLu xx

cLL yy

cLLu xx

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.

SKA Japan Workshop 9

(u, v) Loci and Frequency Step

► (u, v) change with the earth’s spin.► The loci are ellipse if we can observe 24

hours.

2010/11/04-05

cLL yy

cLLu xx

length

area2

1

Frequency :

Frequency : 1

222

11

► The numbers of points are same for both loci.

► The point distribution is more uniform whenconstant

: :

SKA Japan Workshop 10

Simple Simulation►Considering SKA…

Band : 1 – 10 GHz 10-hour observation Time step : 48 s 48 stations

2010/11/04-05

~ 5 km

~ 180 km12 stations

~ 500 km12 stations

24 stations

30o S nort

h

► uv loci of one baseline, one frequency point

SKA Japan Workshop 11

(u, v) Loci of One Baseline

2010/11/04-05

constant constant

SKA Japan Workshop 12

(u, v) Loci of All Baselines

2010/11/04-05

constant constant

SKA Japan Workshop 13

Sampled Grids

2010/11/04-05

constant

constant

462382 grids

1024 grids

1024

gr

ids

Total : 1048576 grids

758383 grids

SKA Japan Workshop 14

Synthesized Beam

2010/11/04-05

constant constant

0.109

0.122

0.235

0.371

►Width of main beam is smaller.

►First sidelobe is slightly higher.

~ 14 pixels

~ 14 pixels

SKA Japan Workshop 15

Imaging Simulation : Method►Making model visibilities with Fourier

transform►Picking up the grids covered by (u, v) loci►Getting simulated images with inverse

transform

2010/11/04-05

model image

model visibilities

FTinverse Fourier transformobserve

d image

0 0

0

0

0

0

0 0 00 0 0

0

0

SKA Japan Workshop 16

Imaging Simulation : Result (1)

2010/11/04-05

model image

constant constant

1024 pixels

1024 pixels

1024 pixels

SKA Japan Workshop 17

Imaging Simulation : Result (2)

2010/11/04-05

model image

constant constant

100 pixels

SKA Japan Workshop 18

Imaging Simulation : Result (3)

2010/11/04-05

model image

constant constant

25 pixels

SKA Japan Workshop 19

Summary►We have proposed a new type of

frequency integration for decade/century-band imaging. Setting the frequency step as

►From a simple simulation, we have found The sampled points distribute more

uniformly on (u, v) plane Synthesized beams and images become

more sharp2010/11/04-05

constant

SKA Japan Workshop 20

Thank you!

2010/11/04-05

2010 Oct 24 Triathlon in Tokunoshima(swim 2 km / bike 75 km / run 21 km)