DIAGNÓSTICO DE LA SITUACIÓN ACTUAL
4.5. LA INFRAESTRUCTURA VERDE EN EL MARCO DE LAS POLÍTICAS SECTORIALES
4.5.1. La Infraestructura Verde en las normas básicas del Estado
CLEAN algorithm
V(u,v) V(u,v)
Above:
Above: sampling sampling of the of the VisibiVisibilitylity function in uv-plane is incomplete function in uv-plane is incomplete
FT
FT of the sampling function FT of the sampling function produces the Point Spread produces the Point Spread Function (PSF)
Function (PSF) usually referrusually referreded to as the DIRTY BEAM in radio to as the DIRTY BEAM in radio astronomy
astronomy. Note (above) . Note (above) thethe high side-lobes that extend far high side-lobes that extend far from the central response.
from the central response.
In radio astronom
In radio astronomy we know the PSF very well - y we know the PSF very well - its just the its just the FT of the sampling function FT of the sampling function in thein the uv-plane. The sampling function has a value of “1” where we have measured data and “0”
uv-plane. The sampling function has a value of “1” where we have measured data and “0”
everywhere else.
everywhere else.
We also have the concept of the We also have the concept of the
“dirty image” (sometime also
“dirty image” (sometime also
“dirty map”) - this is the fourier
“dirty map”) - this is the fourier inversion of the Visibility function:
inversion of the Visibility function:
Dirty image Dirty image
W
We can write that te can write that the dirty ihe dirty image is the convolution of the true image with mage is the convolution of the true image with the dirty the dirty beambeam (sampling function):
(sampling function):
IIDD(x,y) = I(x,y) = I * * B B where where B B is is the the dirty beadirty beamm
The CLEAN algorithm attempts to deconvolve the dirty beam from the dirty map.
The CLEAN algorithm attempts to deconvolve the dirty beam from the dirty map.
In its simplest
In its simplest guise (Hogbom CLEAN) it works as follows:guise (Hogbom CLEAN) it works as follows:
(i)
(i) Assume the sky is +ve and t Assume the sky is +ve and that sources can be represented by a collectihat sources can be represented by a collection of point source deltaon of point source delta functions.
functions.
(ii) make the dirty map, and
(ii) make the dirty map, and find the position and intensity of strongest source find the position and intensity of strongest source in mapin map (iii) subtract some scaled fraction (e.g. 10%)
(iii) subtract some scaled fraction (e.g. 10%) of the dirty beam response at of the dirty beam response at this position from the dirty mapthis position from the dirty map and store the position and intensity as
and store the position and intensity as a “CLEAN component” of the dirty a “CLEAN component” of the dirty map.map.
(iv) find strongest source in
(iv) find strongest source in the new dirty map, add this to the new dirty map, add this to the CLEAN component file and repeat thethe CLEAN component file and repeat the same process many times (e.g. 1000
same process many times (e.g. 1000 iterations) until only noise is left in dirty map.iterations) until only noise is left in dirty map.
(v) The final clean map is produced
(v) The final clean map is produced by taking all the CLEAN components, adding back by taking all the CLEAN components, adding back the residual noisethe residual noise left in the dirty image (see iv),
left in the dirty image (see iv), and then convolve this image with a and then convolve this image with a Guassian that was fitted to the centralGuassian that was fitted to the central lobe of the dirty beam.
lobe of the dirty beam.
Below: WSRT dirty map and CLEAN map. Note that the side-lobes seen in the Dirty map (which Below: WSRT dirty map and CLEAN map. Note that the side-lobes seen in the Dirty map (which are artefacts associated with incomplete u-v
are artefacts associated with incomplete u-v plane coveragplane coverage) are much reduced in e) are much reduced in the CLEANthe CLEAN map
map
D
Di ir rt ty y m ma ap p C CL LE EA AN N m ma ap p
W
We will consider CLEAN in e will consider CLEAN in more detail later in this more detail later in this course - I introduce it now because you willcourse - I introduce it now because you will play with it in the practical session.
play with it in the practical session.
The
The VLA can VLA can also obalso obserserve with ve with one of one of the the VLBA VLBA antennas antennas - - “Pie “Pie TTown”. own”. This This telescope telescope increases increases thethe baseline length to 73km -
baseline length to 73km - improvimproving the resolution of the array but also adding a large whole in ing the resolution of the array but also adding a large whole in thethe uv-coverage:
uv-coverage:
This extended array can still
This extended array can still produce good images - especially for produce good images - especially for “full track” observations and “full track” observations and forfor sources located at high declination.
sources located at high declination.
The UK MERLIN array (6 telescopes spread across England) shows that even sparse arrays can The UK MERLIN array (6 telescopes spread across England) shows that even sparse arrays can produce good images from relatively poor uv-coverage:
produce good images from relatively poor uv-coverage:
MERLIN opera
MERLIN operated by the ted by the U of Manchester & SU of Manchester & STFC TFC
A MERLIN image of a nearby radio galaxy 3C293.
A MERLIN image of a nearby radio galaxy 3C293.
Not only can data from different configurations of the VLA be combined, but data can be combined Not only can data from different configurations of the VLA be combined, but data can be combined from many different radio interferometers....
from many different radio interferometers....
A very deep MERLI
A very deep MERLIN+VLA N+VLA image of a image of a radio galaxy radio galaxy in the Hubble Deep in the Hubble Deep Field North (HDF-N):Field North (HDF-N):
VLA and MERLIN data are often combined when sources present scales on MERLIN VLA and MERLIN data are often combined when sources present scales on MERLIN
VLBA - Very Long VLBA - Very Long Baseline Array:
Baseline Array: 10 VLA10 VLA style antennas spread around
Antennas are notnot connected to connected to a central correlator in a central correlator in real- real-time - telescopes are widely time - telescopes are widely separated - real-time
Operates at cm and mm Operates at cm and mm
wavelengths (90 cm to 3 mm) wavelengths (90 cm to 3 mm) Milliarcsec
Milliarcsecond ond resolutionresolution achieved at cm wavelengths.
achieved at cm wavelengths.
Very Long Baseline Interferometry (VLBI) is also a sparse array with many wholes in the uv-coverage.
Very Long Baseline Interferometry (VLBI) is also a sparse array with many wholes in the uv-coverage.
There are
There are several several VLBI arrVLBI arrays around the ays around the world:world:
EVN - European VLBI
EVN - European VLBI Network.Network.
~16 of the largest antennas in Europe, Asia and S.Africa. Part-time array ( 3 x 1 month per year).
~16 of the largest antennas in Europe, Asia and S.Africa. Part-time array ( 3 x 1 month per year).
The EVN correlator is operated by JIVE (Joint Institute for VLBI in Europe), located in Dwingeloo, The EVN correlator is operated by JIVE (Joint Institute for VLBI in Europe), located in Dwingeloo, NL.
NL.
Max. Baseline 9000 km, shortest baseline 200km. Operates at cm and mm wavelengths (90cm to Max. Baseline 9000 km, shortest baseline 200km. Operates at cm and mm wavelengths (90cm to 7mm). Milliarcsecond resolution achieved at cm wavelengths.
7mm). Milliarcsecond resolution achieved at cm wavelengths.
Has a real-time capability (e-VLBI) in which the
Has a real-time capability (e-VLBI) in which the data are corredata are correlated in real-time by connecting thelated in real-time by connecting the telescopes via optical fibre.
telescopes via optical fibre.
VLBI arrays, like the VLBA (see below) and EVN, naturally have large holes in their uv-coverage.
VLBI arrays, like the VLBA (see below) and EVN, naturally have large holes in their uv-coverage.
Using advanced image processing algorithms, good images can still be made of compact objects.
Using advanced image processing algorithms, good images can still be made of compact objects.
The EVN and VLBA often join together to form a Global VLBI Network:
The EVN and VLBA often join together to form a Global VLBI Network:
A higher resolution
A higher resolution VLBI+MERLIN+VLAVLBI+MERLIN+VLA image of aimage of a nearby radio galaxy 3C293 (see previous slides):
nearby radio galaxy 3C293 (see previous slides):
N.B. the nature and resolution of the image changes, depending on how the data from each array N.B. the nature and resolution of the image changes, depending on how the data from each array are statistically weighted. We will return to the topic of data weighting in subsequent lectures.
are statistically weighted. We will return to the topic of data weighting in subsequent lectures.
An e-
An e- VLBI image made with VLBI image made with telescopes of the EVN telescopes of the EVN and others around the and others around the world after observingworld after observing for (a) 1.5 hr, (b) 2.5 hr and (c) 12 hr:
for (a) 1.5 hr, (b) 2.5 hr and (c) 12 hr:
Note that while the noise level improves, the real improvement in the quality of the image is the Note that while the noise level improves, the real improvement in the quality of the image is the increasing cov
increasing coverage of the erage of the uv-plane as the uv-plane as the observation is observation is being made.being made.
(c) (c) (a)
(a)
(b)
(b)
VLBI array
VLBI arrays like the s like the EVN & EVN & VLBA have most of their VLBA have most of their telescopes located in the telescopes located in the NorthernNorthern
hemisphere. The uv-coverage for sources in the southern sky (-ve declinations) is poor. The EVN hemisphere. The uv-coverage for sources in the southern sky (-ve declinations) is poor. The EVN can make use of telescopes located
can make use of telescopes located in the in the Southern hemisphere at European longitudes e.g. SouthSouthern hemisphere at European longitudes e.g. South africa:
africa:
At lower so
At lower source declinations (< +15 urce declinations (< +15 degrees) the degrees) the covercoverage of the EVN age of the EVN + + VLBA array (“Global VLBA array (“Global VLBI”) becomesVLBI”) becomes
foreshortened (above left), resulting in an increasingly elongated beam and poorer uv-coverage. For the EVN this can foreshortened (above left), resulting in an increasingly elongated beam and poorer uv-coverage. For the EVN this can be improved in the
be improved in the N-S direction by incN-S direction by including Hartebeesthoek, luding Hartebeesthoek, in South Africa (above right).in South Africa (above right).