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This page describes the software and some pointers for using beam cuts through the Moon or Sun for determining the approximate correlation length-scales of errors of a telescope surface.
Please note that this page is very much a work in progress! Any corrections/suggestions very much welcome.
At the moment the software can generate a synthetic beam shape at any frequency with a surface errors which are a sum of distributions with Gaussian-spectrum fluctuations. The blockage due to the sub-reflector and the support structure is correctly taken into account.
This synthetic beam shape can then be convolved with an analytic approximation of the Moon as a tapered top hat distribution, as done in Greve et al 1998. The resulting two-dimensional map can then easily be manipulated to make cuts at various angles.
The basis of the software is the OOF (Out-Of-Focus (OOF) Holography) reduction
data package as it provides the necessary tool for modelling
beams. I’ve created for automatised installation of this software onto
the ALMA data reduction machines – see Building the OOF package: worked solutions in
particular section for building on ALMA machines. If you do not want
to edit any of the source that makes up the main OOF package then you
could just use my installation which is at /users/bnikolic/p/bnoof
on sco-red
.
The second part of the software is the “driver” script which actually
contains the commands specific to the moon scan analysis. It is named
moonscans.py
and the version current at the time of writing is
attached below. No doubt we will want to make edits to this so the
version below may not be definitive at all times.
First consult the section Explanation of my Python scripts and how to use them.
Next, try following commands, which should be used interactively and illustrate simulating a beam map using the Moon:
# Creates a pair of maps which represent the the aperture plane
# phase and amplitude distributions
mphase, mamp = mkALMAAperture(phaserms=[0.4, 0.4],
errscale=[1.0, 0.4])
# Plot the phase map
implot.plotmap(mphase, transf=0, colmap="heat")
# Plot the amplitude
implot.plotmap(mphase, transf=0, colmap="heat")
# Create the object that transforms the aperture plane
# distribution to far field. The second parameter is the
# wavelenght of the radiation
farf= pyoof.FarF(mamp,
3.5e-3)
# Create a map to store the far field pattern in
mbeam=pyplot.Map(512,512)
# Compute the far-field power pattern
farf.Power(mamp, mphase, mbeam)
# Plot the beam as on log-scale (second parameter, it has the same
# meaning as the convention in PGPLOT)
implot.plotmap(mbeam, transf=1, colmap="heat")
# Convolve with a Moon simulation
mb3=mkMoonSim(mbeam)
# Plot the beam as on log-scale
implot.plotmap(mb3, transf=1, colmap="heat")
Next, email me with questions!
# Bojan Nikolic <b.nikolic@mrao.cam.ac.uk>, <bojan@bnikolic.co.uk>.
# The initial versions of this file appeared in 2005 and was
# signficantly extended in 2006.
#
# Updated in 2010, and also deleted a lot of the GBT specific old code
"""
Tools for analysis of scans across the Moon and similar data used to
constrain error correlation scales on radio telescopes
"""
import os
import math
import numpy
from matplotlib import pylab
import pyplot
import pybnlib
import pyoof
import implot
def mkALMAAperture(npix=512,
phaserms=0.5,
errscale=1,
ant="vertex",
justPhase=False):
"""
Make an aperture plane amplitude-phase map appropriate for an ALMA
12m telescope
:note: phaserms and errscale can take lists of as parameters. In
this case it is assumed that there are multiple error distribution
present on the telescope. Example:
>>> mphase = mkALMAAperture(phaserms=[1.0, 1.0],
errscale=[1.0, 0.1],
justPhase=True)
Has two distributions, one with scale of 1m and the other with
scale of 10cm.
:param phaserms: Magnitude of errors, expressed as unweighted,
*wavefront* error in radian
:param errscale: Correlation length scale of errors in units of m
"""
tel=pyoof.MkALMA()
mphase=pyoof.MkApMap(tel,
npix,
2.0)
# Size of one pixel (in x direction, but they will be the same
# size in both)
pxscale=mphase.cs.x_pxtoworld(1,0)-mphase.cs.x_pxtoworld(0,0)
if type(phaserms) is not list:
phaserms=[phaserms]
errscale=[errscale]
else:
if len(phaserms) != len(errscale):
raise "The magnitude of errors and error scale lists must be of same length"
mtemp=pyoof.MkApMap(tel,
npix,
2.0)
for _rms, _scale in zip(phaserms, errscale):
pyplot.CorrGaussGauss(mtemp,
1.0,
pxscale/_scale*npix)
mtemp.mult(_rms/pyplot.MapRMS(mtemp))
mphase.add(mtemp)
if justPhase:
return mphase
mamp=pyoof.MkApMap(tel,
npix,
2.0)
ilmod=pyoof.GaussAmpMod( tel, mamp)
ilmod.SetSigma(0.3)
ilmod.Calc(mamp)
ALMABlockDict[ant](mamp)
return mphase, mamp
def supportWidthVertex(r):
"""
Calculate the width of the support leg for Vertex
:param r: Radius from centre of dish in metres
"""
r=r*1e3
rblock=[375.0, 3897.0, 4197.0, 4497.0, 4797.0, 5097.0, 5397.0, 5697.0, 6000.0];
hblock=[40.0, 40.0, 46.1, 48.9, 58.7, 60.8, 66.5, 72.4, 78.3,];
k1=0
for k in range(len(rblock)-1):
if rblock[k]<r:
k1=k
delta=(hblock[k1+1]-hblock[k1])/(rblock[k1+1]-rblock[k1])
return (hblock[k1] + (r-rblock[k1])*delta)*1e-3
def supportWidthMelco12(r):
"""
Calculate the width of the support leg for the 12-m Melco antennas
:param r: Radius from centre of dish in metres
"""
r=r*1e3
rblock=[375.0, 620.0, 625.0, 1470.0, 6000.0]
hblock=[48.5, 48.5, 39.0, 39.0, 76.5]
k1=0
for k in range(len(rblock)-1):
if rblock[k]<r:
k1=k
delta=(hblock[k1+1]-hblock[k1])/(rblock[k1+1]-rblock[k1])
return (hblock[k1] + (r-rblock[k1])*delta)*1e-3
def ALMABlock(m,
vblock=True,
blockf=supportWidthVertex,
hole=None):
"""
Mask areas of the antenna blocked by the support structure etc.
:param vblock: True for antennas with + type support, False for
antennas with X type support
:param blockf: Width of the support structure as a function of
radius from centre (note that this is passed in as a function)
"""
for i in range(m.nx):
for j in range(m.ny):
x=m.cs.x_pxtoworld(i,j)
y=m.cs.y_pxtoworld(i,j)
r=(x**2+y**2)**0.5
# Outside primary or inside secondary
if r>6.0 or r<0.75/2:
m.set(i,j,0)
if vblock:
rq=min(math.fabs(x), math.fabs(y))
else:
rq=min(math.fabs(x) + math.fabs(y),
math.fabs(x) - math.fabs(y)) / 2.0**0.5
if rq < blockf(r):
m.set(i,j,0);
if hole:
hx, hy, hr = hole
r=((x-hx)**2+(y-hy)**2)**0.5
if r<hr:
m.set(i,j,0);
# This dictionary defines the aperture blockage functions for each of
# the telescopes
ALMABlockDict= {"vertex":
lambda m: ALMABlock(m, vblock=True,
blockf=supportWidthVertex,
hole=(-3.530, 0.290, 0.14)),
"melco12":
lambda m: ALMABlock(m,
vblock=True,
blockf=supportWidthMelco12,
hole=(-3.572951*math.sin(math.radians(85.5)),
3.572951*math.cos(math.radians(85.5)),
0.145)),
}
def MkMoon(m,
Cm=0):
"""
A rough function to generate a simulated Moon
"""
# moon radius 15 arcmin
mradius=15 * math.pi / 180 / 60
moonfn = pybnlib.TaperedTopHatDD()
moonfn.radius = mradius
moonfn.Cm = Cm
pyplot.WorldSet( m , moonfn)
def mkMoonSim(mbeam,
Cm=0):
"""
Make a simulation of a Moon observation
:param mbeam: Map of the telescope beam
:param Cm: The softening parameter. See A. Greve et al, A&A 1998
:return: The simulated map
"""
mmoon = pyplot.Clone(mbeam)
MkMoon(mmoon,
Cm=Cm)
res=pyplot.FFTConvolve(mbeam,
mmoon)
return res
def mapCut(mbeam):
"""
Create a cut through a map
"""
pxscale=mbeam.cs.x_pxtoworld(1,0)-mbeam.cs.x_pxtoworld(0,0)
ymid= int(mbeam.ny*0.5)
dx, fnu= [], []
for i in range(mbeam.nx):
dx.append((i-mbeam.nx*0.5)*pxscale)
fnu.append(mbeam.getv(i,ymid))
return numpy.array(dx), numpy.array(fnu)
def ampMapFName(ant, npix):
return "ampchache-%s-%i.fits" % (ant, npix)
def saveAmpMaps(ant, npix):
"""
Create and save the amplitude maps
"""
p, a=mkALMAAperture(ant=ant,
npix=npix)
# Exclamation mark ensures the files are overwritten
pyplot.FitsWrite(a,
"!"+ampMapFName(ant, npix))
return a
def getAmpMap(ant, npix):
"""
Get an amplitude map.
If it exists already as a FITS file, use that. Otherwise create
and save for later reuse
"""
fname=ampMapFName(ant, npix)
if os.access(fname, os.R_OK):
return pyplot.FitsMapLoad(fname,
1)
else:
return saveAmpMaps(ant, npix)
if 1:
# Creates a pair of maps which represent the the aperture plane
# phase and amplitude distributions
mphase=mkALMAAperture(phaserms=[0.4, 0.4],
errscale=[1.0, 0.4],
justPhase=True)
mamp=getAmpMap("vertex",
512)
# Plot the phase map
implot.plotmap(mphase, transf=0, colmap="heat")
# Plot the amplitude
implot.plotmap(mphase, transf=0, colmap="heat")
# Create the object that transforms the aperture plane
# distribution to far field. The second parameter is the
# wavelenght of the radiation
farf= pyoof.FarF(mamp,
3.5e-3)
# Create a map to store the far field pattern in
mbeam=pyplot.Map(512,512)
# Compute the far-field power pattern
farf.Power(mamp, mphase, mbeam)
# Plot the beam as on log-scale (second parameter, it has the same
# meaning as the convention in PGPLOT)
implot.plotmap(mbeam, transf=1, colmap="heat")
# Convolve with a Moon simulation
mb3=mkMoonSim(mbeam)
# Plot the beam as on log-scale
implot.plotmap(mb3, transf=1, colmap="heat")