Download Pointing Model for the Large Millimeter Telescope Computational Physics Project 2

Pointing Model for the
Large Millimeter Telescope
Computational Physics
Project 2
Fitting a Pointing Model for the
Large Millimeter Telescope
About the LMT....
●
50m diameter millimeter-wave
telescope (32m completed)
●
●
●
●
●
75 microns RMS surface
accuracy
1 arcsec relative pointing
Focal plane array
instrumentation
Big single dish complement
to ALMA
Binational Collaboration
●
●
Instituto Nacional de
Astrofísica, Óptica, y
Electrónica. (Mexico)
UMass-Amherst (USA)
Science Interlude....
AzTEC Image of M87
The debris disk of e Eridani.
Deep LMT/AzTEC observations at 1.1 mm
Starburst Galaxies
approx. 1010 ly away
Debris disk
approx. 10 ly away
The structure and dynamics of the debris disk
is sensitive to planet formation process.
LMT 1.1-mm
Herschel 70-micron
Brick
Sgr B2
20 km/s cloud
50 km/s cloud
Galactic Center with BoloCAM at 1.1mm
(Courtesy John Bally/Jason Glenn)
“Brick" in the CMZ
An incredibly dense collection of gas and dust but with little star formation. Why?
0.45mm
3mm
1.1mm
left: JCMT image of the 450 micron dust continuum emission; middle: ALMA image
of the 3 mm dust continuum (e.g., Hand 2012; Rodrguez & Zapata 2013; Kaumann,
Pillai & Zhang 2013; Longmore et al. 2013). Right: AzTEC image.
Ultra Luminous IR Galaxy: Arp 220
LMT's Killer App
Galaxy Evolution
SubMM View
Optical View
Williams et al. 1997
Hughes et al. 1998
What are the “Submm Galaxies”?
ULIRGs at high redshift?
Ultraluminous infrared
galaxies (ULIRGs):
Dusty, LIR>1012LSolar
High rates of Star Formation
Gas rich
interacting/merging
Surace, Sanders, & Evans 1999
Spectral energy distribution:
strong peak near 100 micron
from warm dust
Peak gets redshifted to 1 mm
by z~10
Yun 2000
Observations of Distant Galaxies
Age of Universe (GYr)
13.5 13.3 12.4 10.3
5.9 2.2
TODAY's
LMT 5-sigma
In 10 sqr arcmin
Map with 2 hours
Integration time
Z
Redshift
0.5
●
●
Continuum fux
from dusty
starbursts is
almost
independent of
redshift
In some models
and cosmologies,
objects get
brighter with z.
Atacama Cosmology Telescope Survey
Bright Source Followup
AzTEC Image
Locates the source at high resolution
Redshift Receiver Spectrum
Determines the Redshift
LMT: AzTEC & RSR Observations
SPIRE 350um on AzTEC
FWHM ~ 8”
(3-20 minutes
integration)
Harrington et al. (in prep.)
One or more CO line
detected in 8/8 sources
observed (15 to 30 minutes
per source)
Back to Project 2
Antenna Pointing
●
●
The LMT is fully steerable, meaning that we can
point and track any position on the sky.
LMT moves in two directions:
●
●
Azimuth – rotation about vertical axis. 0 Azimuth is
towards the North. Position rotation towards the
East from North.
Elevation – rotation of the reflector structure about
horizontal axis. 0 Elevation is towards the horizon.
90 degrees elevation is towards the zenith.
Good Antenna Pointing is Needed
to make Good Observations
●
●
●
With 32m LMT, the radio beam is 8 arcseconds
at 1.1 mm wavelength.
We must point the antenna blindly with an
accuracy that is a small fraction of this.
Pointing is one of the most difficult technical
challenges faced by large antennas
●
Mechanical Misalignments
●
Wind
●
Thermal Distortions
How do we achieve high accuracy?
●
●
Main Solution is to create a Pointing Model.
The model includes terms which account for all
the mechanical misalignments which may be in
the system. Examples:
●
●
●
●
Azimuth Axis and Elevation Axis not perpendicular
Axis encoders don't read zero precisely when
antenna is pointer to zero.
Antenna “sags” as elevation changes, resulting in
pointing shifts
Azimuth axis not perpendicular to ground.
Physical Pointing Model
●
●
Azimuth Offset
●
Constant – Telescope Collimation (A1)
●
Sin(El) – Axis Collimation (A2)
●
Cos(El) – Azimuth Encoder Zero (A3)
●
Sin(El) Sin(Az) – Antenna Tilt (A4)
●
Sin(El) Cos(Az) – Antenna Tilt (A5)
Elevation Offset
●
Constant – Elevation Encoder Zero (E1)
●
Cot(El) – Refraction (E2)
●
Cos(El) – Bending (E3)
●
Cos(Az) – Antenna Tilt (E4)
●
Sin(Az) – Antenna Tilt (E5)
Physical Pointing Model
Azimuth Pointing Error is function of Azimuth and Elevation
Elevation Pointing Error is function of Azimuth and Elevation
Fitting the Model
●
●
●
●
Make measurements of sources at known
position and determine pointing errors.
Observe pointing errors over the entire sky if
possible.
Fit pointing model to determine coefficients
A1,A2,A3,A4,A5 and E1,E2,E3,E4,E5
To fit this linear model, we use the standard
least squares approach described in class.
Least Squares Solution (Az)
Single Observation
N Observations for the Fit
Least Squares Solution:
Project
●
Step 1: Look at the Data
●
●
●
●
See Project Description for link to data file and
program to read data.
Calculate Standard Deviation of Data before fit.
Check distribution of errors. We think measurement
error is should be about 1 arcseconds!
Step 2: Fit the Data
●
●
●
Review script given in Lecture on linear least
squares fit.
Modify to fit BOTH Azimuth AND Elevation pointing
data.
Give Parameter Estimates and estimate of errors.
Project
●
Step 3 – Assessing the Fit
●
Compute the residuals to the model fit.
●
Look carefully at residuals and address questions:
●
–
Have you improved the pointing errors by fitting the model? (Compare the
model residuals to the standard deviation of the data before the fit.)
–
Are the residuals in Azimuth the same as the residuals in Elevation?
–
Do the residuals look like they follow a normal distribution?
–
Do points with larger measurement errors have larger residuals than ones
with small errors?
–
Quantitatively, how likely is it that the residuals from the model arise from
random measurement errors assuming that the standard deviation of
measurement errors is about 1 arcsecond?
–
In a graph of the residuals versus Azimuth and Elevation, do you see any
systematic trends that might indicate unmodeled effects?
Conclusions? Do you think the antenna can point well
enough to support observations with an 8 arcsecond beam?
import
importnumpy
numpyasasnp
np
import
importcsv
csv
Example Script
flename
flename=='PointingData.csv'
'PointingData.csv'
f f==open(flename,'r')
open(flename,'r') ##open
openfle
fle
r r==csv.reader(f)
##create
csv.reader(f)
createcsv
csvreader
reader
We use the csv module to
read the data file since it
is in “column separated variable”
(csv) format.
##create
createlists
lists
AzList
AzList==[][]
ElList
ElList==[][]
AzOffList
AzOffList==[][]
ElOffList
ElOffList==[][]
##read
readeach
eachrow
rowand
andget
getdata
datafrom
fromcolumns
columns
for
forrow
rowininr:r:
AzList.append(eval(row[4]))
AzList.append(eval(row[4]))
ElList.append(eval(row[5]))
ElList.append(eval(row[5]))
AzOffList.append(eval(row[6]))
AzOffList.append(eval(row[6]))
ElOffList.append(eval(row[8]))
ElOffList.append(eval(row[8]))
Here we create empty python
lists to receive the data.
##create
createnumpy
numpyarrays
arrays
az
az==np.array(AzList)
np.array(AzList)
elel==np.array(ElList)
np.array(ElList)
azoff
azoff==np.array(AzOffList)
np.array(AzOffList)
eloff
eloff==np.array(ElOffList)
np.array(ElOffList)
Finally, we want numpy arrays
with the data, since we will use
these later for our least squares
fitting routines. We convert the
python lists to numpy arrays
here.
We read the file one row at a
time.
The data in the data file is a
mixture of strings and floats, so
we have to evaluate each entry
in the table to get it to the
correct data type.