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 surfaceaccuracy

● 1 arcsec relative pointing● Focal plane array

instrumentation● Big single dish complement

to ALMA● Binational Collaboration

● Instituto Nacional deAstrofísica, Óptica, yElectrónica. (Mexico)

● UMass-Amherst (USA)

Science Interlude....

AzTEC Image of M87

Debris diskapprox. 10 ly away

Starburst Galaxies

approx. 1010 ly away

The structure and dynamics of the debris diskis sensitive to planet formation process.

The debris disk of The debris disk of ee Eridani. Eridani. Deep LMT/AzTEC observations at 1.1 mmDeep LMT/AzTEC observations at 1.1 mm

Galactic Center with BoloCAM at 1.1mm(Courtesy John Bally/Jason Glenn)

LMT 1.1-mm

Herschel 70-micron

Brick

20 km/s cloud

50 km/s cloud

Sgr B2

“Brick" in the CMZ

left: JCMT image of the 450 micron dust continuum emission; middle: ALMA imageof the 3 mm dust continuum (e.g., Hand 2012; Rodrguez & Zapata 2013; Kaumann,Pillai & Zhang 2013; Longmore et al. 2013). Right: AzTEC image.

An incredibly dense collection of gas and dust but with little star formation. Why?

0.45mm 3mm 1.1mm

Ultra Luminous IR Galaxy: Arp 220

LMT's Killer AppGalaxy Evolution

Williams et al. 1997Hughes et al. 1998

SubMM View Optical View

What are the “Submm Galaxies”?ULIRGs at high redshift?

Ultraluminous infraredgalaxies (ULIRGs):

Dusty, LIR>1012L

Solar

High rates of Star FormationGas rich interacting/merging

Spectral energy distribution:strong peak near 100 micronfrom warm dust

Peak gets redshifted to 1 mmby z~10 Yun 2000

Surace, Sanders, & Evans 1999

Observations of Distant Galaxies

● Continuum fuxfrom dustystarbursts isalmostindependent ofredshift

● In some modelsand cosmologies,objects getbrighter with z.

TODAY'sLMT 5-sigmaIn 10 sqr arcminMap with 2 hoursIntegration time

0.55.9 2.212.4 10.313.3Age of Universe (GYr)

13.5

ZRedshift

Atacama Cosmology Telescope SurveyBright Source Followup

AzTEC ImageLocates the source at high resolution

Redshift Receiver SpectrumDetermines the Redshift

LMT: AzTEC & RSR Observations

FWHM ~ 8” (3-20 minutesintegration)

One or more CO linedetected in 8/8 sourcesobserved (15 to 30 minutesper source)

SPIRE 350um on AzTEC Harrington et al. (in prep.)

Back to Project 2

Antenna Pointing

● The LMT is fully steerable, meaning that we canpoint 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 theEast from North.

● Elevation – rotation of the reflector structure abouthorizontal axis. 0 Elevation is towards the horizon.90 degrees elevation is towards the zenith.

Good Antenna Pointing is Neededto make Good Observations

● With 32m LMT, the radio beam is 8 arcsecondsat 1.1 mm wavelength.

● We must point the antenna blindly with anaccuracy that is a small fraction of this.

● Pointing is one of the most difficult technicalchallenges 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 inthe 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 knownposition and determine pointing errors.

● Observe pointing errors over the entire sky ifpossible.

● Fit pointing model to determine coefficientsA1,A2,A3,A4,A5 and E1,E2,E3,E4,E5

● To fit this linear model, we use the standardleast 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 andprogram 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 themodel 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 oneswith small errors?

– Quantitatively, how likely is it that the residuals from the model arise fromrandom measurement errors assuming that the standard deviation ofmeasurement errors is about 1 arcsecond?

– In a graph of the residuals versus Azimuth and Elevation, do you see anysystematic trends that might indicate unmodeled effects?

● Conclusions? Do you think the antenna can point wellenough to support observations with an 8 arcsecond beam?

import numpy as npimport csv

flename = 'PointingData.csv'f = open(flename,'r') # open fler = csv.reader(f) # create csv reader

# create listsAzList = []ElList = []AzOffList = []ElOffList = []# read each row and get data from columnsfor row in r: AzList.append(eval(row[4])) ElList.append(eval(row[5])) AzOffList.append(eval(row[6])) ElOffList.append(eval(row[8]))

# create numpy arraysaz = np.array(AzList)el = np.array(ElList)azoff = np.array(AzOffList)eloff = np.array(ElOffList)

import numpy as npimport csv

flename = 'PointingData.csv'f = open(flename,'r') # open fler = csv.reader(f) # create csv reader

# create listsAzList = []ElList = []AzOffList = []ElOffList = []# read each row and get data from columnsfor row in r: AzList.append(eval(row[4])) ElList.append(eval(row[5])) AzOffList.append(eval(row[6])) ElOffList.append(eval(row[8]))

# create numpy arraysaz = np.array(AzList)el = np.array(ElList)azoff = np.array(AzOffList)eloff = np.array(ElOffList)

Example Script

We use the csv module toread the data file since itis in “column separated variable”(csv) format.

Here we create empty pythonlists to receive the data.

We read the file one row at atime.

The data in the data file is amixture of strings and floats, sowe have to evaluate each entryin the table to get it to thecorrect data type.

Finally, we want numpy arrayswith the data, since we will usethese later for our least squaresfitting routines. We convert thepython lists to numpy arrayshere.