Pointing and Amplitude Calibration in Theory and Practice

Jay BlanchardJoint Institute for VLBI - ERIC

IVS TOW, MIT-Haystack Observatory, May 2017Image Credit:Jim Lovell

Acknowledgements

● This talk is based off Uwe Bach’s 2015 talk of the same name.

● I have made some small changes.● Material originally also from Bob Campbell and

Alastair Gunn.

Content Part 1: Theory

● Motivation● Antenna Parameters● Effect of beam width, pointing, and focus● System noise and SEFD● Gain calibration

Why Calibrate? Calibrate What?

● For geodesy, the best possible signal-to-noise ratio is required● For astronomy, the absolute source brightness is required● For the station, regular checks of calibration parameters help to

notice problems.● The basic parameters of an antenna/receiver system that can be

calibrated or measured are:– The focus– The pointing– The aperture efficiency– The system temperature– The gain curve

● Also see the maintenance workshops and seminars:– Automated Pointing Models Using the FS (Himwich)– Antenna Gain Calibration (Lindqvist)

Antenna efficiency & temperature

● For a perfect antenna of area Aef, the power received from an unpolarised source of flux density S (in units of 1x10-26 W m-2 Hz-1, or Janskies) in a bandwidth Δν is:

● In practice we define the efective aperture in terms of the geometric surface area Ageom and an antenna efficiency ηA:

● The factor ηA is the fraction of incident power that is actually picked up by the receiver/antenna system

● The antenna efficiency is generally a function of elevation and is usually characterized by a peak efficiency (called the Degrees Per Flux Unit or DPFU) multiplied by an elevation-dependent, normalized gain curve

P=S Aef

2Δν

Aef=ηA Ageom

Antenna efficiency & temperature

● The received power from an observed radio source is equivalent to an antenna temperature Ta such that

● It follows that the antenna temperature of the radio source is

● Larger antennas, more efficient antennas and stronger sources all give larger antenna temperatures

● To find the overall antenna efficiency requires that the true antenna temperature be measured

● Generally, the relative amplitudes of a radio source and a calibration signal are measured

● While it is helpful to know the absolute efficiency of an antenna, it is only the ratio of system temperature to antenna temperature that determines the sensitivity

P=k T aΔν

T a=S Aef2 k

Beamwidth, Pointing & Focus

● The range of directions over which the effective area is large is the antenna beamwidth. From the laws of diffraction it can be shown that the beamwidth of an antenna with characteristic size D is approximately λ/D

Beamwidth, Pointing & Focus

● Most sensitivity is concentrated in a smaller solid angle that is often characterised by the half-power beamwidth (HPBW), which is the angle between points of the main beam where the normalised power pattern falls to 0.5 of the maximum

Beamwidth, Pointing & Focus

● Ideally, a radio source should be centred in the antenna main beam to prevent loss of signal

● A pointing error of 0.1 times the HPBW causes a 3% loss in signal; for an error of 0.2 HPBW, it rises to 10% and for 0.3 HPBW it becomes 22%

● Because of alignment errors, encoder offsets and deformation of the antenna, most antennas require a detailed analysis of pointing errors in order to derive a useful model for pointing corrections to within 0.1 HPBW across the entire sky

● Minor lateral offsets of the feed of up to a wavelength or so will mostly effect the pointing by biasing the main beam off the electrical axis, with very little loss of gain

● Radial offsets in focus position, however, will significantly reduce the apparent gain of the antenna

● Hence, for peak efficiency, the feed should be well within one-quarter wavelength of the radial focal point

Beamwidth, Pointing & Focus

Sub reflector

Main dishWaveguide

Receiver

2.37

cm

1.02

cm

Beamwidth, Pointing & Focus

System Noise & SEFD

● In the usual case where system noise power dominates over noise power from the source, then the net amplitude of the complex correlation coefficient is

where Vij is the visibility amplitude in Jy, β is the dimensionless factor taking into account the effects of digitisation and Ni and Nj represent the system noise of the two antennas expressed as a Source Equivalent Flux Density (SEFD) in Jy

● The SEFD is defined as the source flux density that would contribute an antenna output equal to that due to the system noise, i.e. which would double the total antenna power

● Amplitude calibration is therefore about estimating the antenna SEFD values as functions of time, elevation and frequency, and applying the resulting corrections to the raw correlation coefficients to obtain Vij

C ij=βV ij

√N i N j

● The SEFD of an antenna can be divided into two parts such that

where Ti is the system temperature in K and Gi is the antenna gain in K/Jy

● Ti is defined as the physical temperature of a load in the antenna beam that contributes the same output power as the system noise

● Gi is defined as the increase in system temperature that occurs when looking at a 1Jy source. Gi changes mainly due to elevation dependent distortions of the dish due to gravity

● The SEFD therefore depends on both changes in the system temperature and in the gain

● Antenna calibration can thus be divided into two halves – the system temperature calibration and the antenna gain calibration

● For amplitude calibration of visibilities, only the relative values of system temperature and antenna gain are necessary, i.e. SEFD

N i=T iG i

System Noise & SEFD

System Temperature

T sys=T receiver+T ground+T sky

T sky=T atmosphere×(1−e−τ /sin el)+T CMB+T RB

T sys=T calPcal−ofPcal−on−Pcal−of

● System temperature, the noise in the system, is a combination of noise from various sources:

● We can parametrize Tsky as

● System temperatures can vary unpredictably during a VLBI experiment due to changes in the receiver temperature, the spill-over, RFI etc. and so must be monitored continuously

● A secondary calibration source (usually a broad-band ‘noise cal’ signal) of constant noise temperature Tcal is periodically injected and the change in total power is compared to the power measured when this cal signal is switched off. From these measurements the system temperature Tsys can be derived via:

System Temperature

● Affected by elevation.

System Temperature

T cal=(T hot−T cold )Pcal−on−Pcal−ofPhot−Pcold

● Estimating Tsys obviously needs an accurate estimate of Tcal. This can be measured using hot and cold loads such that

● Tcal is a function of frequency and part of normal calibration procedures is to determine the dependence of Tcal on ν

System Temperature

● Radio sources used for system temperature (and gain curve) calibration must be strong (tens of Janskies), of known flux density, non-variable and point-like for the antenna/receiver used

Y - method

Gain Calibration

G (z )=DPFU ×g (z )

g (z )=(a0+a1 z+ a2 z2

+a3 z3

+…)

● For the purposes of calibration, G must be found experimentally by measuring the change in system temperature going on and off sources of known flux density

● The antenna gain can be parameterised in terms of an absolute gain or DPFU (Degrees Per Flux Unit) and an accompanying gain curve g, usually expressed as a polynomial function of elevation or zenith angle z such that the DPFU multiplied by the polynomial gives the correct antenna gain at each elevation, thus

where the polynomial g(z) is

Gain Calibration

G=Pon−source−Pof −source

P cal−on−Pcal−of

T calS

● The gain is determined by comparing the change in power going on and off a source with the change in power when switching the noise cal on and off, such that

● A convenient way to collect gain calibration data is to use the aquir program in the Field System

Gain Calibration

● Essentially, the combination of DPFU, gain curve and calibration signal temperature Tcal are all that are required to provide accurate calibration information for a given antenna

● The absolute values of these parameters are not important, only that their combination reflects the actual performance of the antenna

● How they are determined and analysed, and how they are used, is described in other workshops at the TOW

● The acquisition of accurate antenna calibration data is very much dependent on the specific features, capabilities and priorities of individual VLBI stations, but

● Tcal versus frequency should be determined regularly● Gain curve should be measured at least once per year

● The tools are already available within the Field System

Conclusions from Theory

Part 2: Generating ANTABFS files

● FS Power measurements● From the astronomer's viewpoint● antabfs and rxg files● Calibration Feedback● Running antabfs.pl & demo

Field System power measurements

● Cal signal: broad-band noise source as specific temperature (caltemp)● Total-power integrators for Mark4 racks/DBBC

● tpi: measured when cal-source is of● tpical: measured when cal-source is on● tpzero: zero levels

● cal-source “fires” only when not recording (i.e., during long-enough gaps, ~15 sec) ● tpi': a tpi measurement close in time to the cal-source firing ● tpdif: the diference (tpical – tpi') – essentially sets the scale between the

TPI counts and the physical temperature.

System Temperature from FS TPIs

● Output with cal-source on & of

● Forming the ratio of these two output powers and solving for Tsys

in terms of TPI counts gives:

● Representative tpical-tpi' value ~1000● too low → larger scatter● ~0 → dead cal source(?) ● jumps → change in attenuation; unstable cal source

VLBA-Rack differences

● Automatic Gain control keeps power-counts in a good range for the samplers

● tpgain in FS log: index for a look-up table for the AGC gain level, 256 levels

# table of dB gain setting against gain number for BBCs (256 levels) taken from nrao code subroutne "module/bblvcode.c" my ($db1,$db2); my (@gaintable)= ( -99.99, -36.16, -30.14, -26.62, -24.12, -22.18, -20.60, -19.26, -18.10, -17.08, -16.16, -15.34, -14.58, -13.89, -13.24, -12.64, -12.08, -11.56, -11.06, -10.59, -10.14, -9.72, -9.32, -8.93, -8.56, -8.21, -7.86, -7.54, -7.22, -6.92, -6.62, -6.34, -6.06, -5.79, -5.53, -5.28, -5.04, -4.80, -4.57, -4.34, -4.12, -3.91, -3.70, -3.49, -3.30, -3.10, -2.91, -2.72, -2.54, -2.36, -2.18, -2.01, -1.84, -1.68, -1.52, -1.36, -1.20, -1.05, -0.90, -0.75, -0.60, -0.46, -0.32, -0.18, -0.04, 0.09, 0.23, 0.36, 0.49, 0.61, 0.74, 0.86, 0.98, 1.10, 1.22, 1.34, 1.45, 1.57, 1.68, 1.79, 1.90, 2.01, 2.11, 2.22, 2.32, 2.42, 2.53, 2.63, 2.73, 2.82, 2.92, 3.02, 3.11, 3.21, 3.30, 3.39, 3.48, 3.57, 3.66, 3.75, 3.84, 3.92, 4.01, 4.09, 4.18, 4.26, 4.34, 4.42, 4.50, 4.58, 4.66, 4.74, 4.82, 4.90, 4.97, 5.05, 5.12, 5.20, 5.27, 5.35, 5.42, 5.49, 5.56, 5.63, 5.70, 5.77, 5.84, 5.91, 5.98, 6.05, 6.11, 6.18, 6.25, 6.31, 6.38, 6.44, 6.51, 6.57, 6.63, 6.70, 6.76, 6.82, 6.88, 6.94, 7.00, 7.06, 7.12, 7.18, 7.24, 7.30, 7.36, 7.42, 7.47, 7.53, 7.59, 7.64, 7.70, 7.75, 7.81, 7.86, 7.92, 7.97, 8.03, 8.08, 8.13, 8.19, 8.24, 8.29, 8.34, 8.39, 8.44, 8.50, 8.55, 8.60, 8.65, 8.70, 8.75, 8.80, 8.84, 8.89, 8.94, 8.99, 9.04, 9.08, 9.13, 9.18, 9.23, 9.27, 9.32, 9.37, 9.41, 9.46, 9.50, 9.55, 9.59, 9.64, 9.68, 9.73, 9.77, 9.81, 9.86, 9.90, 9.94, 9.99, 10.03, 10.07, 10.11, 10.16, 10.20, 10.24, 10.28, 10.32, 10.36, 10.40, 10.44, 10.48, 10.52, 10.56, 10.60, 10.64, 10.68, 10.72, 10.76, 10.80, 10.84, 10.88, 10.92, 10.96, 10.99, 11.03, 11.07, 11.11, 11.15, 11.18, 11.22, 11.26, 11.29, 11.33, 11.37, 11.40, 11.44, 11.48, 11.51, 11.55, 11.58, 11.62, 11.65, 11.69, 11.72, 11.76, 11.79, 11.83, 11.86, 11.90, 11.93, 11.97 );

● Values from this table are used to compute a tpi proxy given a tpi'

The digital backend: DBBC

● The FS supports two calibration schemes for the DBBC1. A non-continuous mode, works similar to MKIV racks2. Continuous calibration, cal-source is switched at a rate of 80 Hz

1. Tsys

measurements are done between scans (record=of) and only tpi is monitored at a specified interval by tpicd. 2013.058.11:01:00.29#tpicd#tpi/1l,152,1u,131,2l,138,2u,130,3l,103,3u,118,4l,91,4u,63,ia,37845

2013.058.11:01:00.29#tpicd#tpi/5l,1008,5u,986,6l,1054,6u,1009,7l,928,7u,968,8l,997,8u,930,ib,380882013.058.11:01:15.30#tpicd#tpi/1l,152,1u,131,2l,138,2u,130,3l,103,3u,118,4l,91,4u,63,ia,378732013.058.11:01:15.30#tpicd#tpi/5l,1011,5u,989,6l,1057,6u,1012,7l,931,7u,971,8l,1001,8u,934,ib,374132013.058.11:01:30.29#tpicd#tpi/1l,152,1u,131,2l,138,2u,130,3l,103,3u,118,4l,91,4u,63,ia,378762013.058.11:01:30.29#tpicd#tpi/5l,1016,5u,995,6l,1064,6u,1020,7l,938,7u,979,8l,1008,8u,940,ib,37452

2. In continuous mode the cal in on half of the observing time and both tpi and tpi' are monitored continuously by tpicd

2013.122.09:00:10.18#tpicd#tpcont/1l,453,436,1u,408,392,2l,350,336,2u,346,332,3l,402,386,3u,497,4782013.122.09:00:10.18#tpicd#tpcont/4l,511,490,4u,438,419,ia,442252013.122.09:00:10.18#tpicd#tpcont/5l,371,356,5u,338,326,6l,354,340,6u,388,373,7l,422,405,7u,395,3792013.122.09:00:10.18#tpicd#tpcont/8l,317,303,8u,277,266,ib,453972013.122.09:00:11.19#tpicd#tpcont/1l,454,436,1u,409,393,2l,351,337,2u,347,333,3l,403,387,3u,498,4782013.122.09:00:11.19#tpicd#tpcont/4l,512,491,4u,438,420,ia,451352013.122.09:00:11.19#tpicd#tpcont/5l,371,357,5u,339,326,6l,354,340,6u,389,373,7l,422,406,7u,395,3802013.122.09:00:11.19#tpicd#tpcont/8l,317,304,8u,278,266,ib,446882013.122.09:00:11.19#tpicd#tsys/1l,40.5,1u,41.0,2l,41.0,2u,40.7,3l,41.0,3u,41.4,4l,40.9,4u,40.72013.122.09:00:11.19#tpicd#tsys/5l,41.1,5u,42.0,6l,40.9,6u,40.9,7l,41.9,7u,40.9,8l,40.7,8u,40.0

What the Astronomer wants

● Tsys(t) within an experiment

● tpical-tpi' provides a tie to the temperature of the cal source at gaps● tpi provides a relative temperature scale between gaps● New: tpcont provides measured T

sys(t) for all times

● SEFD: noise in flux density units [Jy] of telescopes

● DPFU: degrees per flux unit [K/Jy] – an absolute sensitivity or gain parameter

● POLY: the gain curve as a function of elevation (or zenith angle)

● Dimensionless correlation coefficients converted to physical flux densities via geometric mean of SEFD's of two stations forming a baseline

The ANTABFS program

● antabfs.pl a perl program that inputs a FS log and rxg files to:● compute/edit tpical – tpi' values for each VC/BBC● compute/edit resulting T

sys● output an .antabfs file

● Originally written by Cormac Reynolds; subsequently supported/up- dated by Giuseppe Cimò, Jun Yang, and Jonathan Quick

● It can be obtained via anonymous ftp:ftp.jive.nlcd outgoingget antabfs.tar

● This expands into a subdirectory antabfs

● The guide is at antabfs/docs/antabfs.tex

● New Python version being worked on by Pablo at Yebes to handle continuous cal

The rxg files

● Antenna Gain Calibration workshop by Michael Lindqvist

● CL* experiments in EVN sessions

● Tcal

can be a function of frequency & time

Contents of an rxg file

Contents of an antabfs file

! For antenna: EF ! ----- Tsys information for EFLSBERG GAIN EF ELEV DPFU=1.55,1.55 FREQ=4000,5150POLY=ELEV POLY 1.04343 -1.9066E-3 2.7559E-5 -2.1536E-7 /TSYS EF FT = 1.0 TIMEOFF=0 INDEX= 'R1','R2','R3','R4','R5','R6','R7','R8','L1','L2','L3','L4','L5','L6','L7','L8'/! 122 10:48:10 scan=no0008 source=0528+134!Column 1 = R1: bbc01, 4950.49 MHz , USB, BW= 16.00 MHz, Tcal=1.69 K!Column 2 = R2: bbc01, 4934.49 MHz , USB, BW= 16.00 MHz, Tcal=1.68 K!Column 3 = R3: bbc02, 4982.49 MHz , USB, BW= 16.00 MHz, Tcal=1.70 K!Column 4 = R4: bbc02, 4966.49 MHz , USB, BW= 16.00 MHz, Tcal=1.70 K!Column 5 = R5: bbc03, 5014.49 MHz , USB, BW= 16.00 MHz, Tcal=1.71 K…!Column 9 = L1: bbc05, 4950.49 MHz , USB, BW= 16.00 MHz, Tcal=1.70 K!Column 10 = L2: bbc05, 4934.49 MHz , USB, BW= 16.00 MHz, Tcal=1.69 K!Column 11 = L3: bbc06, 4982.49 MHz , USB, BW= 16.00 MHz, Tcal=1.68 K!Column 12 = L4: bbc06, 4966.49 MHz , USB, BW= 16.00 MHz, Tcal=1.70 K!Column 13 = L5: bbc07, 5014.49 MHz , USB, BW= 16.00 MHz, Tcal=1.69 K…122 10:49.68 39.1 38.5 38.6 38.7 39.3 38.5 38.7 38.6 40.4 39.9 39.1 39.1 39.4 39.2 39.2 38.7 122 10:51.03 39.0 39.2 39.1 38.7 38.9 39.2 38.3 39.2 40.2 40.4 39.5 40.6 39.7 39.9 39.2 39.3 122 10:53.75 39.3 39.1 38.5 39.8 39.1 39.2 38.4 39.1 41.8 40.2 39.3 40.0 39.8 40.1 39.4 38.1 122 10:55.10 39.2 39.6 39.0 39.2 39.3 39.1 38.9 39.1 40.7 40.5 40.3 40.1 40.2 40.4 39.1 39.9 122 10:57.82 38.7 38.6 38.8 38.9 38.9 38.9 39.1 38.8 41.7 41.3 39.2 39.8 39.6 39.6 39.2 38.1 122 10:59.85 39.0 38.6 39.1 39.0 39.4 39.1 38.5 38.4 40.4 40.2 39.2 39.8 39.6 39.6 38.8 39.3 ! 122 11:00:00 scan=no0009 source=J2212+2355122 11:06.83 37.1 37.5 37.0 37.3 37.1 37.7 36.8 36.8 38.7 39.2 38.0 38.7 38.0 38.8 37.5 37.9 122 11:08.18 36.9 37.3 36.8 37.1 37.2 36.8 36.8 37.1 38.0 38.1 37.0 37.8 38.1 37.8 36.7 37.0 122 11:10.22 36.5 37.5 37.8 37.2 37.4 36.4 36.9 36.7 38.8 38.5 37.2 38.1 37.5 37.4 36.6 37.9

EVN calibration feedback

● JIVE-correlated experiments get “pipelined”

www.jive.nl/select-experiment

● pdf file: amplitude corrections factors by station/subband/polarization (1 = no correction needed)

● statistical summary: median amplitude correction factor & related stats per ST/SB/pol

● text file: ST/SB/pol amplitude correction factor, time resolution ~scan

EVN pipeline Amp.Cal. plot

EVN pipeline Amp.Cal. text files

statistical summary raw text file

Running antabfs.pl

● some adjustment might be required to antabfs.pl● 1st line for location of perl● $gaindir for location of rxg files● pgplot available via environment PERL5LIB

● Basic syntax: antabfs.pl logfile

● Three main steps: [1] Loop through all VCs/BBCs, showing tpdif(t), together with piece- wise linear fit & ±5σ-deviation bounds to guide editing of data [2] Compute T

sys from edited tpdif values, looping trough VCs/BBCs to

allow editing [3] Color-coded plot of T

sys for all VCs/BBCs to check consistency

➢ Much more details in the antabfs guide in the tarball

tpidiff editing key-codes

● Return: flags values outsie the green & blue N-deviation bounds● “N”: change the N in the N-deviation bounds (dflt: N = 5)● “B”: change the number of values used for the linear fits

● “E”: enter the manual editing via boxes mode● left-mouse / “A”: select the two opposite corners of a rectangle● middle-mouse / “D”: restart the current rectangle● “C”: cancels all previous defined rectangles● “Z” / “U”: makes a zoom box / unzoom● right-mouse / “X”: deletes points in defined rectangles, exits

● “Y”: accept changes made to this VC/BBC and move on the next