Tracking, Pointing, and Focus

• 4 Tracking, Pointing, and Focus 31
  • 4.1 Tracking Capabilities
    • 4.1.1 Ephemeris Objects
  • 4.2 Tracking Limits
    • 4.2.1 Elevation Limits
    • 4.2.2 Azimuth Limits
  • 4.3 Tracking Error Tolerance
  • 4.4 Sequence of Position Computation Operations
  • 4.5 Subreflector Beam Throw
  • 4.6 Pointing
    • 4.6.1 Continuum and Spectral Line Five-Points
      • 4.6.1.1 Continuum Five-Point Analysis
      • 4.6.1.2 Spectral Line Five-Point Analysis
    • 4.6.2 Pointing Model Equations
    • 4.6.3 Pointing Data Analysis Program
  • 4.7 Focus
    • 4.7.1 Axial Focus
    • 4.7.2 Determining the Axial Focus
    • 4.7.3 Lateral Focus

4.1 Tracking Capabilities

 The 12 Meter Telescope can track both stationary (sidereal) sources or fast moving sources such as the Sun, Moon, planets, comets, or satellites (called “ephemeris objects"). The positions of stationary sources may be entered into source catalogs by the observer or directly into the on-line system by the operator. Stationary source positions may be given as

• Apparent equatorial positions (already precessed),
• Equinox B1950 or J2000 equatorial positions, or
• Galactic coordinate positions (lII, bII).

An example of the 12m catalog format is the following:

18:27:17.3       01:13:23.0       B1950 SERMM1        8.0       LSR     RAD

18:27:28.0       01:10:45.0       B1950 SERMM2        8.0       LSR     RAD

18:27:27.3       01:11:55.0       B1950 SERMM3        8.0       LSR     RAD

18:27:24.7       01:11:10.0       B1950 SERMM4        8.0       LSR     RAD

18:27:18.9       01:12:02.0       B1950 SERMM5        8.0       LSR     RAD

18:27:25.4       01:12:02.0       B1950 SERMM6        8.0       LSR     RAD

18:27:22.0       01:12:30.0       B1950 SERCTR         8.0       LSR     RAD

where

column 1 = right ascension (HH:MM:SS.S) or galactic longitude (DDD.DDDDD),

column 2 = declination (DD:MM:SS.S) or galactic latitude (DD.DDDDD),

column 3 = coordinate epoch (B1950, J2000, APPARENT, or GALACTIC),

column 4 = source name,

column 5 = source velocity,

column 6 = source velocity reference frame (LSR, HEL, GEO, or TOP), where

LSR = local standard of rest velocity reference frame,

HEL = heliocentric velocity reference frame,

GEO = geocentric velocity reference frame, and

TOP = topocentric velocity reference frame,

column 7 = source velocity type (RAD, OPT, or REL), where

RAD = radial velocity type, 

OPT = optical velocity type, and

REL = relativistic velocity type

The sky frequency equations corresponding to the above velocity types are given in Equations 5.4.

4.1.1 Ephemeris Objects

To track ephemeris objects (comets, asteroids, etc.), the control system requires three positions, centered upon the present time. The tracking algorithm then makes a cubic spline interpolation to determine the source position at the specific time of observation.

The observer must prepare a catalog in the correct format in order to observe ephemeris objects other than the planets and the Moon. The basic format needed by the control system is show below.

OBJ Hyakutake

VELFRAME LSR

VELTYPE RAD

#

# Ephemeris for Hyakutake, 0.000 H 9 APR 1996 to 23.700 10 APR 1996

#

D  45.7745  D  41.3975  J  50182.000720  0.00  55.84

D  45.7705  D  41.3822  J  50182.017387  0.00  55.86

D  45.7662  D  41.3670  J  50182.034053  0.00  55.89

D  45.7620  D  41.3517  J  50182.050720  0.00  55.91

D  45.7580  D  41.3363  J  50182.067387  0.00  55.93

D  45.7540  D  41.3212  J  50182.084053  0.00  55.94

D  45.7500  D  41.3058  J  50182.100720  0.00  55.95

D  45.7463  D  41.2907  J  50182.117387  0.00  55.96

D  45.7422  D  41.2755  J  50182.134053  0.00  55.97

D  45.7385  D  41.2603  J  50182.150720  0.00  55.97

D  45.7347  D  41.2452  J  50182.167387  0.00  55.97

D  45.7313  D  41.2300  J  50182.184053  0.00  55.97

where the first three lines are descriptors for the object name, velocity frame, and velocity type. The next three lines are comments. Each column thereafter is defined as follows:

D 45.7745 = the topocentric right ascension in degrees.

D 41.3975 = the topocentric declination in degrees.

NOTE: You can also use a geocentric right ascension and declination in the last two locations, but if you do you must enter the correct horizontal parallax (see below).  

J 50182.000720 = the Modified Julian Date (mjd) of this record in the TT (Terrestrial Time, which used to be called Terrestrial Dynamical Time, or TDT) system. Note that  TT = UTC + 63.184 sec after June 30, 1997.

0.0 = the horizontal parallax (the angle from you to the object to the center of the earth in arc seconds). The horizontal parallax is zero in this case since we are using topocentric coordinates. If one uses geocentric coordinates, the horizontal parallax must be non-zero and is given by:

HP = arcsin

 geocentric distance of object

55.84 = the topocentric velocity. Non-planets default to topocentric velocities. Planets default to geocentric positions and velocities.

After you create the ephemeris put it in a file with the extension eph in the observers home directory - /home/obs/ini/comet.eph for example.

If you do not have an ephemeris generation program, we have a copy of the “TBEG4" two body ephemeris generator program written by Don Yeomans which you can use. This program will produce a 12m-format ephemeris file given a set of orbital elements. Contact Tom Folkers if you would like to use this program.

4.2 Tracking Limits

4.2.1 Elevation Limits

Mechanical limits constrain the movement of the telescope on both the azimuth and elevation axes. Under normal source-tracking operation, the control system software prevents the telescope from moving into these limits. The telescope is also equipped with fail-safe hardware limit switches that will turn the drive motors off and apply the brakes before the telescope can be damaged. When the telescope reaches a lower elevation of 15.0º, it begins to depress a safety spring on the elevation stop. Tracking can continue until the elevation drive motor begins drawing excessive current; this usually occurs at an elevation near 14.5º. A final limit switch is tripped at 13.8º elevation.

The control computer will allow a source to be tracked up to an elevation of 90º. The pointing equations diverge at the zenith, however, and elevations greater than 88º should be strictly avoided during observations. For routine observations, we recommend that you avoid elevations >80º if possible, since both tracking and pointing degrade in that range. For maintenance purposes only, the telescope can be driven to an elevation of 92º before tripping a final limit switch.

4.2.2 Azimuth Limits

To prevent the over-wrapping of cables, the telescope has hardware and software azimuth limits. The control system will not allow the telescope to rotate through 66.8º azimuth to acquire or track a source. As they rise, sources with declinations between 27º and 38.75º will pass through 66.8º azimuth above 15º elevation. When a rising source reaches an azimuth of 66.8º, the telescope will rotate 360º to re-acquire the source. The region of the sky where azimuth transitions occur is displayed in Figure 4.1. If an integration is in progress when the transition azimuth is reached, the integration is halted while the telescope rotates around to re-acquire the source. The integration is resumed when the source is reached again. If it is undesirable for this to happen, you should cease the integration before reaching the transition azimuth.

4.3 Tracking Error Tolerance

The 12 Meter Telescope is vulnerable to tracking errors produced by wind gusts. The tracking software has a provision for rejecting from the integration any data sample that was taken with the telescope off source. The basic timing cycle of the 12m control system is 100 milliseconds (0.1 sec). After each 100 ms interval, the system checks for error conditions such as tracking errors or a loss of frequency phase lock. If an error condition is detected, the data sample collected during the last 100 ms interval is not averaged with the rest of the data.

You can choose how much tracking error you are willing to accept. This number is called the “tracking tolerance" and is displayed on the on-line status monitor in the lower left-hand corner under the heading “TOL". The 12m typically experiences 3-4” tracking errors under calm conditions. The tolerance is usually not set to less than 5” for this reason. Typical choices for the tolerance are 5” for 1.3 mm and shorter wavelength observations, and 10” for 2 and 3 mm observations. Figure 4.2 shows the amount of signal that is lost by a given pointing error, expressed as fractions of a FWHP beamwidth.

4.4 Sequence of Position Computation Operations

The sequence of computer operations that is executed when seeking and then tracking a source is as follows:

1. Input RA-DEC (B1950, J2000, or current epoch) or galactic (lII,bII).

2. If B1950 position, precess to current date. If galactic coordinates, first precess to epoch B1950 The precessed position of a source is computed only when the source is first accessed.

3. If source is an ephemeris object, interpolate to current UT.

4. Do spherical coordinate conversion from RA-DEC to AZ-EL.

5. Add azimuth and elevation encoder corrections as computed from Equations A.1, A.2, A.9, and A.10 (Appendix A). 

6. Add azimuth and elevation pointing corrections.

7. Command telescope to the correct AZ-EL position.

8. Once every 10 seconds, go back to spherical coordinate conversion. Between loops, extrapolate AZ and EL drive rates every 100 ms to compute positions.

Figure 4.1: Local hour angle and declination versus azimuth and elevation for the 12m. The hatched region indicates the range of source declination where the telescope will undergo a 360º azimuth transition while tracking a rising source.

Figure 4.2: Loss of signal due to pointing error.

4.5 Subreflector Beam Throw

The 12 Meter Telescope is equipped with a nutating (chopping) subreflector that is used for beam-switched observations in both the spectral line and continuum modes. Other observing modes, such as position switching, are made with the subreflector locked in place. Obviously, the throw position of the subreflector, whether it is chopping or locked in place, affects the pointing of the telescope. The current 12m subreflector switches only in azimuth, although mount misalignments may produce a small component in the elevation direction (usually these are less than 1-2”). The pointing equations for the 12m are set up for 0 offset in subreflector position, i.e. with the subreflector axis aligned with the electrical axis of the primary reflector. When the subreflector is offset so that the telescope must be moved in the positive azimuth direction to bring the source into the beam, the subreflector is said to be in the “+BEAM”. When the telescope must be moved in the negative azimuth direction to acquire the source, at least with respect to the +BEAM, the subreflector is in the “-BEAM”. Figure 4.3 illustrates this convention. Both the spectral line and continuum backends are configured so that the +BEAM signal is positive and the -BEAM signal negative.

Figure 4.3: Subreflector +Beam/Beam conventions.

The control system software takes account of the subreflector throw setting when positioning the telescope. The computer does not read the subreflector setting automatically, however; it depends upon the operator to manually set the throw value. The subreflector is physically set by turning two dials on the subreflector control chassis. Default values of subreflector throw are stored in the computer: for example, ±2′ for 3 mm and ±1′ for 1 mm. You can check the beam throw by making a continuum cross-scan on a strong source.

Continuum mapping rows are explained in detail in Chapter 6.

4.6 Pointing

    You are responsible for determining the residual azimuth and elevation pointing offsets, relative to the nominal telescope pointing. These offsets are usually of the order 10″- 20″ and often vary across the sky. In particular, the offsets often show an elevation dependence. The pointing of the 12m may drift over a period of several months by 10″ or so, and you are cautioned not to assume that old pointing data are still valid. If a project requires accurate pointing, observers should budget 5 - 10% of their total observing time to pointing checks. High frequency projects, for which the FWHP of the main beam is 30″ or less, obviously require more attention to the pointing.

You may perform pointing checks in either continuum or spectral line mode. Pointing sources must have an angular brightness distribution that is compact compared to the antenna beam. In addition, they must have well-determined positions and must be strong enough to point on in a reasonable amount of time, e.g. 10 minutes or less. The best pointing sources are the major planets Venus, Mars, Jupiter, Saturn, and Uranus, observed in continuum mode. These sources have strong flux densities throughout the millimeter band, although Uranus is faint at 3mm and longer wavelengths. To obtain complete sky coverage, particularly north of the zenith, the planets must be supplemented with other pointing sources. A tabulation of these sources and approximate flux densities at 3 and 1 mm is given in Table 4.1. This table includes the sources traditionally used at the 12m together with sources found useful at the IRAM 30m telescope. The sources with no listed flux density are on the order of 1 Jy in strength. It should be noted that the flux densities of many of the extragalactic sources in the table can be highly time-variable. For an up-to-date listing of measured 3mm fluxes, see http://dopey.haystack.edu/cmva/quasar.list.

The spectral line emission from a number of sources can be used for pointing purposes. Emission from rotational transitions of CO, HCN, and SiO are often strong enough and angularly compact enough to provide good pointing results. A list of spectral line pointing sources and their strong molecular emission lines are listed in Table 4.2.

4.6.1 Continuum and Spectral Line Five-Point Measurements

The five-point mapping option is the standard observing technique for determining the antenna pointing of the 12 Meter Telescope. Continuum five-point measurements can also be used to measure the flux density of a strong source with the highest precision, or the flux density of a source whose position is not exactly known. The five-point map consists of five successive ON/OFF sequences (for continuum and beam-switched spectral line measurements), or five successive ON and OFF measurements (for position-switched spectral line measurements), or five successive ON measurements with one associated OFF measurement (for total power spectral line measurements). The five sequences or ON measurements are positioned in azimuth and elevation relative to the nominal source position, as shown in Figure 4.4. The numbers identifying the positions give the time order in which the sequences are taken. The offset for each position (“HP” in Figure 4.4), is a selected offset (in arcsec) that is usually chosen to be close to half the HPBW of the telescope at the observing frequency. HP should be somewhat larger if the source is extended; for a planet that is resolved by the beam, chose HP to be approximately the semi-diameter of the source.
 

Table 4.1: Galactic and Extragalactic Continuum Pointing Sources