Testing the Laser Metrology System on the 140 Foot Telescope

Introduction

It has been proposed to use the laser rangefinder for two different metrology applications on the GBT: the surface measurement system and the precision pointing system [1], [2], [3]. The panel experiment is an attempt to simulate the surface metrology application, and it is difficult to see how we can go much further with this.

A crucial part of the precision pointing application of the rangefinders is the ability to track a moving target several hundred feet from the ground and generate its three-dimensional position coordinates with an update rate of around twice per second. The 140 Foot Telescope would be suitable for such a test, and this memo gives details on how such a test could be implemented.

To make this test valid for the GBT application involves a first cut at the requirements for both the laser rangefinders and their controlling computer in the GBT application. This is attempted in this memo by needs refinement.

System Requirements

Our initial proposal for the laser precision pointing system is shown in Figure 1. Twelve laser rangefinders surround the GBT at a radius of 70 meters. Twelve retrospheres placed around the edge of the reflector are tracked by these twelve rangefinders. Measurements of the coordinates of the retrospheres in the ground-based coordinate system may then be determined by rotating the antenna in azimuth so that each retrosphere passes over each rangefinder. Overall pointing corrections will, of course, involve measurement of the subreflector position and also the measured surface figure by these are not considered here.

Very simple-minded approximations yield figures for the required accuracy on the position determination of the retrospheres and also their rates of change of position.

Considering the GBT to have an aperture of 100 meters, to determine its angular position with respect to some reference place to an accuracy of one arcsecond, we need to know the position at the edge of the reflector to 250 µm. The maximum rate of change of range will occur at high elevation angles and will probably correspond to a rate of 5º /minute, 2º away from zenith [4]. For a rangefinder tangential to the surface, this rate corresponds to around 70 mm/sec. The practical case will be around a factor of 2 less than this and note that at high elevation angles, the position of the RF beam becomes less dependent on azimuth angle so the required accuracy on the position of the retrosphere is less at these high rates.

The conservative values are then

although these are not required simultaneously.  We should derive more accurate figures soon, but these very rough numbers are good enough for initial planning.

For the 140 Foot Telescope test, the requirements will be less stringent. The only motion when tracking a source is rotation around the polar axis at the sidereal rate. My best guess at the maximum rate of range change for a rangefinder 50 meters away from the antenna, looking at the reflector rim, is around 1 mm/sec.

An additional requirement arises from the second derivative of range with respect to time, i.e., acceleration. The GBT will exhibit many modes of oscillation varying in frequency from a fraction of a hertz up to several tens of hertz. The laser rangefinders will be a useful diagnostic tool for investigating the amplitude and frequency of these modes of oscillation.

These considerations lead to performance specifications for those laser rangefinders used for the pointing system. Two modes of operation are suggested: a normal operation mode and a diagnostic mode.

1. Normal Mode
   The normal mode for the pointing laser rangefinders will be to track retrospheres on the edge of the reflector and to periodically range to other ground-based rangefinders in order to continually reestablish the scaling due to refractive index changes. The following is suggested as a suitable output of each rangefinder:

   Time

   Target Range

   Target Velocity

   Target Acceleration

   Each rangefinder should output this information at a 2 Hz rate, i.e., an update every 500ms.
   
   There are also requirements on the update of the input coordinates to the rangefinders. In the worst case, the rangefinder will be required to track a retrosphere around 80 meters away moving at 40 mm/sec. The divergence of the beam is 1 mR, so the spot size at 80 meters will be 80mm. The maximum rate of change of the target retrosphere moving across the beam is 40 mm/sec, so an update rate to the mirror tracking servos of 5 times per second would also be appropriate. Position interpolation within the rangefinder computer would be possible and perhaps desirable.
   
   

2. Diagnostic Mode
   It is anticipated that the diagnostic mode will be useful for measuring the movements of different parts of the structure either when excited deliberately or during normal operation. Such measurements will be useful in confirming the amplitude and phase of the different modes of oscillation, for example.
   
   A suitable mode of operation would be as follows. A rangefinder locks onto a retroreflector placed at a point of interest, either tracking or stationary, and at a determined time takes a series of range measurements at a rate of one measurement every 10 ms (100 Hz). After ten seconds, these 1,000 numbers are transmitted to the controlling computer over the link with time information. By examining the output of different rangefinders, the response of the structure in different places at the same time may be measured.

Summary of Ground-Based Rangefinder Modes

The following is suggested for implementing the two modes of operation for the ground-based rangefinders. The "division of labor" between the rangefinder computers and the "controlling computer" must be discussed and firmed up soon. The following seems to be one reasonable method.

1. Pointing Mode -- Summary
   On the GBT we will assume twelve ground-based rangefinders and twelve retrospheres on the rim of the telescope. We assume that the positions of the ground-based rangefinders are known in the ground-based coordinate system. We assume that the positions of the retrospheres are know in the telescope coordinate system as determined by rangefinders on the structure. We assume that the nominal positions of the retrospheres in the ground-based coordinate system are determined by simple geometric relationships, the only two variables being telescope azimuth position and telescope elevation positions. (Note that in the 140 Foot Telescope experiment these are hour angle and declination.) The purpose of the ground-based ranging system is to continually reference these nominal positions of the retrospheres in the ground-based coordinate system to a high precision (±250 µm). This is in the presence of thermal deformations within the telescope structure. The result is that we now have 12 points on the telescope structure, the position of each now determined with respect to the ground coordinate system. These points are also accessible to the surface measuring metrology system so enabling the axis of the best-fit parabola to be directly related to the ground coordinate system. So, at least in principle, a major part of the pointing problem is solved. Not included here, of course, are corrections involving the movement of the subreflector, but these will not be considered in the 140 Foot Telescope experiment and are solvable on the GBT.
   
   
2. Pointing Mode -- Detail
   Here the "controller" refers to the "pointing controller" that we presently believe will be a SUN remote from the rangefinders communicating over Ethernet. For the 140 Foot Telescope experiment, this will certainly be the case.
   
   The "rangefinder" refers to the PC-based system within the rangefinder. The rangefinder should be capable of outputting the following time tagged data every 500 ms:
   
   

   Range

   Velocity

   Acceleration

   The rangefinder should also be capable of interpolating between mirror command signals issued by the controller once per second. Note that here the mirror movement will be smoothly tracking, in contrast to the surface measuring application.
   
   A sequence of operations is envisioned as follows:
   

   1. Calibration
      At the start of a calibration initiated by the controller, each rangefinder first calibrates itself internally (this is transparent to the controller) and then measures a distance to as many neighboring rangefinders as possible. The controller has stored coordinates and a "reference length" for each of these distances. A ration of "measured distance" to "referencing length" is taken for every measured distance, an average ratio taken, and this value then is "the scaling value" by which every measured distance will be divided by between this calibration period and the next. The "scaling value" will be nominally 1.0003 and a range of values from 1.00025 to 1.00035, depending upon air temperature and pressure, may be expected. The present scaling value should be displayed as an important parameter and the measured scaling values, along with temperature and pressure will be an important part of the data obtained from the 140 Foot Telescope experiment. So after each calibration, at least for the initial experimental work, the following should be recorded:
      

      Measured Distances

      Computed Scaling Values

      Time

      Temperature

      Pressure

      Humidity

      
      A calibration will probably take place once per minute but this should be an input variable.
      
      

   2. Tracking and Measurement
      At the end of the calibration period, the controller reads the azimuth and elevation (for the 140 Foot Telescope hour angle and declination) of the telescope and makes a decision which rangefinders will track which retrospheres. The AZ-EL coordinates for each rangefinder are then calculated and will be updated once per second until the next calibration period. Each rangefinder then outputs time tagged values of range, velocity, and acceleration at a 2 Hz rate. The mirror servo mechanisms within the rangefinders interpolate at a rate of 5 times per second.
      
      During each 500 ms period, the controller must divide the measured ranges by the scaling values, compute the position, velocity and acceleration of each retrosphere in the ground-based coordinate system (Fred Schwab is developing programs for this), fit a plane through these measured points (with corrections for initial positions of retrospheres), calculate the AZ-EL coordinates of this plane and also the angular velocity and acceleration of the plane.
      
      In the final application, this information will be combined with information regarding the position and tilt of the subreflector to yield absolute pointing for the telescope. Note that the belief is that the most significant modes of oscillation for the whole structure are below 0.2 Hz, so, in theory at least, we will have the ability to predict where the structure will be several measurement cycles ahead. Only telescope tests will comfirm this.

The 140 Foot Telescope Experiment

A block diagram of the experiment is shown in Figure 2. The declination and hour angle values are output from the Honeywell 316 onto the Ethernet via a buffer (a PC). The controller remains in the computer lab at the laser calibration building. Initially, we will start off with one retrosphere mounted on the moving structure and will demonstrate an ability to track this with one rangefinder. The other three rangefinders will then be added and the calibration procedure outlined previously will be implemented. The experiment may then be extended by adding rangefinders and retrospheres if time permits and there is general agreement.

References:

[1] "Pointing and Surface Control of GBT." J. M. Payne. GBT Memo 36.
[2] "Pointing the GBT." J. M. Payne. GBT Memo 84.
[3] "The GBT Precision Pointing System." D. Wells. GBT Memo 85.
[4] "Azimuth and Parallactic Angle Tracking near the Zenith." F. Ghigo. GBT Memo 52.

Comments or Problems:

• Please direct any comments regarding content to John Payne,
  jpayne@nrao.edu
• Regarding matters of style, please direct all comments to Ramón E. Creager,
  rcreager@nrao.edu.

This page was last modified on September 11, 1997.

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