Absolute/Relative Measurement

J. Payne

December 1991

The original concept for the active surface/pointing system envisioned using the laser rangers for measuring changes in distance only--that is, no attempt would be made to measure absolute distance. After "initialization" by other means, the laser system would monitor changes from this initial value and issue corrections based on these changes. For the surface, the initialization would be obtained by microwave holography and for the pointing, initialization would be pointing on a calibration radio source. In this scheme we measure changes in distance (or, more precisely, changes in distance differences). Zero point differences in the instruments are of no concern (provided they are stable). We recognize also that the range recorded by an individual ranger is affected by the prevailing atmospheric conditions, but all paths are affected equally (we have demonstrated this, at least in the horizontal plane) and, as pointed out by Von Hoerner, this is simply a scale change. This whole concept of initialization, measurement, and correction is viable and is certainly a good "minimum" system.

Development of the laser system has come along very well and, recently, Dave Parker and I have been discussing the possibility of using the rangefinders in a system that comes closer to an "absolute" system, although, perhaps not "absolute" in a rigid sense.

Rather than spend time defining what an absolute system is, I'll just describe a procedure that stands a good chance of giving us a well-adjusted, correctly pointed telescope early in the commissioning process.

The laser ranging system in its present stage of development is equipped with a kinematic mounting system that refers the intersection of the pointing mirror axes to a tooling ball on the mounting monument. By the end of the year, we will have three complete ranging systems. We would like to set up a permanent calibration range consisting of two monuments, one equipped to receive the laser ranger, the other with a tooling ball that will act as a mount for a retroreflector. The distance between the two tooling balls will be measured by means of an invar measuring wire or an HP laser interferometer. A range of 40 meters may be measured to an accuracy of around 100 µm. A suitable range distance would be 30 to 50 meters. For a 50 meter range, the refractive index variations are such that a 1ºC change in temperature will produce a range change of 50 µm and for this reason an indoor range where the temperature is reasonably constant would be preferable. An alternative that would be most acceptable would be two stations separated by 50 meters connected by an underground tube (a sewer pipe would be fine). With the calibration range in place, we will now be able to mount each ranger on the range and calibrate out the zero point error in each instrument. Note that the modulation frequency of each instrument is exactly the same and is known to an accuracy of 1 part in (locked to the maser) so the agreement in range reading between the instruments should be determined solely by the instrumental noise (10 to 20 µm). The agreement between the measured range and the range displayed by each instrument will depend on several factors:

  1. The corrections applied to the instrument reading for refractive index. Hopefully, the maximum error from this source will be 50 microns.
  2. Errors in the initial range calibration. Error - 100 µm.
  3. Errors in determining the "reflection point" of the retroreflector. Probably 50 µm maximum.

So, we could reasonably expect agreement between the instrument reading and the independent range calibration of around 120 µm.

This is an oversimplified picture of the calibration procedure -- probably at least two targets would be involved -- but such a procedure would be fairly simple and would result in rangers that have identical calibrations. The establishment of this permanent calibration range will enable the calibration of any ranger to be checked at any time in the future.

Use on the GBT Pointing System

In the original proposal, the pointing system had eight (or twelve) rangers around the antenna. If each one of the ranger monuments is equipped with the kinematic mount, the tooling balls on top of each monument may be surveyed, first with normal surveying instruments, then with the calibrated ranging units. Fast, computerized, measurements made between ranging units with many redundant measurements will result in a highly precise knowledge of the position of each tooling ball. The distances between the tooling balls are now used to establish a length standard for the whole telescope structure that is independent of refractive index. We now have the capability of determining the position of any point on the telescope structure in three dimensions with respect to the ground monuments in absolute length units. We can now determine the position of the reference plane absolutely with respect to the ground reference monuments. It's worth pointing out that we can also measure the absolute position of any point on the structure on which we care to put a retroreflector. A ranging unit can measure up to 1,000 ranges per second when locked onto a single retroreflector, so the dynamic behavior of any telescope member could be investigated at frequencies up to a few hundred Hz.

Use on the Surface Metrology System

With the accurate calibrated ranging units, absolute setting of the surface now becomes a possibility. In this year's budget, I had included money for a prototype surface setting tool that would measure the relative positions of the panels and also the position of the corner cube with respect to the panels. I haven't had time to work on this, but it will certainly be possible to measure the retro with respect to the surface panels to a high degree of precision. Once this is done, absolute measurement of the surface will be possible. I also included money for purchase of a laser interferometer, but, again, I simply haven't had time to do it.

Summary

The change from a relative system to an absolute system will not involve any change in the hardware. The only changes involve calibration, both of the ranging units and the retroreflectors on the surface.

The advantage of the absolute system is that, if successful, we will end up with a well-adjusted telescope very early in the commissioning process. We give up nothing -- the original relative system is still completely valid.

To do a first rate job on the calibration, a laser interferometer is highly desirable. This is included in this year's budget, although the price is a lot lower than my original estimate. The price has come down to around $25,000 from my estimate of $50,000.

What to Do?

I'd like to discuss the possibility of setting up an indoor calibration range. Possible locations would be the basement of the residence hall, the warehouse, the basement of the 300 Foot Telescope control building, or the interferometer basement. The absolute ideal set-up is shown in Figure 1. I have no idea how much it would cost.

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