J. M. Payne, D. Parker and R. Bradley
February 1992
A rangefinder is described that uses the propagation time of a beam of infrared radiation to measure distances of up to 120 meters with errors of less than 50 µm. The instrument is capable of measuring up to five different distances per second by directing an amplitude modulated infrared beam to a retroreflector located at the far end of each path. The instrument is being tested with the expectation that such a system could be used to make precise and rapid measurements on a large radio telescope. Such measurements would be used to adjust the shape of the telescope reflector surface to correct for thermal and gravitational deformations taking place during astronomical observations. It is possible that the measuring system could be extended to relate the positions of certain moving parts of the structure to a reference system fixed in the ground, thus opening the possibility of making corrections to the telescope pointing.
The National Radio Astronomy Observatory (NRAO) is constructing a fully-steerable radio telescope at Green Bank, West Virginia, to be known as the Green Bank Telescope (GBT). The telescope design provides a reflector surface which is a part of a paraboloid, so positioned that radiation can reach the reflector and then pass to one of two focal points without meeting any obstructions. This clear aperture collects radiation from a circular area of 100 meters diameter. The goal of the design is to have an instrument which performs well at radio wavelengths down to 6 mm. It may be possible in the future to lower this short-wavelength limit to 3 mm; this depends on several factors, one of which is the outcome of the present work.
To achieve satisfactory performance at short wavelengths, a radio telescope
must meet two main requirements:
These can be thought of as the "surface" and "pointing" requirements; the precision with which they must be met is related to the shortest wavelength at which the telescope is to be used, and both are very dependent on the environmental conditions at the telescope site. As an example, if the GBT were being used at a wavelength of 3 mm, it would be expected to have a surface whose departures in shape from perfection had an RMS value of at most 0.2 mm, and the astronomer would wish to point the telescope beam to within one arcsecond of any desired point in the sky.
The most significant environmental effects are due to wind and temperature. Even in the absence of wind, unavoidable temperature variations result in a short wavelength limit of approximately 8 mm for a steel structure the size of the GBT. Winds can somewhat reduce temperature differentials across the structure, but wind is a major enemy of good pointing. As the telescope moves in elevation, many parts of the structure deform as the relative direction of the force of gravity changes. Although these deformations can to some extent be computed, it is not easy to allow for all their effects.
A rangefinder system for the GBT, based on the design outlined in this paper,
is being planned to carry out the following tasks:
The reflector surface of the GBT has been designed to facilitate the measurement and adjustment of the surface. 2,004 accurately made reflective panels are mounted onto a steel backup structure, the surface of each panel deviating from the required parabolic surface by less than 75 µm RMS. In order to maintain the correct surface shape in the presence of deformations in the backup structure, connections between the surface panels and backup structure are made through linear actuators located at each junction of four panel corners. The reflecting surface is then a continuous sheet that may be adjusted to remove both the gravitationally-induced deformations resulting from tilting the telescope and thermally-induced changes in the backup structure. These deformations will change slowly compared to the speed at which the surface can be measured. Wind-induced deformations, however, will be too rapid to be corrected by movements in the main surface so, at least in the early years of operation, short wavelength operation will be restricted to calm conditions.
The proposed metrology system for measuring the surface of the antenna is shown in Figure 1. Three rangefinders located on the feed arm support will measure the distance to every one of 2,209 retroreflectors, each one of which is located directly above a surface adjusting actuator. Each rangefinder may measure a distance to a surface retroreflector and also to each of its neighboring rangefinders. The range data will then be processed in a computer to give the best-fit paraboloid surface. The adjustment required at each actuator to correct the departure from the best-fit surface will then be calculated and sent as a command to the actuator.
At its shortest operating wavelength, the GBT will have a diffraction beam of approximately seven arcseconds and accurate pointing of this beam presents a formidable problem. The determination of the best-fit surface is the first step towards a solution, since this means that the location of the paraboloid and the direction of its axis are known in reference to the surface measuring rangefinders. The position of these rangefinders with respect to fixed points on the ground will be derived using measurements from 12 ground-based rangefinders surrounding the telescope. If these ranges are known to an accuracy of 50 µm, the telescope beam direction will be known to an accuracy of approximately one arcsecond over most of the sky.
The specifications for the rangefinder result from the requirements of both accuracy and measurement speed. The accuracy requirement is straightforward and stems from the precision required in the surface setting and pointing. The speed of measurement is dictated by the rate at which the ranges to be measured are changing due to thermal effects and the excitation of various modes of oscillation of the telescope structure. An instrument with an accuracy of 50 µm for ranges up to 120 meters, capable of measuring five ranges per second, is needed to meet these requirements.
Many commercial rangefinders are available [1], but none of these come close to meeting the required accuracy. Several experimental instruments have been constructed [2], [3], but none have demonstrated both the required speed and accuracy in an outdoor environment. The instrument described in this paper demonstrates both improved accuracy and speed over previous instruments.The improved accuracy is a result of increased modulation frequency, made possible by the availability of low-cost laser diodes developed for the consumer electronics industry. The improved measurement speed stems from a high signal-to-noise ratio, the result of higher modulated power levels and a more sensitive detector. This is aided by the digital signal processing now available using inexpensive personal computer technology.
[Principle of Operation] [Block Diagram] [Transmitter] [Receiver] [Oscillator] [Steering Mirror] [Phase Detection]
The principle of operation of the method is shown in
Figure 2. An intensity modulated light
beam is transmitted over the path to be measured, is reversed in direction
by a retroreflector at the far end of the path, and is returned to the
instrument. The phase of the intensity modulation envelope of the returned
beam is retarded with respect to the phase of the outgoing beam by
where d is the distance
to be measured and lambda is the wavelength of the intensity modulation envelope
and depends on the group refractive index of the atmosphere. If
, the phase will be
retarded by more than one cycle and ambiguities in distance reading
arise. The phase detector output in
Figure 2 is proportional to
where
is a constant and
. The phase detector
repeats every 2 Pi radians and will be
*2*Pi
where 
and n is an integer.
The instrument described here uses a modulating frequency of 1.5 GHz so the output of the phase detector will repeat every 10 cm. In some applications, this ambiguity is resolved by a change of modulation wavelength but here all distances should be known well enough so that resolving the ambiguity is unimportant.
[Block Diagram] [Transmitter] [Receiver] [Oscillator] [Steering Mirror] [Phase Detection]
A detailed block diagram of the instrument is shown in Figure 3. The transmitter is a laser diode emitting at a wavelength of 780 nm. Sinusoidal variation of the current through the diode modulates the intensity of the transmitted beam which is directed to the distant retroreflector by a series of mirrors. The final mirror is a computer-controlled beam steering mirror which also accepts the expanded returned beam from the retroreflector. Careful optical alignment ensures that the transmitted and received beams are coaxial. The divergence of the transmitted beam is such that the beam received at the distant retroreflector has a diameter several times that of the retroreflector. Consequently, positioning of the light beam with respect to the retroreflector is not critical; an angular positional accuracy of 20 arcseconds is more than adequate.
The returning light beam is focused onto a fast silicon detector, the resulting electrical signal is amplified and then mixed with a frequency offset from the transmitter frequency by 1 kHz. The phase of the resultant 1 kHz intermediate frequency is directly related to the phase of the 1.5 GHz modulation envelope of the returned signal and is a measure of the path length to the retroreflector with the restriction of the ambiguity previously mentioned.
In order to calibrate slow drifts of the zero point of the instrument, the beam steering mirror is used to measure a reference path within the instrument at regular intervals. One calibration measurement per minute is sufficient to reduce the zero point error to less than 5 µm.
The layout of the instrument is shown in Figure 4 and Figure 5. An exploded view of the optical path is shown in Figure 6. The instrument is constructed on an aluminum base with three tooling balls arranged on the underside in such a manner as to form a kinematic mounting to a fixed mount either on the ground monuments or the telescope. A photograph of the complete rangefinder is shown in Figure 7.
The beam steering mirror is controlled by a personal computer that also calculates the phase difference between the 1 kHz reference frequency and the 1 kHz intermediate frequency. This instrument computer can act in a stand-alone mode or may be controlled via a serial link from a central computer. A typical sequence of operations would be for the central computer to issue a series of retroreflector positions, the instrument computer then drives the beam steering mirror to the first of these, computes a range, stores the result and moves on to the next retroreflector. At the end of the sequence, all the measurements are passed to the central computer.
The instrument uses several commercially-available parts, but some components especially critical to its performance deserve a more detailed description than given above. Some of these components are shown in Figure 8.
[Principle of Operation] [Transmitter] [Receiver] [Oscillator] [Steering Mirror] [Phase Detection]
The output of the transmitter laser diode is modulated by varying the bias current about a fixed dc value. The matching and bias circuitry is shown in Figure 9. To obtain a usable modulation depth, the 1.5 GHz RF modulating signal must be power matched to the diode impedance (approximately 10 ohms) in the presence of the parasitic capacitance and inductance associated with the diode package. The package lead inductance is series resonated at 1.5 GHz using a chip capacitor. The dc bias is supplied to the diode through a RF choke. The diode impedance is transformed to 50 ohms using a microstrip quarter-wave transformer. A return loss of less than -15 dB was measured at the transmitter RF input port. A modulation depth for an RF drive level at 1 mW is estimated to be 30%. The laser diode and all associated biasing components are contained in a well-shielded enclosure. The collimated 1.5 x 2.0 mm beam emerges from the transmitter through a small aperture.
[Principle of Operation] [Block Diagram] [Receiver] [Oscillator] [Steering Mirror] [Phase Detection]
The circuit diagram for the receiver is shown in Figure 10. The receiver consists of a photodetector, RF amplifier (20 dB) and double-balanced mixer. The 1 kHz IF signal, which is dc isolated from the mixer, is further amplified (x300) using low-noise op-amp circuits. The RF components are interconnected using 50 ohm microstrip and all the components are mounted within a metallic enclosure. Particular care was taken to filter all power supply connections.
Leakage of signals at the transmitter frequency into the receiver circuits is highly undesirable and will lead to a nonlinear response to changes in target distance. In order to keep the resulting errors below 10 µm, any leakage signal at the phase detector must be less than one-thousandth of the voltage resulting from the optical return signal. This level of isolation requires some care in design and construction.
[Principle of Operation][Block Diagram] [Transmitter] [Oscillator] [Steering Mirror] [Phase Detection]
The phase of the returned signal is measured using digital signal processing techniques. To achieve an accurate measure of the phase, the 1 kHz IF signal is sampled at 64 samples per cycle, thus requiring high spectral purity for both the 1.5 GHz transmitter and the 1.5 GHz + 1 kHz local oscillator. Any noise on either of these two oscillators at a frequency offset 1 kHz from the desired frequency will add noise to the 1 kHz intermediate frequency and, consequently, degrade the accuracy of the range measurement.
Another requirement in the design of the oscillator system is that of absolute
stability. An accuracy of 10 µm in a range of 120 m is better than 1
part in 
, so the stability
of the oscillators must be greater than this. A hydrogen maser was available
at the site where the instrument was tested so the 100 MHz output from the
maser was used as the frequency standard, giving a long-term stability of
1 part in 
.
The oscillator circuits are shown in Figure 11. A commercially-available X15 multiplier accepts the 100 MHz standard and outputs a stable 1.5 GHz modulating signal to the laser diode. A 1 kHz signal internally generated in the instrument's computer serves to offset the local oscillator from the transmitter frequency by 1 kHz and is also used as the reference against which the phase of the returned signal is compared. The local oscillator frequency is generated by a voltage-controlled crystal oscillator.
A phase-lock loop using the reference signal as an offset frequency locks this oscillator to 1 kHz above the 1.5 GHz transmitter frequency.
NOTE: The first several units used the prototype oscillator assembly described here, but the final production run of 20 instruments used a commercially constructed unit with a slightly different configuration.
[Principle of Operation] [Block Diagram] [Transmitter] [Receiver] [Steering Mirror] [Phase Detection]
The basic requirements of the beam steering mirror are a positioning accuracy of around 20 arcseconds and an ability to switch between positions separated by approximately 2 degrees in less than 70 ms. This follows from the requirement to measure five points per second on the surface of the GBT (we assume that adjacent measurement points will have a separation of one panel width). If we allow 128 ms integration time per point, then 72 ms remain for mirror movement and settling.
Motion in two orthogonal axes is provided by a simple two-axes mount, each
axis being driven by a direct drive torque motor. Each axis position is sensed
by an incremental encoder having a resolution of
pulses per
revolution. A commercially-available servo controller card is used to complete
a closed-loop servo for accurate positioning of the mirror and contains the
hardware required to realize a high performance positioning servo without
the need for velocity sensors or analog compensation.
[Principle of Operation][Block Diagram] [Transmitter] [Receiver] [Oscillator] [Phase Detection]
A 16-bit, analog-to-digital converter, synchronized to the 1 kHz reference
signal, is used to sample the 1 kHz signal into a sequence of samples
. The Fourier components
of the fundamental harmonic for retroreflector i are
where n = number of samples per cycle and m = number of cycles sampled.
The signal amplitude and phase are
.
In our case, the number of samples per cycle was chosen to be 64.
The effectiveness of this phase detection method is illustrated in Figure 12 which is a record of received amplitude and computed phase as the transmitted beam is scanned across a retroreflector. The computed distance remains constant over a change of amplitude in received signal of several orders of magnitude.
[Principle of Operation][Block Diagram] [Transmitter] [Receiver] [Oscillator] [Steering Mirror]
After initial laboratory tests, the instrument was set up in an isolated building suitably equipped to transmit the laser beam over an outdoor horizontal path to a distant retroreflector mounted on an accurately calibrated translation stage. The first test performed was a measure of the linearity of the instrument as shown in Figure 13. This test was made at a range of 100 m with an integration time of one second per data point. The slope of the response was correct and the standard deviation of a single point was less than 20 µm, a very satisfactory value. There was no sign of the cyclical error that would be expected if there was RF leakage at the transmitter frequency into the receiver circuits.
The instrumental noise was investigated with results that are summarized in Figure 14, a plot of the standard deviation (RMS) on a range reading plotted against the number of intermediate frequency (IF) cycles per reading. The IF is 1 kHz; thus, 10 IF cycles is an integration time of 10 ms. The noise introduced by the data-taking circuitry is seen to be small, around 0.7 µm for 128 cycles. The noise in this case is seen to decrease as the square root of the integration time, as would be expected for random noise. A similar result is observed for the instrument measuring a short (1 meter) range, but in this case the noise is higher, around 6 µm for 128 ms.
The source of this higher noise was found to be due to phase noise on both
the transmitter and local oscillator sources. This could undoubtedly be reduced,
either by increasing the 1 kHz IF or by increasing the spectral purity of
the oscillators, but the performance was judged to be more than adequate
for this application. The final curve in
Figure 14 hows a corresponding plot
for a range of 30 m. In this case, atmospheric turbulence causes the phase
fluctuations to decrease more slowly with integration time,
instead of
, due to the Kolmorogorov
spectrum of phase variation with time for path lengths greater than the size
of the turbulence cells [4].
Atmospheric turbulence consists of "bubbles" or "blobs" of air at slightly
differing density to the surrounding air and is characterized by the so-called
structure function, 
,
which may be loosely considered a measure of the refractive index difference
between the "blobs" and the surrounding air. Various references exist relating
the structure function, ,
to variance in range measurement [5]. A large body
of references also exists on the characteristics of
; a good summary
is contained in [6].
The instrument was eventually set up to measure distance to a retroreflector at a range of 120 meters. Measurements were taken once per second with an integration time of 128 ms. Each minute the mean and RMS of the 60 measured ranges were calculated and stored. The values obtained for the RMS departures from the mean were then plotted as shown in Figure 15. In this example, the RMS values cluster around 20 µm, with no values over 50 µm. Over tests which continued for several months, RMS values varied from 9 µm to 45 µm. The lowest values occurred early on still, foggy mornings and generally the highest values on sunny afternoons.
The bulk refractive index of the atmosphere is greater than unity and over a path length of 100 meters, the corresponding reduction in group velocity leads to a measured path length that is around 30 mm longer than that which would be measured in a vacuum. The exact value of the group velocity depends on pressure, temperature, and humidity [7]. Changes of several millimeters in the measured distance over a hundred-meter path are possible as a result of normal diurnal variations. However, due to the close proximity of the distances, all measurement paths should be affected equally, and the overall shape and pointing of the structure are therefore maintained. If absolute distances are required, then correction to the measured path lengths is possible by measuring the temperature, pressure, and relative humidity and computing a corresponding refractive index. This is common practice in commercial surveying instruments but may not be necessary for this application. A more practical solution would be to use the measured distances between the various fixed ground-based instruments and to scale all distances measured on the structure accordingly.
Of crucial importance is the homogeneity of the atmosphere. The change in refractive index must be the same over all measurement paths. In order to demonstrate this, at least in a preliminary way, the instrument was set up to measure two ranges separated by 15 degrees in azimuth, one range was 50 m, the other 120 m. The two ranges were measured and recorded once a minute for two days during which ambient conditions varied considerably. Figure 16 is a plot of each measurement point (with arbitrary zero point) and demonstrates that the changes in measured distance due to changes in group refractive index of the atmosphere are proportional to distance. The slope of the line is correct (12/5) and the standard deviation of a measurement point from this line is 18 µm. This error includes all sources of error; the stability of the monuments, for example, is included.
The prototype instrument described in this paper satisfies the basic requirements for measuring a large structure (approximately 100 m in diameter) with sufficient speed and accuracy to apply real-time corrections to an accuracy of better than 100 µm.
Recently, a production rangefinder has been used to measure ranges of up to a kilometer. Rangefinder monitoring of small amplitude structural deflections was tested by mounting a retroreflector atop a large derrick used for construction of the GBT. The rangefinder was approximately 725 meters from the retroreflector. Range was measured before and during hoisting of a 45 ton telescope section load. Deflections of 50 µm in amplitude were easily measured (see Figure 17). The entire experiment is further described in GBT Memo #160.
Differential ranging observations were also made to two target retroreflectors 1 km away on a nearby mountain. One target prism was mounted on an optical bench with micrometer distance drive. Measured range of the stationary retroreflector, at fixed position, was used to normalize each range measurement of the moving retroreflector for refraction along the common path. Ten range scans were taken for each distance. Measured range of the moving prism versus its translation indicated by the micrometer is shown in Figure 18.
The authors would like to acknowledge R. Hall for support from the GBT Project, R. Creager and A. Dowd for software support, and R. Becker for help with the construction of the instrument. The contributions of the Green Bank machine shop are gratefully acknowledged, as are the many helpful suggestions from J. W. Findlay and D. Hogg.
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