Precision Telescope Control System
PTCS Project Note 16
Analysis of Laser Rangefinder Return Signal Amplitudes and
Pointing Inferences, 1 July 2003 Experiment
K. Constantikes
3 July 2003
GBT Archive: PR028
File: Projects
Keys: Laser
Abstract
Measured return signal amplitudes from the data collection experiment conducted on 1 July, 2003 are
briefly analyzed to infer laser rangefinder pointing performance for ZY101-ZY104 looking at the
retroreflector located near GBT node 41040L. Several collections were performed: One with no offset
pointing corrections ("tweaking"), one with a FEM table modified to take into account the difference
between the model 97 asymmetric FEM model and a survey of cardinal points taken in 2000 1 and
tweaked pointing, and finally one with the original FEM model and tweaking.
While the experiments are hard to interpret as to the causes of signal loss in rangefinder returns, it is
clear that experiment 2 data adequate for further trilateration analysis.
History
n.1 3 July 2003. Original Version (KTC)
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Table of Contents
1
Experimental Method
3
2
Environmental Conditions
3
3
Comparison of signal returns for all rangefinders by experiment
5
4
Comparison of up and down passes in experiment 2
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5
Comparison of all ZY amplitudes versus pointing method and elevation.
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6
Consequences of low return signal strengths
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3
Experimental Method
The rangefinders on monuments ZY101-ZY104, ZY107, and ZY111 were operated to collect range data
from the retroreflectors ZEG41040L, ZEG20440L, ZAG731P, and ZAG731D (respectively, near the
prime feed boom attachment, near the end of the horizontal feed arm, and near the elevation bearing).
The GBT was positioned at 145.3 azimuth, and a GLISH/GO script was used to move the GBT from 94
to 6elevation and back in 5 increments (except for the first and last steps), with the elevation held
constant at each elevation for 180 seconds. Ancillary data (e.g, structure temperature) was recorded via
the M&C system Archivist, with project names TPTCSKTC_FATIP, TPTCSKTC_FATIP2, and
TPTCSKTC_FATIP3. The first experiment was conducted with untweaked rangefinders (i.e., pointing
offsets were not applied), tweaked rangefinders (i.e., at 50 elevation the rangefinder pointing was
modified to maximize return signal and the resulting pointing offset applied at all GBT elevations) and a
modified FEM (where the 2000 cardinal point survey was used for node 41040L, via a linear structure
model, rather than the Model 97f FEM outputs), and finally with the Model 97F FEM and tweaked
rangefinders.
Data were collected via the normal Metrology group methods and with the EMS data protocols. The
latter data are intended for use in EMS algorithm development. The EMS datasets are, respectively,
070103_141630.txt, 070103_181135.txt, and 070103_204858.txt. The analysis that follows is restricted
to the rangefinders on ZY101-104, and retroreflector ZEG41040L.
2
Environmental Conditions
Figure 1 shows the air temperature and wind speed and direction for the second experiment taken by
GBT weather station 2. Note that the air temperature was relatively stable with a total change of 2C,
wind direction was essentially constant, and wind speed showed a significant increase in the second half
of the experiment. Otherwise, the sky was totally overcast and there was no rain during the test. Figure 2
shows the air temperature measured by Metrology weather station 1 and the structural temperature sensor
prototype mounted on the horizontal feed arm near the upper man lift.
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Figure 1. GBT Weather 2 Data
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Figure 2. Comparison of Metrology air temperature and GBT structural temperature
3
Comparison of signal returns for all rangefinders by experiment
This comparison of signal return strength and hence the inference of laser rangefinder pointing
performance for the different experiments is shown in Figure 3. Rangefinder ZY101 has an occluded path
for elevations below 25 and ZY104 is occluded for elevations above 55. The error bars at each data
point represent  1  of the return signal at that elevation, and the marker is placed at the mean value.
Note that the return signal strength can be quite variable at a fixed location, e.g., ZY103 at 50. Also note
that there is no systematic improvement of signal strength for any of the methods, when assessed for all
rangefinders. For ZY101, the untweaked performance is worse than the tweaked, but for ZY103 the
opposite is true. For ZY103 the modified FEM improves signal strength, but for ZY104 the opposite is
true.
There may be some geometric reason for tweaking and FEM modification to not have an effect (viewing
angles desensitize the return with respect to pointing). Reduction of return signal with better pointing
(e.g., ZY104 at 50) defies an direct explanation.
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Figure 3. Comparison of rangefinder returns by experiment.
4
Comparison of up and down passes in experiment 2
The behaviour of signal return strength as a function of elevation in experiment 2 (tweaked, modified
FEM model) seems approximately repeatable between up and down passes. Keep in mind that wind
speed had significantly increased for the up pass, but it's unlikely that 4 m/s winds would cause a motion
of the feed arm tip of the order of 7 cm ( the laser footprint at 150m, i.e., 0.5 millirad). In particular note
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the dips in return for ZY103 at 30 and 60. These are not likely to be due to FEM model errors, nor
environmental conditions since in the first case the corrections to pointing are smoothly varying and in
the second case the conditions were significantly different ( structure temperature and wind speed)
between the two passes.
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Figure 4. Comparison of up and down passes
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5
9
Comparison of all ZY amplitudes versus pointing method and elevation.
Figure 5 shows this comparison, and it appears that the tweaked, modified FEM data provides the best
signal levels for all elevations and rangefinders. Note that multilateration will be possible for elevations
from 30 to 50 with signal strengths above ~0.2 volts, and trilateration possible for elevations from ~25
to 85 with signal strengths in excess of ~0.1 volts.
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Figure 5. Comparison of all amplitudes (ZY's) for each pointing method.
6
Consequences of low return signal strengths
From Application of Laser Metrology to GBT Precision Pointing and Active Surface Control 2, rangeequivalent quantization noise associated with the sampling and conversion of the detected IF is
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q 
L
2  3N
c
L
2 f m ng
M
(1)
where L is the characteristic length of the instrument (one half of the modulation envelope wavelength in
media), M is sampling resolution in bits, and N is the number of samples taken per period of the
measurement clock. This formulation assumes that the detected signals occupy the entire dynamic range
of the ADC. For their configuration, the error is less than 1m (N=128, M=14, L ~ 1 m). The GBT laser
rangefinder parameters are selectable, but typically set with N=64, M=16, L ~ 10 cm, resulting in a
approximately 0.1m quantization noise, which is then further reduced by averaging of many cycles
(128). The quantization noise contribution is thus effectively zero when the input signals are close to
ADC full scale levels. In practice the input levels may only occupy 12 bits (one volt return IF), for a
quantization noise 0.6m for one cycle, and assuming the noise process is IID (independent and
identically distributed), about 0.05m for the average of 128 cycles. Figure 6 shows the relationship for a
16 bit converter (10 volts full scale). Apparently, signals of 0.1 volt are more than adequate for robust
phase estimation in the absence of other noises. Since the path and instrument noises are much larger
than the quantization noise2, experiment 2 data signal strengths are adequate for further analysis.
Figure 6. Quantization noise as a function of signal
1
D. Parker, GBT Cardinal Point Survey and Analysis, GBT Archive A0223, 1-24-01.
2
K. Constantikes, PTCS Project Note PR019, 3-19-03.