Aim
In 1998, the School of Geomatic Engineering of the University of New
South Wales purchased ten Topcon precision digital levels DL101C and the
associated invar bar code staffs. The main purpose of this thesis
was to find out whether these Topcon DL101C precision digital levels suffer
from the cyclic errors found in earlier Topcon DL101. Only the cyclic
error was tested and considered. Special techniques were used in
order to eliminate the other errors inherent in digital levels. The
project included field experiments, least squares adjustments for the processing
of data and the estimation of the cyclic errors.
Field Experiment
Only four Topcon digital levels DL101C were used to measure to an
invar staff on twelve bolts. The bolts were placed at a height step of
30 mm giving a total difference in height of 330 mm. Measurements
were also made with a Zeiss Ni1 automatic precision level with a threemetre
Wild line scale invar staff in order to obtain reference data.
Each Digital level was setup at sighting distances of 2.0 m, 3.0 m, 5.0 m,
8.0 m, 15.0 m, and 20.0 m from the line of bolts. At each sighting
distance, measurements were made to the staff on the very first bolt and
then to the staff on all other bolts. After that, the bolts were
immediately measured to in reverse order. The complete sequence of
measurement was: 1 > 2 > 3 > 4 > 5 > 6 > 7 > 8 > 9 > 10
> 11 > 12 > 12 > 11 > 10 > 9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 >
1. Before and after measuring all bolts with each Topcon Digital
Level Dl101C, the Zeiss Ni1 precise level was setup, at a sighting distance
of 2.0 m, to measure the bolts in the same sequence. The above procedures
were repeated for all four of the Topcon digital levels DL101C tested.
The figure above shows the instruement and the invar staff at the test site. The bolts (obscured) were on the ramp behind the hand rail. The instrument setups were on a perpendicular to the row of bolts, intersecting the row of bolts between Bolts 6 and 7.
Least Square Modelling
Where
H_{Corr}
~ Corrected height of collimation (mm)
T_{i}
~ Staff reading at ith bolt with a Topcon Digital Level (mm)
from instrument station j
a
~ Coefficient of the sine term of the cyclic error (mm)
b
~ Coefficient of the cosine term of the cyclic errors (mm)
H_{i}
~ Height of the ith bolt (mm)
Z_{ki}
~ Staff reading at ith bolt in scale k using Zeiss automatic
Levels (mm)
Lambda
~ Wavelength of fitted cyclic error (taken as 315 mm)
Plot of "a priori" Standard Deviation versus Distance (Outliers Removed)
The "a priori" standard deviations were computed from the differences
between the forward and reverse measurements to the 12 bolts from each
setup. Less that 30 minutes elapsed between the forward and return
measurement to a bolt. Each diamond in the diagram represents the
precision pooled over a maximum of eights values from four instruments.
Cyclic Errors Found
Below are the results of eight least squares adjustments that returned
significant cyclic errors. The uncertainties are given at 95 percent
confidence level. The cyclic errors in the remaining 16 least squares
adjustments were not significant.






















































Conclusion
The largest statistically significant cyclic error found in four of
the School's ten Topcon DL101C digital levels was 0.039 mm. It should
be noted that in most surveying applications, a cyclic error of 0.039 mm
in amplitude is not important, as it averages out over consecutive setups,
for example in a first order levelling network.
The measuring precision under field conditions is about ±0.02
mm at sighting distances below 8 m and then increases with the square of
the distance.
Further Information
For more information, please contact:
A/Prof. J.M. Rüeger
Email:
J.Rueger@unsw.edu.au
Mail: School of Surveying
& Spatial Information Systems
University of New South Wales
Sydney NSW 2052
Australia
Phone: +61293854173
Fax: +61293137493
Mr. H.C. Lok
Email: HC_LOK@mail.com
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