published by Van Heel (1950), employing diffracted
light only. A coherent wavefront in the form of a
narrow pencil proceeding through or from a circular
diaphragm is caught by a zone plate. The inter
ference patterns formed at any arbitrary distance
from this plate will consist of concentric coloured
rings with a clear centre. In the case of a monochro
matic wavefront the pattern shows light and dark
rings. An index (circles or crosswires etched on
glass) can be set on this interference pattern with a
micrometer.
This will effect the alignment of the centres of the
first diaphragm, the centre of the zone plate and the
index. It is noted instantly in comparison with the
conventional use of telescopes, that focussing has
been eliminated as a source of errors. Van Heel
claims a precision of pointing (under laboratory
circumstances) of 0,01 mm (standard deviation) for
distances of 0.5 to 30 metres. This linear measure
is independent of the distance. A second advantage
of this method is, that a diffraction pattern is form
ed at any arbitrary place passed the zone plate,
where the index can be set without loss of precision.
This eliminates the error-theoretical difficulty that
becomes apparent in continuating a line by extra
polation.
For these reasons a similar set up was selected for
the experiment. A 1.5 mW LS-32/E.N.L. HeNe gas
laser system provided a coherent pencil of optical
red (632.8 nm) light, the diameter being 2 mm at
the exit aperture. The zone plate produces a pattern
of red and black rings on which could be pointed
with an index of three concentric rings etched on
glass. It is possible to use the centre of the beam
for the alignment, or the centre of the circular
aperture of the optical system with which the con
vergence of the beam can be adjusted. As could be
expected, however (see a.o. Geilen 1971), the direc
tional stability of the beam was by no means suffi
cient to maintain the required high precision of
alignment especially during the three hours after
first triggering the laser. Deviations could amount
to 0.2 mm at a distance of a few meters. This diffi
culty was avoided by locating an independent
circular diaphragm at a few centimeters in front of
the laser. This diaphragm (diameter 0.1 mm) then
acts as an independent source of coherent light and
produces a high quality pattern as long as it
remains situated within the laser beam. The line
could now be held fixed perfectly between the centre
of this diaphragm and the index.
After the arrangement of the alignment in the lab
oratory with an intial total length of approximately
30 meters, the internal precision of pointing was
checked. The zone plate, being attached to a micro
meter reading directly to 0.01 mm and an estimation
of 2 pm, could be moved by remote electronical
control from the observer's place (at the index).
The observations were subdivided into groups of
10 settings in order to avoid long term influence of
refraction.
The position of the diffraction pattern reacted
sharply to short term turbulence, caused mainly by
walking along the line; therefore one should wait
observing until the unrest in the atmosphere settles
down. It then appeared that the internal precision
of pointing (s.d.) was 6.5 pm. This agrees with the
findings of Van Heel, the difference being caused
by the use of a more precise micrometer and the
fact that the laser did not exist at the time of Van
Heel's experiment.
The influence of refraction cannot be eliminated,
at least not the horizontal refraction. The question
arose whether the alignment could be improved in
a vertical direction by the use of a liquid level
surface as a reference surface.
A number of points should be considered when
using a liquid surface in this way:
1. The surface is in fact an equipotential surface,
which can be taken as spherical over the short
distances involved.
The corrections Ah to the horizontal direction
at a point of the surface can be calculated with
the formula (see Fig. I
where a is the distance from the tangent point
and R the radius of the earth (6378 km).
2. It is a known fact in hydrostatic levelling, that
the tidal forces cause the liquid to follow a
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