An experiment with a high precision method of alignment*
6e jaargang no. 8, oktober 1976
Peter Richardus and Robert H. Masée
1 Introduction
The requirement of the highest possible precision
of a three point alignment at relatively short
distances is particularly stringent in respect of
industrial and other technical purposes. Refraction
and the many mechanical inaccuracies of the optical
instruments have a considerably detrimental in
fluence on the precision particularly of the pointing
at short distances. The standard deviation (sq. root
of the variance: s.d.) of pointing (horizontal as well
as vertical) may be expressed (in sex. sec. of arc) by
the formula (Richardus 1963, 1968)
ap=* 1.48^f£j2 0.0642r/* (1)
where Cis the "vernier acuity" of the observer; M
the magnification of the optical system and d the
distance to the target in meters.
One may allow for laboratory circumstances by
taking fapThis formula is based on a very large
number of observations by Washer and Williams
(1946); Washer (1947) and Anon. (1968). It is note
worthy that very few references to this problem are
found in the literature to this date.
Characteristic for the optical systems is that the
influence of diffracted light is eliminated as much as
possible.
A very high precision method of alignment has been
SUMMARY
It is generally known that the alignment of three points at a maximum distance of say
30 meters as applied to industrial purposes frequently constitutes a problem in respect
of the precision required.
One of the most precise methods of alignment is described by Van Heel (1950) employing
a beam of coherent light, and a zone plate between two fixed points represented respectively
by the centre of a circular diaphragm and the intersection point of crosswires. It owes its
high precision to the fact that it does not apply an optical lens system, thus obviating the
influence of the non-symmetric aberrations of such a system, and the detrimental influence
of the need of focussing at various distances. The precision of each setting is therefore
independent of distance. The method is, however, just as well liable to the influence of
refraction.
An experiment has been conducted in the laboratory investigating the possibilities of
improving the precision of alignment in a vertical sense by trying to eliminate - at least
partly - the influence of the vertical refraction. This improvement is thought to be obtained
by the application of a liquid level surface (water) as a reference surface, the alignment
in a horizontal direction still being performed with the conventional Van Heel's arrange
ment.
The results are very encouraging. It appeared that by the instrumentation and the method
described in this paper, one may measure the vertical distance of two fixed (terminal)
points of the alignment in respect of this surface with micrometers; calculate the position
of intermediate points by interpolation and set the micrometers accordingly. The internal
standard deviation of alignment is estimated at approximately 3-5 (xm (single setting).
The total length of the line in the experiment was 13£ meter, with 4 intermediate points
at equal distances. An extension to 30 meters is possible maintaining the same precision.
Paper presented at the VII International Course of Tech
nical Measurements of High Precision and The Symposium
F.I.G. Commissions 5 and 6, Darmstadt, W.-Germany,
29th September-8th October 1976.
ngt 76
137
