Logo of the Physikalisch-Technische Bundesanstalt
symbolic picture: "magazines"

Angle measurement under pressure

Air pressure – an underestimated factor in angle measurement carried out by means of autocollimators

PTB-News 2.2019
Especially interesting for

high-precision mechanical engineering

the optical industry

users of synchrotron radiation and free-electron laser radiation

High-precision angle measurements carried out by means of autocollimators are significantly influenced by the refractive index of air – and thus in particular by the ambient pressure. When comparing measurements that have been carried out at different locations, it is therefore necessary to take changes in pressure into account. PTB has developed suitable strategies both to correct the measurement results and to assess the measurement uncertainty.

Simultaneous changes in the air pressure (top) and in the relative angle measurement error of the autocollimator (bottom; ppm: parts per million) as a function of time.

Autocollimators allow the contact-free measurement of the inclination angle of reflecting surfaces. These devices are used for various applications in industry and research, in particular to measure the straightness and levelness of mechanical and optical components, for example for ultra-precise form measurements on Xray mirrors for synchrotron radiation and free-electron laser radiation.


The measurement principle of autocollimators is as follows: the objective of the autocollimator converts the angle of the measuring beam which is reflected by conthe surface into the spatial displacement of a measuring mark that is imaged onto the detector. The objective thus acts as a kind of optical lever that transforms small angles into measurable displacements. The leverage effect depends on the focal length of the objective, which, in turn, is influenced by the refractive index of air.

As recent investigations have shown, the influence which changes in the refractive index of air have on angle measurements that are carried out by means of autocollimators must not be neglected. These changes are due to changes in the environmental conditions (air pressure and humidity, temperature). Here, it is particularly important to emphasize the importance of air pressure, which is not only subject to variations due to the weather, but which also depends on altitude. In contrast to this, temperature and humidity are precisely controlled in air-conditioned laboratories, so that they remain practically constant. The error in the angle measurement of the autocollimator increases proportionally to the angle and to the ambient pressure. In addition, it is also scaled along with the distance (i.e. the air clearance) between the autocollimator and the reflecting surface in relation to the focal length of the objective.

Environmental data, which were collected over a decade in PTB᾽s Clean Room Center, have exhibited an ambient pressure range of 84 hPa, and thus a relative change in pressure of more than 8 % compared to the standard pressure. An international comparison was carried out with laboratories located at heights ranging from 2 m to 712 m above sea level. This comparison revealed pressure differences of up to 89 hPa. The resulting relative angle measurement errors were each on the order of up to 10-4.

As shown by these figures, both quantities that have an influence on the ambient pressure (the meteorological conditions and the geographical elevation) must be taken into account when comparing angle measurements carried out by means of autocollimators at different locations and at different times in order to avoid substantial angle measurement errors.


Ralf D. Geckeler
Department 5.2
Dimensional Nanometrology
Phone: +49 531 592-5220
Opens window for sending emailralf.geckeler(at)ptb.de

Scientific publication

R. D. Geckeler, P. Křen, A. Just, M. Schumann, M. Krause: Influence of the air’s refractive index on precision angle metrology with autocollimators. Meas. Sci. Technol. 29, 075002 (2018)