Traceability of small force measurements and the future international system of units (SI)

¹ Laboratoire Commun de Métrologie: LNE-Cnam, 61 rue du Landy – Case 2LAB10, 93210 La Plaine Saint-Denis, France
² Laboratoire National de Métrologie et d'Essais: LNE, 1 rue Gaston Boissier, 75015 Paris, France

^⁎ Corresponding author: naceur.khelifa@cnam.fr

Received: 11 September 2016
Accepted: 13 September 2016

Abstract

The unit of force is connected to the international prototype of the kilogramme, unit of mass in the international system of units (SI), via dead weight machines using calibrated masses. However, forces below 10 μN, ubiquitous in nature and in some devices cannot be measured with a traceability to the SI. The measurement, with the uncertainty of these forces has implications for both basic and applied science. Today, many emerging sectors in micro/nanotechnology and biotechnology have started producing and using systems to implement low forces that, for various reasons, require them to be traceable. Also, the revision of the SI, scheduled for 2018 year, of linking the definitions of the kilogramme, the ampere, the kelvin and the mole to fixed numerical values of fundamental constants, has aroused particular interest in the measurement and calibration of small forces. In this paper, we will give some indications of the state of the art on the small force with a focus on the development of a force sensor using a photoelastic crystal as a monolithic solid-state laser. Basically, the force to be measured is applied to the crystal induces a birefringence in the laser medium which in turn manifests itself by the appearance of a splitting between the frequencies associated with the two polarization components of the oscillating laser mode. This difference is then exploited because, within the elastic limit of the crystal, it is proportional to the force acting on the laser.