Gaussian Beams and Spatial Modulation in Nanopositioning

The kilogram is the last base unit of the systeme international d´unites (SI) that is still defined by an artifact. The watt-balance experiment is one of the promising methods that can produce a new definition of the kilogram based on fundamental constants. In this experiment, to compare an electromagnetic force and a gravitational force with a relative uncertainty of 10^-9 by means of a beam balance, an absolute position sensor with nanometric resolution is needed. A novel method in position sensing based on the Gaussian beam propagation properties and their spatial modulation is presented. Two modulated and collimated Gaussian beams are focused into a slit. The slit is fixed to the object to be positioned. The resulting beams at the slit illuminate a photodetector whose signal is demodulated by a lock-in amplifier. The lock-in amplifier output signal is a function of the slit position with respect to the two modulated Gaussian beams. A resolution of 25 pm/(Hz)^1/2 can be achieved. The long-term stability is 3.5 pm over 2 h and 20 min.