Laser Displacement Interferometers with Subnanometre Resolution in Absolute Ballistic Gravimeters

The absolute ballistic gravimeter (ABG) realizes the free motion of the test body in the gravity field and the free-fall acceleration g is obtained from the measurement of the length and time intervals using the motion equation of the falling body. Laser displacement interferometers (LDI) and precise clocks are used in such measurements. To obtain a relative uncertainty of a few parts in 109 (or a few units of 10-8 ms-2) in a g-measurement on the Earth the uncertainty in the length measurement (for the path length in the range from 0.025 m to about 0.5 m for different types of gravimeters) should be less than 0.025 nm and 0.5 nm, respectively. In addition, the rate of interference fringe counting achieves more than 6 MHz. A high accuracy in the measurements length and time is crucial for the ABG but a direct calibration of its LDI in terms of the length unit is not possible due to the design of the absolute gravimeter and because the required uncertainty in the calibration is difficult to reach. The design of the LDI for an ABG represents practically the task for length metrology with the subnanometre uncertainty in the dynamical measurement mode.