Abstract
Displacement measurement with laser interferometer is based on measuring the laser Doppler frequency shift that a beam of radiation undergoes upon reflection from measuring prism connected to a moving stage. The principle error in fast ultra-precision laser heterodyne interferometric measurement is proposed in this paper. Only 1-dimension motion of the measuring prism is usually thought about in the laser Doppler frequency shift calculation. The formula of laser Doppler frequency shift taken in account of 3-dimension motion of measurement prism is established, and the error introduced by the velocity of other dimensions is analyzed. There is a lack of the second-order in v/c in traditional model of displacement measurement with laser heterodyne interferometric. The distance error lead by the second-order in v/c in Doppler frequency is analyzed and emulated, the emulation result shows that there is a residual cumulative error that is up to 17.7nm when the highest speed is up to 1m/s and the displacement is long to 3m. The residual cumulative error is cumulatived.
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