Data Age Error Compensation for Nonconstant Velocity Metrology

Positioning calibration under dynamic conditions is becoming increasingly of interest for high precision fields, such as semiconductor lithography and additive manufacturing. Because heterodyne interferometry has high dynamic range and direct traceability to the meter, it is widely used in stage position calibration. When processing measurement and reference signals of heterodyne interferometry, the signal processing algorithm and optical receiver introduce time delay and phase shift to the measurement data, which leads the measurement data cannot precisely represent the current position of the stage. That error is called data age error and depends on the velocity of the stage, which will become significant when stage's velocity is nonconstant in dynamic calibrations. This paper presents a comprehensive data age error model and a compensation method by tracking the derivatives of the phase and solving for the data age error in a field programmable gate array (FPGA) in real time. The FPGA hardware-in-the-loop simulation shows that this method can significantly decrease the displacement error from ±600 to ±0.8 nm (fixed delay time) in dynamic cases, and it will still keep subnanometer resolution for quasi-static calibrations.