Data Age Error Compensation for Nonconstant Velocity Metrology

Chen Wang, Jonathan D. Ellis

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Article number7544472
Pages (from-to)2601-2611
Number of pages11
JournalIEEE Transactions on Instrumentation and Measurement
Issue number11
StatePublished - Nov 2016


  • Data age
  • displacement measurement
  • error compensation
  • field programmable gate arrays (FPGAs)
  • interferometry
  • phase measurement

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering


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