Nonlinear Compensation Techniques in Interferometric Measurement Systems
Summary
Interferometric systems underpin high-precision displacement and dimensional metrology but are susceptible to nonlinear errors that degrade accuracy. These nonlinearities—often manifesting as periodic deviations known as cyclic errors—arise from polarisation mixing, phase-shift imbalances, ghost reflections, multi-order Doppler effects and imperfections in demodulation electronics. Compensation approaches can be broadly classified into optical techniques, algorithmic corrections and model-based strategies. Optical techniques include passive realignment of polarising components to suppress cross-talk and optimise polarisation purity. Algorithmic methods exploit ellipse-fitting, iterative digital phase-demodulation or peak-value estimation to transform distorted quadrature trajectories into idealised signals, often implemented in real time on programmable hardware. Model-based strategies develop detailed mathematical representations of ghost reflections or Doppler-shift contributions to guide targeted mitigation. Together, these techniques have driven interferometric measurement capabilities to the picometre and sub-nanometre domains, with critical applications in semiconductor lithography, machine-tool calibration and gravitational-wave detection.
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Nonlinear Compensation Techniques in Interferometric Measurement Systems publication trend
The graph below shows the total number of articles in nonlinear compensation techniques in interferometric measurement systems across all publications each year (not limited to Nature Index journals).
Technical terms
Heterodyne interferometry: Measurement technique using two light beams with slightly different frequencies to produce a beat signal whose phase encodes displacement.
Homodyne interferometry: Technique employing a single-frequency source split into two optical paths and recombined to extract phase via quadrature detection.
Cyclic error: Periodic deviation in interferometric phase measurement repeating every optical cycle or fringe.
Jones matrix: Mathematical formalism describing polarisation transformations of optical components.
Lissajous curve: Parametric plot of two orthogonal signal components used to visualise and correct phase and amplitude imbalances.
References
- Error Analysis of Heterodyne Interferometry Based on One Single-Mode Polarization-Maintaining Fiber. Sensors (2023).
- Quadrature phase-shift error analysis using a homodyne laser interferometer.. Optics Express (2009).
- Nonlinearity error in homodyne interferometer caused by multi-order Doppler frequency shift ghost reflections.. Optics Express (2017).
- A passive method to compensate nonlinearity in a homodyne interferometer.. Optics Express (2009).
- Compensation for the Variable Cyclic Error in Homodyne Laser Interferometers. Sensors (2015).
- Iterative compensation of nonlinear error of heterodyne interferometer.. Optics Express (2017).
- Toward a nonlinearity model for a heterodyne interferometer: not based on double-frequency mixing. Optics Express (2015).
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