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Single-frequency interferometer with bidirectional fringe counting is frequently used in accurate length measurements due to its high resolution, stability and compact hardware. Meanwhile, in order to obtain nanometric path length resolution, corrections have to be introduced to the phase quadrature signals of a real interferometer due to its systematic deviations such as phase quadrature error, dc bias, unequal gains, etc. Conventional approaches to correct nonlinearity in a single frequency interferometer are generally based on ellipse fitting proposed by Heydemann, i.e. fitting an ellipse to instantaneous phase quadrature signals as the interferometer path length is varying. Consequently, when interferometer path length variation is far larger than light wavelength, the highest correction accuracy could be obtained by the largest number of data points.
In some cases like nanoindentation instruments in particular, however, the path length variation of an interferometer cannot be large enough to produce a closed Lissajou figure. Simulation and experimental results show that the accuracy of conventional calibration techniques drops quickly as the range of the optical path length variation reduces.
A new approach to correct nonlinearity in single-frequency interferometry was introduced, which was based on the concept of model reference control technique. Firstly, a Neural Network (NN) model was created and trained to predict the instantaneous phase of an ideal interferometer. And then the NN model was used as a reference model due to such characteristic that its outputs would be quite different from those obtained by conventional instantaneous phase computation methods when the input data were not on an ideal Lissajou figure. Better correction results could be achieved through minimizing the phase error between the NN model outputs and the conventional computation results. Theoretical derivation and analysis of the new approach are detailed in this paper. Simulation and experimental results show that this new
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