A new method for the synthesis of wavenumber series before and after mode hopping is proposed for depth-resolved wavenumber scanning interferometry. The classical Fourier transform is not suitable for mode hopping; consequently, the wavenumber scanning range of diode lasers is rather narrow, reducing the depth resolution and measurement accuracy. We show that the discontinuity in wavenumber domain interferograms caused by mode hopping can be removed by introducing the phase compensation of the interference spectrum. Thus, the wavenumber series before and after mode hopping can be synthesized. Experiments and numerical simulations validate the proposed method, and the measurement error is within 5nm.
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