White light interferometry (WLI) provides noncontact, high-precision surface profiling and inspection for ultra-precision machining. This paper presented a signal time-domain mode-decomposition denoising based surface recovery algorithm for WLI. In this work, the captured correlogram is firstly decomposed into a series of modes with different central spectrums by means of the variation mode-decomposition (VMD), and the spectral component of each intrinsic mode can be derived through the Fourier transform. Afterwards, the noise existed in each spectral component is eliminated through windowed Fourier filtering (WFF), where the filtering threshold is decided by the ratio of spectral energy of intrinsic mode comparing with that of the correlogram. The denoised correlogram could then be extracted as the sum of filtered intrinsic modes. And the surface height isfinally retrieved through envelope peak location by applying Hilbert transform. The effectiveness of the proposed method on noise suppression is investigated under different levels of additive noises occurred on simulated correlograms. Moreover, a height step standard with calibrated values 1.762±0.010μm is further testified, where the measurement accuracy of the proposed method is totally verified.
This paper proposed a Gamma effect correction method based on the probability distribution function (PDF) for suppressing phase nonlinearity error in fringe projection profilometry. In this work, the periodicity of phase with Gamma effect is first analyzed, and nonlinear wrapped phase is modeled as superposition of normal wrapped phase with a sinusoidal function. Afterwards, a series of reference phases with Gamma factors ranging from 1 to 3 is constructed and the corresponding PDF is calculated. Then the optimal precoding factor γp of projected fringe is obtained by applying Jensen-Shannon (JS) divergence matching between the PDF of measured phase and constructed reference phases. In simulations, the availability of proposed method is investigated, where RMSE decreases from 0.218rad to 0.016rad. In experiments, the turbine blade is tested and compared with calibrated values where RMS of measured deviations after correction has decreased from 0.269mm to 0.095mm. All the investigations have proved the high reliability of proposed method.
This paper proposed a frequency-domain-decomposition denoising algorithm for nano-scale measurement in white light interferometry (WLI). In this work, the captured correlogram is firstly divided into a series of short-time stationary signals, the phase distribution can then be derived as the sum of the corresponding phase components after Fourier transform. By applying windowed threshold filtering, the noises existed in phase map can be eliminated, and a denoised correlogram is precisely reconstructed. Afterwards, the surface height is retrieved through phase-frequency least-square fitting. In simulations, the phase noises with different levels are investigated. By comparing the noise deviations in the reconstructed phase map with the original one, the effectiveness on noise suppression of the proposed method is properly verified. In the experiments, a height step standard with calibrated values 182±2.0nm are tested, where the height deviations below 3nm and the repeatability of 0.5% has proved the robustness of our proposed method.
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