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.
As an important ultra-precision measurement method, white light interferometry is widely used in 3D measurements with nanometer resolution. In this paper, a white light interferometer is designed with a random phase noise insensitive algorithm. A discrete interferogram is established by analyzing the phase noise, which is modelized by the combination of random noise and systematic deviation. After Fourier analysis, the mathematical expression of the discrete interferogram in frequency domain is derived, where the random noise can be estimated by least square method and then be corrected. As a result, a more accurate relationship between phase distribution and surface height is established. To set up an stable system, the scanner of white light interferometer is driven by a precision step motor with scanning range 100 mm, and the travel range of the object stage in x and y directions is 60 mm. In the experiment, a step height standard (VLSI, 182.7±2.0 nm) and the end face of a multi-mode optical fiber are tested, where the repeatability error for the step height is less than 0.28%, which proves the measurement accuracy and robustness of the system.
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