White Light Interferometry (WLI) is a widely used technique for surface recovery. However, it is extremely sensitive to various external disturbances, increasing the uncertainty on measurement results. In this paper, a time-domain guided filtering-based surface recovery algorithm is proposed for WLI. The reference signal is firstly simulated according to the spectral map of illuminator employed in the system. The correlation between the actual correlogram and the simulated one is then analyzed through the generalized cubic correlation delay estimation method. The corrected correlogram is obtained as a local linear transformation of the reference one that has been shifted, where the linear coefficients are estimated using least squares analysis. The surface height is then retrieved based on mapping relationship between the phase and frequency. The capability of the proposed method on noise suppression is investigated through simulation under different levels of additive noise. In the experiment, a step height standard (VLSI,181.0nm±2.1nm) is employed, which verifies the performance of the proposed method on measurement accuracy and reliability.
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.
In this paper, we proposed an aero-engine turbine blade measurement technique based on photometric stereo, which can reconstruct the blade surface quite accurately and efficient from the images captured under multi-illuminations. In this work, a measurement system is designed by using 8 LEDs as the point light sources, a light propagation process under the point light illumination is developed. Based on this process, a normal estimation method is provided for the reconstruction process. The system calibration is implemented on a USAF resolution target manufactured by Edmund, which proves the method is capable of performing the surface recovery with the repeatability error down to 0.0272mm. The experiments are performed through a turbine blade from aero-engine, where the comparison result is also provided by using a commercial portable laser scanner from Creaform, which shows the better performance of the methodology presented in this paper.
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.
Borescopes are widely used for civil aviation engine inspection. In this paper, a novel scaled shape from shading (SFS) approach is proposed to measure the civil aviation engine chambers with 3D information from the borescope images. In this work, a more accurate point light source model is firstly investigated. By introducing the matrix of camera, the relationship between the CCD grayscale image and the surface depth map is developed, which enables the new method can recover the 3D information of the surface with only one image. Under the constraints of brightness, smoothness and integrability, the depth map of surface is calculated through iteration. To evaluate our method, three synthetic images were simulated. By using the ratio of RMSE as criteria, the simulation results show a perfect match with the errors of 1.19%, 1.01% and 1.16%, respectively. In the experiment, the nozzle inner wall with clear features of Turbomeca Turmo IV C, a helicopter engine of Safran, is measured and its 3D shape is successfully recovered. The results prove the effectiveness of this method and show great potential of applications in civil aviation engine inspection.
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