White light scanning interferometry (WLSI) has been an extremely powerful technique in precision measurements. In this work, a phase noise estimation based surface recovery algorithm is proposed, which can significantly improve the measurement accuracy by decreasing the noise level in phase map coming from the systemic and environmental disturbances. The noise existed in phase map is firstly researched in spectrum domain and defined as the linear combination of complex terms at each angular wavenumber. Afterwards, based on the theoretical linearity of the phase distribution, the surface features can be redefined through establishing the function with respect to phase noise. By applying least square estimation (LSE), a spectral coefficient is defined to determine the optimal estimation of phase noise that represents the best statistical consistency with the actual case, from which a more accurate surface after removing most phase noise will then be generated. In order to testify the noise elimination ability of the proposed method, a nano-scale step height standard (9.5nm±1.0nm) is scanned, and the measurement result 9.49nm with repeatability 0.17nm is successfully achieved. Moreover, a leading edge of an aero-engine blade is also tested to investigate the potential of this method in industrial inspections. The measurement comparison with AFM is also displayed.

White light interferometry is a well-established surface recovery technique. In this paper, a white light signal processing algorithm based on phase error compensation using spectrum selection is proposed. The derived nonlinear phase distribution from the correlogram is modeled as the combination of random errors and systemic deviations. By developing a new, to the best of our knowledge, recovery algorithm, the phase noise can be separated from the linear map and significantly attenuated. Based on the proposed algorithm, the spectrum features of white light LEDs and halogen lamps are investigated in detail. The inner products defined by three selected points are employed to generate a coefficient to evaluate the linearity of an unwrapped phase map within a certain spectrum region. The optimal spectrum range corresponding to the best measurement performance can then be located where the coefficient approximates 1 and the spectrum energy stays relatively high. The simulations are carried out under different levels of SNR and scan step noises, which show that the new method can effectively reduce additional disturbance from the recovered topography. In experiments, the system with the proposed method is first calibrated by a step height standard (VLSI, 182.7 ± 2.0 n m ) with the repeatability of 0.44 nm. A silicon wafer and three roughness standards are also tested to further verify the robustness of the new method.

In this paper, a calibration method for non-isotropic point light source is developed, which is capable of calibrating position and orientation of the point light source with a single image synchronously. Based on the bidirectional reflectance distribution function (BRDF), the relationship between the shape of observed surface and the recorded grayscale image is firstly investigated in a more accurate way. Based on this model, a cost function is proposed to evaluate the estimation error, and a new cumulative, error-free iteration method is designed to recursively estimate the point light source parameters. The average simulation rebuilding root mean square error (RMSE) is below 0.9. The experiments are performed by calibrating a point light source in a photometric stereo measurement system, and the corresponding RMSE is below 1.2 in the unit of grayscale. Further analysis shows one image is enough to achieve the precision calibration using our proposed method.

This paper describes a new peak detecting algorithm combined Carré phase shifting interferometry with white light interferometry. The new method can carry the fast, accurate, and noncontact measurements. The testing system employs a Mirau objective on a piezoelectric transducer based on a Zeiss microscope. Several numerical simulations are first carried to analyze its phase calculation errors due to the visibility variation in the white light correlogram. Afterwards, the centroid method is adopted to concentrate the phase extraction on the zero-order fringe, which not only decreases the phase error, but also frees the data processing from the phase unwrapping procedure. The capabilities of the system and the proposed algorithm are evaluated through the measurements of a microresonator and two standard step heights. In the measurement of the 44-nm standard step height, no overshoot shows up on or close to the edge of the sample. At last, three different methods include: white light phase shifting interferometry, phase shifting interferometry and white light interferometry are employed to make a comparison on the measurement precision.

A Lambertian surface is a kind of very important assumption in shape from shading (SFS), which is widely used in many measurement cases. In this paper, a novel scaled SFS method is developed to measure the shape of a Lambertian surface with dimensions. In which, a more accurate light source model is investigated under the illumination of a simple point light source, the relationship between surface depth map and the recorded image grayscale is established by introducing the camera matrix into the model. Together with the constraints of brightness, smoothness and integrability, the surface shape with dimensions can be obtained by analyzing only one image using the scaled SFS method. The algorithm simulations show a perfect matching between the simulated structures and the results, the rebuilding root mean square error (RMSE) is below 0.6mm. Further experiment is performed by measuring a PVC tube internal surface, the overall measurement error lies below 2%.