Gaussian Processes Based Surface Topography Measurement

A great many functional performances such as wear,bearing,lubrication,wetting,antireflection and corrosion are closely related to surface topography.Nowadays,quantitative measurement of surface topography is essential in a variety of sciences and engineering fields.Demanding for high efficiency and high precision measurement is also growing.Unfortunately,every kind of measurement instruments has its own advantages and disadvantages,and no instrument can meet all measurement requirements.Measurement instruments such as scanning probe microscopes(SPM)and coordinate measuring machines(CMM)have high measurement accuracy.However,this kind of point by point scan has a low measurement efficiency and a small range of SPM measurements.Optical microscopy(OM)has the advantages of high measurement efficiency,high data density and non-destructive.However,complex interactions between light and surface structures may induce a relatively large bias.Therefore,in order to meet the measurement requirements of high efficiency and high precision,this paper performs the following research work from the algorithm,simulation and experiment based on the Gaussian processes machine learning algorithm.1.We studied the surface reconstruction under four special scan paths,namely,an extended range pattern,a chessboard pattern,a fractal Hilbert curve and a spiral pattern based on the Gaussian processes.For random rough surfaces,freeform surfaces and structured surfaces,it is obtained from simulation and experiments that this special trajectory scanning has the advantages of reducing measurement points and improving measurement efficiency without sacrificing measurement accuracy.2.With the aim of reducing sampling density while having minimal impact on surface reconstruction accuracy,an adaptive sampling method based on Gaussian process inference is proposed.Besides,we verified the effectiveness and robustness of the algorithm.In each iterative step,the current sampling points serve as the training data to predict surface topography and then a new sampling point is adaptively located and added at the position where the maximum inference uncertainty is estimated.The updated samples are trained in the next step.By such an iterative training-inference-sampling approach,the reconstructed topography can converge to the expected one efficiently.Demonstrations on different structured,freeform and roughness surfaces ascertain the effectiveness of the sampling strategy.It can lead to an accurate inference of the surface topography and a sufficient reduction of data points compared with conventional uniform sampling.Robustness against random surface features,measurement noise and sharp height changes is further discussed.Such an adaptive sampling method is extremely suitable for discrete point-by-point measurements.3.The effectiveness of data fusion algorithm based on Gaussian processes in surface measurement is studied.Datasets with characteristics of high accuracy low density(HALD)and low accuracy high density(LAHD)are frequently encountered in hybrid dimensional measurements.To enhance the accuracy and efficiency when measuring structured surfaces,fusion of the two datasets based on Gaussian processes was established and the fusion framework was demonstrated to be rather effective for various kinds of structured surfaces in simulation and experiment.Influencing factors in data fusion such as measurement bias,noise and sampling points were investigated systematically.The fused surface has better accuracy than the LAHD dataset and higher data density than the HALD dataset.Furthermore,data acquisition efficiency may also be improved.The advantages of hybrid measurements are therefore fully maximized.