Correlation and convolution filtering and image processing for pitch evaluation of 2D micro- and nano-scale gratings and lattices

Abstract

We have mathematically explicated and experimentally demonstrated how a correlation and convolution filter can dramatically suppress the noise that coexists with the scanned topographic signals of two-dimensional (2D) gratings and lattices with 2D perspectives. To realize pitch evaluation, the true peaks' coordinates have been precisely acquired after detecting the local maxima from the filtered signal, followed by image processing. The combination of 2D filtering, local-maxima detecting, and image processing make up the pitch detection (PD) method. It is elucidated that the pitch average, uniformity, rotation angle, and orthogonal angle can be calculated using the PD method. This has been applied to the pitch evaluation of several 2D gratings and lattices, and the results are compared with the results of using the center-of-gravity (CG) and Fourier-transform-based (FT) method. The differences of pitch averages which are produced using the PD, CG, and FT methods are within 1.5 pixels. Moreover, the PD method has also been applied to detect the dense peaks of Si (111) 7×7 surface and the highly oriented pyrolytic graphite (HOPG) basal plane.

A novel SPM error measurement method based on peak detection of nodes centers in a 2D orthogonal lattice as standard

“…The method based on 2D CC filtering, combined with local maximum detection and image processing to detect various peak positions or valley-positions in morphology signals related to 2D micro lattices/grids positions, is named as peak detection (PD) method [19]. Whether PD method detects peaks or valleys depends on the structure of the 2D lateral standard which is an array of hills, columns or holes.…”

“…In response to the high complexity and limitations of existing SPM measurement methods, this paper proposes an SPM measurement method based on lattice node center detection. By using the cross correlation/ convolutional filtering peak detection (PD) method [18,19], the x and y coordinates of each lattice center are quickly extracted from the 2D orthogonal lattice standard image scanned by SPM, thereby achieving the measurements of the x-y planar motion geometric errors and drifting rate of SPMs.…”

Dimensional artefacts to achieve metrological traceability in advanced manufacturing

“…2D gratings are usually calibrated by either diffractometry or scanning probe microscopy (SPM) (typically AFM) [109], [193]. Suitable vision algorithms help in aligning the artefacts [201] and in suppressing the noise [54]. Detailed analyses of the diffracted wavefront can be used for deriving flatness information [55], [107].…”