Elsevier

Measurement

Volume 95, January 2017, Pages 82-92
Measurement

Shape descriptors and statistical classification on areal topography data for tile inspection in tessellated surfaces

https://doi.org/10.1016/j.measurement.2016.09.044Get rights and content

Abstract

Verification of conformance to design specifications in production, and identification of defects related to wear or other damage during maintenance, are key metrological aspects that must be addressed for micro-scale tessellated surfaces. A new algorithmic approach is presented that operates on topography datasets as obtained by areal topography instruments. The approach combines segmentation algorithms with a novel implementation of the angular radial transform, originally adopted by the MPEG-7 standard, to implement shape descriptors and associated similarity metrics. Applications to the inspection and verification of laser-manufactured micro-embossing topographies are illustrated. The topographies are first segmented to extract the individual tiles; the tiles are then encoded through shape descriptors. Principal component analysis and cluster analysis are used to investigate the behaviour of the angular radial transform coefficients. Finally, an algorithmic classifier based on supervised learning (k-nearest neighbours) is implemented and shown to be effective at identifying defects and at discriminating between defect types.

Introduction

Structured surfaces are surfaces whose micrometric or sub-micrometric texture is characterised by a deterministic pattern of (often high aspect-ratio) features, designed to achieve a specific functional role [1], [2]. The topography of a structured surface is explicitly defined by design specification, as opposed to conventional, unstructured surfaces, where topography is only partially and indirectly defined through compliance to provided texture descriptors (for example, areal surface texture field parameters as defined in ISO 25178-2 [3], [4]). “Tessellated” is a term commonly used to refer to a particular class of structured surface whose topography can be thought of as comprised of a pattern unit, or tile, replicated multiple times in order to create a regular, periodic pattern [1]. Tessellated surfaces have increasingly found successful uses in a wide array of industrial applications. Typical examples include optical surfaces (retroreflectors, Fresnel lenses, etc.) [5], mechanical surfaces (for example, low-friction patterns [6]), and biocompatible/biomimetic surfaces (prosthetic implants, microfilters, high-adhesion, hydrophilic, etc.) [7]. Designed topographies are constantly evolving along with the high-precision micro- and nanomanufacturing processes needed to generate them. In this scenario, the importance of providing a dedicated and effective solution for metrological inspection and verification is paramount.

The test case used in this work consists of micro-embossing patterns obtained by means of different manufacturing processes. Two example surfaces are shown in Fig. 1; albeit fabricated from the same nominal specification, they feature significant topography differences, thus obtaining a quantitative assessment of such differences can be used as a means to obtain information on the performance of the two manufacturing processes.

As typically happens for tessellated surfaces [8], the small size of the topographic features that need to be measured and verified (i.e. checked for compliance to specifications, according to ISO 17450-1 [9]), makes areal topography instruments, such as 3D digital profilometers and 3D digital microscopes, ideal candidates for acquiring quantitative information useful for obtaining 3D reconstructions of measured topography [10], [11]. Therefore, the test topographies were measured with an interferometric probe based on conoscopic holography [8], [12] operating in single-point, raster scanning mode. Aside from the differences in the two topographies, each tile is dale-shaped, with an approximately 280 μm × 280 μm square footprint, and a 50 μm nominal depth.

Typical analysis solutions based on computing surface texture parameters, as provided by current surface metrology literature [13], [14] and standards (in particular ISO 25178-2 [3]), are often not capable of capturing some of the defining properties of tessellated surfaces, such as their degree of regularity/periodicity. Many researchers in surface metrology have thus begun exploring alternative approaches. For example, some authors have explored the possibility of devising new parameters that better capture the correlation between topography and functional performance (see the work in [15] for an application to anilox printing rollers). Several researchers have been approaching the characterisation problem as a two-step process: firstly the tiles (or the notable topographic features within the tiles) are identified and extracted as separate geometric entities; then dedicated, custom parameters are devised aimed at capturing properties pertaining to the shape of the tiles, and/or their layout over the surface. Notable examples have been shown for hard disk drives [13], abrasives and optical depixelator surfaces [1] and microlens arrays [5], [16]. The same two-step, tile-centred approach has been adopted by the authors of this paper. Two alternative characterisation routes have been investigated. The first route aims at computing dimensional and geometric attributes from measured topography, so that a one-to-one mapping with design specifications is achieved (thus allowing for direct verification akin to common practice in dimensional metrology for standard-sized mechanical parts). Examples of this approach can be found in previous publications [17], [18], and have been specifically applied to tessellated surfaces [19]. The second characterisation route, which is the subject of this paper, is about computing shape descriptors; that is, fast transforms turning topography data into a finite series of numbers useful for shape encoding. Given the high degree of similarity between the mathematical representation of topography data and conventional, digital intensity images (and also equivalently, range images), a large number of techniques, originally developed in computer vision/image processing, can be adapted to generate shape descriptors that efficiently operate on surface topography data [18]. The underlying premise is that the overall size of the tessellated surface is in general large, in comparison to the size of the unit tile; which implies that hundreds, if not thousands of tiles may need to be inspected/verified in an industrial application. Therefore, processing speed becomes a primary issue, and tile characterisation approaches that favour this aspect, sometimes at the expense of a less accurate depiction of tile topography, are given priority.

Section snippets

The angular radial transform

The angular radial transform (ART) is a moment-based description method adopted by the MPEG-7 standard for shape encoding in video frames [20], [21], [22], [23]. The ART is defined on a unit disk and based on complex orthogonal sinusoidal basis functions in polar coordinates. The ART coefficients Fn,m of order n and m are given by:Fn,m=02π01Vn,m(ρ,θ)f(ρ,θ)ρdρdθ,where f(ρ,θ) is the image function in polar coordinates (ρ[0,1], θ[0,2π]) and Vn,m(ρ,θ) is the basis (complex) function separable

Tile inspection and verification with ART distance to nominal

Assuming the tile nominal geometry is available, which is usually the case with a manufactured structured surface, the simplest way to use ART shape descriptors for tile inspection is based on comparing the topography of each manufactured tile with the nominal reference. The ART distance between the two ART encoding results provides a quantitative indication of cumulative shape error between the manufacturing process and the nominal specification. For the example test case, the nominal

Investigation of the discriminating power of the ART shape descriptor

In addition to the difficulty in setting an appropriate threshold value, the main drawback of using statistical process control in univariate space with simple ART distance is that different types of departures from nominal topography (for example, different types of tile defects) may not be properly discriminated if their distances to the template are similar. In order to better understand how the ART shape descriptor really behaves, it is necessary to go back to analysing the descriptor in

Development of a classifier based on supervised learning

Regardless of whether the ART shape descriptor is sufficiently capable of discriminating between defect types by means of simple multivariate clustering statistics, an effective performance at identification and discrimination of tile states can still be obtained by devising alternative means of classification, for example, based on supervised learning approaches. Amongst the wide array of supervised learning alternatives available from the literature, for the specific micro-embossing test

Computational speed against quality of shape information

In this work, the choice of encoding tile topography through a general-purpose shape descriptor (such as the one based on the ART, presented in this work), against adopting dedicated algorithmic procedures aimed at directly computing specific geometric/dimensional attributes of the tile (for example, depth, footprint area, etc.) is fundamentally driven by computational speed. For example, for detecting a recessed singularity (pit), one could develop a case-specific, dedicated algorithm for

Conclusions and future work

The characterisation of tessellated surfaces presents unique challenges. On one hand, being structured surfaces, tessellated surfaces are not easily specified in terms of conventional surface texture parameters, but instead are suitable to be subjected to dimensional and geometric verification against a nominal topography specification, akin to what happens in verification of standard-sized manufactured components. On the other hand, tessellated surfaces are intrinsically defined as comprised

Acknowledgements

N.S. and R.K.L. would like to thank the EC for supporting this work through the grant: FP7-PEOPLE-IEF-METROSURF. R.K.L. would also like to thank the EPSRC (grant: EP/M008983/1). N.S. and M.M. would also like to acknowledge the grant: UM12024L002, POR Umbria FSE 2007-2013, awarded by Regione Umbria.

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