Information-rich surface metrology

Nicola Senin, associate professor, Department of Engineering, University of Perugia, and visiting researcher, Faculty of Engineering, the University of Nottingham

Richard Leach, professor of metrology, Faculty of Engineering, University of Nottingham

A paper from the 15th CIRP Conference on Computer Aided Tolerancing (CIRP CAT 2018), which took place on 11–13 June 2018, in Milan, Italy.

In press: Procedia CIRP, Elsevier.

There have been several significant developments in surface metrology over the last two decades, for example, the transition from contact to optical instruments, the transition from profile to areal characterisation and a number of advances in the use of surface topography data to control advanced manufacturing processes. However, if the field is to be progressed further—thus allowing for increased area coverage, improved accuracies, higher measurement speeds, and more intelligent process control—perhaps a fresh perspective is required. In this article, the authors present one approach to aiding the development and enhancement of surface metrology; an approach called information-rich metrology (IRM). 

Introduction

IRM is a term that is here introduced to refer to the use of any type of additionally-available information to improve a measurement process1. The concept is not new, as the conceptual ties between measurement and information theory have long been explored, for example, by seeing measurement as a means to decrease the uncertainty associated with our knowledge of a quantity or event ² . Even more generally, Thomas Bayes first proposed that knowledge can be refined by using a priori information³ . IRM is therefore here proposed as an umbrella concept to gather many concepts and methods currently being developed in industrial metrology, all sharing the common idea of using additionally available information to improve a measurement process.

Information may come from knowledge of the manufacturing process, knowledge of the object to be measured, and/or knowledge of the physical interactions/principles underlying the measurement technology itself. Information may come from pre-existing knowledge (i.e. a priori), mathematical modelling, or simulation, or from other measurement processes, even performed concurrently to the measurement one is aiming to improve. An overview of how information sources and information flow change when the IRM paradigm is adopted is provided in figure 1. The idea of using available information related to the product, process, or product-measurement-instrument interaction makes intuitive sense because metrology in manufacturing takes place in controlled and very predictable conditions, with a sensible amount of information known in advance.

Information about the measured object and the manufacturing process

When a part or product is manufactured—in particular, when using digital manufacturing methods—a large amount of information about it is typically available. For example, CAD data provides information about the nominal form. Analogously, a significant amount of information is available or can be easily acquired about the manufacturing process, in terms of its capability, the features and defects it generates, the materials it is designed to operate with, and the types of geometries and surfaces it typically produces. Most of such information is generated and exploited through product design and manufacturing process planning. In IRM, the aim is for such information to be used to improve metrology, for example, in the inspection and verification of part quality or in manufacturing process monitoring.

Information about the measurement instrument and the instrument-surface interaction

One of the most promising paradigms for IRM is based on using additional information about the manufacturing process and the object produced to develop improved mathematical models that describe the interactions between the measured object and measuring instrument. In practice, mathematical models that describe physical principles and phenomena underlying many measurement technologies are already available, although one has to be careful that over-simplifications are not abused. In optical measurement, for example, many models have been developed over the last decades to support the theories of focus variation microscopy (FVM), coherence scanning interferometry (CSI), confocal microscopy, fringe projection, photogrammetry, etc. ⁴

It is safe to say that all current, commercial optical measurement systems already use complex mathematical models to interpret the raw data acquired through their probes. However, because such models aim to be general, which means that they must be applicable with little prior knowledge of the measurement scenarios, they can make very few assumptions about the nature of the surface to be measured, the material properties to be encountered and other factors. Thus, such models are limited in the information they can provide. A typical example is the interpretation of optical signals captured by the detector after multiple reflections and scattering. Trying to reconstruct what determined the patterns captured by the detector implies the solving of complex (often non-linear) inverse problems, which are typically unsolvable or ambiguous without resorting to additional sources of information.

The advantage of working in the scenarios typically encountered in manufacturing metrology is that such additional information is often readily available; at the macroscopic scale, there is information about part shape and expected dimensions, at the microscopic scale, there is information about the expected surface texture and about signature features left by the manufacturing processes. All such information is exploited to a small extent in conventional manufacturing metrology, but it is rarely used to develop a better understanding of how measurement instruments interact with surfaces, useful in turn to achieve a better interpretation of raw measurement data.

Smart aggregation of information

The IRM paradigm requires a fundamental re-design of the data analysis processes that are typically adopted in conventional metrology applications. The addition of a potentially high number of heterogeneous information streams raises a whole series of challenges regarding how such information should be homogenised, aggregated and finally exploited towards achieving a better measurement result overall. These challenges are in:

• how to handle large amounts of data in increasingly shorter times (possibly verging towards big data issues);
• how to data mine the relevant relationships between variables; and
• how to obtain mathematical and statistical models that ultimately support what can be referred to as the ‘smart’ measurement paradigm, as opposed to the conventional metrology pipeline of ‘blind’ processing (i.e. where knowledge is extracted exclusively from the raw data provided by the measurement instrument, with no help from any other sources of information).

As in many other applications involving big data, a fundamental role in such a paradigm shift may be covered by artificial intelligence (AI) technologies. Machine learning, in particular, can provide significant support to the development of the smart measurement solutions of the future (for example, see reference 5).

The IRM advantage

Central to the IRM paradigm is the aim to improve measurement quality. Quality is here intended as a generic term encompassing multiple facets; improving quality may mean reducing measurement times, improving measurement performance indicators (accuracy, precision, etc.), expanding the range of covered scales (spatial resolution and range) and improving coverage, intended as the capability to reach surfaces that may be harder to reach, for example, measuring beyond the maximum permissible slope for a given measurement technology.

The IRM advantage

Central to the IRM paradigm is the aim to improve measurement quality. Quality is here intended as a generic term encompassing multiple facets; improving quality may mean reducing measurement times, improving measurement performance indicators (accuracy, precision, etc.), expanding the range of covered scales (spatial resolution and range) and improving coverage, intended as the capability to reach surfaces that may be harder to reach, for example, measuring beyond the maximum permissible slope for a given measurement technology.

The IRM advantage

Central to the IRM paradigm is the aim to improve measurement quality. Quality is here intended as a generic term encompassing multiple facets; improving quality may mean reducing measurement times, improving measurement performance indicators (accuracy, precision, etc.), expanding the range of covered scales (spatial resolution and range) and improving coverage, intended as the capability to reach surfaces that may be harder to reach, for example, measuring beyond the maximum permissible slope for a given measurement technology.

Improving coverage and metrological quality of measurement is a key strategic objective in manufacturing metrology, as many emerging measurement applications (for example, in additive manufacturing) are creating new challenges related to geometric complexity and lack of uniform material properties^6–9. Improving measurement speed is almost as essential in many in-process and in-situ measurement applications^10–13, as well as the need to overcome the fundamental limits of individual measurement technologies¹⁴. The idea of overcoming the aforementioned limitations by manipulating the acquired data (as opposed or in addition to creating new measurement technologies) is not new (see references 15 and 16 for examples of adaptive or intelligent data reduction and sampling techniques) and is the fundamental conceptual paradigm that defines IRM.

A final consideration is that IRM is not only about improving the quality of a measurement, since the information-rich paradigm may also lead to an improved interpretation of the same measurement result. Thanks to an information-rich approach to measurement, more advanced conclusions or further insight on the system under observation can be gained, specifically the information-rich paradigm affords a new perspective from which to look at the data.

Information-rich surface metrology

Whilst the previous considerations are general to any metrology application, this article focuses specifically on the measurement of surface topography and on what it means for surface metrology to embrace the information-rich paradigm in terms of challenges and new opportunities.

The paradigm shift illustrated through an example

The conventional data processing pipeline adopted by surface metrology is shown in figure 2. The pipeline is based on ISO 25178-2¹⁷ terminology, but equivalent concepts also apply to the older ISO 4287 standard¹⁸. A form operator (F-operator) is used to de-trend the signal (i.e. level) and remove any trace of the underlying form of the part. An S-filter is used to remove high-frequency noise and an L-filter is used to separate and remove the waviness component. Data processing is designed to ensure that the resulting scale-limited surface (SL-surface) is as close as possible to a stationary random signal, suitable to be described by texture parameters that are for a significant part derived from sample statistics.

Very little information is required to apply this procedure; some knowledge of the surface nominal form is required for the F-operator, and previous information about relevant spatial frequencies (typically coming from the manufacturing process and the measuring instrument) is required to choose suitable nesting indices for the S and L filters (cut-off frequencies in ISO 4287 terminology). The paucity of information requirements is an advantage, as it makes the procedure of very general applicability. But generality is also the main limitation of the procedure, as further case-specific information cannot be exploited to delve deeper into the analysis of measurement data.

An example of the information-rich paradigm is shown in figure 3 for a simple case of profile measurement in cylindrical turning. In this case, the expected topography is modelled using the geometrical construction introduced by Schmalz²⁰, which relates the spacing, depth and shape of the machining grooves to process parameters, such as feed rate and tool tip geometry. Whilst measurement can proceed in the same way as in the conventional method, what changes is the way the data is analysed; the simulated, expected topography can be subtracted from the measured profile, and then the residuals can be characterised, again possibly with the conventional means of isolating a stationary random signal. The advantages are immediately visible, for example, it is possible to investigate aspects, such as the regularity and geometric properties of the machining marks (i.e. how much they deviate from the expected results), and in turn identify effects of machining error at multiple scales (chatter phenomena, oscillations of the workpiece, worn tool, etc.).

The drawbacks of a potentially much more in-depth investigation are: the method is not generic (it only applies to cylindrical turning); knowledge of nominal manufacturing parameters is required; and the whole process of fitting to a nominal geometry and investigating the residuals requires more preparation and is more challenging to implement.

Introduction to feature-based representations

The use of modelling to predict topography from manufacturing process parameters—as exemplified in the previous section—introduces the concept in IRM that additional information layers pertaining to topography can be added to the characterisation pipeline, for example, where topography itself is described in terms of its constituent features. For the cylindrical turning example, such features are the machining marks, but in general, multiple higher-level information overlays can be added to represent additional viewpoints. For example, in figure 4, an areal topography dataset acquired by an atomic force microscope (AFM) is shown—again representing a cylindrical turned surface—where further overlays, in addition to machining marks, are used to identify scratches from functional life or artefacts from the measurement process.

Feature-based representation is the term introduced in IRM to refer to the use of additional, higher-level information overlays where topography is partitioned into regions, and the relevant ones are mapped to classes defined within some user-defined ontology. As ontologies may be case-specific (i.e. refer to a specific manufacturing process, application, or measurement technology), once again, IRM sacrifices generality for depth and breadth of investigation possibilities.

The feature-based characterisation pipeline and examples

For feature-aware topography characterisation, a new data processing pipeline is introduced within the information-rich surface metrology paradigm²¹. This is summarised in figure 5 and comprises three phases, namely:

• feature identification (the features of interest are identified through template matching of their shape and size properties to those defined in the ontology of reference);
• feature extraction (the features of interest are isolated through a partitioning/segmentation of the original dataset, and then extracted as independent geometric entities); and
• feature characterisation (the features of interest are described in terms of their relevant shape and size properties).  

 Feature-based overlays are a core concept of information- rich surface metrology, as they allow mapping of low-level topography information (point cloud or structured grid of height values) to multiple layers of higher-level information, each designed to allow some type of context-specific reasoning, for example, to investigate manufacturing signature features, measurement artefacts, or elements of structured surfaces.

An example application of feature-based characterisation is shown in figure 6 for a metal laser powder bed fusion (LPBF) surface measured using CSI. In figure 6a, spatter formations are algorithmically identified in the measured dataset, and in figures 6b and figure 6c, some of such formations are isolated and characterised in terms of footprint area and protruding height from the surroundings²².

In figure 7, a similar feature-based characterisation pipeline is used to isolate and characterise LPBF weld tracks and weld ripple spacing²². In figure 8, the feature-based characterisation pipeline is used to quantify the regularity of the cross-section of a manufacturing artefact specimen designed to study the process capability of ink-jetting to fabricate micro-conductor lines made of metal particles in a polymer matrix²³.

In figure 9, unit dimples from a regular pattern designed to reduce friction in bearing applications are algorithmically identified and isolated²⁴. In addition to the characterisation of their diameters, the regularity of the pattern layout is investigated by reconstruction of the network of distances between feature centroids.

Depending on the degree of determinism of the studied topography, different feature identification and characterisation solutions may be adopted. For example, high variability of shape and size of feature instances suggest the use of statistical modelling tools for shape representation and comparison, the main goal being to pursue robustness to intrinsic variability of feature instances, while still ensuring discrimination of features belonging to different classes. Additional challenges for shape-based reasoning are related to possible lack of information due to sub-optimal sampling density, occlusions, re-entrant portions or too steep to measure portions of the features, all of which are typical issues of micro-scale topography measurement.

Currently investigated approaches for feature identification range from CAD-compare techniques, to the use of a variety of template matching technologies based on shape descriptors (for example, the ring projection transform²⁵ and the angular radial transform²⁶). CAD-compare approaches work well in the presence of highly deterministic structures, for example, when inspecting micro-parts or products (MEMS, microfluidics), and share significant resemblances with the inspection and verification of standard-sized parts as shown in figure 10 in terms of procedural choices and in terms of issues.

However, since typical applications of information-rich surface metrology are at the micro-scale, the availability of surface-specific point sets—akin to what is obtainable from a touch probe coordinate measuring machine (CMM)—is seldom achievable (because of the low market penetration and challenges of using micro-CMMs^{4, 21}), and thus in most circumstances, characterisation proceeds with blanket measurements (typical of range imaging techniques) that require point set partitioning to isolate the point subsets to fit to each datum²¹. For step-like features, edge detection combined with morphological segmentation methods^27-29 has also proven effective. For the identification and isolation of feature instances subjected to significant variability, the use of shape descriptors has been explored, for example, applied to super-abrasives as shown in figure 11a²⁵ and micro-embossing patterns as shown in figure 11b²⁶, or for identifying correspondences between topographies to be aligned³⁰.

Incorporating knowledge about measurement instruments and instrument-surface interaction

Another primary venue of investigation in the development of the information-rich surface metrology paradigm pertains to the incorporation of instrument-related information and, in particular, to the use of models that explain instrument- surface interaction and are thus capable of predicting instrument performance and behaviour when encountering specific topography features. A simple example is shown in figure 12, where the algorithm applied has been specifically designed to identify and reduce batwing and other spike-like artefacts that appear in CSI measurement in correspondence with abrupt height changes in the topography, as typically happens when measuring step-like features³¹.

The challenge when incorporating knowledge of a specific measurement technology in the surface data processing pipeline is that aside from general well-known effects that are clearly recognisable and fairly easy to predict in correspondence of specific topographic features (such as the aforementioned batwing artefacts), a wide range of additional problems are more challenging to spot and handle, as they are related to specific combinations of topographic properties, material properties and instrument configurations at the time of measurement. In recent work by the authors, it was shown how the assessment of topographic reconstruction error has a key relevance in contemporary surface metrology^{32, 33}, as measurement error across technologies may sometimes be the same order of magnitude as the features one is trying to measure. The same LPBF region measured via different technologies is shown in figure 13; recessed features and high-spatial frequency topographic components are most likely to result in very different reconstructions when acquired with different technologies.

Research work is therefore in progress, not only to better understand each and every one of the major measurement technologies and how their performance and behaviour is affected by measurement set-up parameters^34–36, but also to investigate instrument-surface interaction by focusing on specific test-cases of interest, for instance, the non-contact (optical and X-ray) measurement of metallic LPBF surfaces^{32, 33}. As an example, the reconstruction of the topography of an individual LPBF spatter formation is shown in figure 14, as obtained from focus variation (FV) and CSI measurements.

^{32, 33}. In figure 15, repeated measurements of a metallic LPBF surface with multiple instruments are used to build confidence intervals on local mean height. As the results indicate, some regions of the topography are associated with higher measurement dispersion, which can be used as a starting point to build predictive models of measurement dispersion as a function of local topographic properties, to use in characterisation approaches.

The same method shown in figure 15 can be used to assess statistically relevant discrepancies between reconstructions obtained with different measuring instruments; discrepancies corresponding with the regions where confidence intervals do not intersect³³. This, in turn, is equivalent to determining the local bias of the topographic reconstruction of one instrument, if another can be assumed as a more reliable (i.e. accurate) reference.

Statistical modelling of topographies from replicate measurements is a first step towards building a wide array of regression models capable of predicting measurement error from information about the topographic properties of the region being measured. Such predictor models could eventually be extended into simulation tools capable of predicting measurement error and behaviour when confronted with any surface.

The incorporation of measurement error models is a first step towards a measurement-aware approach to feature identification and characterisation, as shape/size information pertaining to the relevant features could be modified to accommodate for variability owing to performance and behaviour of the measurement technology used to acquire information. As a minimum, for example, both local bias and precision information arising from statistical topography models could be used to formulate uncertainty budgets associated with topography, which in turn could be propagated through the feature-based characterisation pipeline, ultimately determining the uncertainty of the feature characterisation result. Ultimately, though, the determination of traceability for feature-based characterisation is still fundamentally undermined by the need to establish traceability of surface topography measurement first, a long-time running endeavour^{37, 38}.

Conclusions and outlook

In its attempt to incorporate useful knowledge about the surface, manufacturing process and measurement process into the data processing pipeline, information-rich surface metrology surely loses generality with respect to the conventional approach to surface characterisation, where only minimal information is necessary and the same data processing pipelines can be applied, at least in principle, to any surface measured by any instrument. On the contrary, additional, often significant, effort is needed in information- rich approaches to collect, understand and appropriately integrate additional data and models into the data processing pipeline. Such effort is typically tied to the specific aspects that define the application, i.e. expected part geometry, the manufacturing process used to produce it and/or the measurement technologies used to collect data.

The methods of conventional surface metrology, the specification standards around it, and even the instruments around it have been designed to ensure satisfactory results— almost in a fool-proof manner—from any surface, in any operating conditions. On the contrary, it is evident that the information-rich approach requires more preparation and careful fine tuning, tailored to each and every specific application domain.

To make the matter more difficult, as the application changes, it is not unlikely that much additional modelling effort will need re-visiting to adapt to the new circumstances. Manufacturing processes evolve and improve over time, as do the signature features they generate. Measurement instruments also evolve and so do their performance and behaviour. Customer specifications on what is relevant to measure and to what accuracies and precisions also evolve, as products with increasingly higher value added are designed and produced. At each and every iteration, information-rich approaches require significant extra work to collect extra data, to develop the appropriate support models and finally to integrate all the sources of heterogeneous information into a coherent pipeline, ultimately aiming at achieving better metrological performance. This process of data gathering and organisation is typically not straightforward.

IRM, in general, and information-rich surface metrology, in particular, pose a series of challenging issues from the viewpoint of knowledge representation, as a multitude of heterogeneous sources and many different viewpoints encompassing shape, process and function-related information must be gathered and merged into a coherent whole. Fundamental challenges of information handling, communication, processing and storage must be addressed, involving a wide array of disciplines and competencies such as ontologies, AI, etc.

Ultimately, the application of the IRM paradigm is far from effortless or straightforward and may not be suitable in all manufacturing metrology scenarios. Where it is applicable though, it is asserted that such a significant price to pay is hopefully counterbalanced by the value added to the characterisation results, as dedicated analysis pipelines can be developed that are custom-tailored to specific characterisation requirements and are capable of providing information that may more directly address specific inspection requests.

Faculty of Engineering, University of Nottingham www.nottingham.ac.uk/engineering

Department of Engineering, University of Perugia http://www.ing.unipg.it/en/

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