# Surface metrology

Surface metrology is the measurement of small-scale features on surfaces, and is a branch of metrology. Surface primary form, surface waviness and surface roughness are the parameters most commonly associated with the field. It is important to many disciplines and is mostly known for the machining of precision parts and assemblies which contain mating surfaces or which must operate with high internal pressures.

Surface metrology is the study of surface geometry, also called surface texture or surface roughness. The approach is to measure and analyze the surface texture in order to be able to understand how the texture is influenced by its history, (e.g., manufacture, wear, fracture) and how it influences its behavior (e.g., adhesion, gloss, friction).

## Equipment

A full list of standardized instruments can also be found in the part 6 document of the ISO series ISO 25178.

### Contact (tactile measurement)

The following instruments are well established technologies. There are many manufacturers implementing these technologies into products:

### Non-Contact (optical microscopes)

Optical measurement instruments have some advantages over the tactile ones. The main advantages are:

• no touching of the surface (the sample can not be damaged)
• the measurement speed is much higher (up to a million 3d points can be measured in a second)
• they are designed primarily for 3D surface topography rather than single traces of data
• they can measure surfaces through transparent medium such as glass or plastic film
• they have lower vertical noise

Vertical scanning:

Horizonal scanning:

### Choice of the right measurement instrument

Because of every instrument has advantages and disadvantages the operator must choose the right instrument depending on the measurement application. In the following some advantages and disadvantages to the main technologies are listed:

• Interferometry: This method has the highest vertical resolution of any optical technique and lateral resolution equivalent to most other optical techniques except for confocal which has better lateral resolution. Instruments can measure very smooth surfaces using phase shifting interferometry (PSI) with high vertical repeatability; such systems can be dedicated for measuring large parts (up to 300mm) or microscope-based. They can also use vertical scanning interferometry (VSI) mode with a white-light source to measure steep or rough surfaces, including machined metal, foam, paper and more. The interaction of light with the sample for this instruments is not fully understood. This means that measurement errors can occur especially for roughness measurement.[1][2]
• Focus variation: This method delivers color information, can measure on steep flanks and can measure on very rough surfaces. The disadvantage is that this method can not measure on surfaces with a very smooth surface roughness like a silicon wafer. The main application is metal (machined parts and tools), plastic or paper samples.
• Confocal microscopy: this method has the advantage of high lateral resolution because of the use of a pin hole but has the disadvantage that it can not measure on steep flanks. Also, it quickly loses vertical resolution when looking at large areas since the veritical sensitivity depends on the microscope objective in use.
• Confocal chromatic aberration: This method has the advantage of measuring certain height ranges without a vertical scan, can measure very rough surfaces with ease, and smooth surfaces down to the single nm range. The fact that these sensors have no moving parts allows for very high scan speeds and makes them very repeatable. Configurations with a high numerical aperture can measure on relatively steep flanks. Multiple sensors, with the same or different measurement ranges, can be used simultaneously, allowing differential measurement approaches (TTV) or expanding the use case of a system.
• Profilometer: this method is the most common surface measurement technique. The advantages are that it is a cheap instrument and has higher lateral resolution than optical techniques, depending on the stylus tip radius chosen. New systems can do 3D measurements in addition to 2D traces and can measure form and critical dimensions as well as roughness. However, the disadvantages are that the stylus tip has to be in physical contact with the surface, which may alter the surface and/or stylus and cause contamination. Furthermore, due to the mechanical interaction, the scan speeds are significantly slower than with optical methods. Because of the stylus shank angle, stylus profilometers cannot measure up to the edge of a rising structure, causing a "shadow"or undefined area, usually much larger than what is typical for optical systems.

### Resolution

The scale of the desired measurement will help decide which type of microscope will be used.

For 3D measurements, the probe is commanded to scan over a 2D area on the surface. The spacing between data points may not be the same in both directions.

In some cases, the physics of the measuring instrument may have a large effect on the data. This is especially true when measuring very smooth surfaces. For contact measurements, most obvious problem is that the stylus may scratch the measured surface. Another problem is that the stylus may be too blunt to reach the bottom of deep valleys and it may round the tips of sharp peaks. In this case the probe is a physical filter that limits the accuracy of the instrument.

## Roughness parameters

The real surface geometry is so complicated that a finite number of parameters cannot provide a full description. If the number of parameters used is increased, a more accurate description can be obtained. This is one of the reasons for introducing new parameters for surface evaluation. Surface roughness parameters are normally categorised into three groups according to its functionality. These groups are defined as amplitude parameters, spacing parameters, and hybrid parameters.[3]

### Profile roughness parameters

Parameters used to describe surfaces are largely statistical indicators obtained from many samples of the surface height. Some examples include:

Table of useful surface metrics
Parameter Name Description Type Formula
Ra, Raa, Ryni arithmetic average of absolute values Mean of the absolute values of the profile heights measured from a mean line averaged over the profile Amplitude $R_a = \frac{1}{n} \sum_{i=1}^{n} \left | y_i \right |$
Rq, RRMS root mean squared Amplitude $R_q = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} y_i^2 }$
Rv maximum valley depth Maximum depth of the profile below the mean line with the sampling length Amplitude $R_v = \min_{i} y_i$
Rp maximum peak height Maximum height of the profile above the mean line within the sampling length Amplitude $R_p = \max_{i} y_i$
Rt Maximum Height of the Profile Maximum peak to valley height of the profile in the assessment length Amplitude $R_t = R_p - R_v$
Rsk Skewness Symmetry of the profile about the mean line Amplitude $R_{sk} = \frac{1}{n R_q^3} \sum_{i=1}^{n} y_i^3$
Rku Kurtosis Measure of the sharpness of the surface profile Hybrid $R_{ku} = \frac{1}{n R_q^4} \sum_{i=1}^{n} y_i^4$
RSm Mean Peak Spacing Mean Spacing between peaks at the mean line Spatial $RS_{m} = \frac{1}{n} \sum_{i=1}^{n} S_i$

This is a small subset of available parameters described in standards like ASME B46.1[4] and ISO 4287.[5] Most of these parameters originated from the capabilities of profilometers and other mechanical probe systems. In addition, new measures of surface dimensions have been developed which are more directly related to the measurements made possible by high-definition optical gauging technologies.

Most of these parameters can be estimated using the SurfCharJ plugin [1] for the ImageJ.

### Areal surface parameters

The surface roughness can also be calculated over an area. This gives Sa instead of Ra values. The ISO 25178 series describes all these roughness values in detail. The advantage over the profile parameters are:

• more significant values
• more relation to the real function possible
• faster measurement with actual instruments[clarification needed] possible (optical areal based instruments can measure an Sa in higher speed then Ra.

Surfaces have fractal properties, multi-scale measurements can also be made such as Length-scale Fractal Analysis or Area-scale Fractal Analysis.[6]

## Filtering

To obtain the surface characteristic almost all measurements are subject to filtering. It is one of the most important topics when it comes to specifying and controlling surface attributes such as roughness, waviness, and form error. These components of the surface deviations must be distinctly separable in measurement to achieve a clear understanding between the surface supplier and the surface recipient as to the expected characteristics of the surface in question. Typically, either digital or analog filters are used to separate form error, waviness, and roughness resulting from a measurement. There are three characteristics of these filters that should be known in order to understand the parameter values that an instrument may calculate. These are the spatial wavelength at which a filter separates roughness from waviness or waviness from form error, the sharpness of a filter or how cleanly the filter separates two components of the surface deviations and the distortion of a filter or how much the filter alters a spatial wavelength component in the separation process.[4]