Surface topography measurement: 3D areal measurements

This post discusses the procedure to perform a reliable 3D areal surface texture measurement and analysis.

Like 2D profile, 3D areal surface texture analysis also follows three steps: fitting, filtering and analysis.

Let’s briefly repeat the short explanation of the three steps as follows.

Fitting process is to remove form components, the very low frequency component, from surface data points captured by a tactile or optical surface texture measuring instruments.

Filtering process is to extract high-frequency components from the surface data and to separate roughness and waviness components (high or low spatial frequency components) for further analysis.

Analysis process is to calculate 3D areal parameters from the filtered surface data. This filtered 3D areal data is called scale-limited surface data.

Remember, different procedures or set values on one or more of the three fundamental steps, we will get a noticeable difference in calculated surface texture parameters [1].

Unlike 2D profile, all standards related to 3D areal surface texture analysis are unified into a single standard series, that is ISO25178 series [2].

Tabe 1 presents the standard comparison between 2D profile and 3D areal surface texture analysis. In table 2, standards for 2D profile measurement are diverse and spread into several standards. Meanwhile, 3D areal measurement standards are unified into a single ISO25178 series.

Another particular difference we can observe between 2D profile and 3D areal surface analysis is that the standards that explains “Measuring instrument classification” is not available for 2D profile. This is because, 2D profile data is typically obtained using a stylus (tactile/contact) instrument.

Meanwhile, for 3D areal data, in addition to stylus instruments, there are various optical (non-contact) measuring instruments we can use, such as focus variation microscopy, point autofocus, confocal microscope, coherence scanning interferometry and other optical instruments [1].

Table 1: Comparison of standards between 2D profile and 3D areal analysis.

Currently, 3D areal surface analysis becomes a trend and widely adopted. Because 3D areal surface analysis describes surface condition more comprehensively and more complete, with more parameters, compared to 2D profile surface analysis which only represent an area with a single profile!

Representing a surface with only a single 2D profile analysis is very incomplete and ambiguous.

Incomplete means a single profile cannot represent the whole area of a surface. Maybe, the obtained profile missis the critical feature on a surface!

Ambiguous means totally different 2D profile can have the same calculated 2D profile parameters [1]. A simple example is two different 2D profile, one is the flipped version of the other, will have the same Ra and Rz and other parameter values.

General procedure for 3D areal surface analysis

There are specific procedures to following order to extract scaled-limited surface and to perform 3D areal surface analysis.

Figure 1 below shows the procedure or steps for 3D areal surface analysis. The procedure is as follows:

1. Capture 3D surface data by using either stylus instruments or optical instruments.

2. Apply S filter with $S_{1}$ nesting index to remove very high frequency components, such as high frequency noise, from optical instrument data. If the data is captured by using a stylus or contact instruments, the stylus tip already perform the S filtering by means of mechanical morphological filtering.

3. Obtain primary 3D areal data.

4. Perform fitting to remove form. The process is by applying F operator to remove nominal geometry in the data such as parabolic or tilted surface components.

5. Obtain first S-F surface data as form-removed primary surface data.

5. If needed, we can calculate 3D areal parameters from the first S-F surface data (the form-removed primary surface data).

6. If we want to perform areal waviness:

6.1 Apply S filter with $S_{2}$ nesting index.

6.2 Obtain S-F surface.

6.3 Calculate 3D areal parameters from this S-F surface data.

7. if we want to perform areal roughness:

7.1 Apply L filter with $L$ nesting index.

7.2 Obtain S-L surface.

7.3 Calculate 3D areal parameters from this S-L surface data.

Note that the values for $S_{1}$, $S_{2}$, F and L nesting index can be obtained from ISO25178-3 [3]. In this standard, the relation between S and F-operator L filter, bandwidths ratio between F-operator/L-filter, as well as the appropriate sampling distance on the surface data are explained in detail.

Figure 1: The general procedure for 3D areal surface analysis: from 3D data capturing, S-filter (first), F-filter (form removal) and S-filter (second) for surface waviness (S-F surface) and L filter for surface roughness (S-L surface).

Figure 2 below shows the illustration of various filter nesting index on selecting and removing components on a measured surface data.

The final goal is to get “scale-limited surface” data (as shown in figure 2). From this scale-limited surface, we can then calculate 3D areal parameters to quantitatively represent our measure surfaces and to get understanding.

Some understandings from our 3D areal surface texture analysis include understanding about expected functionalities and manufacturing process understandings.

Figure 2: Illustration of filter nesting index and the scale regions for a surface (adapted from [4]).

Fitting: Form removal from captured 3D areal data

After we get the primary surface data, obtained after filtering the first S-filter with S1-esting index since typically areal data are obtained by using optical instruments [3], we need to remove the form component on a measured surface.

The operation to remove the form is F-operator with F nesting index [3]. Typical form removal is flattening or parabolic surface linear second order regression curve removal.

Other form removals with complex geometrical shapes, such as free-form surface or higher order type of form/shape, can only be used if we exactly know our specific application and analysis needs.

Figure 3 below shows an example of form removal from a measured surface data. In this case, the form is a tilting of the surface. After removing the tilt (form), we get an approximately a flat surface.

Figure 3: Example of form (tilt) removal from a captured surface data. After removing the form (tilt), we get a relatively flat surface to apply filters and extract a scale-limited surface.

Filtering: Extracting the roughness components from form removed 3D areal data

After removing the form component from a surface data, we can do two different filtering processes:

We can apply the second S-filter with S2-nesting index [3] to get S-F surface which contains the waviness components on the surface.
We can apply L-filter with -nesting index [3] to get S-L surface which contains the roughness components on the surface.

Figure 4 below shows an example of S-F surface and S-L surface extracted from the same original measured surface. From figure 4, we can clearly see the different components (waviness and roughness) we get after the filtering process.

Typical filtering method is linear Gaussian filter. Unless we know exactly what we need to our unique applications at hand, we can use a specific filter.

ISO16610 series provides guides for various filtering process of 3D areal data as follows:

ISO16610-61: Linear Gaussian filter for surfaces.
ISO16610-62: Cubic Spline filter for surfaces.
ISO16610-69: Wavelets filter for surfaces.
ISO16610-62: Robust Spline filter for surfaces.
ISO16610-81: Morphological filter for surfaces.
ISO16610-89: Multiscale filter for surfaces.

Figure 4: Example of extracted S-F surface for waviness component (left) and S-L surface for roughness component (right) from the same measured surface data [2]. From these scale-limited surfaces, we can calculate 3D areal parameters.

Analysis: Calculating 3D areal roughness parameters

After obtaining the scale-limited component (S-F or S-L surfaces) from a measured surface (after the F and S or L filtering processes), we can then calculate 3D areal texture parameters from these S-F and/or S-L surfaces.

With 3D areal analysis, more surface texture parameters can be calculated to specifically represent a surface condition [4].

Like the corresponding 2D profile parameters, Sa and Sq are ambiguous parameters because two different surfaces can have identical or similar Sa and Sq values. However, Sa and Sq are still important parameters to have basic representations of a surface.

Hence, we need to calculate other parameters to reliably quantitatively represent a surface condition for our further analysis and understanding on the functionality and manufacturing processes of a surface.

The list of some parameters for 3D areal surface measurement are defined in ISO 25178-2:2021 [4]:

Height parameters: Maximum height (Sz), maximum peak height (Sp), maximum pit depth (Sv), Arithmetic mean height (Sa), root mean square height (Sq), skewness (Ssk), kurtosis (Sku).
Spatial parameters: Autocorrelation length (Sal), texture aspect ratio (Str).
Hybrid parameters: Root mean square gradient (Sdq), developed interfacial area ratio (Sdr).
Functions and related parameters: Core height (Sk), reduced peak height (Spk), reduced valley height (Svk), material ratio (Smr1), material ratio (Smr2), peak extreme height (Sxp), dale void volume (Vw), core void volume (Vvc), peak material volume (Vmp), core material volume (Vmc).
Others, for example, angular spectrums (APS) and 3D feature parameters.

Figure 5 and figure 6 below show example of why we need different 3D areal parameters to reliably quantified surface conditions.

In figure 5, $Sa$ and $Sq$ parameters alone cannot differentiate the two different surface conditions. In this case we calculate other parameters, such as $Sal$, $Sdq$ and $Sdr$ to be able to differentiate the two surfaces.

In figure 6, two different surfaces with two different feature orientations are presented. In this case, $Str$ parameter cannot different the two different feature orientation on the two surfaces.

Then, we use another parameter $Std$ to capture how many features orientation and what orientation degree a surface has. With the $Std$ parameter, we can extract a single feature orientation on the first surface and two feature orientation on the other surface.

From these two examples in figure 5 and figure 6, we can acknowledge the important of having several 3D areal parameters to calculate.

Figure 5: Example of different areal parameters to quantify surfaces. In this example, Sa and Sq parameters cannot differentiate the two surfaces. Hence, we need other parameters to differentiate the surfaces (adapted from [2]).

Figure 6: Example of different areal parameters to quantify surfaces. In this example, feature orientation parameters can differentiate the two surfaces by capturing the orientation on main features on the surfaces (adapted from [2]).

Conclusion

In this post, we have discussed 3D areal surface texture analysis.

Currently, more and more people adopt 3D areal analysis, instead of the traditional 2D profile analysis. Because 3D areal analysis provides a better “picture” and “representation” of a surface texture.

Standards governing 3D areal analysis is unified into a single ISO 25178 series. These unified standards ease people to navigate guides related to 3D areal analysis.

There are more parameters for 3D areal analysis. These parameters can provide more distinctive quantitative representations on a surface and hence provide a better understanding of our surfaces in term of their functionalities and manufacturing processes.

Reference

[1] Leach, R. ed., 2013. Characterisation of areal surface texture. Berlin: Springer.

[2] Olympus. 2017. Introduction to Surface Roughness Measurement. Roughness measurement guidebook.

[3] ISO 25178-3:2012 Geometrical product specifications (GPS) — Surface texture: Areal — Part 3: Specification operators

[4] ISO 25178-2:2021 Geometrical product specification (GPS) - Surface texture: Areal, Part 2: Terms, definitions and surface texture parameters

You may find some interesting items by shopping here.

amazon #ad