Substrate Surface Analysis: Get the Most from Roughness Data

TAGS:  Science-based Formulation    

Sometimes we like a gloss paint, sometimes we like a silk paint and sometimes we like a matt paint. Although the paint itself might be basically the same, the crucial difference is in the surface. Of course, the gloss surface is smooth while the silk and matt surfaces are rough.

But how are the surfaces smooth or rough? This is just one of many examples of how we need to control the roughness of a surface for the look, feel or function. And to control something we need to measure it.

Measurement can be via an AFM, a white light interferometer, or some sort of confocal microscopy. But the most common method is via a scanning stylus probe, basically a fine diamond style that is pulled gently across the surface while monitoring and recording the ups and downs of the stylus.

Here is a typical plot from such a stylus probe, as seen in the top left of this screenshot from my free Surface Profile Explorer app.

Across a length of 12.5mm (12500µm), the fine stylus tip has followed the ups and downs covering a vertical range, in this example, around 5µm. From the large number of individual data points, the device can calculate and output some values that characterize your surface.

If you are unlucky, you will have a machine that simply gives you some “roughness” numbers, with no visualization of the surface. This guarantees that you will be strongly misled.

If you have a more modern machine that allows you to view the digital scan and allows fuller analysis, you have the chance to really understand your surface. Yet many people don’t take advantage of the data because (as you can see in the screenshot) there are so many different numbers offered by the instrument. Few of these numbers have any obvious meaning or clear advantage compared to the well-known Ra and Rz values.

The combination of this article with the app easily helps you to get a good understanding of your surface, and how it affects your product.

• The app lets you choose from a set of different, known surface profiles. Although the app also lets you load your own dataset, here I will only use the standard examples.
• The point is that by knowing exactly what the surface is like (because it’s created through our own choices) we can make a rational comparison between the different measurement values, to show when they are useful or, as is often the case, misleading.

Let’s start with all those R numbers which are various measures of the amplitude of the roughness...

Amplitude Measurements

Ra and Rz are familiar to most of us. Some industries tend to focus on Ra and others on Rz. They are just different ways of averaging over the peaks and troughs, trying not to over-emphasize anomalies while trying not to ignore too much that’s of significance.

For those interested in gloss measurements, Rq, also known as RMS should be used because it happens to correlate more strongly with gloss than Ra or Rz.

The important thing to realize is that often these standard values can be completely misleading. Go to the app and click the High option. Then, having looked at the numbers, click the Deep option.

The important thing to note is that Ra and Rz are identical for the two cases, even though the two surfaces are clearly very different.


By comparing the values from the two datasets you find that Rpm is large for the High structure and Rvm is low, while for the Deep structure it’s the other way round.


There are plenty of other R metrics and each of them is described in the text of the app. Instead of exploring them all, I want to look at another metric that is little known and rather important.

The opening image seems to show an amazingly rough surface. If you:

• Imagine yourself as an ant having to walk across the surface, you can see that you would have to walk a very long distance up & down those hills and valleys.
• Compare the distance you actually walked to the distance of the smooth surface (i.e. 12500µm), you can get an idea of how much extra surface area there is.

The intuition of most people, especially in the adhesion science community, is that Lr ratio will be large (maybe a value of more than 2), showing that the surface area has been doubled. Yet when we look at the Lr box in the output, you see that it says 1.000.


The reason for this difference between intuition and reality is the different X and Y scales. If you zoom the X scale by changing View Length to, say, 25µm and then slide the View Offset to scan across the surface, you find that it is a very gentle surface – no amazing mountains and no deep valleys to trap adhesive in order to increase adhesion:


There is one more thing to know about roughness amplitude measurements which you can test for yourself. Use the Slope slider to create a small slope of 5µm along the 12500µm. You haven’t changed the true nature of the roughness, but the Rz increases from ~4.2 to 4.5 while the Ra increases from ~0.6 to ~1.35. This is a reminder that different metrics have different susceptibilities to errors such as an accidental slope.



If you are not aware of the slope, which might be due to a slight misalignment of your instrument, and if you rely on Ra as your customer spec, then you would be spending a lot of time trying to make your surface flatter before shipping, and therefore delivering a product unfit for purpose because the true roughness would be less than required.

Of course, good stylus probe machines allow you to add low-pass filters to remove such simple errors, but every filter adds potential distortions. The human eye is really good at spotting systematic errors and correcting them.

I like creating Abbott rules for real-life science, and the first Abbott rule for surface roughness measurements is: “Never use a machine that does not give you a visual output of the scan”. It is amazing how much you can learn from a quick glance.

• If there is a slope it is obvious.
• If there are a few spikes from, say, a piece of dirt, they can really distort the values.

So only use reported values when your scan makes visual sense and you have corrected, for example, for slope errors.

Wavelength Measurements

Let’s compare two different samples:


These have been created using the Synth option and are simply sine waves with wavelengths that differ by a factor of 10. Not surprisingly, their Ra, Rz and other amplitude values are identical. Yet clearly the surfaces are very different in practice. This is seen in the λ & S values which are a factor of 10 different each.

The λ values are measures of the representative wavelength of the surface, and the S values are a sort of equivalent, the average local slope (not to be confused with an accidental global slope). Because I have chosen simple sine waves, the values are obvious; when you have a real rough surface, they are less intuitive but still important. They are the missing link in so many surface effect puzzles.

Here’s a typical problem. You have two surfaces that are each within spec in terms of amplitude and which avoid elementary errors of, say, peaks versus troughs, yet visually they are obviously different. They might also have a very different “feel” when touched with the fingers, something of great importance to those creating objects that need to be handled by consumers.

Our visual and tactile senses are very sensitive to the wavelength of the surface structure and those who rely on amplitude-only measures will never be able to tune such surfaces and ensure their quality control. I say this with feeling. Many years ago, I was involved with a project where something changed in our process and although everything stayed in spec with Ra and Rz, the product was visually unacceptable.

I created the very first version of the Surface Profile Explorer (written in a now ancient language) because of my inability to understand what our measurements were providing. It was a lightbulb moment when I started to see the wavelength effects as being as important as the amplitude ones. It was then that I pronounced the second of Abbott’s laws of surface roughness: “Never rely on just amplitude, always check the wavelength values”.

Those who want to see how amplitude and wavelength interact in terms of gloss level, an important measure for many products, can visit my page https://www.stevenabbott.co.uk/practical-coatings/gloss.php, though they should be warned that the app is at first a bit tricky just like the topic of gloss.

The Take-home Message

Here is a serious suggestion. Now you’ve read this article, assemble your team of colleagues involved in a project where the surface structure is important.

• Set up Surface Profile Explorer on your video screen and together play around with each of the different surfaces, noting the changing values and identifying which seem to be most sensitive and relevant to your projects.
• If you can’t remember what, say, R3z means don’t worry – you can scroll down and find the definition. Make sure you focus as much on the wavelength metrics as on the amplitude ones.
• If you wish to know more, together you can look at some other values such as peak count, Pc, which are a bit more complex.
• You can also explore the graph on the top right, the ADF, Amplitude Distribution Function, from which parameters such as Rsk (skew) and Rku (kurtosis) are obtained.
• If you have some digital datasets but no software to view them, by transforming them into a simple text file containing two columns with X and Y values separated by a tab, you can load them into the app.

From this process, you will be able to work out which metrics are important and diagnostic for your purposes. If you need to agree on these metrics with a supplier or customer, bring them into the discussions so that everyone is clear which metrics have been chosen and why.

Especially important is to include the chief budget holder in the meeting. If your surface profile machine only gives a few R values with no possibility of viewing the raw data and obtaining wavelength values (i.e. it contravenes both Abbott laws) then maybe the meeting will be convincing enough that some weeks later you will have a profile that is fit for purpose.

One story to end with! I was involved in a project with a major Asian customer who wanted a sophisticated surface with the right look and feel. They had lots of Ra and Rz data but could not correlate them with the like/dislike judgements of panels of test users, so they had no way to define an optimal surface.

On a Friday, I said that they needed to re-measure all their samples so I could extract all the data, especially the wavelength metrics, and aim for a correlation. To my surprise, on the Monday morning a few MB of raw digital data were sitting in my email inbox – they’d worked the whole weekend to get the data.

Extracting the data wasn’t hard, but how was I supposed to get an optimum correlation. A colleague said “Just use Excel’s Pearson correlation technique”. I had no idea what this meant, but it wasn’t so hard to set up. I pressed the button and instantly it was clear that in this specific case, almost any reasonable amplitude metric coupled with any reasonable wavelength metric gave a strong, predictive correlation. Because it was especially easy for them to measure Rz and λa, those became their metrics during development and QC measures during production.

In this example, a problem that had baffled a large, serious team for months was solved with a weekend’s work and a click of an Excel button. I hope that by using Abbott’s two rules and, therefore, a good surface profile measurement system, you will similarly find that your surface analysis puzzles will become a thing of the past.