Roughly, small measured area means that longer features are not even captured in the image – and then any levelling makes it even worse.

No, the units of the distribution are 1/height_units. It is a probability distribution which must integrate to 1. Hence the product of the abscissa and ordinate units must be also 1. It does not count anything. It is the distribution of heights.

When the area is very small, it becomes difficult to even estimate how much the result can be wrong because the information just isn't in the image. So take 40–50% value as an educated guess (from someone who wrote paper about this). It can be 30%. It can be more than 50%.

If you measured larger areas, almost everything you now consider waviness would become roughness (the split is kind of arbitrary). You may insist on splitting the texture to waviness and roughness because a standard say so, but then your scan lines may have to be 1.25 mm long – because the standard says so.

Please note that Surface SMP85 should be more rough than SMP43 which is kind of evident from the topography. But RMS values are contrary. I also tried 2nd order flatenning on both images before calculating Overall RMS. These values also match with the Asylum Research Software. What I think might be happening is that the crystal growth is kind of lateral in case of SMP85, due to which the surface roughness is contrary.

That is explained in the paper. The accepted version has some nice improvements and additions, but you can get the original submission from arXiv https://arxiv.org/abs/2001.00433.

Also note that the scan sizes are way too small for roughness measurement. For SPM43 roughness will be underestimated maybe by 40-50%, for SPM85 a bit less. In addition the value will have a huge variance (i.e. uncertainty). See https://iopscience.iop.org/article/10.1088/1361-6501/ab8993. The scan cannot contain just a few bumps in it, it must have lots of them.

One last question and it is little bit silly to ask but- when we show height distribution an entire image, the unit of Y-axis reads rho( µm^-1), is it density distribution of the mountains?

Please do not evaluate roughness from single profiles if you have image data. Use the Statistical Quantities tool (for start).

0.9 mmhexnearby

If you think I should proceed with PSD and its more wise choice for accurate results, is there a protocol with steps or examples I can learn how to use?

One last question and it is little bit silly to ask but- when we show height distribution an entire image, the unit of Y-axis reads rho( µm^-1), is it density distribution of the mountains? If I put an intersection line and if coordinates are (0.200µm, 0.915µm^-1)- does it should read as- "there are 915 mountains per nm which has height of 200nm. Is this correct? If not what is? Kindly help.

I have couple of questions regarding roughness estimation. I am working with very rough surface (.ibw files attached along with images). When I choose "calculate roughness parameter" option, I have to select a line on the topography. Here the have to specify the "cut-off" and then the algorithm takes out surface waviness texture and separates roughness for that " line.

I have another query I wanted to ask you. Please see the attached image. Before asking this, I understand that the size of my image is not enought to give accurate value of the roughness. But just wanted to know this. 1. The Row and Column statistics, when used, the curve generated, is it the average roughness profile for the whole topography? 2. The value 198, is the average Roughness value? 3. Again, I wish to request you exactly in words, how will you read the graph? For the position on X, the roughness is Y, is it? 4. Since row is generally fast scanning axis, for angle 0, should I prefer choosing row? 5. Last question is, if this is roughness profile, does it filters the waviness and texture out?

The height distribution is a probability distribution. So, technically, values at a single point have no meaning, only its integral over some finite interval has meaning. The sentence can be read as for any probability distribution:

As per literature PSD, might be more accurate in this case. I spend some time reading about this but still I can't apply this in my case and also I am not sure how to "PSD" option in "Data process". When I use it anyways, I get a picture which seems more intense at the center and thats it. I don't know how to proceed after this or even if I started it correctly.

For SPM43 roughness will be underestimated maybe by 40-50%, for SPM85 a bit less. How are you saying this, I mean how can we be knowing that there will be underestimation by 40-50% ? Secondly, Why will SPM85 a bit less?

The cut-off values are manually adjusted for each case, and should be very carefully choosen. This seems very non-reproducible result to me. What is the correct value, how should find out so that my results becomes reproducible?

Also note that the scan sizes are way too small for roughness measurement. What scan size should it be in general for more appropriate estimation?

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Hi David thanks for reply. I found the paper thanks for the reply. I will read the papaer and if I might any question I will ask you. I hope thats ok with you.

My questions are- 1. When using " calculate roughness parameter", is it anyway possible to have "line" thickness to equal to whole image such that I can remove the waviness 3-dimensional, ending up with only 3D roughness profile. Similar to what we see the upright curve but in 3D form or for whole image? I am imagining this as when I can increase the line thickness to equal to 15µm (my image size), I will see something like 3D texture, 3D waviness and 3D roughness images.

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You may have an a priori physical reason for considering the texture as composition of long-wavelength (‘waviness’) and short-wavelength (‘roughness’) components. In such case calculate the 1D PSDF using Statistical Functions tool, export it and fit it with your two-component theoretical model.

If you take a small interval of heights Δz around 0.200µm, then Δz × 0.915µm^-1 is the fraction of surface heights which lie in this interval.

0.9 mmhexscrewdriver

It is probably possible (for sufficiently small images), but never do this. You do not want to average profiles over the entire image.

See https://iopscience.iop.org/article/10.1088/1361-6501/ab8993, being off campus, my institute id is not working to get this paper.

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It is definitely not evident, if ‘being more rough’ means the usual ‘irregularities having larger vertical size’. The vertical scales are comparable. It is entirely possible SPM43 is more rough.

My last question is "If I put an intersection line and if coordinates are (0.200µm, 0.915µm^-1)"- does it should be read as. I am requesting for a sentence which reads the values. think it as physical significance.

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