# How to measure 8 μm surface bumps?

I want to measure surface bumps which are larger in size than $8\ \mathrm{\mu m}$ on a uncoated plastic mirror. So it can be any number of smaller bumps and that would not effect the application.

I don't want to count them only estimate if there are many or few.

The mirror is curved (spherical). The theoretical sphere is about $160\ \mathrm{mm}$ radius and the total size of the mirror is about $30\times20 \mathrm{mm}$. I have to buy every thing and can't borrow any equipment. So cost is an issue.

How can this be done?

EDIT: The mirror is curved (spherical). The theoretical sphere is about 160mm radius and the total size of the mirror is about 30x20 mm. I have to buy every thing and can't borrow any equipment. So cost is an issue.

• An atomic force microscope (AFM) would certainly do it. The instrument is expensive, but many college campuses have them. – Spirko Dec 4 '15 at 16:27
• The problem is that I can't borrow equipment since it will be used for many years. – Johan Holtby Dec 4 '15 at 16:57
• IF cost is an issue then you're not charging enough for your product. Check your business model. And no, I'm not kidding. – Carl Witthoft Dec 4 '15 at 18:14
• @CarlWitthoft Huh? Don't people work on lowering cost in order to make a product economically viable? – DanielSank Dec 4 '15 at 21:02
• The lowest price is most interesting to the customer. – Johan Holtby Dec 7 '15 at 7:43

Since your substrate is a mirror you can simply place a partially transmitting mirror on top of it and illuminate it with coherent light:

Wherever you have a bump on the substrate it will be visible as a series of Newton's rings. Examine the system with a low powered microscope and you'll easily be able to count the number of bumps in some specified test area.

Eight microns is huge as these things go, and easily visible. For my PhD I was trying to measure features 10 nm high, which was a lot, lot harder!

• I'm not counting only estimating to sort bad mirrors from good mirrors. However i like the approach. – Johan Holtby Dec 4 '15 at 16:42
• You've just edited your question to say the mirror is curved, which makes life harder. However given that it's a mirror I'd say an interferometric technique has to be the easiest solution. – John Rennie Dec 4 '15 at 16:45
• It's an black plastic piece which is not coated yet. But I agree. As most post on this page has mentioned the best approach would probably be using some interference measurement (interferometric interesting new word to search). – Johan Holtby Dec 4 '15 at 16:49
• How about a Shack-Hartmann test with an array of pinholes on the order of the desired defect diameter? – Carl Witthoft Dec 4 '15 at 18:17
• That sounds very interesting. I have read some about it but don't understand the setup to use. I have only found lenslet arrays no pinhole arrays. I'm familiar with the pinhole camera setup. Is the ninhole array just a lowpas filter for defects in the wave front or is the use more like lenslet arrays? Could you elaborate on the setup? It would be most appreciated! – Johan Holtby Dec 7 '15 at 7:50

You could possibly use a 1 um laser (wavelength smaller than bumps) and make a hologram type of measurement - see wiki article and https://upload.wikimedia.org/wikipedia/commons/3/34/Holography-record.png for experimental setup.

The idea is that a change in path length from a bump would lead to some interference change on a detector. Of course, the final setup would be more complicated and would depend on your sample size and other considerations.

• Sounds very interesting. But i don't understand the concept of hologram type measurements. Is there a more basic link? – Johan Holtby Dec 4 '15 at 15:53
• The wiki page is a good start for beginners: en.wikipedia.org/wiki/Holography also watch some youtube videos. The basic underlying principle is "interference" (see en.wikipedia.org/wiki/Interference_(wave_propagation)) – StarStrides Dec 4 '15 at 15:55
• Sounds like I have some reading to do. I kind of understand but not really how to evaluate if there is many or few bumps. – Johan Holtby Dec 4 '15 at 16:44