# Moire Pattern



## goldsilverpro (Feb 1, 2018)

Sorry. Another long windy story.

Although this happened 50 years ago, this year, it posed a question or two that haven't been answered to my satisfaction.

One of my first jobs in LA was to head up the lab in a large plating facility. This place had about 100 active plating tanks, plus a ton of cleaners, acid dips, etc., ranging from 50 gallons to maybe 4000 gallons, of about every type of plating under the sun. My job was to analyze the solutions and keep them up to snuff. I also was the head troubleshooter and, in a plating shop, troubleshooting is a daily, if not hourly, thing. 

Something that set this place apart was that they were a licensee for the Kanigen electroless nickel system developed by the General American Transportation Co. This was originally developed to plate the inside of railroad tank cars The round tank from a car was rotated on rollers while the 200F solution was pumped in constantly and drained out constantly and reheated. The solution plated catalytically and deposited about 1 mil, 25 microns, in an hour. We maintained 4200 gallons of the solution. The solution crapped out after about a month and had to be re-made from scratch. It was made up with 6 or 8 chemicals.

At night, it was pumped into 3 holding tanks and allowed to cool. During the day, it was pumped from the storage tanks to whatever tanks were needed to fit the particular shapes and sizes of the parts being plated that day. There were 20 or 30, 300 series SS tanks, of all shapes and sizes, all connected with about 2 or 3" pyrex piping. The solutions were heated with live steam from a big boiler. At night, when all the tanks were empty, a 20% nitric solution was pumped into all the SS tanks used that day. This dissolved any nickel plated on the SS and, at the same time, passivated the SS so that nickel wouldn't plate on the SS unless a part were dropped in the tank and that damaged the oxide layer on the SS, thus exposing nickel to the solution.

Patience, please. I'm getting there.

One big job we had was plating large SS screens, with holes in them, which were used to line centrifuges in large sugar plants. I think that the sugar was dissolved and then the solution was put into the centrifuges to remove undissolved crystals, etc. The flat SS sheet panels were about 18" X 24" and a number of them were used in a circle to line the centrifuge. They had many 100s, and probably, many 1000s, of these fabricated before discovering that the holes were too big. What we were doing was to plate nickel thick enough to fill in the holes until it met their spec. Since electroless nickel doesn't use a power supply, it plates extremely evenly over the entire part.

The holes were chemically machined and were hexagonal, about 1/32" (.8mm), or so, and were very close together. There was an immediate discussion on how QC should best measure the resulting hole size(s) after plating. Several methods were tried but found innacurate, tenuous, or time-consuming. I discovered that if a plated sheet were placed on top of an unplated sheet and the pair placed on a light box and the top plated sheet rotated, a moire pattern appeared. When the top sheet was rotated to a certain angle, the images of the holes were magnified from 1/32" to maybe 3 or 4", or more. I assumed that the magnified image was an average of all the holes in the area covered by the 4" hole image. The 4" hole image was measured along with the spacing between 4" holes and the hole diameter was calculated. Whether my thinking was correct, or not, in my assumptions, the hole size came out correct and the customer was pleased.

Questions: Was the large image truly an average of all the holes in that large area? If so, what is the math involved? 

Every few years, I rehash this problem in my mind and lose sleep thinking about it. I just Googled again and could find no instant answer. I downloaded a file on Moire Patterns from Wolfram along with a viewer. Maybe it will help solve this problem. 

*NOTE:* The Wolfram stuff was worthless - just drawings.


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## g_axelsson (Feb 1, 2018)

Interesting problem...

I can imagine that this can be described in terms of fourier analysis. It is a repeating pattern of another pattern (a single hole). Coupled to a similar pattern but with a twist and you got interference between the two plates.
This could definitely be modeled with fourier analysis and I think you have the answer there... though, there are quite a bit of work to formalize the solution.

In electron microscopy a similar phenomenon occurs, I haven't experienced it myself and I've only read about it, it is possible to measure the size of cells on a slide by interference over a large area covered with cells.

Here is an article about electron diffraction that might dive into some details.
https://ac.els-cdn.com/S0006349569864374/1-s2.0-S0006349569864374-main.pdf?_tid=fb5a1682-0793-11e8-8f2a-00000aab0f6b&acdnat=1517519459_a565fa6450c635cc8b6a22d52b837705

Göran


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## Palladium (Feb 1, 2018)

This is way over my head, but what you are describing relates to me the function of a pin hole camera for viewing a eclipse. I wonder if anything can be found in the mathematical formulas used for that?

https://en.wikipedia.org/wiki/Pinhole_camera_model


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## goldsilverpro (Feb 1, 2018)

https://www.google.com/search?q=moire+pattern&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjYo6v8gIbZAhVh_IMKHSKsD9AQ_AUICigB&biw=1138&bih=497

You've all seen it driving in the country when you are viewing 2 fences, one in back of the other. If you watch, the pattern changes as your car moves. Here's a few good pictures and a lot of bad. 
https://www.google.com/search?q=moire+fences&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwi-4JWcgobZAhVi3IMKHeOHCnsQsAQIXA&biw=1138&bih=497

A pretty good article on fences. You've all seen these patterns,
https://www.interviewmagazine.com/art/todd-kreher-nominated-by-kelley-walker

There is also moire silk, fairly common inside the covers of old books. I would guess they make it by overlapping 2 layers of silk and rotating one layer slightly, until they get the desired effect. I could very well be wrong. I didn't research it.
https://www.google.com/search?q=moire+silk&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiX6eWrg4bZAhVr1oMKHSlNAzkQ_AUICigB&biw=1138&bih=497

Still, I can't find anything similar to the phenomenon I observed, the enlargement of the hexagon.

I think moire is pronounced like a moray eel and, when written, there's a hickey over the e.

In writing this, I kept trying to remember whether we had to sync the two sheets, or not. I don't think it was necessary. I think the QC girls just shifted the top sheet around until a large hexagon appeared and then held it down tight while they measured it with a ruler.


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## Smack (Feb 2, 2018)

That's also the patter that is created on TV if you wear something with vertical stripes and that's why they tell you not to wear cloths with stripes if you're going to be on TV.


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## Palladium (Feb 2, 2018)

So horizontal stripes are ok?
Just checking! :mrgreen:


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## rickbb (Feb 2, 2018)

Look to the printing industry, modern lithography uses this Moiré effect to print full color from just 4 inks. It's a well established science there. There are formulas to calculate various patterns by overlaying screens at different angles/resolutions.

Some math on it here;

https://en.wikipedia.org/wiki/Moir%C3%A9_pattern


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## goldsilverpro (Feb 2, 2018)

That Wiki article is the best so far, Rick. Can't believe I missed it.


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## everydayisalesson (Feb 2, 2018)

This is why I try to read everything posted by many of you. As you stated in references to the fences GSP, we do see it everyday. I never would have looked into it as a named phenomenon though. 

Something that may or may not be related to this is something I seen twice in my life, I have tried to duplicate it but have yet to do it. I was standing about 15 feet in front of a fence one day, and there was a bush with very small petal like leaves just the other side pressing up against and through the fence. Just as I looked up, a gust of wind fluttered the leaves in such a manner that my brain was unable to keep up with all of the changing colors, shapes, and shades. My brain kind of just blurred it into what I can only describe as a smudge.

That was about 30 years ago, I seen it again about 10 years ago. The second time, I told my wife about it. She was at one time in the medical field and said that people can have strokes or seizures when the brain is presented with so much information at one time. She said flashing lights can do the same thing. Didn't mean to go off topic here but I thought I would share it with you guys anyway. Interesting topic either way.

Mike


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## Smack (Feb 2, 2018)

Palladium said:


> So horizontal stripes are ok?
> Just checking! :mrgreen:



Well I thought it was just vertical, guessing I'm wrong then? Been a very long time since I heard about it, I think it was during a Johnny Carson show. No worries it won't kill ya.


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