Tag Archives: moiré

Moiré Patterns

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Moiré pattern

Some time ago I reblogged a post from El Ojo Inoportuno showing Moiré pattern, which resulted from taking a photo of a circular pattern of (beautiful) tiles. This phenomenon is caused by undersampling and is also called space aliasing. There’s a very good explanation of space aliasing and another stunning Moiré example on Agile Geoscience’s post N is for Nyquist.

Creating Moiré patterns

One way to get Moiré pattern is to superimpose two identical, transparent line gratings and rotate one by an angle. You can see an animation of this on Wolfram Mathworld here; notice that the pattern varies with the angle. In the same page there’s also an example of Moiré Patterns generated by plotting series of curves on a computer screen, which is very similar to taking the photo of circular tiles shown in the Ojo Inoportuno photo. Again the interference is caused by representing circles with a finite size pixel grid. If you are interested you can experiment with these effects and many more by downloading templates from this site. Figure 1 shows my own Moiré from circular patterns.

circ2

Figure 1

 

There is a program for interactive Moiré pattern experiments called iMoiré.

Another way to get a Moiré pattern is to scan a picture printed with halftone. There’s a simple explanation of this scanning-generated interference here. Again this is a matter of aliasing, or undersampling. Here’s a good example:

Figure 2

The original image is a lovely watercolor by  Ettore Roesler Franz showing medieval houses along the Tiber river in Rome. The Moiré Pattern results from scanning the watercolor from one of the book collections (the image was posted on Flickr here).

How to remove Moiré pattern from digital images

For a quick solution, there’s a good article with detailed instructions on how to remove Moiré pattern in Photoshop, Paint Shop Pro, etcetera. For a more advanced workflow there’s an excellent top hat filter in Photoshop included in Reindeer Graphic’s FoveaPro plugin. In Figure 3, I created a sort of pictorial chart of this workflow using low resolution copies of examples in The Image Processing Cookbook, by John C. Russ.

Figure 3

 

In future posts I plan to show how to remove Moire’ pattern with open source code images  using Python, and then to extend the workflow to the removal (or attenuation) of acquisition footprint in seismic data, which has a very similar appearance in the 2D Fourier domain, and can be filtered with very similar techniques.

 

 

Mo(r)iré

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I love this photo (thanks to Carlos Mario del Rio for posting it)!
There’s something about tiled floors (and tiles in general) that has always mesmerized me and this is a really good one. I like the unusual perspective too.
There’s a radial pattern and a circular pattern of tiles, but if I stare at the photo I also see hints of an interference pattern, an intriguing flower pattern. I think this is a genuine Moiré pattern, one quite well known to photographers, generated by interference between circles of varying distance with the camera’s sensor pixel grid.
In my next post I will look in more detail at Moiré patterns and try to explain how they form.
I will show how the effect can be removed, or at least reduced, particularly from scanned images. Similar techniques can be used to remove acquisition footprint from reflection seismic data, which will be the topic of an upcoming series on MyCarta.