Monstein moiré


I have just posted a video of a moiré pattern I generated earlier


The two gratings encrypt the images of Albert Einstein and Mona Lisa, hence Monstein. The two gratings are in green and purple — two opposite colors to combine into a gray image.


Here are some online applications that let you play with moiré patterns:

1. Project LITE at Boston University
2. Elisabeth Sylvan student project at MIT
3. Moire videos at phidelity blog
4. iMoire by Vincent Scheib

A common misconception of shadows is that they must be binary, producing images comprising only black and white areas.

The following figures are adapted (with some conceptual changes) from a patent application I filed while employed at General Electric (US 20080037709A1: METHOD AND SYSTEM FOR CONTROLLING RADIATION INTENSITY OF AN IMAGING SYSTEM). The invention uses shadows from superposed opaque gratings to control the spatial distribution of x-ray radiation intensities in an x-ray beam.

First, we produce two gratings comprising curved opaque bars:

Then, we superpose them with some distance separating them and shine light through them at different angles as shown:

The bars are curved so that the same two gratings together cast shadows containing two different detailed images (not just contours):

Yet, this is not the whole story. If the light comes not from a point source but from a somewhat diffuse source (e.g. the sun), then the shadow will be blurred somewhat by penumbra or half-shadows producing a full-grayscale image:

The blur removes the sharp edges and, paradoxically, improves the images. Notice for example the wrinkles on Albert’s face that only come through after the images has been blurred.

Another way to achieve blurring is to rapidly shake the gratings perpendicularly to the bars. Motion blur will then remove the sharp edges from the image producing a similarly smooth image.

You can print the gratings in (a) and (b) on transparencies and superpose them with slight offsets to see the effect for yourselves.

What if such gratings are built as sculpture pieces or are integrated into the facade of a building or as sundials that would cast various artistic shadows at various times of the day at various seasons? What do you think?

Moirés in architecture can add a sense of motion to the building. As you walk past the building, the pattern will appear to move and dance – I can almost see it.

Such patterns could be dramatically improved by using color, generating meaningful images instead of simple geometric patterns, and making the patterns vary with the position of the sun.

Before exploring moiré patterns more systematically and mathematically, let’s look at a few examples.

Most moirés are incidental: they arise naturally when two or more gratings, sheets of fabric, wire screens, fences, or dot screens are superposed.

Fence moiré, by Prof. David Eppstein at UC Irwine

In signal processing and imaging, moiré patterns are often known as aliasing. They arise when the sampling rate of a digitized signal is too low to accurately represent the signal. This effect may be a big nuisance in photography and television. In this case in the role of the two gratings play the periodic features in the image and the regular arrangement of pixels in the camera.

Moiré patterns are responsible for adding funky colors to Al Gore’s collar in this photo, arguably improving its appearance:

These aliasing artifacts can be easily resolved by either increasing the sampling resolution or by applying proper filtering techniques prior to sampling as described by the Nyquist theorem.

Moiré patterns are commonly treated as a problem. However, they also have many useful applications. For example, their ability to magnify small offsets is exploited for strain and deformation analysis of materials by means of moiré interferometry.

The intentional synthesis of moirés appears to be largely unexplored. The most interesting and sophisticated examples of moiré art I have found to date are animated pictures in children’s books:

Animated Illusion, Solved!Funny videos are here

Invariably, the words magic and amazing are used to describe moiré phenomena, even the most basic ones.

These examples are but a small fraction of what could be done with moirés. Through this blog, I would like to expand the definition of moirés and their applications.

Digital sundials


As my friends know, I have a fetish for moiré patterns and shadow sculpture: I have designed a few interesting patterns and have patented an application for moiré synthesis for x-ray fluoroscopy. I believe that shadows and moirés remain largely unexplored as an artistic medium since their generation may be computationally and conceptually daunting.

A company already markets moiré-based digital sundials. As any other sundial, it has no moving parts and no electronic components – only shadows and reflections.

The idea is computationally simple yet the the design is slick!

What else can be done with this? Color? Full grayscale? Larger scale? Artistic expression?