The 3D Moire Law

Updated: Nov 11, 2019

The Moire pattern is created when two grids are superimposed one on the top of the other. This effect is known for a long time, and is often used to create curious visual effects. However, can it be used for 3D imaging?


The Moire pattern created by the superposition of two grids which are disposed in different planes moves with the position of the observer. In other words, it has a parallax. Whenever there is a parallax, there is 3D.


Barriers or parapets are often constructed from dense grids. In some instances it is possible to view two such structures one behind the other. The 3D Moire pattern appears spontaneously in such circumstances, and it is likely that you were exposed to this curious phenomenon more then once.


The 3D Moire phenomenon raises three questions:

1. What is its 3D shape?

2. Where in space it appears?

3. Is it possible to control the 3D Moire shape and use it for 3D imaging?


Although the 3D Moire is a common phenomenon, it appears that these questions were never researched methodologically. It is not possible to expose the 3D Moire research in a Blog. Instead, we present here the 3D Moire law, which answers questions 1 and 2. The answer to Question 3 is much more elaborate; here we will just state that it is positive.


The 3D Moire law is stated with respect to the scheme below. It shows three physical objects: a point light source, an opaque grid and a white diffusive screen. It is assumed that the planes of the screen and the opaque grid are parallel. The opaque grid casts a grid of shadows on the screen as shown in the scheme.


Let us assume that this scenario is viewed from a point behind the light source. The observer will see two grids: the opaque grid and the grid of its shadows (the shadow grid will be partially obscured). These grids are in different planes, and their pitch is slightly different. The 3D Moire Law states the following:

The 3D Moire pattern will appear on a plane parallel to the screen and passing through the light source

The remarkable thing about the 3D Moire phenomenon is that its shape and position in space does not depend on the observation point. To the best of my knowledge, there is no other 3D optical illusion phenomenon which has an infinite viewing space, both in angle and in range.


Obviously, one does not need to use light sources and shadows to create a 3D Moire pattern. The shadows grid in the scheme can be replaced by a suitable physical grid.

The 3D Moire effect is used already in flyeye pictures, like the one below (taken from https://www.swissqprint.com/en/3d-moire-effect.html):

3D Moire effect in flyeye picture

3D Moire effect can be also created in lenticular pictures, like this one:

"ORB512" 3D Moire art picture

In this picture the 3D Moire pattern was sculptured to appear on a ball rather than on a plane.

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Herzliya, Israel

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