Moir� Patterns & Fringes

Ethereal shapes, tessellations darting and flickering with the slightest head movement.

Curved and shimmering fringes on fabrics, distracting flashing false colours on a TV announcer's check jacket, lines and artifacts when scanning printed pages - all manifestations of moir� patterns and fringes.

Mario Freitas of Universidade Tecnológica Federal do Paraná saw this hexagonal moiré pattern on a pair of overlapping doors at the entrance of a mall in Curtiba, Brazil.

Each door had a near identical screen made up of an hexagonal array of circular holes ~2mm diameter. The screens were ~50mm apart.

Light rays passing through, or being blocked by, the screens made the patterns.

The top image was taken with a zoom lens some distance away. 

As Mario then approached the doors (smaller images a and b) the hexagonal pattern surprisingly got smaller rather than larger as might at first have been expected.

Close up (c) the ever smaller moiré pattern dissolved into the screen design itself.   Really close (d) we see the nearer screen's hexagonal hole array.

What the eye or camera sees is a mosaic of the distant scene. The two screens act as masks that in places open to reveal the scene and in other places block it.

An element of the scene or background is visible when a line from it to the eye can pass through a hole in each screen. Angular directions where the holes do not align at all have light blocked and appear dark.

The conditions for alignment or transmission occur periodically with the result that a moiré pattern forms. The pattern generation is most easily visualised for a pair of simple linear arrays of holes as at left.

The condition of transmission through a given pair of holes in the two screens is extremely sensitive to the position of the eye or camera. The slightest movement shifts the pattern dramatically.

Moir� patterns are generally are very sensitive to movement, a property used in some rotation and position sensors.
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From the eye's viewpoint, holes in the two masks periodically line up and then become out of line.

In the diagram every eight holes or so on the front mask line up with the back one to give light.

As the eye gets closer the spacing between holes in the front mask that line up with those in the back mask decreases. The one dimensional moiré pattern then shrinks.

A one dimensional moiré pattern

The blue and green masks have identical arrays of equally spaced circular holes.

Viewed from a distance the two sets of holes are periodically aligned and let through light. At other angles the light is blocked.

The result is a repeating pattern of light.

Create moir� patterns

Make a pattern containing transparent holes or spaces. Save the pattern as a layer in Photoshop or equivalent.

Alternatively, download this PSD file example.

Duplicate the layer.

Enlarge, reduce, rotate or distort the top layer to generate moiré patterns.
hexagonal mask
stacked mask
Top mask slightly enlarged and rotated generates a hexagonal moir� pattern. This one is equivalent to being far away from the two mall doors
Top mask further enlarged. Equivalent to moving closer to the mall doors.
Regular repeating grids produce moir� patterns that are a highly enlarged version of the grid.

The hole shape is less important. This rectangular array of rabbits gives a rectangular moiré pattern with only a hint of rabbit.
Moiré and interference

Moiré patterns are the result of two masks that let through light when their apertures overlap and block it otherwise.

When the masks are regularly spaced lines or circles the effect is akin to optical interference where two sets of light waves superpose and interfere. There is light in directions where wave crests (lines) coincide and darkness where they are out of phase.

At right, two overlapping masks of equally spaced circles reproduce the positions (but not intensities) of interference fringes generated when a coherent light beam impinges on two slits.

Masks where arrays of lines are distorted give the twisting and curved moiré fringes often seen on fabrics.