Moiré artifacts and other forms of aliasing often appear in electronic imaging systems due to insufficient sampling of the optical images. Spatial aliasing occurs when the optical image bandwidth exceeds that of the image detector. Spatial aliasing manifests itself when a TV host wears a fine-striped shirt, producing distracting moirés.

George's moirés

George's moirés

Temporal aliasing occurs when the temporal bandwidth of the imaged scene exceeds the frame rate of the camera. Temporal aliasing manifests itself in the wagon wheel illusion in a Western movie. A rotating wagon wheel will appear to freeze or even to reverse its rotation.

Why don’t biological systems experience aliasing — or do they? Does the eye or brain circuits exhibit aliasing and moiré phenomena?

The human eye appears to avoid spatial aliasing by supersampling the optical signal: the point spread function of the eye optics covers several photoreceptors. What limits the resolution of the eye is the optics. The cornea, aqueous humor, the lens, vitrous humor, and three layers of retinal cells in front of the photoreceptors blur the signal and efficiently remove the very high-frequency content in the image. In addition, the arrangement of photoreceptors is not strictly regular as happens in a CCD chip for example. Thus chances of producing a spatial moiré pattern in the eye are nil.

However, temporal or spatiotemporal aliasing may occur, probably in motion processing areas of the visual cortex. One manifestation of this glitch is the motion reversal illusion sometimes perceived when a spoked wheel accelerates and decelerates through a range of RPMs. Skeptical that this could be the result of the stroboscopic effect of electric lighting, I made a black-and-white pinwheel and spun it. Even in daylight, at some rotation rates, I perceived subtle and transient episodes of illusory reversal. You can try this for yourself.

I spun this wheel to reproduce the rotation reversal illusion.

Spinning wheel to reproduce the rotation reversal illusion.

Is this evidence that the visual system has a semi-regular ‘frame rate’ similar to video and film cameras? I found it hard to believe. Temporally subsampled signals indicate inefficiencies undercutting the quantum efficiency (ie overall sensitivity) of the system, a problem that’s too easily fixed by introducing additional blurring (low-pass filtering) to limit the bandwidth before sampling. Temporal blurring is something very easy for cells to do and evolution would have long found a way to blur the signal, even if vision did work in regular discontinuous frames. There has to be something else to account for the illusory motion reversal.

In a recent paper by Kline and Eagleman (2008) in the Journal of Vision titled “Evidence against the snapshot hypothesis of illusory motion reversal”, the authors staged a series of experiments that argued against the snapshot hypothesis (frame-rate hypothesis).
The experiments support the rivalry hypothesis of the illusory motion reversal, ie that “the continuous stimulation of one direction of motion eventually causes rivalry with the opposite direction of motion, and the balance of the rivalry eventually tips, engendering the perception of reversed motion”. In other words, motion detection is hypothesized to consist of multiple motion detectors that each have undersampled spatiotemporal responses, many of which produce aliasing. Normally, those motion detectors that detect correct motion are stimulated stronger than their aliased counterparts resulting in correct perception. However, in continuous exposure, the strongly stimulated detectors desensitize and the aliased detectors get their opinions heard. That’s the putative mechanism, but no specific circuits responsible for this illusion have yet been described.


dappled designs


image courtesy Edward Tufte

As sunlight passes through the crown of a tree, every small opening in the crown serves as the aperture of a pinhole camera that casts an image of the sun on the ground. These sun images vary in size and brightness and may overlap, forming shadows of intricate detail and rich intensity gradations.

Artists call this dappled light. As the sun makes its way across the sky, the shapes change relatively quickly (a property of the moiré phenomenon).

If we could carefully design a tree-shaped sculpture with precisely positioned twigs and leaves, we could make a sundial that marks the passage of times and seasons by casting intricately detailed transient shadow images. For example, a tree sculpture installation that casts shadow portraits of persons whose birthday it is on that day — every day of the year, at a specific time.

The artist Danny Rozin has created “mirrors” that create shadow images of the viewer by actuating simple elements such as blocks or pegs.

Randy Cooper uses copper mesh as his medium. The resulting figures appear somewhat like three-dimensional pencil drawings. Furthermore, the sculptures cast wispy shadows that often complement the overall composition.

Meshes are also an ideal medium for moiré synthesis. The moirés in this photo are probably an artifact of digital photography. However, the sculptures themselves can generate rich moiré patterns by interfering with themselves or their own shadows. The moirés could make the figures appear to move and shimmer as the viewer moves past them. Or, with a fair amount of craftsmanship, meaningful secret moiré patterns could be integrated in these figures visible only from a specific vantage point.

Originally uploaded by alwasaga

Another interesting property of shadow sculptures that can be exploited in computer-aided sculpting to enhance the visual surprise is that shadow shapes depend on the geometry of the surface onto which they are cast and the viewing angle.

I liked the artistic touch: the book appears to be a dictionary opened on imaginary and imagination.

In this piece by Kumi Yamashita titled Landscape, the shadow is cast by a straight edge and the shadow is shaped by the surface.

Another interesting property of shadows is that their meaning can change as the light source moves, even without resorting to moiré patterns, as in this sculpture by Markuz Raetz.

… or in this God-Ego duality shadow sculpture by Fred Eerdekens.

With the introduction of moiré effects, the number of possible distinct meaningful shadows can quickly multiply. So far, I have not seen anyone trying this medium.

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.