This is a magical 3D image! Hold the picture to your nose, and then very slowly move it away from your face. Keep staring through the picture and a 3D image will magically appear before your eyes!

You've no doubt seen one – a picture consisting entirely of seemingly arbitrary dots and whirls and squiggles, that only an abstract artist or theoretical particle physicist could appreciate, with accompanying captions promising that if you looked at the picture the right way you'd see magical 3D structures appearing before your very eyes. And yes, without LSD.

What is a 3D stereogram?

To put it simply – a flat two-dimensional image viewed in such a way that it produces a three-dimensional effect.

The objects we encounter every day are three-dimensional – that is to say, they have height, width and depth. A graphical representation of the object in the form of a painting or photograph is only two-dimensional; however, by cunning use of angles and shadows it is possible to give the portrayed object the illusion of possessing three dimensions.

As early as 15,000 BC, man has endeavoured to add a third dimension to his paintings by means of natural textures on cave walls. Thanks to today's technology – which combines computers with artistic flair – a three-dimensional object may now be convincingly rendered upon a perfectly flat piece of paper.

The history of 3D pictures and stereograms

Stereography in the Victorian age

The grandfather of 3D art and stereographical headache is Charles Wheatstone, who in 1833 accidentally discovered that because human eyes are set a short distance apart, objects viewed through one eye differs slightly from the other, thus creating an illusion of depth. Five years later, after the discovery of this stereoscopic phenomenon, he invented the stereoscope¹ – a binocular device through which a pair of monocular images was projected to both eyes in such a way that the optic axes converge at the same angle, thus giving the impression of a solid 3D image.

In 1839, barely a year after the stereoscope was introduced, the Frenchman Louis Daguerre ushered in the new age of photography by combining the camera obscura, which had been constructed by Joseph Nicephore Niepce² only 17 years earlier, with a silver-coated copper plate treated with iodine vapours to permanently fix camera obscura images. The invention was bought by the French government and publicly announced on August 19. These photographs were named daguerrotypes in Daguerre's honour.

We now have two important inventions critical to the development of the modern stereogram: the stereoscope and the durable photograph. However, Wheatstone's stereoscope was impractical for use with photographs and stereoscopy thus languished until 1844 when Sir David Brewster³, a Scottish physicist and experimenter of optics, discovered that a three-dimensional effect could be observed in repeated patterns with small differences. He applied this principle in building the stereo camera, which combined a refracting stereoscope with a twin camera consisting of two separate cameras placed slightly apart. When viewed through the stereoscope, the monocular pictures provided by the twin camera gave the resulting image a three-dimensional effect. This new invention, exhibited at the 1851 Great Exhibition in the Crystal Palace in London, caught the attention of both Queen Victoria and the public and not surprisingly, became a popular craze.

Two years later, W Rollman made another innovation in stereography in the form of 3D anaglyphs - two sets of superimposed identical line drawings (one in blue and the other in red) which, when viewed through red and blue glasses, appeared to be three-dimensional. The Frenchman Joseph D'Almeida decided to bring this to the masses in 1858 in the form of 3D magic lantern slide shows whereby the colours were separated using red and blue filters⁴, and the audience used red and blue goggles to view the images. However, it wasn't until 1891 that Louis Ducas du Haron created the first printed anaglyphs - photographs consisting of two negatives (one in blue or green, the other in red) printed on the same sheet of paper to form a stereoscopic photograph.

3D anaglyphs were taken to the big screen in 1889 when William Friese-Green created the world's first anaglyphic motion pictures. These movies, made using a single film with green image emulsion on one side and red on the other, became immensely popular in the 1920s, and many science fiction movies of this sort were televised in the 1950s. Today, 3D anaglyphic movies continue to be made and screened in theatres - theme parks have in recent years shown several such movies, eg 'Captain EO' (starring Michael Jackson) as seen in Disney theme parks, and 'Terminator 2: 3D', as seen in Universal Studios parks.

Modern stereography

But why produce images on two separate sheets of paper when one will do? It may have been this question that drove inventor Edwin Land to improve on du Haron's anaglyphs in the 1930s by replacing the red and green filters method with two planes of polarised light, thus making it possible for stereoscopic images to be produced on a single sheet of film. He named these images vectographs, but it was his polarising filters that would make him famous - as the genius behind the Polaroid Corporation.

Holography - the science of recording images in three dimensions (holograms) - was in fact invented by accident in 1947. The scientist responsible for this was Hungarian physicist Dennis Gabor, who had been doing research with the intention of improving on electron microscopes by making them capable of resolving atomic lattices and seeing single atoms; instead he produced three-dimensional images. He named these images 'holograms', combining the Greek words 'holos', which meant whole or complete, and 'gram' meaning message. These magical pictures caught the interest of many scientists, who embarked on their own quest to develop the holographic technique. Unfortunately, hologram development went nowhere for the next decade because the most coherent light source then was the mercury arc lamp, which did not allow production of holograms of any depth. It was only in 1960 when laser was invented that hologram research truly advanced⁵.

Meanwhile, the age of Magic Eye stereography began in 1959 when Dr. Bela Julesz, a psychologist researching on depth perception and pattern recognition, created random-dot stereoimages – pictures consisting of a uniform, random distribution of dots – as an experiment to study stereopsis, or the ability to see in 3D. His experiment led to the discovery that three-dimensional images are produced in the brain, and not on both retinas as previously thought.

Twenty years later, Julesz's student, Christopher Tyler pioneered the merging of two stereograms into a single image, also known as an autostereogram. He collaborated with Maureen Clarke to generate the world's first black-and-white single image random dot stereograms using an Apple-II Computer. Programmed in BASIC, the computer generated single images of mostly random (but some constrained) selected pixel colours which could be viewed independent of equipment.

Julesz' and Tyler's work caught the interest of programmer Tom Baccei and artist Cheri Smith who, in 1991, collaborated with programmer Bob Salitsky to improve on this new art form. Together they developed a full-colour stereogram program which, when used in combination with sophisticated 3D modeling software and colourful art techniques, could create incredibly bizarre repetitive squiggles and anomalous shapes in glorious technicolour which, when viewed the right way, produced 3D objects. But of course you already knew that.

Types of 3D stereograms

1. Stereo Pair

A stereogram that consists of two images viewed through a stereoscope. This forms the base of all stereograms.

2. Stereo Pictures

A pair of images taken from two different angles.

3. Random Dot Stereogram (RDS)

A stereogram generated by a random distribution of dots in place of texture. The first of these was published in 1972 by Dr. Bela Julesz. This was how Julesz created the images: He first created a rectangle of randomly arranged dots. These dots were to eliminate the depth cues that are inherent in recognisable images. A group of dots within the rectangle were selected to make up a basic shape. A second rectangle similar to the first was created, this time with the 'shape' shifted slightly to one side. Thus when a person capable of seeing in 3D viewed the two rectangles as a pair, the image of the 'shape' would be seen to float above the background of random dots.

4. Shutter

Also called a tachistoscopic technique, this is used by some virtual reality systems. Images are generated for the left and right eye, which are separated by alternating shutter glasses. The shutter closes one eye's view whilst the other receives the proper image, but because the alternation is so fast, it is not noticed at a conscious level.

5. Anaglyphs

This is a stereoscopic method using different coloured or polarised images. A pair of spectacles equipped with special filter glasses gives each eye the proper information, creating a three-dimensional effect. In its simplest form, two identical images are designated two separate colours – such as green and red – and overlapped in such a way that they are slightly offset. The image is then viewed through a pair of spectacles with one green filter and one red one. The eye that looks through the green filter will see only the red image; the eye that looks through the red filter will see only the green one. The brain then creates a composite of these two images in the form of a 3D object.

6. Single Image Stereogram (SIS)

Tyler's improvement on Dr. Julezs' Random Dot Stereogram, whereby the two images are merged into one picture. There are several variants:

1. Single Image Random Dot Stereogram (SIRDS⁶) - Consists of a single image stereogram with a random pattern instead of a texture.
2. Single Image Random Text Stereogram (SIRTS) – Instead of dots, ASCII text is used for two-dimensional image information.
3. Single Image Texture Stereogram (SITS) – This SIS uses texture in place of a random pattern. There are three basic forms of SITS – those with internal 3D elements integrated into a 2D picture, floaters (visible elements that appear to float in space at different depths) and floaters integrated with a hidden 3D image.

7. Lenticular

This is perhaps the most common amongst children, and does not require special visual abilities. The lenticular is a thin, portable, full-colour stereo picture which consists of a photo over which are placed thin plastic 'lenses' which restrict one's view to a particular region of the picture. When the lenticular is tilted, one may see two different images, or perhaps a series of them in such a way that they suggest movement. The Harry Potter chocolate frogs trading cards available in the market make use of this method, and so does the first hardcover edition of Douglas Adams' 'So Long, And Thanks For All The Fish'.

8. Vectographs

A Polaroid vectograph is a print whereby the image itself is a light polariser. Normal unpolarised light comprises rays vibrating equally in all directions crosswise to the path in which they travel⁷; it becomes polarised when it is transmitted through a polaroid filter that allows only light of a particular polarity to pass. A vectograph print, like normal polaroid filters, freely transmits one component of light while absorbing the other; unlike normal polarizers however, the amount of the absorbed component is in proportion to its density. Each of the two images comprising the stereoscopic pair are printed on either side of a sheet of vectograph film in stereoscopic register. To view the pair of images as a three-dimensional picture, the observer wears a viewer whose eye filter polarisation axes are perpendicular to one another, as well as to the corresponding vectograph.

Why can I see in 3D? Or why can't I?

T.S. Quint: Oh yeah, look it's a sailboat.
Willam Black: You saw it, too?! Damn it!
T.S. Quint: What?
Willam Black: I've been staring at this thing for a week now - from opening 'til closing - and I can't see a Godd*mn thing!

- From Mallrats (1995).

People who are not visually impaired in either eye have a binocular view of the world. That is to say, when we look at each object, the image falls on both eyes separately. Because our eyes are separated by a small distance, the perspective at which each eye views object is slightly different. When we look at the object through each eye on its own, we can only see the height and width of the object – but when both eyes work together, an amazing phenomenon occurs. When presented to our brain, it automatically merges the two images into one, matching up all the similarities in both images and presenting the minor differences in a way that is intelligible to the viewer – by adding a depth dimension, thus giving us the ability to determine the location of the object in relation to our bodies.

Unfortunately, if you suffer from eye problems such as lazy eye (amblyopia); wandering eye, wall-eye, crossed-eyes (strabismus, exotropia, esotropia); double vision, or convergence insufficiency, then the novelty of 3D stereograms are lost to you. There have been reports of success in using stereograms to treat such problems, but we'll discuss that later.

How do I see these blasted 3D images?

There is nothing more infuriating than having companions insist, "But there are two frogs mating in the lower left corner, can't you see them yet?" and of course not being able to see diddly- squat! (Unless of course, in desperation you have turned to psychedelic drugs, in which case you will be able to see not only 3D images, but technicolour dancing refrigerators and singing frogs)

But fear not. Unless there is something dreadfully wrong with your eyes, there is no reason why you shouldn't be able to see a 3D image, if you're willing to sacrifice a little time and shreds of sanity. Basically there are four ways to do it:

1. The reflection method

This is perhaps the simplest way of doing it, although it's generally thought of as cheating. All 3D stereograms are printed on high-gloss paper, which tends to reflect light very well. The trick is to position yourself in such a way that light bounces off the picture, and then to focus all your attention on the glare and not the picture itself. Your peripheral vision will automatically pick up on the image and convey the information to your brain, which will eventually resolve the strange squiggles into a recognisable 3D shape.

2. The parallel-viewing method (recommended)

Parallel-viewing is generally recognised as the correct method of viewing 3D images; it is also perhaps the hardest one to pull off. Theoretically, you look right through a picture – as though it's not there – so that your focus seems to be a far-off object, hence the parallel lines of sight. The trick is to bring the picture close to your nose so that the image is blurry and unfocused, and then to draw the picture back while all the time allowing your eye muscles to stay relaxed, until eventually the weird shapes resolve into something more readily recognisable. Alternatively, you can hold the picture at a fixed distance and force yourself to stare at it in the same manner as when you're drunk and unable to focus on anything. Unfortunately (unless drunk) most people will initially find their eyes wandering off-course, usually to focus upon the picture itself. A lapse of concentration will result in a confused alternation of focus, and subsequently, a major headache.

3. The overlapping images method

Sometimes a 3D stereogram consists of repetitive images that are easily recognised, such as teddy bears or balls (these are more common in floater images than in hidden 3D pictures). The trick is to focus your eyes on two adjacent objects of the same sort until they merge into one. When this happens, you will be able to move your eyes freely over the picture in search of the 3D element.

4. The cross-eyed method

This method calls for the deliberate focusing or your eyes by crossing them so that their lines of sight cross in front of the image. Unfortunately, this will result in the image appearing to be inside-out.

What's in it for me, besides a headache?

Because the correct method of viewing Magic Eye stereograms is by relaxing the eye muscles, research has been carried out to determine if viewing 3D stereograms is of value in improving vision. Some optometrists in the United States, Europe and Australia are, in fact, incorporating 3D viewing into their vision therapy programs. There has been reported success of using stereograms to train eyes to work as a binocular team and improve depth perception.

However, whilst people with binocular vision impairment may have benefited from this therapy, there is nothing to prove that viewing stereograms can improve non-binocular vision problems, such as astigmatism and myopia. And anyway as Gene Levine, creator of stereograms and webmaster of www.colorstereo.com, lamented,

"I was nearsighted before I began creating stereograms, and I am even more nearsighted now. Who's to say I am not less nearsighted than I might have become?"

Bibliography & Further Reading

• Curtis, M and S Zwicker. 2003. Digital stereograms.

• Gulick, WL and RB Lawson. 1976. Human Stereopsis: A psychological analysis. Oxford University Press.

• Julesz, B. 1972. Principles of cyclopean perception. MIT Press.

• Marr, D and T Poggio. 1976. Cooperative computation of stereo displarity. Science, 194: 283-287.

• McAllister, DF. (ed) 1993. Stereo computer graphics and other true 3D technologies. Princeton University Press.

• Thimbleby, HW and C Neesham. 1993. How to play tricks with dots. New Scientist, 140(1894): 26-29.

• Tyler, CW and MB Clarke. 1990. The Autostereogram. SPIE Stereoscopic Displays and Applications 1258: 182-196.

Other resources on the Internet

• Dennis Gabor: Inventor of Holography
• Dr. Bela Julesz: Short Vita
• Heineken Prizes – 1985: Julesz & Reichardt
• Historical Development of Stereograms
• Kondo's Stereogram Workshop
• Magic Eye
• Natural Vision Improvement Frequently Asked Questions V1.1
• Seeing 3D: Stereographic Carpeting?
• SIRDS FAQ
• Stereograms Theory
• Stereoscopy FAQ
• Summit View Eyecare
• The Stereo Vision project