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Stereograms and how they work

This page attempts to explain how various types of stereograms work whether they are SIRDS; Red/green; double image or whatever.

First we need to know what happens when we see something normally . . .

Normal Sight

Figure 1.
(viewed from above)

Figure 1 shows us how normal eyes (eyes that do not need correction) focus and converge on an object in the same plane. As an object moves closer to our head, our eyes converge at the new distance (your brain knows this because the images overlay best at this new convergence) and an automatic bit of computational apparatus in our brains works out the new focusing distance for the lenses in our eyes. By altering the distance between parts of the image seen by the left and right eyes, we can make a stereoscopic image that presents each of the two different images to each respective eye.

Figure 2.
(without colour information)

On paper, this is done (usually) by having a red filter over the left eye and a green filter over the right eye (the right eye is usually a little more dominant than the left eye and by giving it a colour that our eyes are more sensitive to - green - the resulting image is brighter) and viewing a composite (Figure 2 - made from monochrome images - Method 1) where red light remains reflected in the image for the left eye and green light remains in the image for the right eye. One of the drawbacks of this method is that colour information is lost to a large extent as only the primary colours that make red through yellow and orange to green are left to view (see the dried Snap-dragon seed pod) - it should be remembered that if an object is red or green, it can only be seen with one eye thus losing the 3D information and making the user feel uncomfortable (Figure 3 - made from the red layer of the left image and the green layer of the right image - Method 2).

Figure 3.
(with colour information - look at the top inside of the D which happens to be red)

On the silver screen (literally a silvered screen) a stereoscopic pair of images are shone onto the metalised projection screen with one image polarised 90║ from the angle of polarisation of the other (these are usually +45░ and -45░ so that the glasses may be work either way - it being difficult to wear glasses that are upside down - and therefore without reversing the front/back qualities of the image) there being similar polarising filters over the projection lenses (Method 3). The silvered screen is used so as to preserve the angle of polarisation. In this way, the image from the right picture is blocked out from the left eye but allowed to pass to the right and vice versa. This method now replaces the red green method that used to be used in the cinema.

Figure 4.
(showing how the images for the left and right eyes are fucused on different strips of the image)

Another method that can be used, where the user is fed different images for each eye, is to use the plastic lens layer that has been used for animating images for decades. In the past, the lens sheet, a sheet of plastic that is flat on one side (to be stuck to the image) and with half-lens cross-section lenses on the other, has been placed so that the lenses run across the sheet. This meant that both eyes were getting the same image and that by tilting the sheet up or down, the image received by the viewer would change. Make the image from slices of motion and you have animation. Printing has improved so that now, sheets can be aligned sufficiently accurately so that the lens sheet can be run vertically and each eye gets a different image (Figure 4 - showing how the images for the left and right eyes are focused onto different strips of the image - Method 4). One for the left and one for the right. This stereoscopic image method was used recently on the cover of a Guiness Book Of Records.

One other method that was tried for television (where, like the printed page, you cannot make things polarised) was to show one image in one scan and the other image in the next scan and so on. A special pair of glasses would block out the light to each eye in time with the image on the screen giving the impression that you were looking at a real object (Method 5). Unfortunately, there were a number of problems associated with this: high cost of the specs (liquid crystal lenses are a little more expensive than coloured plastic in cardboard); distribution of the technology, getting a sufficiently large number of films to warrant the expense; and so on.

All of these methods involve the user looking at one plane - no mirrors. If you use a special contraption with mirrors, having diverted the line of sight for each eye (in opposite directions) or use lenses to magnify a slide pair, you can view the separate images in full. These contraptions, however, are cumbersome and are reserved for virtual reality (Method 6) or viewing slides (Method 7).

Back to flat images on paper and screens. . .

Not so normal sight - using the lessons from correcting dysfunctional focussing

Figure 5.
(viewed from above)

A person needs glasses (to correct hypermetropia or myopia) when they are no longer able to make the in-focus images overlay - the corrective lenses adding to or subtracting from the power of the adjustable lenses in our eyes. When someone is hypermetropic on one eye and normal in the other, the hypermetropic eye will become lazy - only being used to judge distance - and will not develop the necessary high-definition capabilities of normally developed eyes. This condition is known as amblyopia and, although largely irrelevant to this subject, is interesting in that the affected eye will pick out detail differently - such as stars, nebulae et cetera in low light levels - and may be used to see things easily that the unaffected eye finds difficult.

Figure 6.
(viewed from above)

Figure 5 shows how a myopic person focuses in one plane but converges his sight on another (the virtual image plane)- Figure 6 showing the same for a hypermetropic person (note that in Figure 5, L & R are the correct way around but in Figure 6, they are reversed). If it is possible to create an image that can exist in the focal plane (thus remaining in focus) and provide the respective information that each eye needs, you can produce a stereogram that will convey the three dimensional information and will remain sharp, especially when the person with corrected eyesight takes off their glasses.

There are two ways of doing this: by putting two images side by side (Method 8); or, by creating a special image called a SIRDS (Single Image Random Dot Stereogram) (Method 9). In each case, there will be a different image to suit myopic and hypermetropic individuals. People with normal sight could perhaps borrow someone's glasses.

Method 8 - Stereoscopic pairs

Figure 7 shows hypermetropic and Figure 8 shows the myopic versions of this method. Figure 9 shows a useful mixture of the two - the latter being adopted in some of the more enlightened books that display stereograms of this sort.

Figure 7 (Right Image on left . . .)
Figure 8 (Right Image on Right . . .)
Figure 9

Notice that there are only two images used in the above three figures - the first two of these simply have them swapped and the latter's outer images are identical. Figure 9 (assuming that it is done consistently throughout) allows the user to get used to looking at a particular set of pictures (the left pair or the right pair). With this method, all of the colour information is retained, although for myopic viewers, there is a limit for the maximum image width in that if the repeat distance is greater than their interocular distance, their eyes will have to diverge to see the image correctly (yuk). If you are attempting to view the myopic pairs (Figure 8 and the right hand pair of Figure 9) and you are having trouble diverging your eyes enough, you can right click on the images concerned and select 'zoom out' from the menu to make them smaller and therefore closer together. One disadvantage of this method is that the images are limited in size.

Method 9 - SIRDS (a stereogram in one image)

Single Image Random Dot Stereograms (SIRDS, sometimes called Autostereograms) allow the viewer to perceive three dimensional information using one image. Elevation on maps and so on, is easy to see, giving the viewer a good appreciation of regional topography.

To view a SIRDS, cross your eyes (or relax them if you are looking at a myopic SIRDS) so that the two black dots overlap to become three, with the middle dot darker (this is because the middle dot is the left dot and right dot overlaid) and then, with the dots in focus, transfer your gaze to the field of dots below it. It is possible to do this without the guide dots after a little practice.

Figure 10

Figure 10 shows how the dots of a SIRDS pattern for the impression of depth. Note that it is only the edges of the shapes in an autostereogram that give the impression of depth - the pictures that you often see in books display little stereoscopic information and are usually merely art works (for want of a better term). Use the black dots at the top of the figure to converge and focus your eyes and you will notice that the red triangles appear in the same plane whereas the orange squares appear in front, the green pentagons behind and the blue hexagons at various positions (the front back positions will be reversed if you look at it by diverging your eyes as though it is a myopic SIRDS). SIRDS may be monochrome but taking into consideration the fact that the stereo information only comes from the edges of the dots, using coloured dots allows for an increased dot density (unlike monochrome dots, coloured dots may be placed next to each other and remain distinct) and therefore more detail.

Figure 11 shows a SIRDS of a woven pattern (shown here because it transfers well to various browsers on systems configured differently) and illustrates the fact that what seems to be a meaningless pattern of dots can function as an image. To make your own, see the SIRDS page.

Figure 11. (A full SIRDS image (hypermetropic) of a woven pattern - with a little cheating so that it will reproduce on any modern browser that will take tables on any screen size - to print, you will have to turn on background printing (View / Internet Options / Advanced / Printer / Print background colors [sic] and images))


Table 1 below summarises the key factors when choosing between the methods described above. Each has its own advantages and disadvantages - being suited to one medium rather than another.

Method Eyesight Viewer
for flat
Rough order
of Cost
Number Description
1. 3D red green composite
Without colour information
Normal Simple
No No Yes 0.1 results in
2. 3D red green composite
Retaining colour information
Normal Simple
Yes but
with serious
No Yes 0.1 image
quality is
3. Polarised stereoscopic
pair for projection
onto metalised screen
Normal Simple, Filter
Specs - Complicated
Yes No No 1,000 Image is good
and specs are
4. Linear lens sheet laid in
front of image so that
each eye receives
differnet picture
Normal None Yes No Yes 0.1 (A4 size) Lens sheet
alignment needs
to be good
to work
5. Temporally separated image
with liquid crystal specs
Normal Complicated
Yes No No 100 Expensive,
6. Viewer for separate real-time
computer generated
images that move with head
(virtual reality)
Normal Complicated
Head-gear and
Yes No No 10,000
Used to
create a
virtual world
7. Viewer for separate still
images (slides or prints)
Normal Cumbersome Yes No No 1 Results as
detailed as
images used.
used in
books and toys
8. Printed stereoscopic pairs Corrected
None Yes Yes Yes 0.01
9. Single Image Randome Dot
Stereograms (SIRDS)
None No No Yes 0.01 Monochrome
image. User
must be trained
Table 1
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