Notes on Stereography

Stereography is the science (mostly) of rendering a 3-d image in the mind of the viewer by using a pair of 2-d images.

Theory

The process takes advantage of the binocular nature of human vision - each eye sees a slighly different 2-dimensional image, and the brain uses the differences to reconstruct the third dimension, often called depth.

Stereography mimics this process. By "tricking" each eye into viewing a different image, where each image represents the same scene but from slightly different angles, the brain will reconstruct the third dimension just as in normal binocular vision. There are several ways of accomplishing this.

Anaglyphic stereography

Anaglyphic stereography is the kind used in 3-d movies: each image is presented in a different color, and colored filters in front of each eye allow only the appropriate image to pass. Some international standards body has decided that the right eye filter should be blue, while the left eye filter is red, but this can vary. For example, the image below requires the red filter over the right eye.

Anaglyphic Stereogram
Anaglyphic Stereogram of a Dragonfly Nymph
Right Eye Red

These images can be produced using just about any graphics program - just combine the blue and green channels of the left image with the red channel of the right image. It is possible to use other colors, but cyan and red, being complementary colors, produce a true-color image in the mind of the viewer. The subject of the images should be coincident on the image (as in the dragonfly nymph's head in the above image) to make the image easier to view.

Anaglyphic Stereogram
True Color Anaglyphic Stereo

One problem with true color anaglyphs is that any item that happens to be the same color as either filter will only be visible to one eye. Try viewing the above cyan and red images above through anaglyph glasses and you'll see why this is a problem.

Orthostereography

Orthostereography uses images presented side-by-side. This kind of stereography goes back a long time, and was quite popular around the turn of the 19th century.

Orthostereogram
An c.1900 Orthostereogram

Orthostereographs have a distinct advantage over anaglyphic stereographs - many stereographs may, with sufficient practice, be viewed without special equipment. There are two basic ways to accomplish this.

In the parallel viewing method (aka the free viewing method), the viewer points his left eye at the left image, and right eye at the right image. This is done by "gazing into the distance" between the two images until the middle two of the four perceived images (due to "double vision") coincide. This method is restricted to images less than 2.5" across, as larger images would require the viewer's eyes to point away from each other. (I've actually managed this with images as far apart as 3.6", and believe me, it feels weird.)

Distance method of viewing a stereogram without a viewer
Distance method of viewing a stereogram without a viewer

The "cross-eye" method circumvents the size limitation by switching the two images; the image intended for the left eye is on the right, and the image for the right eye is on the left. Thus, the viewer must become cross-eyed to see them, but becoming cross-eyed is a lot easier than forcing your eyes to diverge. The disadvantages are that being crosseyed is a bit unpleasant, and the resulting perceived image appears quite small and close to the viewer. I much prefer the parallel viewing technique.

Crosseye method of viewing a stereogram without a viewer
Crosseye method of viewing a stereogram without a viewer

Special viewing equipment provides the best of both worlds - larger images can be presented and at a much larger percieved distance.

Early 1900's stereogram viewer
Early 1900's stereogram viewer

Viewers simplify the process of distance viewing in two ways: they provide a path from each photograph to the appropriate eye, and block each eye's the view of the wrong photograph. Very often they also change the focus of the image to match the apparent distance - it feels very odd at first to have to focus in on an image that seems far away.

Hyperstereo images

Hyperstereo images are images that use a much longer baseline (the distance between points from which the photos were taken) than the standard 2.5" of the human eyes. The result is that the subject appears much smaller than it really is, but depth can be perceived much more readily.

Hyperstereogram
Hyperstereogram of my car - note how small it looks

Normal human binocular vision can only directly perceive depth out to a distance of about 30 feet, with decreasing precision. Objects, such as cities or buildings, at greater distances may seem to have depth, but the mind also takes queues from other effects, such as shadows. Hyperstereo images are sometimes used in aerial photography so that map-makers can literally "see" the hills and valleys. Before the advent of radar, battleships used special binoculars, with widely separated occulars, to allow gunners to perceive distance over dozens of miles.

Optical Rangefinder

Hypostereo images

Hypostereo images are just the opposite - they use a baseline much shorter than the 2.5" human standard to produce an image that appears much larger than life. I've used this effect in the image below of a Dragonfly Nymph. The baseline between the two images is approximately an inch.

Hypostereogram of Dragonfly Nymph

Methods

Commercial Stereocamera

Viewmaster stereocamera
Sawyer's "Viewmaster" Stereocamera, c. 1940

Of course, stereocameras are commercially available, as well, though they're not anywhere near as common as they once were, so you may only be able to find used cameras. eBay is a good source for these older models. Brands include Sputnik, Realist, Viewmaster, Vivid, Graflex, an a bazillion others. While old, many are still operable.


Vivitar's 3D Cam - a relabled Loreo 321?

Vivitar makes a 3D camera, called (who would have guessed?) the 3D Cam, duh. It typically goes for about $60 on eBay.


Loreo's Mk II stereo camera

Loreo makes the Mk II and the 321 (I believe the Vivitar 3D Cam is actually a relabeled 321) as well as viewers and a whole mess of other neat stereophotography stuff. I've never seen one go on eBay, but you can get them new for $66 plus $13 shipping to the US from Hong Kong. ($45 plus shipping if you pass on the viewer.)

Using a normal camera

This actually is a lot easier than it sounds. Simply take a picture, sway a bit (2.5" specifically) to one side, and take another. With practice, it becomes surprisingly easy. The process can be made more precise by using some kind of jig to move the camera an exactly 2.5" while keeping it pointed in the right direction.

The above method has a serious drawback - the images are taken at different times. If anything in the field of view is in motion, such as a moving person or even wind swaying the branches of a tree, the result will be, at the least, weird. In many cases, the result will be impossible to view. This problem must be resolved by taking the two images concurrently.

Homemade Stereocamera

The simplest way to take two images concurrently is just to use two cameras. I took a pair of "PhotoFlex Deluxe 110" cameras bought at a flea market for $1 each (they're junk) and epoxied them to a piece of wood sized to produce a separation of exactly 2.5" center-to-center.

Homemade stereocamera and viewer
Homemade stereocamera and viewer

The big metal bracket on the top is to trigger both shutters at once. It takes a bit of adjustment to get it right. In front is an experimental stereoviewer. It basically makes using the distance method of viewing possible for images that are up to 4" center-to-center (such as a pair of 4"x 6" photos layed side by side).

The same two cameras could be arranged side-by-side on a piece of angle-iron, held in place by rubber bands. The lenses would be too far apart for true orthostereography (i.e. hyperstereography), but it would still work.

It is even possible to mate two normal cameras together to produce a "siamese camera" very similar to a commercial stereocamera. Sam Smith has done a lot of this.

Homemade Stereo Viewers

The simplest homemade stereo viewer is just two pair of mirrors set up as "periscopes" aimed in opposite directions. All it does is brings a pair of widely separated images closer together for easier viewing.

Homemade stereoviewer

  1. Start with a block of wood, 3/4" x 1-1/8", at least 3-3/4" long.
  2. Mark the centerline along the length of it on the 3/4" side.
  3. 1/2" along the centerline from the end, cut it at 45°.
  4. 2-1/2" along the centerline from the cut, cut it at 45° the other way.
  5. Trim the remaining piece to 1/2" long along the centerline.
  6. Glue the three pieces as shown to anything that will hold them rigid, such as a 5" x 3/4" piece of wood.
  7. Using silicone, glue the four 1-1/8" diameter mirrors in place.

There few things that can go wrong. Keep everything nice and square, and keep the primary mirror separation to exactly 2.5". If you use larger secondary mirrors, make sure they are separated by at least the diameter of the smaller primary mirror, or you'll get lots of weird double reflections to confuse the hell out of you and give you a headache. If you can, use first-surface mirrors to avoid surface and internal reflections, but if they're very thick, you'll have to trim the center piece shorter. Don't worry too much about it, though, it's not brain surgery.

My first homemade stereo viewer is in the image above of the homemade stereo camera.

Digital Stereography

Of course, it is possible to use computers to create stereograms.


Local Star Map

This is one of my all-time favorites: a stereogram of the 100 stars within 75 light years of Earth. The double star directly below Sol (in the center) is Alpha and Beta Centauri (Gamma is not shown, as it is too close to Alpha and Beta to show), our closest neighbor at only 4.3 light years away. The size of each star is proportional to it's absolute luminosity, and it's color is proportional to, well, it's color. Here's another, same as above, only without the green frame of reference.

Animated Digital Stereography

And once you make it that far, it's a simple process to animate stereograms - many programs (such as AutoCad) support Lisp, a scripting language, that can be used to automate the process. Here are a few I've whipped up over the years. They are all viewable without special equipment using the distance method.

Spheres
Spheres in motion

The thing to remember when creating digital stereograms intended to be viewed without a viewer is that the images cannot be more than 2.5" wide. Given the vast number of monitor sizes and screen resolutions, what works on one monitor may not work on another. These images were originally intended for a 17" monitor running at 1280x1024 resolution. Chances are, you'll find them too big. (If you use a good browser, like Opera, you can resize the images.)

Update - 1/28/2004

Spirit and Opportunity, twin rovers, have landed on Mars! And guess what? They're equipped with stereocameras! Many of the photos they've been sending back are stereograms (others are RGB triplets). Here is a sample stereogram (use the distance method to view):


Spirit's view, near Gusev Crater

Here is same image presented as an anaglyphic stereogram (left eye red):


Spirit's view, near Gusev Crater
(I can see my house from here!)

As an aside, here is a quote from Space.com:

Too many memory files, too many tasks being fulfilled, and not enough deleting of less-needed data appears to have conspired to upset Spirit.

Ah, so that's the problem! It's running Windows!

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© 2003 W. E. Johns