Gale Rhodes
Contact Information
Dom
St. Stephan, Passau, Deutschland
(convergent stereo)
The sky at night, a loon's call,
autumn's first apple, a
spider's web,
a crystal, a protein's core—
my life is full of cathedrals.
Too often, people try only briefly and halfheartedly to view in stereo, and never try again. Almost anyone can view in stereo with a little effort and practice. The only ones who simply cannot are those who have acute amblyopia (one very weak eye). And those who say they can see just as much without stereo simply cannot imagine what they are missing. You can be a much more effective explorer of molecular structure if you learn to see in 3D. Most structural biologists learn to view stereo views by two methods: convergent and divergent viewing.
First turn on stereo viewing with your molecular graphics program. For most graphics programs, set the stereo viewing angle to -5 degrees (that's minus five). RasMol is backwards; for convergent viewing, set the angle to 5 degrees with the command stereo 5 (this is the default in RasMol).
Or work with this convergent stereo pair of the heme (space filling) and histidine ligands (ball and stick) in cytochrome b5*:
To view most computer and projected stereo images, you need to look at the left-hand image with your right eye, and at the right-hand image with your left eye (called convergent or cross-eye viewing). Here's how to develop the skill at your computer.
Gaze at the stereo pair, keeping your eyes level (don't tilt your head left or right), and cross your eyes slightly. As you know, crossing your eyes makes you see double, so you will see four images. Try to cross your eyes slowly, so that the two images in the center come together. When they converge or fuse, you will see them as a single 3D image. The fused image will appear to lie between two flat images, which you should ignore. When you are viewing correctly, you see three images instead of four. The center image is three-dimensional. At first, the 3D image may be blurred. Keep trying to hold the stereo pair together while you focus. The longer you can hold it, the more time your eyes have to adjust their focus. Usually, even before you begin to get the hang of focusing, the two central images lock together, because your mind begins to interpret them as a single 3D object.
Having trouble? Here's another approach. With your head level and about 2.5 feet from the screen, hold up a finger, with its tip about 6 inches in front of your face, and centered between the stereo pair on the screen. Focus on your finger tip. Without focusing on the screen, notice how many images you see there (they will be blurred). If you see four images, move your finger slowly toward or away from you eyes, keeping focused on your finger tip, until the middle pair of images converge. With your finger still in place, partly covering the converged pair, change your focus to the screen. The image partly hidden by your finger should appear three-dimensional. Your finger should still appear single, but blurred. With some practice, you can remove your finger and still keep the screen images converged into a stereo image.
Now try your skill with the stereo image at the top of this page. If you are viewing properly, the golden hangings at the right should look much closer to you than the high vaults of the cathedral interior.
These instructions are for a printed stereo pair, which you can find in some biochemistry textbooks or in journal articles (try a recent issue of Science -- look for an article announcing a new protein structure determination).
If you have no printed pairs, print this page with a color printer, and use this divergent version of the previous stereo pair*:
If you can't print the image, use it on the screen, or use your molecular graphics program to make a satisfactory image. First, turn on stereo viewing. Shrink the graphics window so that the stereo pair is small -- about the same size as a stereo pair in a textbook. The distance between image centers must be no more than the distance between your eyes, 6 to 7 cm (for those still in the Dark Ages, that's about 2 & 1/2 inches). For divergent viewing in most graphics programs, set the stereo angle to 5 degrees (that's plus five -- this is often the default setting). RasMol is backwards; for divergent viewing, set the RasMol stereo angle to -5 degrees (thats minus five) with the command stereo -5.
To view most printed images, you need to view the left image with the left eye, and the right image with the right eye (called divergent or wall-eye viewing). Here are two methods to try.
Put your nose on the page between the two views. With both eyes open, you will see the two images superimposed, but out of focus, because they are too close to your eyes. Slowly move the paper away from your face, trying to keep the images superimposed until you can focus on them. (Keep the line between image centers parallel to the line between your eyes.) When you can focus, you will see three images. The middle one should exhibit convincing depth. Try to ignore the flat images on either side.
Another method -- the one I used when stereo pairs first appeared in the biochemical literature (can anyone tell me where?): Photocopy a stereo pair from a text or journal article, and cut off the copied page above the pair, leaving the pair at the very top of the page. Then hold the page just below eye level, and look out above it at a distant object. You will notice below your line of sight that the two views are blurred, but superimposed on each other, because your eyes are looking more or less parallel to each other to the distant object. Now move the picture upward into your line of sight, trying to keep the images superimposed, and try to focus on them. As with the first method, you will see three images -- the middle one is three-dimensional.
Here's another technique, suggested by Nicolas Guex.
Tape a divergent stereo pair to a mirror, just below eye level. Then look at your eyes in the mirror above the image. Slowly bend your knees so that your view passes through the stereo pair on the way to looking at your eyes below the image, and then slowly rise again and repeat. At some point, as you cross the pair, the images should fuse, and you should find it easy to focus on the three-dimensional image, because your point of focus for looking at your reflection is not far off.
Finally, try this suggestion from Mitchell Miller of MDL Information Systems.
Use two empty paper-towel or bathroom-tissue rolls like binoculars. Point left roll at left view, and right at right. This should allow comfortable 3D viewing. Then see if you can quickly remove the rolls and keep the views converged.
(In trying for divergent viewing, you may stumble into convergent viewing; after all, it's actually a more natural thing for your eyes to do. With the image above, if you mistakenly view it cross-eyed instead of wall-eyed, it will appear very strange because the depth cues of the image (light, shadow, and hidden surfaces) conflict with those provided by the double image. In addition, the space-filling heme atoms will appear to be inside out, or concave rather than convex. Finally, the histidines (ball and stick) will appear closer to you than the front edge of the heme, while they are actually near the middle of the heme.)
Viewing either convergently or divergently becomes easier with practice. Once your mind sees a pair as a single 3D image, it recalls the experience, and resists your efforts less with each try. I can automatically snap a stereo pair -- convergent or divergent -- into superimposition, and I no longer think about exactly what I am doing. Suddenly, there is a vivid, three-dimensional object floating above the screen or page. I've been doing it since 1969 (that's a hint about the source of the first biochemical stereos!), and I've suffered no damage to my vision. It's very handy to be able to use the stereo pairs in Science and other journals without digging up a viewer. Such important tasks as interpreting electron-density maps from x-ray crystallography are practically impossible without this skill.
* Stereo images prepared with SwissPdbViewer (well, all but one).