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Instructions for watching in 3-D using your bare eyes

Now, here is how one uses one’s own eyes, in a very natural way (without contortions) to see the stars of this applet in 3-D.

Suppose you are given a figure like the following, which is called a “stereogram”, and you want to see it in three dimensions using only your bare eyes:

But I mean seeing it in 3-D really; that is, seeing the yellow dot standing in front of the plane of this page, the red ball approximately on the page plane, and the cyan ball behind the other two. Please follow these instructions:

First, select a spot on the opposite wall: it could be the door knob — or anything at a distance of more than 2 m. (7 ft.). It can even be some faraway object that you see through your window. Place your two index fingers at arm’s length, as shown in the above figure, while watching the object — let’s say a door knob — between your two fingers.

If you are focusing on the door knob, then you actually see four fingers!

If you don’t believe me, shake your fingers slightly (but always focusing on the door knob), so their four moving images will become apparent. Don’t focus on them! The trick is to be aware of all four fingers while still focusing on the door knob. If you feel your eyes becoming de-focused from the door knob whenever you move your fingers, have patience! The experiment will not work if you cannot pass this first step.

Are you in a position to “see” four index fingers while focusing at a distance? (There is nothing wrong with your eyes: this is the way our visual system works to perceive depth, i.e., the third dimension.) Now move your fingers inwards slowly (see figure below), until the two innermost of the four index fingers merge into one.

Remember, keep focusing on the door knob while you do the above! I admit this is a bit difficult to do since your index fingers will get in the way, but nothing prevents you from repeating this movement as many times as needed. Practice doing this. If it helps, before you merge your two index fingers, move your hands a little below the door knob, so that it remains at your focusing point all the time, then merge your index fingers (below the door knob), and finally move both hands slightly upwards until the tips of the two index fingers cover the door knob.

If you have successfully merged your two index fingers you are effectively seeing three fingers now (shake them a bit to see them better), while you never de-focused from the door knob. We will need to refer to this position, so let’s call it “Position A”.

Now the following action is the key to our attempt.

Since you still focus at a distance, slowly de-focus (without moving your hands) and look (focus) straight on one of the two fingers (or in the space between). Don’t move your fingers! No other part of your body must move, except your eyes. Do the de-focusing slowly, feeling how your eye muscles move while you change focus from door to fingers. This is important, because now I will ask you to do the reverse movement! Try to bring your two index fingers back to Position A (as they were before you de-focused) without moving your fingers, just your eyes. Can’t do it? Don’t be discouraged. And read on, you are very close to completing the job.

I assume you had some difficulty in doing the reverse movement (merging your two index fingers without moving them). So here is what to do.

Go back to Position A, and this time do the de-focusing in a very careful and controlled way: do not de-focus all the way, but only a little, hesitating, and going back to Position A immediately. Do this several times, seeing your fingers becoming separated and merged again. As you become more confident, gradually increase the separation distance between your fingers, and do the merging and un-merging again. (Remember, no other part of your body moves during the merging/un-merging save for your eyes.) As you become more and more familiar with this movement you will find yourself being able to separate the two fingers all the way, and bring them back to the merged position (Position A) at will.

You have essentially learned to control your eye muscles. Don’t worry, there is no problem of getting in some kind of eye-strain trouble because of muscle contortions: you don’t contort anything; this is the natural position of your eyes when you focus at a distance. (Except that usually there are no other objects — such as fingers — in front, so you probably never noticed it.)

Moving your eyes at will so that they come to Position A is all these instructions are attempting to teach you. Why is this sufficient? Because if you can merge your two index fingers at will, you can also merge the two almost-identical-but-not-quite parts of a three dimensional figure (a stereogram), such as in the one below.

Just pretend the two repeated parts of the image (left-half and right-half) are your index fingers, and do the same thing. You will know when you manage to merge them, because you will see the yellow dot standing out in front of the page, while the red one stands in the middle, and the blue one stays in the background! You may find it easier to do the merging if you position yourself at some distance from the screen (e.g. at ½ meter, or 1.5 feet).

Isn’t this much better than red-and-blue goggles to see in 3D? (Such goggles eliminate the colors, by the way.) You also don’t need any tool to do it, such as a mirror.

Notice that it’s also possible to do the same thing by crossing your eyes, but this has the disadvantage of really contorting your eye muscles, which might make you feel tired after a while. It also reverses the front-and-back (you’ll see the yellow dot in the back and the cyan one in front in the above stereogram), which means you’ll get the wrong perspective with the stars. Plus it makes the entire scene appear a bit smaller. If, however, you don’t mind about all these, feel free to watch this page cross-eyed.

Instructions for watching in 3-D using a mirror

The button on the tool bar that allows you to watch the stars in 3-D using a mirror is this one:

This is the technically easiest way to see in 3-D, if you have not trained (or don’t want to train) your eyes to see in 3-D without tools. The way to use the mirror is as follows. Suppose we have this “stereogram”:

As you see, the right-side repetition of the left side is mirrored. (It is also not identically mirrored, but suitable for seeing it in 3-D.) Now place a mirror perpendicularly to the plane of the image, as shown in the following figure:

Watch the scene with both eyes focusing on the left side of the image. But because of the intervening mirror, your right eye will not be seeing the left side but the right side; which, because it is mirrored, will appear normal through the mirror.

By slightly adjusting the perpendicularity of the mirror with your hand, you can make the two images coincide.

Notice also that you can adjust how far away or close together the two mirrored sides are, so that the mirror fits comfortably between them. You do this adjustment by dragging the right-side of the main area at its middle point, shown by the arrow, below:

However, make sure you find a good and clean mirror without spots; especially one that doesn’t create a faint shadow next to the main mirrored image. Low-quality mirrors usually do that.

You may select and line up stars, like this:

Or like this:

You can do that in various ways:

The easiest way is by simply clicking on a star that appears in the main screen. If you click on a single star, then that star will appear in a window above the main 3-D screen, as the previous images show. If your click results in multiple stars being clicked (because many times stars have smaller companions that are not shown on the main 3-D screen) then a dialog box will permit you choose which stars you intend to see.

But maybe the star you want to see is not in the main screen already. In that case, use this button of the tool bar:

Doing so will open up a dialog box above the main screen, which looks like this:

The name “Arc” is already shown as being typed in the box, at which point hitting [Enter] (or clicking on the green “Accept” button) will add the star Arcturus in the list of displayed stars:

The system of accepting names of stars is case-insensitive (so you could type “arc”, with the same result), accepts Greek letters and constellation names, abbreviated or in full (so you could type “α Boo”, “α Bootis”, “alpha Boo”, or “alpha Bootis”, with the same result), and also accepts Hipparcos id number specifications (so you could type “HIP 69673”, with the same result).

After that, you may click on the bluish “Find” button:

to add a star or stars.

This will open up the following dialog within the same screen:

in the text area of which you can type any names of stars, separated by commas, as the instructions above the text area explain.

For example, after typing “aldeb, gamma cru” in the text box, you reach and display the stars Aldebaran and Gacrux:

The largest star (in this case, Aldebaran) is always shown with the maximum diameter, and the sizes of all other stars are adjusted accordingly.

You may remove any star from this display by clicking on button , drag and shift stars around, or add more stars by the same method. Clicking on the info button opens the Wikipedia information page for that star on a separate tab of your browser. You may always add the Sun by clicking on the yellow round button at the left, labeled “Sun”, although in the example we’re demonstrating here the Sun will appear as a tiny yellow dot (on the left):

You may select and line up stars, like this:

You may use this program as a database of stars by clicking on this button of the tool bar:

Doing so will open a dialog box just above the main area of the program:

You may use this dialog to form queries about stars. To help you in forming queries, there is the selection box titled: “Choose by star type:”. Clicking on it, you get a drop-down list of various types of stars:

Now suppose you select the first option, “Brown Dwarfs”:

The selection completes some of the data in the other fields of this dialog, necessary to search for brown dwarfs: a diameter less than or equal to 0.5 X the diameter of the Sun, and a temperature of 2000°K or cooler. There are the controls of how many stars to show (up to 20) and that the two conditions will be used in conjunction. Clicking on the green OK button, the display of stars appears as shown below:

Try adding Jupiter to the above display, by clicking on the button with the image of Jupiter You then get this display:

You may add the Earth although in most cases our planet becomes invisible in the display compared to the sizes of stars. There are a few stars, however, that are comparable to Earth in size. You can find some such stars, however. Given that the Earth’s diameter is 0.0091 times the diameter of the Sun, you may search for stars with a diameter less than 0.02 of the Sun and that are within a distance of 12 light years from us. Here is the query:

The above query returns the following display, after clicking also on :

As you see, there is a nearby and super-hot star (Sirius B, the dwarf companion of Sirius) that is even smaller than our planet!

Many other peculiarities among stars can be discovered by using the database-queries feature of this program.