This is the setup and preparation for the AF sensor optics experiment that I have been discussing. This should be performed in the evening, so that the room can be dark to aid in seeing the projected images.
Recommended lens is a 50mm f/1.4 or f/1.8 prime. Good alternatives would be a 35 f/2 (or faster), or an 85 f/1.8 or f/1.4. D-type lenses, with an aperture ring, should be used for this.
Set the lens horizontally on a smooth-top table. It's helpful to have a sheet of paper taped onto the table under the lens, and you may also want to tape some small stops down to the paper, to keep the lens from rolling. Aim the lens toward a bright lamp (use halogen or bare bulb) at least 20' away, and hang a sheet of cardboard, aluminum foil, etc., close in front of the lamp. Make a hole about 3/4 to 1" diameter in the cardboard, and align it so the light shining through the hole strikes the lens. It is best if the light source is at about the same height as the table top.
Cut a sheet of paper about 3" or 4" square, and tape it onto the side of a smooth, square box, such as a Kleenex box or a Nikon lens box; this will serve as our projection screen. Set this behind the lens, adjust the lens focus ring to near infinity, set the lens aperture wide open, and align the screen position until you have a nice, sharply focused image of the light source, which will be a very bright spot.
You can now vary the lens aperture, observing the brightness of the projected spot changing as you do so.
We're ready to begin - on to Part 2.
With everything set up as in Part #1, now put the lens back to maximum aperture.
Slowly slide the screen toward the back of the lens, and observe that the tiny light spot gradually grows into a larger and larger solid circle. The illumination across the diameter of this circle is very even. If we plot the diameter of the circle versus the screen position, we will find a simple linear relationship; as the screen moves, it is sampling cross sections of a 3-dimensional cone of light.
It's a little cumbersome to study the circle diameters this way because of the small space between the screen and the back of the lens. The distance from a focused image to the rear of the lens mount is only about 38mm. To get more working room, we can alternatively look at the rear cone of light, which forms behind the plane of focus.
Set the screen back to position where the light spot is well focused. Set a metric ruler against one side of the screen's box, and slide the box back along the ruler exactly 100mm. We now have a much larger solid circle of light to examine (although it is also much dimmer). Use the ruler to measure the diameter of the circle in milimeters. Calculate the value of 100/diameter; this should be the same as the f-stop of the lens (assuming the lens is still wide open).
Set the lens aperture to a few other values, and observe that as you stop the lens down, the size of the circle reduces. Also, notice that as the circle shrinks, the brightness of its interior does not change. [You can confirm this by photographing the circle at different lens aperture settings (used locked manual exposure settings on the camera when doing this), then checking the images that you obtain.] Thus, changing the lens aperture alters the size of the circle (i.e., the diameter of the light cone), which by itself determines the total amount of light passed by the lens - the intensity or concentration of light within the cone remains constant.
Measure the diameter of the circle for several different lens aperture settings, and for each one, calculate the value of 100/diameter. The calculated value should agree with the f-stop set. This set of measurements does not depend on the lens focal length. You can repeat this experiment with other lenses and you will again find that 100/diameter = f-stop.
Now we know that the width of the light cone relates directly to lens aperture, and in fact the height of the light cone, divided by its base diameter, is the same as the lens focal ratio or f-stop.
For the last demonstration in this part, slide the screen back to position where the light spot is well focused. Set the lens back to maximum aperture. Take a small dot of paper, about 1/4" diameter, and hold it with tweezers or stick it onto the end of a toothpick or similar. You can move this dot across the back of the lens, through the light cone, and no matter what position it is held in, the projected light spot will still be observed. It will drop slightly in brightness while the paper dot is within the light cone, but it cannot be cut off.
On to part 3 . . .
Picking up where we left off in Part 2, we again have the lens at maximum aperture, projecting a focused spot of light onto the screen.
Cut out a rectangle of paper, about 1.5" by 3", and punch a hole in the center of about 1/16" (1.5mm) diameter. Hold this paper across the back of the lens, with the small hole inside the light cone. The projected spot on the screen will become much dimmer, but note that you can move the hole to any position inside the light cone, without the spot disappearing, and in fact, without its brightness changing.
Now punch a second small hole in the 1.5" by 3" paper, centered 12mm away from the first hole, and in line with the length of the paper. Hold the paper so that both holes are within the light cone, and align it so that both holes are on a diameter and evenly spaced from the center (i.e., evenly spaced from the edge of the circle - you want the holes positioned symmetrically). The projected light spot will now be a bit brighter, having the illumination from two holes.
Here's the fun part. You may need a second person to assist. While keeping the paper with the two holes aligned at the back of the lens, rotate the focus ring and observe what happens to the projected spot of light. It will split into two spots, and you control the distance between them by turning the lens focus ring. What you are seeing now, is exactly what is projected onto the AF sensors in the camera. The AF system compares the two small images, and adjusts the lens focus until they line up.
Now, what happens when the lens aperture is adjusted? With the two holes in the paper centered 12mm apart, they have been set up to work with apertures of f/2.8 or faster. If you set the lens to f/1.4, f/2, or f/2.8, the projected spot(s) will appear the same. But, if you try to stop down smaller than f/2.8, the spots will extinguish because the light cone becomes too small to pass light through both holes at the same time (you need to hold the alignment of the paper rather accurately to see both spots go out at the same time).
Of course, there is no such mask with small holes in our cameras, but the mask does simulate the AF optics, which samples a small pair of spots at the back of the lens, for each AF sensor.
There are several more things you can try:
Second light source
Add a second light source to the side of the original lamp. Note that you will have two projected spots on the screen, which you can split or merge with the lens focus ring.
Try moving the second light source closer. Now you will see that the split spots will merge at different focus settings, for each light source.
Combination horizontal/vertical AF optics
You can add a second pair of holes to the paper. If you place these at right angles to the original holes, you will form a combination horizontal/vertical AF optics set. For added interest, make the second set of holes closer together; if they are spaced 5mm between centers, then they will work down to lens apertures of f/5.6. Note, however, that the pair of light spots which they project will be closer together, i.e., the AF sensor requires more precision to use the closer holes.
Additional variations: Up to your own imagination!