Okay, this is my first instructable and I am doing this in my Christmas holiday. I reproduced the camera installation from the film Tim's Vermeer on my job as high school physics teacher. That means I don't have all materials at my disposal to photograph yet, but I will upload them in a week or two.
I will try to keep this instructable as practical as possible. I can imagine that this will raise some questions on the optics behind the machine, so I will answer those in the last step.
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Step 1: What We Need
The camera consists of three components: A tiny flat comparator mirror, a positive lens and a concave mirror. The combination of lens and mirror work as a negative lens and I achieved reasonable results with just a negative lens (with a focal length of -20 cm). The thing is that the installation actually makes your image smaller, so you want a lens that has a long focal length so the image is not extremely tiny. Tim Jenison makes use of a lens with a focal length of 70 cm that he ground himself. Rightfully so, because these lenses are extremely hard to come by. Fresnel lenses with such focal lengths exist in solar ovens, but are useless for image projection because of spherical aberration and grating effects. The concave mirror can actually be any shaving mirror you can find for a few bucks.
So you'll need:
A large as possible positive lens with a focal length of at least 30 cm (embroidery lenses work fine here. (A company called Velleman has a pretty good one here.)
A shaving mirror (any will do, as long as it is concave)
Something to use as a comparator mirror (there's a tool called "inspection mirror" that is perfect for the job, but at my school we took small mirror tile we put at the end of a stick, so we could have entire classes work with those for less than 10 bucks.)
A table to work on
A screen with an angle of 90 degrees with the table top on which to put the concave mirror
some sheets of paper
a flashlight (optional)
Step 2: Setting Up the Comparator Mirror
This is reproduced extensively all over the internet, but I believe this method is the easiest. The mirror should be exactly in the right position for the image not to shift, otherwise you move your head and your image is different. This is how I let 13-year olds do it:
1. Take two identical sheets of paper (like to halves of an a4 or two a4's)
2. Tape one to your screen and put the other down on the tabletop
3. arrange your mirror in such a way that the angles of the paper on the table coincide with the angles you see in the mirror.
4. If you attach a photo to the screen, you can easily trace it on a sheet of paper. (this actually takes some practice and is fun to do. I recommend trying it before building the entire camera.)
Step 3: Enter the Concave Mirror
Put your concave mirror on the screen. That's it.
I know what you are thinking. "but doesn't the image shift forward now? Won't there be any parallax?" No, the virtual image the concave mirror creates is right behind the concave mirror. The only think you should make sure is that the object of the hollow mirror is then right in front of it. And this is where the lens comes in.
p.s Oh, and it is wise to put the concave mirror a little to the side, so the comparator mirror is not between the lens and the concave mirror. As long as it is in this correct plane (see previous section) you are quite allright.
(p.p.s I noticed that it doesn't make a big difference if you change the angle of the concave mirror a bit to center on the lens.)
Step 4: Putting the Lens in Position
Okay, so you got hold of a large diameter lense with a long focal length. You will want to project an image right in front of the concave mirror. So put a sheet of paper in front of the concave mirror (I usually go for a few millimeters, but if you tape the paper to the mirror that works fine). And you put a flashlight exactly where the nearest subject is you want to paint. That would be the object closest to the lens, like the carpet in Vermeer's Music Lesson. From that position, you shine at the sheet of paper. You know your lens is in the correct position when the led's or the bulb of the flashlight are sharply projected on the paper sheet. You can remove your sheet and flashlight now and start painting/drawing. You will notice that your object is projected on your tabletop without any parallax. So you can move your head as much as you want, the image will not shift in relation to the tabletop.
When painting/drawing, try to avoid the edge of the lens to minimise spherical aberration. Vermeer has some in his paintings, but you want to shift your lens a few times to expand your image. For this, you will just need to repeat this step with the flashlight in another position. I guess that if you are Johannes Vermeer or Tim Jenison, you might want to have a wooden framework in wich your lens can move within a set plane. But I never bothered.