Wednesday 18 May 2011

Aperture Science

Looking the the flat mirror you might realise that the rectangular output of the projector won't fit on it entirely, and that the light that misses the mirror will go straight on the screen, thus interfering with the actual virtual reality. One solution would be to but a plate behind the flat mirror which catches the excess output. However, due to space constraints an aperture is the better solution. There is a lot to say about apertures and you can use it for many purposes/effects in optics, but I'm using the term aperture in its most general meaning, here is the first line of its Wikipedia article: "In optics, an aperture is a hole or an opening through which light travels." Yeah, great word for such a simple thing. In microscopy you use an aperture to catch scatter light and thus improve sharpness and contrast of the picture. Here we use it to block unwanted background light. The best  location to mount the aperture in our case are the two black construction cubes you can see in the picture below.

The Aperture will be mounted to the two black cubes which also hold the poles for the flat mirror.

Here is a side view of the entire model. You can see here to location of the projector and at which angle the rays will fall onto the screen. The convex mirror profile was chosen to maximise coverage.

Because we are cutting a plane through a cone at an angle we will need an eliptical opening. Now, if you are a straight A student you'll know how to calculate the dimensions of the eliptical cross section at the level of the intersecting plane. But if you are, like me, a lazy git, you'll just punch it into the modelling software and make the computer do the work.

First of all, we take the projector output and revolve it around the centre axis to get a solid body which we can use for modelling. With that you can create a plane in the desired orientation and level as I've done in the picture below. For clarity I made the raytracing lines invisible. You can probably guess where I'm going with this now.

By taking the raytracing lines and revolving them around the centre we can make a 3-dimensional representation of the projector output.

Next step is to slice the model at the level of the plane. Sounds like a lot of work but really all you need to do is hit F7.

The cone sliced by the plane.

Now all you have to do is project the cut edges of the cone onto your plane, create a sketch and extrude it.

Sketching a simple rectangle with the ellipse projected at its centre.
The extruded aperture with the requried opening.
Cutting the ellipse straight is suboptimal because the rays are passing through at an angle, but given how thin the aperture is (here it is 5mm, but it can be much thinner, depending on which material you use), it is negligible in my view. Here is the final picture:

Aperture mounted to construction cubes with bolts.

To turn the computer model into reality we can easily create a technical drawing which can be handed to the workshop. With sufficient annotation they should be able to create the desired part.

Technical drawing of the Aperture.
From here it is easy to order a plate with the required dimensions, drill holes at the right places and cut the ellipse out. Then two M6 screws will keep it in place. I hope I made my case for 3d modelling once again, it's hard to overstate my satisfaction.

Just a few words of clarification:
- the light cone cuts through the flat mirror, that is just me being too lazy to correct the model. I simply revolve the top half of the lightpath around the central axis, but because the cone is at an angle to the mirror it will cut through it.

- the initial technical drawing missed a few annotations, that is now corrected.

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