Notes for doing complex and exact things with lighting fixtures.
A gobo is a light filter with a pattern. So it is used in focussable lights to get a certain effect. E.g. a logo cut from aluminium, the ball and paddles from the Sonic Pong installation, the coloured glass goibos used for big projections or on the road outside nightclubs.
Problem: I want a logo 1 meter diameter on a wall 15 meters away using a light (e.g. ETC Source 4) with a 5 degree lens. How Big is the gobo?
This is a little exercise for the mathematician in you - well, the multiplier in you. But first we have to work out what the actual dimensions mean!
First problem: what is the actual gobo size? A gobo is cut from a large piece of something (this aluminium or glass) that includes the fitting parts. The actual visible part of the gobo is smaller. And the really usable part even smaller, as one tries to avoid using the edges due to lens aberrations. The ETC source 4 can use A size and B size. I found out that a B size has a visible size of 70mm and a usable size of 65mm or so.
The visible size should correspond to the whole light beam. We know that the light beam has a 5 degree spread, which is 2.5 degrees either side of the axis. Some trig says that the size of the whole image is 15 * 2 * tan(2.5) = 1.31 meters. So it is bigger that the image we want to make (phew!). Thus we just go the other way and say we need (1/1.31) of the image size, i.e. the gobo we make has diameter (1/1.31) * 70mm = 53.4mm.
Note: these dimensions were found through talking to light techs and reading online documentation from the fixture manufacturers. The companies are good at spreading some relevant info online. Lighting techs know a lot about the things they use, but they rarely do anything like work out how to make a 1 meter diameter circle on the floor - they try things out and have a storeroom full of toys.
STAGE 2: It is a bit stranger than what is above. we did an experiment with a light and a different lens (36 degrees) and found that at 15.4m we have 8.5mm on the gobo is 1.00m on the wall. we now use a proportion of tangents to get that the gobosize we need is tan(18)/tan(2.5) * 8.5mm = 63mm.
We then double checked this with the gobo calculator at http://www.gobogroup.com/members/a_members/imagecalculator.html and by messing around with the numbers we found that the original size of the gobo style we were trying to use is 85mm. Then we can change the angle of the lens and find that the gobo size needs to be 63mm. Which agrees with the calculation above quite well. But experience (i.e. the lighting guy) says that more than 60mm gobo size on such a gobo is not good as deformations begin to creep in.
End Result: it's all a mess, but it should be possible to get things done.
Gobos can be made from vector graphics designs, directly rendered with laser, so there are no pixelisation effects. Example: http://www.goboworks.at
Using simple tricks with freehand, a gobo pattern can be squeezed to make it appear correctly on a surface that is not perpedicular to the lighting fixture.
– TimBo - 07 Oct 2004
something else learnt from sonic pong