For a guy that has a background in software development and CG/post production the ever wonderful world of production craft and equipment can be full of small technical hurdles. Sometimes it takes a moment or two to make sense of what others have honed for decades.

When looking into matte boxes and filters one of that “what?!” moments was when I looked at ND (neutral density) filters. Wading through filter stages and form factors like 4x4 and 4x5.65, graduated and what not it took me a while to make sense of their rating. Assuming that a 0.3 filter would let through 30% of the light was quickly ridiculed by filters with a factor of 1.2 or higher. So the guess of a multiplication factor was ruled out quickly.

The number is the optical density which is the logarithm of the ratio of the light passing through the filter to the light entering the filter. Sounds complicated but isn’t really. An optical density of 0.3 reduces brightness by 50%, thus halfing it (1 stop in photography terms). The math is simple:

0.3 = -log_{10} ( 0.5 / 1.0 )

0.5 is the amount of light (intensity) passing through the filter, 1.0 is the intensity before the filter. (You can just get rid of that part in the equation as the intensity in front of the filter always is 1.0)

Still does not make sense?

Reversing it might help: With an optical density of 0.3 the amount of light passing through the filter is:

10^{-0.3} which is 0.5

So suddenly a filter of 1.0 or 1.5 makes sense:

10^{-1.0} = 0.1 or 10%

10^{-1.5} = 0.03 or 3%

Once I was past this hurdle it got a bit easier to grok and I was ready to learn why you should use an hot mirror when stepping down considerable and what the heck a hot mirror actually does - and how it relates to infrared and the properties of sensors (or film, should you still work analog).