Changing a lens opening by "one stop" means either doubling or halving the amount of light that passes through the lens. By definition a .30 log neutral density filter will absorb 50% of the light passing through it (i.e. -1 stop)
If a cinematographer opens up "one stop" he is doubling the amount of light passing through his lens. To compensate he could put a .30 ND filter in front of his lens and be back where he started. If he's shooting under perfect conditions and opens up one stop and exposes a motion picture negative film such as 5247 then twice as much light will hit the film as should. To compensate for a one stop overexposure in the lab the gamma, or contrast, of the film must be considered.
The gamma of all contemporary motion picture color negative camera stocks is around 0.65. This means that for a one stop increase in exposure, the resulting density increases by .30 ND times the gamma of 0.65 which is .195. One laboratory printer point is 0.025 ND. Dividing .195 by .025 yields 7.8 printer points. Therefore to compensate for a one stop overexposure by a cinematographer one must increase the light in the printer by 7.8 printer points to make a print of the proper density.
If a cinematographer asks for the timing of a scene to be "one stop darker" he probably means, "make the scene look as if I stopped down one stop." So to accommodate the wishes of the cinematographer one should add 7.8 points of density.
If an optical house cameraman says that he shot the dupe neg "one stop overexposed" and asks the lab to compensate, the request is quite different: The optical cameraman is probably using 5244 intermediate stock which has a gamma of 1.0, so his resulting density increased by .30 ND times the gamma of 1.0 which yields .30, or 12 printer points, since .30 divided by .025 is 12.
- some wisdom from the old optical printer days in Hollywood.