I was doing some research for an upcoming guide to long exposure photography, and I was struck by how differently the various filter manufacturers name their neutral density (ND) filters. I had a long phone conversation about filters with a friend this week, and the terminology differences also caused some confusion there as well.
Some manufacturers label their filters using what is called the Optical Density of the filter, whereas some of them use what’s known as the Filter Factor.
|F-Stop Reduction||Optical Density||Filter Factor||% transmittance|
|10||3.0||1024 (sometimes called ND1000)||0.09765625|
Filter Factor (ND2, ND4 etc.)
This is simply a representation of the factor by which the neutral density filter reduces the light coming into the lens. For example, an ND filter that reduces light by one stop has a filter factor of 2. A one stop reduction of light is always half the light (see previous tutorial on aperture and f-stop), so the factor by which a one stop neutral density reduces the light, is 2.
The confusion arises because with these smaller filter factor numbers (2,4,8,16), people confuse them the with the reduction of light in f-stops. When they see ND2 on a filter, they think it is a 2-stop ND filter, but actually it’s a 1-stop filter. Similarly, a filter that has ND16 written on the side of it is actually a 4-stop filter and not a 16-stop filter. Please refer to the table above for a full list of common filter factors.
Since the light reduction doubles for each further reduction in f-stop, we can say that where x is the reduction in f-stops, Filter Factor = 2x
A 5-stop reduction in light would give us a filter factor of 25 = 2x2x2x2x2 = 32 , so an ND32 is a 5-stop neutral density filter.
The transmittance number is actually very rarely mentioned on a filter itself, but you might see it mentioned on some packaging. The reason I included it in the reference table is really because I find it’s just a good visual representation of the light that gets cut by neutral density filters. To many people, when I tell them that a 6-stop ND filter only lets in 1.56% of the light, it’s instantly easier for them to visualize the result of that, as opposed to me just saying it has a filter factor of 64. The % Transmittance also comes into play if you want to mathematically calculate the optical density.
Optical Density (0.3, 0.6, 0.9 etc.)
These days this seems to be the most common way for manufacturers to represent the amount of light by which their neutral density filter cuts light. An ND0.3 is a 1-stop ND filter, and an ND0.9 is a 3-stop ND filter for example (see the reference table above).
Optical Density Equation
Being the kind of photo nerd that I am, and also an engineer in a past existence, I couldn’t just trust that these numbers mean what they do, and simply put them into the reference table verbatim! So of course I looked a little deeper and found out how these numbers are achieved.
The formula relating to optical density is: Fractional Transmittance = 10-d
Where d is the optical density we are looking for and fractional transmittance = (% transmittance/100)
This now gives us % transmittance = 10-d x100
But we also know that % transmittance = (100/Filter Factor)
So now we can say 100/Filter Factor = 10-d x100
Additionally, where X is the light reduction in f-stops, we know from the earlier section that Filter Factor is = 2x
Now that gives us 100/(2x) = 10-d x100
To solve the equation for d, we would get: d = log10 (1/((100/2x)/100)
If you simplify all the stuff in the brackets on the right, you are actually just left with 2x
Therefore we can say that d = log10 2x or d=log10Filter Factor
Using this equation we can work out the optical density number using the reduction of light in f-stops.
We want a reduction in light of 3-stops and we want to know which filter to pick because they aren’t labelled in stops. We would do -> d = log10 23 = log10 8 = 0.90308998699
For simplicity we just say 0.9! A 3-stop ND filter is also called a 0.9.
Now you know this optical density number it is simply the Log of the factor by which light is decreased!
Ok, ok… don’t worry, there’s no need to actually remember all that mathematical stuff. All you really need to know is what is in the table above. I just put all the math there for the small minority that might be curious about it, so please don’t let it scare you off. Neutral density filters are a really important thing for photographers, so it is important to know which ones are which, but you can just use the table to memorize the relationships and names.
Hopefully you guys find this useful and it clears up a few things about the naming of neutral density filters.