When you are shopping for the ND filters, you may have been in a situation where the numbers (printed on the filter) confuse you more than help you. All you want to buy is 1-stop, 2-stop, 3-stop or 10-stop filter which blocks 1-stop, 2-stop, 3-stop or 10-stop of lights respectively but the numbers manufacturers use to represent the f-stop creates confusion. When I bought my first ND filter back in 2012, I actually ordered the wrong filter because of this confusion. I wanted to buy a 3-stop ND filter and when I looked online, it was showing Neutral Density 3.0 and I thought it was the right filter. But later when it arrived, it seemed darker than it should be for a 3-stop filter and after doing little bit of research, I realized that the filter I got was a 10-stop filter and not a 3-stop filter. My fault was not to do proper research before buying the item but I think it would be fair to blame the part of the mistake on how manufacturers label their product as well. Why wouldn't they simply market the filters as 1-stop, 2-stop or 3-stop filter and avoid any possible confusion? I don't know the answer for this question yet but the good news is that some of the vendors have started using more sensible naming practice with the detailed description of the products. Today, I was trying to get another ND filter and the past memory came back to me. So, I thought it would be helpful for you guys to share what I have learned so that you can make the right decision when you are shopping for the ND filter. After I made a mistake during my first purchase, I tried to find out why manufacturers use these numbers and how does this naming conventions make sense? After knowing the science behind the numbers, I shifted more blame towards me for the mistake I made but I think there is still some room left to blame the manufacturers as well. It's the manufacturers job to market their products as clearly as possible so that the buyers can easily understand what they are getting.
Let's take an example of the ND filter I was going to get today and see what the numbers tell us about the characters of the filter.
Name of the ND Filter (on Amazon) - B+W 77mm Neutral Density 0.9-8x Filter #103
In the above example, B+W is the name of the manufacturer who built the ND filter and 77mm is the diameter of the filter to fit the 77mm diameter lens. You can't fit 77mm filter on 72mm lens which is obvious. This is also something you have to be careful while shopping for the circular filter. You have to match the diameter of the filter and the lens. Now, the more confusing part of the name is 0.9-8x and #103. Let's see what do these numbers suggest.
The first number 0.9 represents the multiple of the f-stop optical density (0.3) with regard to how much light the filter is letting through the lens to the sensor. The number 0.9 in our example filter is a multiplication of (0.3) and (3) which tells us that this is a 3-stop ND filter. By using this filter, only (1/2) * (1/2) * (1/2) = 1/8th of the light that hits the front of the filter is passing through the lens. The number 1/2 would be the fraction of the lens area opening if the optical density would be 0.3 compared to the full lens opening of 1 for 0.0 optical density (which means no filters are attached to the lens).
The second number 8x suggests that if you use this filter on your lens, you will need 8 times more light than without the filter to get the same level of exposure. You can get 8 times more light by using the longer shutter speed, widening an aperture (if possible), increasing the ISO value or by using the combination of the three. How to adjust the exposure setting depends on what you are trying to achieve by using the filter. Usually, ND filters are used to get the long exposure shot and hence you would want to increase the shutter speed to compensate the loss of light with the introduction of the filter.
The Third number #103 represents the general naming convention (look at the table below) to represent the 3-stop filter. So, if you look closely, all these numbers mean the same thing and that is the filter in our example is a 3-stop ND filter. If we attach this filter in front of our lens, we need to slow down the shutter by 3-stop (or 8 times longer shutter speed is required) to get the same level of exposure as we would get without the filter. If you are shooting with the shutter speed of 1/8th of a second, an aperture of f/11 and the ISO 100, after applying a 3-stop ND filter, your new shutter speed would be 1 second (1/8 * 8 = 1) to get the same exposure considering the other two exposure parameters, aperture and ISO, are same. However, in a real world scenario, you might need to adjust the calculated shutter speed little bit up or down depending on shooting condition and the quality of the filter you are using.
If the filter in our example had a 3.0-1000x number on it, it would mean a 10-stop filter (3.0 = 0.3 * 10) letting in only 1/1000th of the light and requiring 1000 times longer shutter speed to get the same exposure as without the filter. If we do a proper math using the same formula we used before and multiply (1/2) * (1/2) *.....* (1/2) 10 times, the actual number should be 1024x but for the simplicity, 1000 is being commonly used as a rounded number. If you are interested to know how to take a long exposure shot using a ND filter, here is an article I posted earlier last week about Using a 10-Stop ND Filter for a Long Exposure Shot. You can also stack the filters and multiply the effects as well. If you use 0.9-8x filter on top of 3.0-1000x filter, the effective value would be 3.9-8000x requiring to keep the shutter open for 8000 times longer than without the filter.
During my research, I found this table below on the Wikipedia and thought it could shed some lights on the discussion we just had about the significance of the numbers to represent the ND filters. The rest of the article below is an excerpt from the Wikipedia.
In photography, ND filters are quantified by their optical density or equivalently their f-stop reduction.
Note: Hoya, B+W, Cokin use code ND2 or ND2x, etc; Lee, Tiffen use code 0.3ND, etc; Leica uses code 1x, 4x, 8x, etc.