Variable Neutral Density filters are incredibly handy in situations where you need slower shutter speeds than can be achieved by using your camera’s lowest ISO and stopping down the lens. For instance, when photographing a waterfall you might want the water blurred to convey the sense of motion. If the ambient light is too bright, a reasonable aperture like F/16 at your camera’s lowest ISO may not provide a shutter speed long enough for the effect you desire. This is when you need a neutral density (ND) filter, or better yet, a variable neutral density filter.
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Variable ND filters are quite expensive ($300-$400) and difficult to justify for occasional use. But if you already have a circular polarizing filter for your lens, adding a relatively inexpensive linear polarizer of the same size is all you need to do to create your own variable neutral density filter whenever you need it.
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Neutral density filters are simply filters that are tinted neutral gray. They restrict the amount of light entering the lens and do not appreciably change its color. Variable neutral density filters work differently, and are made with two polarizing elements. You may recall from high school physics that if you orient two polarizing elements in a crosswise manner almost no light gets through the pair, and as you change the orientation an increasing amount of light passes through. This is the heart of a variable ND filter.
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If you are as old as I am you’ll remember when all cameras used linear polarizing filters. Stacking two of these worked exactly as I just described to create a great variable neutral density filter. But of course it's not that simple today. Modern cameras require un-polarized light for their light metering and auto-focusing systems to work properly. Enter the so-called circular polarizing filters that are required by most modern cameras. These are made by sandwiching linear polarizing film and a quarter-wave retardation plate between two pieces of glass, with the polarization film in front. The light first passes through the polarization film, which acts exactly like the old polarizing filters to remove unwanted glare based on orientation. But then the light passes through the quarter-wave retardation plate which essentially scrambles or "un-polarizes" the light waves so your camera's light meter and auto-focusing system can work correctly. Because the light waves coming out of a circular polarizer are not truly polarized, stacking two of them does not create a variable ND filter.
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But, if you mount a normal linear polarizing filter in front of a circular polarizing filter you’ll actually have a stack of three filters. In front is the first linear polarizer, followed by a second linear polarizer (inside the circular polarizing filter “sandwich”), which together make exactly the variable ND filter we want. These are followed by the quarter-wave retardation plate (also inside the circular polarizing filter “sandwich”), which makes the resulting light un-polarized so our metering and autofocus systems are happy. Changing the orientation of the two filters relative to one another varies how much light can pass, while rotating the whole assembly on the lens varies the polarization effect.
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There are a couple things you should keep in mind here. First, a stack of two polarizing filters can be rather thick. That can cause vignetting, especially with wide angle lenses. Some filters are thicker than others, and lenses from different makers vary widely in how well they tolerate thick filter rings. Check for vignetting at home before shooting something important with the filters. Then you'll know how wide you can zoom without creating darkened corners in your images. Also keep in mind that smaller apertures lessen the amount of vignetting a filter may cause. Secondly, linear polarizers are less expensive than circular polarizers, so you've probably already spent more than half of what you need for a variable ND filter. But don't buy a bargain basement linear polarizer. Quality coated filters from reputable manufacturers make a difference. Using a thin-mount linear polarizer in front of a standard circular polarizer will cost more, but it will also reduce the chance of vignetting if you use the filters on wide angle lenses.
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Happy shooting!
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