ND filters and the arithmetic of long exposure

A neutral density filter is a piece of dark glass. That is the entire concept. The complications are all in the labelling, which the industry has managed to do three incompatible ways at once, and in the practical business of operating a camera that can no longer see.

Three names for the same filter

Pick up three filters from three manufacturers and you may find them marked ND8, ND 0.9 and 3 stops. These are the same filter.

Stops is the photographer's unit. Each stop halves the light. Three stops means the exposure time must be multiplied by eight.

Filter factor is the multiplier itself. ND8 passes one eighth of the light, so it multiplies exposure time by eight. Three stops.

Optical density is the logarithm: D = log₁₀(1/T), where T is transmission. Density 0.9 means transmission of 10^−0.9, about 1/8. Three stops again. Each 0.3 of density is one stop, because log₁₀(2) is 0.301.

The ND1000 is the one that annoys people who like arithmetic: ten stops is a factor of 1024, and the marketing rounds it down. The difference is under one twentieth of a stop and does not matter.

The conversion, which is one line

New time = base time × 2^stops

Meter the scene without the filter, then multiply. That is the whole calculation.

A frame that meters at 1/250s becomes 1024/250, about 4.1 seconds, behind ten stops. A frame at 1/60s behind six stops becomes 64/60, just over a second. A frame at 1/8s behind ten stops becomes 128 seconds, and you are now well into territory where you need a remote release and a plan.

If you prefer to do it in your head, remember that ten stops is very close to multiplying by a thousand, and that shifting from fractional seconds to whole seconds is the same move as multiplying by the denominator. 1/500 with ten stops is about two seconds. 1/125 is about eight. That approximation is accurate enough that the difference is smaller than the variation in the light while you fit the filter.

The ND filter calculator does it exactly, including the awkward middle cases, and takes shutter speeds in the fractional form the camera displays.

Stacking

Stops add. An ND8 in front of an ND64 is three plus six, nine stops, a factor of 512. You do not multiply the stop numbers, and you do not add the filter factors.

Stacking works, but it costs you three things. Each additional air-glass surface adds reflections, so flare and loss of contrast get worse, particularly with a bright sun in or near the frame. Each filter ring adds physical depth in front of the lens, and on anything wider than about 24mm on full frame you will start to see the stack vignette in the corners. And colour casts compound: two filters that are each slightly warm produce something distinctly warm.

For occasional use, stacking a 6 and a 3 to reach 9 is entirely reasonable. If you find yourself doing it every time, buy the single filter of the right strength.

Operating a camera you cannot see through

Past about six stops, a set of practical problems appear at once, and they are the real difficulty rather than the arithmetic.

Metering stops working. Through ten stops, the camera's meter is guessing. Meter and set exposure before fitting the filter, then apply the multiplication yourself. This is not a limitation of cheap cameras; it is a limitation of measuring almost no light.

Autofocus stops working. Same reason. Focus first, then switch to manual so it cannot hunt, then fit the filter. Fitting a screw-in filter can nudge a focus-by-wire ring, so check afterwards.

Exposures pass 30 seconds. Most cameras stop at 30 seconds in aperture or shutter priority and manual. Beyond that you need bulb mode and something to hold the shutter — an intervalometer, a remote release, or the camera's app. Some recent bodies have a dedicated long-exposure mode that will time it for you.

Light gets in the back. On a DSLR, with your eye away from the viewfinder during a two minute exposure, light enters through the eyepiece and fogs the frame. Cover it; most DSLRs shipped with a small plastic cap on the strap for exactly this and most people threw it away. Mirrorless cameras do not have this problem.

Infrared contamination. Cheap ND filters block visible light effectively and infrared much less so. Over a long exposure the sensor accumulates that infrared, and the result is a colour cast — usually magenta or brown — that is not uniform and is a nuisance to correct. This is the single clearest difference between a budget ten-stop filter and an expensive one, more so than sharpness.

Long exposure noise reduction doubles your time. If it is on, the camera takes a second dark frame of equal length after every exposure. A four minute exposure occupies the camera for eight. It genuinely helps with hot pixels, so the answer is to know it is happening rather than to switch it off blindly.

Reciprocity failure does not apply. On film, very long exposures required extra compensation because the emulsion became less efficient. Digital sensors do not behave this way. If you have come from film, this is one calculation you can drop.

Choosing strengths

Three stops is not much, and that is the point: enough to soften moving water slightly at dusk, or to open a lens up a stop or two in bright light for shallow depth of field. Often the least dramatic and most used filter in the bag.

Six stops is the general-purpose long exposure filter. In shade or overcast light it takes you to a second or two, which is where waterfalls and streams look best — long enough to smooth the water, short enough to keep some structure in it.

Ten stops is for bright daylight, and for the several-minute exposures that flatten water and stretch clouds into streaks. Under a midday sun it lands you around two to eight seconds; in softer light it takes you to minutes.

Variable ND deserves a caveat. It is two polarisers rotating against each other, and at the extreme end of its range you get a dark X across the frame, especially on wide lenses. It also polarises the scene as a side effect, which changes skies and removes reflections whether or not you wanted that. It is excellent for video, where continuous adjustment matters more than absolute quality, and a compromise for stills.

A last practical note

Screw-in filters cross-thread easily, and a jammed filter on a lens in the field is a bad afternoon. Start the thread by turning anticlockwise until you feel it drop into place, then turn clockwise. That one habit prevents nearly all of it.

And check for a polariser underneath before you stack. A circular polariser plus a ten-stop filter is a thirteen-stop combination, which is why the exposure came out four stops darker than the calculator promised and everything looked broken.