A correctly exposed scene sometimes leaves no room to work. Bright daylight forces a fast shutter that freezes the blur of moving water, or a small aperture that pulls more of the frame into focus than intended. A neutral density filter resolves this by removing light without favouring one part of the spectrum, lowering the illuminance reaching the film so the exposure can be re-extended through a slower shutter or a wider aperture. The arithmetic is simple. The traps lie in the labelling, in the meter that can no longer read the scene, and in a strong filter that turns out to be neither perfectly neutral nor exactly its rated strength.

Density, Transmittance and the Logarithmic Scale

The most fundamental rating is optical density, the figure Lee and Tiffen print on their glass. Density is defined logarithmically: transmittance equals 10 raised to the power of the negative density, T = 10^(-D). A filter of density 0.3 transmits 10^-0.3, very close to 50 percent of incident light, a reduction of one stop. Because the scale is logarithmic, densities add: two 0.3 filters stacked give 0.6 and a two-stop loss; 0.9 transmits about 12.5 percent and costs three stops.

The convenient consequence is that each 0.30 of density equals one whole stop. Common values follow directly: 0.6 is two stops (25 percent transmission), 0.9 is three, 1.8 is six (around 1.56 percent), and 3.0 is ten stops, the last passing only 0.1 percent of the light.

The Same Filter, Three Different Labels

The intro promised confusion, and here it is. A second convention, the ND factor, states the multiple by which exposure must increase rather than the density. Since each stop halves the light, the factor doubles per stop: ND2 is one stop, ND4 two, ND8 three, ND64 six, ND1024 ten. The factor equals two raised to the number of stops. A third, looser convention simply prints “3-stop” or “6-stop.”

The number on the glass means nothing until you know which system the maker used. ND2 is one stop, not two. ND16 is four stops, not sixteen. Hoya, B+W and Cokin print the factor (ND8); Lee and Tiffen print the density (0.9); Leica prints the factor as a multiplier (8x). A 0.9, an ND8 and a “3-stop” filter are the same article in three dialects. Buy by the stop count you actually want and translate everything else to it before it reaches the front of the lens.

Reading Through the Filter

Past three or four stops a practical problem arrives that the arithmetic ignores: the camera can no longer see. A six- to ten-stop filter blocks so much light that a through-the-lens meter, and most handheld meters, cannot take a reliable reading through it, and an autofocus or split-image rangefinder cannot lock either. The workflow is therefore fixed in order. Meter the scene unfiltered and note the reading. Focus unfiltered, then switch the lens to manual so nothing hunts in the dark. Only then fit the filter, apply the factor, and set the result.

Applying the factor means landing on a shutter speed the camera offers. A metered 1/250 second behind an ND8 is 1/250 x 8 = 1/31.25 second; there is no such mark, so you set the nearest one, 1/30. Round to the marked value rather than chasing a decimal the shutter cannot deliver.

When the Arithmetic Runs Out: Reciprocity

The factor calculation assumes film responds linearly to light, and below about one second it does. Beyond that, emulsions lose sensitivity, and the calculated time underexposes the negative. HARMAN, who make Ilford film, give the correction in their Film Reciprocity Failure Compensation sheet (David Abberley, 30 May 2024) as a power law: the corrected time Tc equals the metered time Tm raised to a per-film exponent P, with no compensation needed at one second or below. The exponents differ by emulsion: HP5+ is 1.31, FP4+ 1.26, Delta 100 1.26, Pan F+ 1.33, SFX 1.43. Ilford’s own worked example: HP5+ metered at 10 seconds wants 10^1.31 = 20.4 seconds, set to 20.

The same note carries the fact most useful in the darkroom. Long exposures increase contrast, because the brightest and darkest parts of the frame sit at different light levels and so fail reciprocity by different amounts within a single negative; the shadows lose more than the highlights, and the curve stretches.

Grain structure matters here. Kodak’s T-grain films are far more tolerant than classic cubic-grain emulsions: T-MAX 100 needs nothing from 1/1,000 to 1/10 second, only +1/3 stop at one second and +1/2 stop at ten (shoot 15), and +1 stop at 100 seconds. Tri-X is brutal by comparison — roughly +1 stop at 1/100,000 second rising to +3 stops at 100 seconds, where a metered one minute should be given about eight. Choose the film for the exposure length, not only for the look.

A Worked Ten-Stop Frame

Carry one example all the way through. A metered 1/60 second behind a 3.0 / ND1024 filter is 1/60 x 1024, about 17 seconds — and 17 seconds is well past the reciprocity threshold, so the unreciprocated figure is a trap. On HP5+ it becomes 17^1.31, roughly 41 seconds. On FP4+ (P 1.26) about 36 seconds. On T-MAX 100 the same 17 seconds wants only around +1/2 stop, roughly 25 seconds. Same light, same filter, three different exposures because the films fail reciprocity differently. The ND maths sets the starting point; the datasheet finishes the figure.

Not Quite Neutral

The “neutral” in the name is a goal, not a guarantee. Strong filters carry a colour cast: the Lee Big Stopper runs cool and blue, B+W ten-stops tend to warm. On panchromatic black-and-white film this is not cosmetic — a blue-casting “ND” behaves like a weak blue filter on the negative, lifting skies and darkening reds relative to a truly neutral piece of glass. There is a second leak at high density. Around 3.0 the filter blocks so much visible light that residual near-infrared becomes a measurable fraction of what reaches the film, raising shadow density and flattening contrast. IRND glass exists to block it — Lee’s ProGlass IRND, and the IRND ranges from NiSi and Formatt-Hitech.

Two more practical notes. Rated strength is approximate: independent measurements of Lee Big Stoppers have come in around 10.3 to 10.6 stops rather than a clean ten, so one calibration frame on your own filter is worth more than the figure printed on the ring. And variable NDs, built from two crossed polarisers rotated against each other, save space but fail near maximum density, where oblique rays are not extinguished evenly and a dark “X” crosses the frame, worst on wide and ultra-wide lenses; keep below the rated maximum. Stacking fixed filters brings its own costs — vignetting on wide lenses and reflections between the glass surfaces — so reach for a single high-density filter before a stack whenever you can.