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 evenly across the visible spectrum, lowering the overall illuminance reaching the film without altering the relative brightness of one tone against another. The exposure can then be re-extended through a slower shutter or a wider aperture. The only complication is that three different rating conventions describe the same filter, and they are easily confused.

Density, Transmittance and the Logarithmic Scale

The most fundamental rating is optical density, the figure printed on filters from manufacturers such as B+W. Density is defined logarithmically: fractional transmittance equals 10 raised to the power of the negative density. A filter of density 0.3 transmits 10^-0.3, or very close to 50 percent of incident light, which corresponds to a reduction of one f-stop. Because the scale is logarithmic, densities add. Two 0.3 filters stacked give a density of 0.6 and a two-stop loss; a density of 0.9 transmits roughly 12.5 percent and costs three stops.

The convenient consequence is that each 0.3 of density equals one whole stop. Common values follow directly: 0.6 is two stops, 0.9 is three, 1.8 is six, and 3.0 is ten stops, the last transmitting only 0.1 percent of the light.

The ND Factor and the Stops Notation

A second convention, the ND number or filter 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 stops, ND8 three, ND64 six, and ND1024 ten. The factor equals two raised to the power of the number of stops. A third, looser convention simply labels the filter “3-stop” or “6-stop.” All three describe identical glass; a 0.9, an ND8, and a 3-stop filter are the same article.

Recalculating the Exposure

Because the factor is a literal multiplier, exposure time scales by it directly. A metered exposure of 1/250 second behind an ND8 (three stops) becomes 1/250 multiplied by 8, or about 1/30 second. A ten-stop filter multiplies by 1,024: a metered 1/60 second extends to roughly 17 seconds. Equivalently, counting in stops, each stop doubles the existing time, so the calculation can be done by repeated doubling from the unfiltered reading.

One caveat applies to the longest exposures. Most films depart from reciprocity once exposures pass roughly one second, so the calculated time underexposes the negative. Ilford’s technical data for its black-and-white films gives reciprocity corrections for this regime, and a measured time of several seconds may require extending further still. The ND arithmetic sets the starting point; reciprocity compensation, where the film’s datasheet calls for it, completes the figure.