Neutral density filter

In photography and optics, a neutral-density filter, or ND filter, is a filter that reduces or modifies the intensity of all wavelengths, or colors, of light equally, giving no changes in hue of color rendition. It can be a colorless (clear) or grey filter. The purpose of a standard photographic neutral-density filter is to reduce the amount of light entering the lens. Doing so allows the photographer to select combinations of aperture, exposure time and sensor sensitivity that would otherwise produce overexposed pictures. This is done to achieve effects such as a shallower depth of field or motion blur of a subject in a wider range of situations and atmospheric conditions.

For example, one might wish to photograph a waterfall at a slow shutter speed to create a deliberate motion-blur effect. The photographer might determine that to obtain the desired effect, a shutter speed of ten seconds was needed. On a very bright day, there might be so much light that even at minimal film speed and a minimal aperture, the ten-second shutter speed would let in too much light, and the photo would be overexposed. In this situation, applying an appropriate neutral-density filter is the equivalent of stopping down one or more additional stops, allowing the slower shutter speed and the desired motion-blur effect.

For an ND filter with optical density d, the fraction of the optical power transmitted through the filter can be calculated as

where I is the intensity after the filter, and I₀ is the incident intensity.

The use of an ND filter allows the photographer to use a larger aperture that is at or below the diffraction limit, which varies depending on the size of the sensory medium (film or digital) and for many cameras is between f/8 and f/11, with smaller sensory medium sizes needing larger-sized apertures, and larger ones able to use smaller apertures. ND filters can also be used to reduce the depth of field of an image (by allowing the use of a larger aperture) where otherwise not possible due to a maximal shutter speed limit.

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