Neutral density filter
In photography and optics, a neutral density filter or ND filter is a filter that reduces or modifies 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 allow the photographer greater flexibility to change the aperture, exposure time and/or motion blur of subject in different situations and atmospheric conditions.
For a ND filter with optical density d the amount of optical power transmitted through the filter, which can be calculated from the logarithm of the ratio of the measurable intensity (I) after the filter to the incident intensity (I0), shown as the following:
- Fractional Transmittance (I⁄I0) = 10-d, or
For example, on a very bright day, one might wish to photograph a waterfall at a slow shutter speed to create a deliberate motion blur effect. In order to do this, one would need a shutter speed on the order of tens of seconds. There might be so much light that even at minimum film speed and a minimum aperture such as f/32, the desired shutter speed would still let in too much light and the photo would be overexposed—or, if shooting at aperture priority, the camera would select a shutter speed that would be too fast to achieve the desired effect. In this situation, applying an appropriate neutral density filter is the equivalent of stopping down one or more additional stops, allowing for the slower shutter speed and the desired motion-blur effect.
The use of an ND filter allows the photographer to utilize 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 maximum shutter speed limit.
Instead of reducing the aperture to limit light, the photographer can add a ND filter to limit light, and can then set the shutter speed according to the particular motion desired (blur of water movement, for example) and the aperture set as needed (small aperture for maximum sharpness or large aperture for narrow depth of field (subject in focus and background out of focus)). Using a digital camera, the photographer can see the image right away, and can choose the best ND filter to use for the scene being captured by first knowing the best aperture to use for maximum sharpness desired. The shutter speed would be selected by finding the desired blur from subject movement. The camera would be set up for these in manual mode, and then the overall exposure then adjusted darker by adjusting either aperture or shutter speed, noting the number of stops needed to bring the exposure to that which is desired. That offset would then be the amount of stop needed in the ND filter to use for that scene.
Examples of this use include:
- Blurring water motion (e.g. waterfalls, rivers, oceans).
- Reducing depth of field in very bright light (e.g. daylight).
- When using a flash on a camera with a focal-plane shutter, exposure time is limited to the maximum speed—often 1/250th of a second, at best—at which the entire film or sensor is exposed to light at one instant. Without an ND filter this can result in the need to use f8 or higher.
- Using a wider aperture to stay below the diffraction limit.
- Reduce the visibility of moving objects
- Add motion blur to subjects
- Extended time exposures
Neutral density filters are used to control exposure with photographic catadioptric lenses, since the use of a traditional iris diaphragm increases the ratio of the central obstruction found in those systems leading to poor performance.
ND filters find applications in several high-precision laser experiments because the power of a laser cannot be adjusted without changing other properties of the laser light (e.g. collimation of the beam). Moreover, most lasers have a minimum power setting at which they can be operated. To achieve the desired light attenuation, one or more neutral density filters can be placed in the path of the beam.
Large telescopes can cause the moon and planets to become too bright and lose contrast. A neutral density filter can increase the contrast and cut down the brightness, making the moon easier to view.
A graduated ND filter is similar except the intensity varies across the surface of the filter. This is useful when one region of the image is bright and the rest is not, as in a picture of a sunset.
The transition area, or edge, is available in different variations (soft, hard, attenuator). The most common is a soft edge and provides a smooth transition from the ND side and the clear side. Hard edge grads have a sharp transition from ND to clear and the attenuator edge changes gradually over most of the filter so the transition is less noticeable.
Another type of ND filter configuration is the ND Filter-wheel. It consists of two perforated glass disks which have progressively denser coating applied around the perforation on the face of each disk. When the two disks are counter-rotated in front of each other they gradually and evenly go from 100% transmission to 0% transmission. These are used on catadioptric telescopes mentioned above and in any system that is required to work at 100% of its aperture (usually because the system is required to work at its maximum angular resolution).
Practical ND filters are not perfect, as they do not reduce the intensity of all wavelengths equally. This can sometimes create color casts in recorded images, particularly with inexpensive filters. More significantly, most ND filters are only specified over the visible region of the spectrum, and do not proportionally block all wavelengths of ultraviolet or infrared radiation. This can be dangerous if using ND filters to view sources (such as the sun or white-hot metal or glass) which emit intense non-visible radiation, since the eye may be damaged even though the source does not look bright when viewed through the filter. Special filters must be used if such sources are to be safely viewed.
An inexpensive, homemade alternative to professional ND filters can be made from a piece of welder's glass. This has the effect of a 10-stop filter.
ND filter types 
In photography, ND filters are quantified by their optical density or equivalently their f-stop reduction. In microscopy, the 'transmittance' value is sometimes used.
lens area opening, as fraction of the complete lens optical density f-stop reduction % transmittance 1 0.0 100% ND2 1/2 0.3 1 50% ND4 1/4 0.6 2 25% ND8 1/8 0.9 3 12.5% ND16 1/16 1.2 4 6.25% ND32 1/32 1.5 5 3.125% ND64 1/64 1.8 6 1.563% ND128 1/128 2.1 7 0.781% ND256 1/256 2.4 8 0.391% ND512 1/512 2.7 9 0.195% ND1024 1/1024 3.0 10 0.098% ND2048 1/2048 3.3 11 0.049% ND4096 1/4096 3.6 12 0.024% ND8192 1/8192 3.9 13 0.012%
Digital ND Filter 
Ricoh GR V has in-built Digital ND Filter 2x.
See also 
- ND Filters: Everything You Need to Know
- Neutral Density Filters and Graduated ND Filters
- Neutral Density Filters: What are they & when to use them ?
- Neutral Density Filter FAQ at Digital Grin Photography Forum
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