## 14 Apr ND Filters

The main purpose of a Neutral Density filter (ND) is to decrease the amount of light transmitted through a given objective. As a result if the shutter speed is maintained unchanged, for regain the correct exposure, you must increase the lens aperture by a factor dependent on the gradation of the ND filter used.

Likewise, if you want to keep the same lens aperture , with a ND filter installed on the lens, you must set a lower shutter speed .

The diagram clearly shows what happens with the insertion of an ND filter: the red line is the line of the correct exposure for the camera with a certain sensitivity (gain). Its obvious that the correct exposure is obtained with an infinite set of pairs f-stop / shutter speed.

With the insertion of an ND filter a lesser amount of light will pass through the lens, so the red line moves parallel to bottom: with a given shutter speed you should further open the aperture to obtain the correct exposure, in accord with the above described effect of the Neutral Density filter.

Reversing the argument, if we keep the same aperture (ie the same depth of field) it will be necessary to decrease the Shutter speed to regain the correct exposure with the ND filter mounted.

The optical density (D) expresses the measure of the absorption of light by the filter. Theoretically, it should take place in a uniform manner, ie that do not alter the colorimetry of optics on which it is installed. Its easy to understand that the optical density is related to the index of Transmissivity (T), the percentage of the light intensity not reflected by the filter, according to the simple equation:

#### D= log_{10} 1/T

The density is therefore logarithmic function of the transmissivity and implies that when the transmissivity is T= 1, the value of D = 0.5, when the transmissivity decreases to 50% (0.5) D = 0.3, when the transmissivity drops to 25% (0.25), D = 0.6 and so on, according to a first table which is summarized below:

[table]

Light Index | Trasmissivity Index | Density Index |

1 | T=1 | D=0 |

1/2 | T=50% | D=0.3 |

1/4 | T=25% | D=0.6 |

1/8 | T=12.5% | D=0.9 |

1/16 | T=6.25% | D=1.2 |

1/32 | T=3.125% | D=1.5 |

[/table]

Table 1

At this point it is useful to correlate the optical density with the number of F-Stop adjustment to regain the correct exposure. Please note that the F-Stop number is a purely geometrical parameter (in fact, strictly speaking, it would be more appropriate to talk about T-Stop), which indicates the brightness of an image produced by a lens.

This number is intimately tied to the depth of field achievable in a given shot, and therefore also influences the artistic result of a shoot. A smallest number of F-Stop means a brighter image, but also a correspondegly depth of field more compressed.

If “f” is the focal length of the lens and “d” is its effective aperture, then its F-Stop is given by:

#### F-Stop= f/d

In the formula above you can notify that for a given optical, more great is the effective aperture (in direct relation with the diameter of the first lens) more small the F-stop number will be, in other words the brightness of the lens will be greater.

Note, however, that this parameter, as already mentioned, does not reveal anything about the real optical qualities of the lens: in fact does not say if all the light incident of the effective aperture of lens is then actually transmitted through it. It may therefore happen that using two lenses with identical F-Stop, but with different physical characteristics of optical materials are pointed out with several indices of reflection and transmissivity (light loss); this would lead to a different apparent brightness of the picture produced by the camera even with the same F-Stop setting. To avert this danger is preferable to adopt what is called “T-Stop” (Transmission Stop) and defined as:

#### T − Stop = (F − Stop)/√T

The square root of the index of transmissivity (T) in the denominator “weighs” the fraction and it does stretch the value of the F-Stop geometric if and only if the value of T approaches 1, ie the ideal value. In all other cases, ie if a lens is made of optical glass with poor or no adequate antireflection coating, the more the value of T-Stop > F-Stop.

This is a very real situation: the **Canon** lenses are the only ones who declare a value F-stop is very close to the real value of T-Stop. Other manufacturers have actual brightness values that are evident in measurement also significant differences with respect to the data reported.

It ‘s well known that the scale of the Iris (or iris) of a lens for film, television, High Definition, Photography is engraved with a series of markers marked with a series of numbers in a reciprocal relationship

#### √2: 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22.

The reason for this law consists in the fact that the amount of energy collected on the image plane is directly proportional to the area of the entrance pupil of the objective, while on the image plane, the energy per unit area is inversely proportional to the area on which the image is formed. The area of the entrance pupil is proportional to the square of the diameter of the pupil while the area of the image plane is proportional to the square of the focal length:

#### Incident Energy ∞ d2

#### Plan on Energy ∞ Image 1/f2

The relationship between these two quantities is therefore a measure of illumination produced on the image. A doubling of the quantity expressed by the ratio actually expresses a doubling of the brightness of the image produced. The simple relationship between the focal length f and the effective aperture of the lens is rather the relative aperture (F-Stop) and then only the square of the value of the fraction is correlated corresponds to a doubling of the image brightness.

An increase of √2 of this value will correspond to an increase in brightness of 50%. Now and then easy to combine the data in Table 1 by adding opening required in terms of sleep necessary to offset the decrease in light output caused by the presence of the ND filter as:

[table]

Light Index | Trasmissitivity Index | Density Index | F-Stop Aperture |

1 | T=1 | D=0 | 0 |

1/2 | T=50% | D=0.3 | 1 |

1/4 | T=25% | D=0.6 | 2 |

1/8 | T=12.5% | D=0.9 | 3 |

1/16 | T=6.25% | D=1.2 | 4 |

1/32 | T=3.125% | D=1.5 | 5 |

[/table]

Table 2

Note that there is another nomenclature for the ND filters, such as to highlight the corrective action to be made directly on the diaphragm ring. In this case, they are indicated according to the power of 2 having as the exponent the number of correction Stop:

#### ND = 0.3 ND 2, (21 = 2)

#### ND = 0.6 ND 4, (22 = 4)

#### ND = 0.9 ND 8; (23 = 8 )

Therefore, the Table 2 may still be rewritten by adding a final column as follows:

[table]

Light Index | Trasmissivity Index | Density Index | F-Stop Aperture | Alternative Nomenclature |

1 | T=1 | D=0 | 0 | |

1/2 | T=50% | D=0.3 | 1 | ND2 |

1/4 | T=25% | D=0.6 | 2 | ND4 |

1/8 | T=12.5% | D=0.9 | 3 | ND8 |

1/16 | T=6.25% | D=1.2 | 4 | ND16 |

1/32 | T=3.125% | D=1.5 | 5 | ND32 |

[/table]

Table 3