The different Angle-of-View measurements

Look at any lens spec, and they will normally talk about the angle-of-view (AOV), sometimes used interchangeably (and incorectly) with field-of-view (FOV). But there are three forms of AOV, and they can be somewhat confusing. The first form is the diagonal AOV. It is one of the most common ones found in lens literature, but it isn’t very easy to comprehend without viewing the picture across the diagonal. Next is the vertical AOV, which makes the least sense, because we generally don’t take pictures, or even visualize the vertical. Lastly is the horizontal AOV, which makes the most sense, because of how humans perceive the world in front of them.

Showing the diagonal AOV of a lens is hard to conceptualize. It’s a bit like the way TV’s are described as being, say 50″, which is the diagonal measurement. In reality through, the TV is only 43.6″ wide. Horizontal is how people generally conceptualize things. As an example of a lens, consider a 24mm full-frame lens – it has a diagonal AOV of 84°, and a horizontal AOV of 74°. This isn’t really a lot, but enough to get a little confusing. A 16mm lens that has a AOV of 180° in the vertical, may only have a horizontal AOV of 140° An example of this is shown below.

FOV and AOV

Photography, like many fields is full of acronyms, and sometimes two terms seem to merge into one, when the reality is not the case. DPI, and PPI for instance. Another is FOV and AOV, representing Field-Of-View, and Angle-Of-View respectively. Is there a difference between the two, or can the terms be used interchangeably? As the name suggests, AOV relates to angles, and FOV measures linear distance. But look across the net and you will find a hodge-podge of different uses of both terms. So let’s clarify the two terms.

Angle-of-View

The Angle-of-view (AOV) of a lens describes the angular coverage of a scene. It can be specified as a horizontal, vertical, or diagonal AOV. For example, a 50mm lens on a 35mm film camera would have a horizontal AOV of 39.6°, a vertical AOV of 27°, and a diagonal AOV of 46.8°. It can be calculated using the following formula (calculated in degrees):

      AOV = 2 × arctan(SD / (2×FL)) × (180 / π)°

Here SD represents the dimension of the sensor (or film) in the direction being measured, and FL is the focal length of the lens. For example a full-frame sensor will have a horizontal dimension that is 36mm, so SD=36. A visual depiction of a horizontal AOV is shown in Figure 1.

Fig.1: A horizontal AOV

A short focal length will hence produce a wide angle of view. Consider the Fuji XF 23mm F1.4 R lens. The specs give it an AOV of 63.4°, if used on a Fuji camera with an APS-C sensor (23.6×15.6mm). Using this information the equation works well, but you have to be somewhat careful because manufacturers often specify AOV for the diagonal, as is the case for the lens above. The horizontal AOV is 54.3°.

Field-of-View

The Field-of-view (FOV) is a measurement of the field dimension a lens will cover at a certain distance from the lens. The FOV can be described in terms of horizontal, vertical or diagonal dimensions. A visual depiction of a horizontal FOV is shown in Figure 2.

Fig.2: A horizontal FOV

To calculate it requires the AOV and the distance to the subject/object. It can be calculated with this equation:

      FOV = 2 ( tan(AOV/2) × D )°

Here D is the distance from the object to the lens. Using this to calculate the horizontal FOV for an object 100ft from the camera, using the AOV as 0.9477138 radians (54.3°). The FOV=102 feet. It does not matter if the value of D is feet or metres, as the result will be in the same units. There is another formula to use, without the need for calculating the AOV.

      FOV = (SD × D)/FL

For the same calculation (horizontal FOV) using SD=23.6, FL=23mm, D=100ft, the value calculated is 102ft.

Shorter focal lengths will have a higher FOV than longer focal lengths, hence the reason why wide-angle lenses have such as broad FOV, and telephoto lens have a narrow FOV. A visual depiction of a the effect of differing focal lengths is shown in Figure 3.

Fig.3: FOV changes with focal length

FOV also changes with sensor size, as the dimension of the sensor, SD, changes. A visual depiction of the effect of differing sensor sizes on FOV is shown in Figure 4. Here two different sized sensors use lenses with differing focal lengths to achieve the same FOV.

Fig.4: FOV changes with sensor size

AOV versus FOV

The AOV remains constant for a given sensor and lens, whereas the FOV varies with the distance to the subject being photographed.

Quite a good AOV/FOV visualizer can be found here.