FPV Cameras Focal Length and FOV

[quadfather]

Everyone flying FPV has their own preference when it comes to the field of view (FOV).  The FOV depends on the focal length of the lens (f) and the image sensor';s width and height (w, h).

A note on terminology: When reading about cameras and lenses and you see FOV given as an angle it';s the angle of view (AOV).  The FOV is an area, as in width x height.  There';s no point trying to correct this, it';s been done wrong for yonks.  Just as a note for those who may want to look into optics a bit deeper. 

Sensors are sized in inches for historical reasons, with the most common sensor size in FPV cameras being 1/3".  As usual, there';s no standard.  Sensors sold as 1/3" don';t necessarily have the same dimensions, and since the sensor';s dimensions affect the FOV not all cameras will give you the same FOV.  Having said that, the variation is probably not significant and only important to those that fine tune the living cr@p out of their rigs.

A typical 1/3" sensor (SONY 960H Super HAD CCD II) is 4.8 mm wide, 3.6 mm high, and 6 mm diagonally.  Here';s an overview using this sensor and common lenses available (angles converted from rad to deg).

Sony CCD	2.1 mm	2.8 mm	3.6 mm
AOVhor	97.63o	81.20o	67.38o
AOVver	81.20o	65.47o	53.13o
AOVdia	110.02o	93.95o	79.61o

These are calculated angles, not advertised angles.  The maths behind is quite simple:
AOV_hor = 2 * arctan( w / ( 2 * f ))
AOV_ver = 2 * arctan( h / ( 2 * f ))
AOV_dia = 2 * arctan( d / ( 2 * f )), where d = sqrt(w² + h²)

When an angle is advertised by a seller, you need to know what axis it';s for.  Typically it';s the horizontal AOV, but because "bigger is better" you may find that the diagonal AOV is given instead.  12 degrees do make a difference.

The FOV is the area you can see at a given distance and depends on the horizontal and vertical AOVs.  If someone quotes a FOV at you, you also need to know the distance from the camera.  Without the distance the FOV is meaningless.

Here';s another overview, again using the above sensor and lenses.  This time the left hand column is the distance from the camera, and the values are the areas of the image (FOV) that you can see in meters (width x height).

Sony CCD	2.1 mm	2.8 mm	3.6 mm
FOV @ 2 m	4.6 x 3.4 m	3.4 x 2.6 m	2.7 x 2 m
FOV @ 5 m	11.4 x 8.6 m	8.6 x 6.4 m	6.7 x 5 m
FOV @ 10 m	22.9 x 17.1 m	17.1 x 12.9 m	13.3 x 10 m

To calculate the FOV you can use these formulas:
FOV_width = s * 2 * tan( AOV_hor / 2 )
FOV_height = s * 2 * tan( AOV_ver / 2 )
where s is the distance from the camera.

A good illustration why it';s so difficult to see small branches and such at distance on wide angle cameras (size of the area and low resolution).  Perhaps, for fast proximity flying, the widest angle isn';t necessarily the best.

If you know your sensor size and focal length you can plug any of the above formulas into Google and it will give you the angles and FOV.  Note, they will be in rads, so just add "in deg" after it (or multiply by 180/π) where necessary.  Feel free to compare these values to what you thought you have bought.