FOV And Lenses

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FOV and Lenses

The field of view (FOV) described the angular span seen by any camera/lens combination. It is split into the horizontal and vertical components, HFOV and VFOV, respectively, although by the HFOV is usually meant by default. When designing a new station, there is a usually a criterion to sample over some span of horizontal view. For instance on a straight beach we often need to span 180 degrees. Only a fisheye lens could see this span with a single camera (and with terrible optics) so we usually rely on using multiple cameras with slight overlap between each. It is important to know the HFOV for different lens choices in order for us to make good decisions on the number of cameras and which lenses to use.

If we know the calibrated focal length, f, of a lens/camera combination measured in pixels (for example from a Caltech lens calibration procedure), then the HFOV can be found by finding

HFOV = 2*atan(NU/(2*fU))      (1)

In other words, a right triangle is formed with sides NU/2 and f that represents half the field of view (so must be doubled).

Often, only the focal length given by the manufacturer is known and it is not measured in pixels (since that depends on the camera chip) but instead is known in millimeters, the distance from the effective pinhole to the film plane. The same math then requires us to know the width of the sensor chip, also in the same units (usually millimeters). Otherwise the math is the same as above. Note that the same lens will then yield different fields of view for different cameras, or equivalently different lenses are needed to achieve the same FOV for different cameras. For example the ‘average view’ 35 mm lens for an old SLR film camera would usually be the equivalent of a 9 mm lens on a ½” chip sensor like a Grasshopper (remember to convert the chip size to mm). Usually there are only a limited number of choices for lens focal lengths. Also note that manufactures listed chip sizes are usually not accurately defined (they may be chip size versus the size of the sensing part, or they may exaggerate for marketing reasons). A better estimation of horizontal chip size for any sensor can be found by multiplying the listed pixel dimensions (pixel pitch) times the number of pixels.

Routines to compute field of view for typical lenses are included here under the Support Routines. fov is a Perl scripts and fov.m is a Matlab equivalent. There is also an example routine FOVexample.m.

Lenses are also rated for different image resolution. For example, if you wish to use a 5 Megapixel camera you should use a lens that is rated to at least 5 Mpixels. Otherwise you be wasting the sensor resolution.

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