# Linear is better than angular field of view

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Linear is better than angular field of view

A recent thread suggested that it would be better to label a lens with its field of view instead of its focal length.

I don't think that camera manufacturers are going to change the labelling on lenses any time soon, but it is interesting to speculate on how the field of view of a lens could be used to simplify some calculations.

However, it strikes me that it is much more useful to specify the field of view in linear terms rather than as an angle as is often assumed.  Suppose that the field of view is specified as the relative linear field of view, defined as the ratio of the length of the image diagonal to the focal length of the lens.

Then there is a very simple formula for working out the hyperfocal distance:

h = Rfa,

where
R = the ratio of the image diagonal to the circle of confusion,
f = the relative linear field of view as defined above,
a = the aperture (entrance pupil) of the lens.

The hardest part of this formula to compute is working out the values of R, f and a.  If the latter two were marked on the lens, then the formula would be very easy indeed.

The most commonly used value of R is about 1440, corresponding to a CoC of 0.030mm on a FF sensor (diagonal = 43.3mm).  Personally, I usually prefer to use R = 2000 because it makes the arithmetic a lot simpler and it gives somewhat sharper images. The value of R is a matter of choice, of course.

Knowing the hyperfocal distance, it then becomes easy to work out an approximation to the depth of field.  Simply work out the subject distance as a fraction of the hyperfocal distance, double it, and multiply by the subject distance.  This gives a good approximation to the depth of field, provided the subject is much closer than the hyperfocal distance:

d = 2(s/h)s,   if   s<<h,

where s is the subject distance from the lens (the subject is assumed to be in the plane of focus).

I know that many people will find this approach unfamiliar and perhaps confusing.  Over time I have become sufficiently familiar with this way of thinking to find it much easier than the more conventional formulae for depth of field and hyperfocal distance, but I would be interested in hearing the comments and opinions of others.

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