From: jacobson@cello.hpl.hp.com (David Jacobson)
Subject: Re: Hyperfocal distances
Date: Mon, 5 Oct 1992 15:58:03 GMT
Organization: Hewlett-Packard Laboratories
Keywords: lens, depth of field, hyperfocal

In article <1992Oct5.115020.21377@cbnews.cb.att.com> fohl@cbnews.cb.att.com (mark.e.fohl) writes:
>
>I've got a question for the optics gurus in the group.  Is depth of field
>the same for all lenses of a given focal length and aperture?  

Yes.  

>That is, for
>a 50 mm lens at f16, is the depth of field the same for Nikkor, Zeiss, Ritz,
>etc.?  

Yes.

>I've got a Mamiya C220 twin lens, and I need some work on my depth of field.
>I'm trying to determine hyperfocal distances for the lenses I've got.  I seem
>to remember seeing depth of field charts for those lenses, but I can't find
>them.  If the depth of field charts for any lenses will do, my search will be
>easier.  Any help would be appreciated.
>
>Thanks,
>
>Mark

The hyperfocal distance is at F^2/(c f)
where


        f       geometrical f number of lens 

        c       allowable circle of confusion, say .000030 meters
        
        F       focal length of lens

And here are the exact formulas for depth of field.  If we let

        s       distance beyond front nodal point of lens (approx. center)

the distance from the point of perfect focus to the nearest point in
focus is given by

              c f s (s-F)
doffront = -------------------
             F^2 + c f (s-F)

And the depth to the fartherst point is given by 

              c f s (s-F)
dofrear = -------------------
             F^2 - c f (s-F)

except that if the denomintor is zero or negative then all points
beyond the subject, clear out to infinity, are in focus.

A simplified version of all this results from making the approximation
that F^2 >> c f (s-F) and that s/F = (s-F)/F = 1/M, where M is the
magnification.  This yeilds dof = c f / M^2, which is valid if your
are at least several focal lengths away and no farther away than a
small fraction (say 1/3) of the hyperfocal distance.

An implication of this approximate formula is that within the range of
applicability, the depth of field does not depend on focal length, but
only on magnification and aperture.  However, the rendering of
extremely out of focus distant objects (eg background of a portrait)
does depend on focal length, and will be more blurred with longer
lenses.

The only property of a lens that affects focusing and magnification
that is not given by the standard specifications of focal length and
f-stop is the position of the front nodal point, which is the point
from which the lens-to-subject distance should be measured from for
all the textbook formulas (and those above).  You can usually find it
taking the lens off the camera and pointing the rear of the lens
toward a distant object and noting where the image is formed.  Then
measure one focal length to the rear.  That's the front nodal point.

The generally accepted value of c, the acceptable circle of confusion,
is .03 mm for 35mm film.  Obviously this is subjective.  A
semi-frequent topic of discssion on rec.photo is "should this value be
different depending on the magnficiation used in printing?" and
"should this value be different for medium and large format?".  I'm
sure the answer is yes, but I'll leave it up to others to decide the
"correct" values.  Let me conclude by observing that it doesn't make
sense to quibble about the difference between a lens that can resolve
100 lpmm and one that can resolve 120 lpmm, and then depend of depth
of field that is based on a 1/33 mm circle of confusion.

Sorry for the length of this.  I think I said everything :-).

  -- David Jacobson




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