Front tilt loses middle

Leonard Evens wrote:

Tom Phillips wrote:
One might point out that circles of confusion are those points of
non-critical focus which lie either in front of or behind the film
plane, i.e., object or image points which are not in critical focus.
What is in focus on the actual film plane is a point, not a circle.

I think this is misleading. The circles of confusion are in the film
plane. They arise when images points come to exact focus either in
front or in back of the film plane.

Yes. I meant this. I perhaps should have said "circles of
confusion "arise" from those points of non-critical focus
which lie either in front of or behind the film plane."

But I understood you to be saying from your eariler post
that everything on the film plane was a circle of confusion,
since you did not mention that what is in critical focus
on the film plane is either not a circle, or is small enough
to be considered a point.

You then consider a cone with
vertex at the point of focus and base the exit pupil of the lens. That
cone intersects the film plane in a region. When that region is small
enough, you can't distinguish it from a point. Deciding just when that
happens is the basis of DOF calculations.

Thus when one tilts or swings one is bringing into focus objects
beyond the plane of critical focus. So, the reason one uses circle
of confusion size in determining DOF is to determine the extent
of non-critical focus one wants to _appear_ in focus at a given
print size.

You have the general idea, but I think you haven't quite visualized the
geometry.

After 30 years, I think I do this well enough...

Also, circles of confusion are used in the analysis whether
or not you tilt or swing.

I never said otherwise. In fact, I attempting to point out
that even though you can tilt or swing to bring objects
(not in critical focus) into focus on the film plane you
still need to calculate DOF...

When the lens plane is parallel to the film plane, if you assume the
exit pupil is a circle, the blurry regions in the film plane described
above are circles. If the lens plane is tilted with respect to the
film plane, they are ellipses whose exact shape and orientation depend
of position in the field. But usually they may be approximated by
circles, and that is good enough in almost all situations for practical
large format photography.

Well, we don't and never have called them "ellipses of
confusion." Perhaps we should just recognize descriptive
language and communication, even when sometimes related to
scientifically inclined technical jargon, is an inexact
science. Plus people make mistakes...