Front tilt loses middle

Tom Phillips wrote:



The complete paragraph on p. 128-129, 5th edition, which
follows a discussion on hyperfocal distance-based DOF, says:

"The effect that swinging or tilting the camera lens or
back has on DOF can be observed on the graph since the
camera is actually focused on a series of object distances
that vary from side to side with the swings and from top
to bottom with the tilts. If the camera is adjusted so that
the plane of sharp focus in the object space is at an angle
of 45 degrees, the DOF will not only change from side to
side or from top to bottom, but the near and far limits of
depth of field will be curved..."

In my empirical experience (but not scientific tests)
this would appear to be true. But if in the 7th ed.
he has repudiated and retracted this perhaps you could
provide the relevant quotes in context.

I would have to look at exactly what appears in the 5th edition to see
the context and what follows what you quoted. But the above quote
certainly seems to say something wrong.

It would be best if you got hold of the 7th edition and read all of
Chapter 7 and particularly the material on tilts and swings. But here
is the direct quote of section 7.5.

"When the front and back of a view camera are in their normal or zero
positions, the plane of focus and the near and far limits of the depth
of field are planes that are parallel to each other and to the lens
board and film planes. When the back or front of the camera is tilted
or swung to satisfy the Scheimplfug rule with a r receding subject
plane, the camera is simultaneously focused on a continuum of different
object distances. Since the depth of field increases approximately with
the square of the object distance over a large range of distances, it
might be assumed that the near and far depth of field limits would be
curved, like the near and far limit lines with increasing distance, on
depth-of-field graphs. The drawing in Figure 7-13 illustrates that the
near and far limits are planes rather than curved surfaces because the
near and far object points associated with a given point of focus must
be on the same central ray of light to the lens as the point of focus,
rather than on a straight line parallel to the lens axis as when the
camera adjustments are zeroed. The near and far limit planes meet the
plane of sharp focus at a distance of one focal length in front of the
camera lens of the camera lens. Figure 7-14 shows the change in the
angles of the near and far depth-of-field limits as the lens is stopped
down."

I find this quote interesting in that he gets the basic fact more or
less right in this edition. But his argument is a bit mysterious to me
since it doesn't seem to explain anything. Also, as I've repeatedly
tried to say, the bounding surfaces are not exactly planes. They could
depart substantially from planes in certain extreme circumstances such
as a very short lens used close-up. But in situations actually
encountered in practice, they are so close to being planar that the
difference can be ignored.

Be that as it may, the above quote contains a statement which is clearly
at odds with what Merklinger and Wheeler say. They say quite clearly
that the surfaces bounding the DOF region meet in the hinge line. I've
verified this myself starting from first principles. The hinge line is
in a plane through the lens parallel to the film plane and at a certain
distance below it. The hinge line is NOT one focal length in front of
the lens. See

www.trenholm.org/hmmerk/HMbooks5.html

for a picture illustrating this.

Here is one way to roughly understand what is going on. Suppose you tilt
the lens plane. As you move the film plane back and forth, the subject
plane which would come to exact focus on it pivots about the hinge line.
Suppose instead you leave the film plane where it is, but you
consider other subject planes through the hinge line. The image points
corresponding to each such subject plane come to focus in a shifted
image plane parallel to the film plane but displaced from it. They
produce small blurs in the film plane, and to a first approximation, all
these blurs are the same size, depending only on how far the shifted
image plane is from the film plane. If these blurs are too large, the
images in the film plane look too fuzzy and you are outside the DOF
region. Otherwise you are inside it and there are two bounding planes
on either side of the film plane characterizing the transition. The
subject planes, through the hinge line, corresponding to these bounding
image planes bound the DOF region in the subject.

Perhaps Stroebel will get it right in the next edition, but as of now, I
wouldn't recommend him as a reference in the subtleties of what we have
been discussing.

As far as your empirical evidence is concerned, let me point out again,
that there is no theoretical justification for it based on the optical
theory of a diffraction limited perfect lens. Stroebel is not saying it
now, and no recognized authority I've seen says it. Moreover, I don't
see it with my lenses. So if you see it, then it must have something to
do with the specifics of your lenses or the way you are using them, and
it is sheer coincidence that it seems to agree with what Stroebel
appeared to say, incorrectly, in his 5th edition.

"Leonard Evens" wrote

www.trenholm.org/hmmerk/HMbooks5.html

Aha! I had always used the lens/film/subject plane
intersection line as the 'hinge line', but I see now:

The hinge line is the closest point that can be imaged
assuming a perfect lens with 180 degree coverage and
infinitely large sheet of film. So logically it
is the point where the DOF wedge must begin.

Normally it is about 1 focal length in front of the
focusing intersection line, so for practical purposes the
two lines are the same - there not being many people taking
pictures with tilts and a fish-eye lens.

Perhaps Stroebel will get it right in the next edition, but as of now, I
wouldn't recommend him as a reference in the subtleties of what we have
been discussing.

Photographers are not mathematicians but mathematicians
are sometimes photographers - though not of the Annie Leibowitz
type.

--
Nicholas O. Lindan, Cleveland, Ohio
Darkroom Automation: F-Stop Timers, Enlarging Meters
http://www.nolindan.com/da/index.htm
n o lindan at ix dot netcom dot com

Nicholas O. Lindan wrote:
"Leonard Evens" wrote

www.trenholm.org/hmmerk/HMbooks5.html

Aha! I had always used the lens/film/subject plane
intersection line as the 'hinge line', but I see now:

The hinge line is the closest point that can be imaged
assuming a perfect lens with 180 degree coverage and
infinitely large sheet of film. So logically it
is the point where the DOF wedge must begin.

Normally it is about 1 focal length in front of the
focusing intersection line, so for practical purposes the
two lines are the same - there not being many people taking
pictures with tilts and a fish-eye lens.

Your point is well taken. Unless subjects quite close to the len are in
the field of view, the exact location of the hinge line won't matter
much. But you can under some circumstances include subjects close to
the lens in the field of view without using an ultra-wide angle lens.
This would happen if you use a significant tilt combined with a large
drop of the front standard. For example, I was able easily to include
something three feet in front of my 150 mm lens in my field of view
using a tilt of about 10 degrees and a drop of about 40 mm. The
distance between the hinge line and the subject was about 900 mm and the
distance between the hinge line and the Scheimpflug line was something
over 150 mm.



Perhaps Stroebel will get it right in the next edition, but as of now, I
wouldn't recommend him as a reference in the subtleties of what we have
been discussing.

Photographers are not mathematicians but mathematicians
are sometimes photographers - though not of the Annie Leibowitz
type.+

Charles Dodgson, who wrote under the name of Lewis Carroll, was a
talented early photographer. His best known pictures are portraits of
of Alice Liddell, the Alice in "Alice in Wonderland", and her sisters.

He was also a talented mathematician who did research in logic.

I don't know if any other well known photographers have strong
backgrounds in mathematics or if any famous mathematicians are talented
photographers, but I suspect there may be examples of both.

Certainly, a knowledge of mathematics will help with the technical
aspects of photography, but it won't help much with aesthetic matters.
On the other hand, it won't hurt either. A mathematician stands as
good a chance of doing good work in photography as anyone else.

Of course to excel in either field, one must devote one's full attention
to it, so these days we are unlikely to find a famous photographer who
is also a working mathematician or vice versa.

So is everyone in agreement that the wedge shape in the illustration noted
below is the way DOF works with a "perfect" lens of normal design?

"Nicholas O. Lindan"

www.trenholm.org/hmmerk/HMbooks5.html

Aha! I had always used the lens/film/subject plane
intersection line as the 'hinge line', but I see now:

The hinge line is the closest point that can be imaged
assuming a perfect lens with 180 degree coverage and
infinitely large sheet of film. So logically it
is the point where the DOF wedge must begin.

"babelfish" wrote
So is everyone in agreement that the wedge shape in the illustration noted
www.trenholm.org/hmmerk/HMbooks5.html

Aye.

--
Nicholas O. Lindan, Cleveland, Ohio
Darkroom Automation: F-Stop Timers, Enlarging Meters
http://www.nolindan.com/da/index.htm
n o lindan at ix dot netcom dot com

Leonard Evens wrote:

Tom Phillips wrote:



The complete paragraph on p. 128-129, 5th edition, which
follows a discussion on hyperfocal distance-based DOF, says:

"The effect that swinging or tilting the camera lens or
back has on DOF can be observed on the graph since the
camera is actually focused on a series of object distances
that vary from side to side with the swings and from top
to bottom with the tilts. If the camera is adjusted so that
the plane of sharp focus in the object space is at an angle
of 45 degrees, the DOF will not only change from side to
side or from top to bottom, but the near and far limits of
depth of field will be curved..."

In my empirical experience (but not scientific tests)
this would appear to be true. But if in the 7th ed.
he has repudiated and retracted this perhaps you could
provide the relevant quotes in context.

I would have to look at exactly what appears in the 5th edition to see
the context and what follows what you quoted. But the above quote
certainly seems to say something wrong.

That's really all it says, in context. The next
paragraphs/sections go on to discuss DOF in relation
to focal length, DOF tables, and calculating DOF...

It would be best if you got hold of the 7th edition and read all of
Chapter 7 and particularly the material on tilts and swings. But here
is the direct quote of section 7.5.

"When the front and back of a view camera are in their normal or zero
positions, the plane of focus and the near and far limits of the depth
of field are planes that are parallel to each other and to the lens
board and film planes. When the back or front of the camera is tilted
or swung to satisfy the Scheimplfug rule with a r receding subject
plane, the camera is simultaneously focused on a continuum of different
object distances. Since the depth of field increases approximately with
the square of the object distance over a large range of distances, it
might be assumed that the near and far depth of field limits would be
curved, like the near and far limit lines with increasing distance, on
depth-of-field graphs. The drawing in Figure 7-13 illustrates that the
near and far limits are planes rather than curved surfaces because the
near and far object points associated with a given point of focus must
be on the same central ray of light to the lens as the point of focus,
rather than on a straight line parallel to the lens axis as when the
camera adjustments are zeroed. The near and far limit planes meet the
plane of sharp focus at a distance of one focal length in front of the
camera lens of the camera lens. Figure 7-14 shows the change in the
angles of the near and far depth-of-field limits as the lens is stopped
down."

I find this quote interesting in that he gets the basic fact more or
less right in this edition. But his argument is a bit mysterious to me
since it doesn't seem to explain anything.

Well, that is interesting, to say the least...

Also, as I've repeatedly
tried to say, the bounding surfaces are not exactly planes. They could
depart substantially from planes in certain extreme circumstances such
as a very short lens used close-up. But in situations actually
encountered in practice, they are so close to being planar that the
difference can be ignored.

I haven't noticed any extreme DOF circumstances
when using a short lens in close up photography,
but I typically haven't used extremes of movement
with a short lens, as this is rather an oyxmoron

But there certainly appears a significant, if
unexplained difference between the 5th and 7th
editions. In any case, I readily accept that DOF
is for the most part a wedge as you earlier said
and wouldn't argue with this. But you also stated
DOF curves, just that it is "insignificant." In
any case the site below is an interesting web site,
plus I've never read Merklinger, so I'll investigate
further when I have more time. Appreciate the link.

Be that as it may, the above quote contains a statement which is clearly
at odds with what Merklinger and Wheeler say. They say quite clearly
that the surfaces bounding the DOF region meet in the hinge line. I've
verified this myself starting from first principles. The hinge line is
in a plane through the lens parallel to the film plane and at a certain
distance below it. The hinge line is NOT one focal length in front of
the lens. See

www.trenholm.org/hmmerk/HMbooks5.html

for a picture illustrating this.

Here is one way to roughly understand what is going on. Suppose you tilt
the lens plane. As you move the film plane back and forth, the subject
plane which would come to exact focus on it pivots about the hinge line.
Suppose instead you leave the film plane where it is, but you
consider other subject planes through the hinge line. The image points
corresponding to each such subject plane come to focus in a shifted
image plane parallel to the film plane but displaced from it. They
produce small blurs in the film plane, and to a first approximation, all
these blurs are the same size, depending only on how far the shifted
image plane is from the film plane. If these blurs are too large, the
images in the film plane look too fuzzy and you are outside the DOF
region. Otherwise you are inside it and there are two bounding planes
on either side of the film plane characterizing the transition. The
subject planes, through the hinge line, corresponding to these bounding
image planes bound the DOF region in the subject.

Perhaps Stroebel will get it right in the next edition, but as of now, I
wouldn't recommend him as a reference in the subtleties of what we have
been discussing.

Stroebel, of course, is usually the most
referenced work for view camera...

As far as your empirical evidence is concerned, let me point out again,
that there is no theoretical justification for it based on the optical
theory of a diffraction limited perfect lens. Stroebel is not saying it
now, and no recognized authority I've seen says it. Moreover, I don't
see it with my lenses. So if you see it, then it must have something to
do with the specifics of your lenses or the way you are using them, and
it is sheer coincidence that it seems to agree with what Stroebel
appeared to say, incorrectly, in his 5th edition.

If so Stroebel should have admited he was wrong in
no uncertain terms...

babelfish wrote:
So is everyone in agreement that the wedge shape in the illustration noted
below is the way DOF works with a "perfect" lens of normal design?

Yes, except for the minor quibbles I've discussed before.

The reason for the quibbles is that DOF is usually calculated assuming
the 'circles of confusion' on the film plane are circular discs of size
depending on the distance of the image point to the film plane. In
fact, when the lens plane is tilted with respect to the film plane, they
are ellipses with size and orientation varying over the field. It is
not easy to analyze this variation, but it can be done. Wheeler did it
just for the center line of the field, but I did it more generally. It
turns out this is a second order effect which changes things by a
negligible amount in ordinary large format photography.


"Nicholas O. Lindan"
www.trenholm.org/hmmerk/HMbooks5.html
Aha! I had always used the lens/film/subject plane
intersection line as the 'hinge line', but I see now:

The hinge line is the closest point that can be imaged
assuming a perfect lens with 180 degree coverage and
infinitely large sheet of film. So logically it
is the point where the DOF wedge must begin.

Yes, a fine point that I never considered, but worth noting. I just want to
tell people with confidence that a good lens should remain "flat" and not
curve its DOF when it's tilted, and except for the minutia, I think we've
established that.

"Leonard Evens"
The reason for the quibbles is that DOF is usually calculated assuming the
'circles of confusion' on the film plane are circular discs of size
depending on the distance of the image point to the film plane. In fact,
when the lens plane is tilted with respect to the film plane, they are
ellipses with size and orientation varying over the field. It is not
easy to analyze this variation, but it can be done. Wheeler did it just
for the center line of the field, but I did it more generally. It turns
out this is a second order effect which changes things by a negligible
amount in ordinary large format photography.

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.
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.


babelfish wrote:

Yes, a fine point that I never considered, but worth noting. I just want to
tell people with confidence that a good lens should remain "flat" and not
curve its DOF when it's tilted, and except for the minutia, I think we've
established that.

"Leonard Evens"
The reason for the quibbles is that DOF is usually calculated assuming the
'circles of confusion' on the film plane are circular discs of size
depending on the distance of the image point to the film plane. In fact,
when the lens plane is tilted with respect to the film plane, they are
ellipses with size and orientation varying over the field. It is not
easy to analyze this variation, but it can be done. Wheeler did it just
for the center line of the field, but I did it more generally. It turns
out this is a second order effect which changes things by a negligible
amount in ordinary large format photography.

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

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.