film plane flatness vs depth of focus

I have been reading discussions of the math for depth of focus vs
format, CofC, and aperture.

For 5x7 and 8x10 the distance is significant. (Up to several mm)

I want to understand how this relates to film plane flatness.

I built a 5x7 box camera and am stressing over 'skew' between my front
and rear 'standards' (thin aluminum plates over a 4-sided wood box.
The problem was due to achieving nice miters at the expense of a
warped box.

Before I spend too much effort figuring out a shimming scheme that
gives me reasonably parallel front & rear, I want to know if the
depth of focus 'range' gives me some leeway here.

I am trying to apply d = 2*c*N to film plane flatness, with c= CofC, N
= f-#. I hope this 'd' is not lens-to-subject (bellows extension
variation), but actually lens-to-film distance variation.

One example cited for 5x7 and CofC = 0.12 mm, d @ f/45 = 10.9 mm.

If I have 1 mm peak-to-peak of 'waviness' in my front standard-to-
film holder film plane distance, and 10.9 mm applies behind the lens,
I should be fine.

If I need to have parallelism within the flatness expected for
groundglass spacing (say +/- 0.007"), then I have an ugly problem and
I better make this a pinhole camera!

I measured distances with a digital depth gauge and steel gauge blocks
on a rigid steel base, so it's not measurement error I'm seeing.

Thanks

Murray

MurrayatUptown wrote:
I have been reading discussions of the math for depth of focus vs
format, CofC, and aperture.

For 5x7 and 8x10 the distance is significant. (Up to several mm)

I want to understand how this relates to film plane flatness.

I built a 5x7 box camera and am stressing over 'skew' between my front
and rear 'standards' (thin aluminum plates over a 4-sided wood box.
The problem was due to achieving nice miters at the expense of a
warped box.

Before I spend too much effort figuring out a shimming scheme that
gives me reasonably parallel front & rear, I want to know if the
depth of focus 'range' gives me some leeway here.

I am trying to apply d = 2*c*N to film plane flatness, with c= CofC, N
= f-#. I hope this 'd' is not lens-to-subject (bellows extension
variation), but actually lens-to-film distance variation.

That d is the the depth of focus. But let me explain it a bit. Assume
you focus exactly on a subject confined to a plane which is parallel to
the lens plane (i.e., lens board or front standard, assuming the lens is
mounted properly). Then the exact image plane would be parallel to the
subject and lens planes at at some distance in back of the lens.
(Exactly where is determined by the lens equation, but that is another
matter.) Points in the subject plane will be imaged as points in the
image plane, ignoring diffraction. So the question is where the film is
in relation to the exact image plane. The idea of depth of focus is
that for each point in the image, if the film is within plus or minus Nc
of the image plane, the corresponding image in the film will be a small
disc which, if smaller in size than c, will be indistiguishable from a
point. So you should visualize the exact image plane and a very thin
"slab" of thickness d = 2Nc which is centered on it. As long as the
film lies within this slab, the film image of the exact subject plane
will be sharp enough for all practical purposes. (Actually, that
formula only works for distant subjects. A more accurate formula is
2Nc(1+M) where M is the magnification of scale of reproduction. For
normal subjects, M is so close to zero it can be ingored. Also,
there are some other approximations which go into the mathematical
analysis, which in almost all practical situations don't lead to any
significant errors.)

Now the film can depart from the exact image plane for several reasons.
One might be just that the film is not flat in the holder. A second
is that the rear standard(i.e. film holder) makes a slight angle with
the image plane and hence with the lens plane.

I think it is the second issue that you are concerned about. Another
way to think about it is as follows. If the standards are not exactly
parallel, then you in effect are introducing a slight rear swing/tilt.
That will in turn produce a shift in the exact subject plane. If the
resulting subject plane is still within the depth of field for the focal
length and aperture, you will be okay. If not, part of the subject
plane will be blurry.


One example cited for 5x7 and CofC = 0.12 mm, d @ f/45 = 10.9 mm.

If I have 1 mm peak-to-peak of 'waviness' in my front standard-to-
film holder film plane distance, and 10.9 mm applies behind the lens,
I should be fine.

You would be fine if you only take pictures of perfectly flat subjects
parallel to the lens plane. It gets more complicated with real
subjects. Any error you introduce in effect changes the position of
the surface out in space, which will almost always be pretty close to a
plane, which is in exact focus. It will also change the region about
that surface which is in the depth of field region. Whether the results
will be acceptable or not can depend on many factors, e.g., the subject,
the focal length of the lens, how carefully you focus, whether you are
using tilts or swings, etc.

It would be better to make that variation as small as possible. 10.9 mm
is enormous, and you should be able to do a lot better than that.


If I need to have parallelism within the flatness expected for
groundglass spacing (say +/- 0.007"), then I have an ugly problem and
I better make this a pinhole camera!

I doubt if many view cameras maintain parallelism of the standards in
the null or detent positions to that degree of accuracy. As you've
correctly reasoned, the tolerance of gg spacing is a separate matter.
(Of course, with a view camera with movements, you can always adjust
it.) But if I calculated correctly, being out by as much as 10.9 mm for
5 x 7 would introduce a rear tilt/swing angle of almost 3 1/2 degrees.
You are entering the range of what might be considered a normal tilt
or swing in some situations.


I measured distances with a digital depth gauge and steel gauge blocks
on a rigid steel base, so it's not measurement error I'm seeing.

Thanks

Murray

MurrayatUptown wrote:
I have been reading discussions of the math for depth of focus vs
format, CofC, and aperture.

For 5x7 and 8x10 the distance is significant. (Up to several mm)

I want to understand how this relates to film plane flatness.

I built a 5x7 box camera and am stressing over 'skew' between my front
and rear 'standards' (thin aluminum plates over a 4-sided wood box.
The problem was due to achieving nice miters at the expense of a
warped box.

Before I spend too much effort figuring out a shimming scheme that
gives me reasonably parallel front & rear, I want to know if the
depth of focus 'range' gives me some leeway here.

I am trying to apply d = 2*c*N to film plane flatness, with c= CofC, N
= f-#. I hope this 'd' is not lens-to-subject (bellows extension
variation), but actually lens-to-film distance variation.

That d is the the depth of focus. But let me explain it a bit. Assume
you focus exactly on a subject confined to a plane which is parallel to
the lens plane (i.e., lens board or front standard, assuming the lens is
mounted properly). Then the exact image plane would be parallel to the
subject and lens planes at at some distance in back of the lens.
(Exactly where is determined by the lens equation, but that is another
matter.) Points in the subject plane will be imaged as points in the
image plane, ignoring diffraction. So the question is where the film is
in relation to the exact image plane. The idea of depth of focus is
that for each point in the image, if the film is within plus or minus Nc
of the image plane, the corresponding image in the film will be a small
disc which, if smaller in size than c, will be indistiguishable from a
point. So you should visualize the exact image plane and a very thin
"slab" of thickness d = 2Nc which is centered on it. As long as the
film lies within this slab, the film image of the exact subject plane
will be sharp enough for all practical purposes. (Actually, that
formula only works for distant subjects. A more accurate formula is
2Nc(1+M) where M is the magnification of scale of reproduction. For
normal subjects, M is so close to zero it can be ingored. Also,
there are some other approximations which go into the mathematical
analysis, which in almost all practical situations don't lead to any
significant errors.)

Now the film can depart from the exact image plane for several reasons.
One might be just that the film is not flat in the holder. A second
is that the rear standard(i.e. film holder) makes a slight angle with
the image plane and hence with the lens plane.

I think it is the second issue that you are concerned about. Another
way to think about it is as follows. If the standards are not exactly
parallel, then you in effect are introducing a slight rear swing/tilt.
That will in turn produce a shift in the exact subject plane. If the
resulting subject plane is still within the depth of field for the focal
length and aperture, you will be okay. If not, part of the subject
plane will be blurry.


One example cited for 5x7 and CofC = 0.12 mm, d @ f/45 = 10.9 mm.

If I have 1 mm peak-to-peak of 'waviness' in my front standard-to-
film holder film plane distance, and 10.9 mm applies behind the lens,
I should be fine.

You would be fine if you only take pictures of perfectly flat subjects
parallel to the lens plane. It gets more complicated with real
subjects. Any error you introduce in effect changes the position of
the surface out in space, which will almost always be pretty close to a
plane, which is in exact focus. It will also change the region about
that surface which is in the depth of field region. Whether the results
will be acceptable or not can depend on many factors, e.g., the subject,
the focal length of the lens, how carefully you focus, whether you are
using tilts or swings, etc.

It would be better to make that variation as small as possible. 10.9 mm
is enormous, and you should be able to do a lot better than that.


If I need to have parallelism within the flatness expected for
groundglass spacing (say +/- 0.007"), then I have an ugly problem and
I better make this a pinhole camera!

I doubt if many view cameras maintain parallelism of the standards in
the null or detent positions to that degree of accuracy. As you've
correctly reasoned, the tolerance of gg spacing is a separate matter.
(Of course, with a view camera with movements, you can always adjust
it.) But if I calculated correctly, being out by as much as 10.9 mm for
5 x 7 would introduce a rear tilt/swing angle of almost 3 1/2 degrees.
You are entering the range of what might be considered a normal tilt
or swing in some situations.


I measured distances with a digital depth gauge and steel gauge blocks
on a rigid steel base, so it's not measurement error I'm seeing.

Thanks

Murray

Thank you for the reality check.

I think I have 0.030-0.040" worst case total spread. Interestigly,
it's 5-10 thousandths over most of it and a couple weird spots.

I may have bent the plate that I drilled/filed etc by hand.

The front one I had a machinist do, so the camera fits nice and
tight(ly) in the box back (big extension box, basically).

Thanks again.

Murray

Thank you for the reality check.

I think I have 0.030-0.040" worst case total spread. Interestigly,
it's 5-10 thousandths over most of it and a couple weird spots.

I may have bent the plate that I drilled/filed etc by hand.

The front one I had a machinist do, so the camera fits nice and
tight(ly) in the box back (big extension box, basically).

Thanks again.

Murray

I forgot to mention it is undoubtedly experimental...I expect quite a
bit of aberration... from the lens contraption I hacked.

(Polaroid 130mm triplet (150 or 95B) with internal shutter + a
Rodenstock-Ysarex front cell (2-element, approx -4.5 diopter) glued on
the back.

It's about 310-320 mm f.l. now and will 'illuminate' the better part
of an 11x14 ground glass, with definite blur on the outside.

There is another a vignetting baffle inside the lens that I figure I
better leave well enough alone.

I just hope that the blur is interesting and not horribly
distorted...we shall see.

Thanks again.

Murray

"MurrayatUptown" wrote in message
om...

I am trying to apply d = 2*c*N to film plane flatness, with c= CofC, N
= f-#. I hope this 'd' is not lens-to-subject (bellows extension
variation), but actually lens-to-film distance variation.

In order to understand how to apply formulas, like the one you mention, it
is always helpful to know were they come from, in this case:

If you assume a thin lens with an aperture with diameter "D", an object
point at a very large distance from the lens will describe a cone of light
from itself to the edges of the lens' aperture and then the lens will focus
it onto an image point "P" (ignoring diffraction) at a distance equal to
the focal length "F" of the lens, the focused light emanating from the lens
will describe another cone of light, that if we draw it on paper (2D), it'd
be represented by a triangle with base = "D" and height = "F", the apex of
that cone being the image point of light "P". Your film plane has to be at
a distance "F" from the lens for optimum focusing. If the film plane is
closer to the lens, the image point would not be a point anymore but a small
disc of light with diameter equal to the diameter the cone of light has at
the point where the film plane is intersecting it. If that disc of light is
equal or smaller than the CoC = "c", the image on the film plane of the
object point is considered to be sharp enough. We can then have the film
plane a distance "d" units closer to the lens and still have an acceptable
sharp enough image point, if and only if the diameter of the cone at that
point is still equal or smaller than "c", the smaller the "c" value you
select, the smaller the distance "d" could be.

We then have 2 equivalent triangles, one with base "D" and height "F" and
another with base "c" and height "d", since the triangles are equivalent, we
can write:

D / F = c / d (1)
then:
d = c * F / D (2)
But the focal length "F" divided by the diameter of the aperture "D" is
equal to the f/stop "N" of the lens, we then have:
d = c N (3)
The same depth of focus in front of the image point "P" is at the rear of
it, therefore the total depth of focus is "2 c N"

If the distance from the object point to the lens is short, the image point
"P" will not be at a distance "F" from the lens but at a distance "F (m +
1)", where "m" is the magnification, so the formula (2) becomes:

d = c * F(m+1) / D
but because F/D is equal to "N", we then have:

d = c N (m + 1)
for a total depth of focus of "2 c N (m + 1) as per above.

Hope the above is not confusing.

Guillermo

Hi

True depth of focus can be expressed as

(f-stop x f-stop) x wavelength.005) x 2.

So a f-1 lens has 1 micron of true depth of focus.

At f-32 the lens has about 1.024 mm of true depth of focus. This means that
racking the lens in and out for 1.024 mm you will not see any focus change what
so ever under high magnification.

Now add CoC calculations on top of that for the degree of focus forgivness you
wish.

Larry

Hi

True depth of focus can be expressed as

(f-stop x f-stop) x wavelength.005) x 2.

So a f-1 lens has 1 micron of true depth of focus.

At f-32 the lens has about 1.024 mm of true depth of focus. This means that
racking the lens in and out for 1.024 mm you will not see any focus change what
so ever under high magnification.

Now add CoC calculations on top of that for the degree of focus forgivness you
wish.

Larry

No, no confusion...

I just usually don't have all the numbers because it's not a
functional camera yet..., particularly 'm' is unknown.

Thanks again.

Murray