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Hello all,
I have a Scheimpful admission to make: I don't understand this rule. I know how to use it, but the theory I knew crumbled under a little thinking. One answer is not to think (generally a good idea), but I am hoping you might have another answer. Right, this is the problem:
(i) the rule states that "subject, lens board, and film planes must be parallel to each other or meet at a common point" (ref Stroebel, View Camera Technique)
(ii) for a start planes wouldn't meet at a common point but at a common line, right?? For a given focus (ie bellows length) and a given angle between lens and film boards, there is a single line L that defines the intersection of the two planes corresponding to the film and lens boards.
(iii) In geometrical terms, the rule states that two objects A and B must be on a line M that belongs to a plane P to which L also belongs (L and M coplanar). Now it strikes me there are an infinite number of planes P containing L. Therefore the number of possible lines M must also be infinite. So why isn't the whole of space in focus?
If planes P, P' and P" are all planes that contain L, there must equally be lines M, M' and M" defined by the pairs of points (A,B), (A',B') and (A",B"), such that each pair of points defines a pair of objects which are both in focus. The Scheimpflug rule applies for each pair of points. So why doesn't it apply for non-paired points such as (A,B") or (A,A") (which define lines that are not coplanar with L). It seems to me there is an inherent contradiction within the rule. Is there a corollary to the rule which defines the angle between P and the planes corresponding to the lens and film boards?
This is really bugging me. Any help will be appreciated.
Thanks,
Charles

for a start planes wouldn't meet at a common point but at a common line, right??

Yes, but out of Stroebel's attempt to simplify comes a measure of confusion. The plane is the reality, as you understand, but (re forward tilt, for example) stand beside your camera and the planes appear as no more than lines - as in, sideways on. Hence his use of the word point.

I'm lost on your point (iii), I'm afraid, as a sketch speaks more clearly to me by way of explanation. You must have seen the sketches in Stroebel on page 28 (7th edition) so I'm wondering if this is where you're coming unstuck, or whether in some deeper zone of physics?



It's an area that fascinates as much as it frustrates.

OK here goes for a simpler side-on view AND a sketch:

So we are agreed that objects A and B are in focus. And we are also agreed that objects A' and B' are in focus. Logical conclusion: A, A', B and B' are all in focus. But I know from experience that I need a different lens to film board angle to get both A and A' in focus (agreement with Scheimpflug).
Confused? I am.
Charles

I'm no expert, but this is how I understood it to be.

The three planes are just that, flat planes, film, lens and focal plane. If these planes are tilted at all by any amount, they will eventually meet at some point in space. The only situation where they wouldn't meet is if they are all absolutely parallel to each other, and in this circumstance it is explained away with the mathmetician's old scapegoat, that they meet at infinity.

The focal plane is flat, but surrounded by a field of focus ( roughly 1/3rd in front, 2/3rd behind, which isn't accurate but as a simple approximation is useful here ), I'm sure you've heard all of this before. Even when we tilt the plane of focus, that field still exists in the same proportions in front and behind the plane, but I understand the width of the field increases with distance. With a parallel focal plane, there is only one distance, so the depth of field is uniform.

To quote from what I was led to believe was the "bible" ( "Using the view camera", Steve Simmons ) : "The Scheimpflug Rule states that a subject plane will be rendered with greatest sharpness when the planes of the film, subject, and lensboard are extended and meet at a common line above, below or to the side of the camera".

In essence, work out your subject plane, and tilt the lens plane until it meets the point where the flim and subject plane cross ( or switch film/lens planes there for back tilt ). That's how I've tried to do it. That said, actually implementing it on my camera is another feat altogether... ( what wouldn't I give for asymmetric tilts... )

Erm, I don't know if any of that is going to help, but hey, worth a try.

So we are agreed that objects A and B are in focus. And we are also agreed that objects A' and B' are in focus.

My question here has to be "Why so?" Or, why the plural "Planes of critical focus"? My approach (as in the image above) would be to say I want points A and B to be in equal focus (and for that reason I use a tilt) ... but I want points A' and B' to be out of focus. I ensure that my tilt avoids the A'B' plane, and I use a wide aperture.

Let's call the plane AB (distinguished from plane A'B') ... my tilt allows everything along that plane to be in focus, and only along that plane if using a wide aperture. Close down the aperture and my plane of focus thickens to include anything adjacent to that plane - another plane, if you will, that is as good as parallel to AB. Stop down to f260 and my plane of focus would encompass even A'B'.

However, enter the good Captain ... Because points A and B are not in the same position as points A' and B', the Scheimpflug result will be different. The angle between the lens plane and film plane may remain the same, but the relative position of lens and film plane changes and therefore the intersection must move - because you are focusing by moving the lens plane forwards or backwards.

Move the subject position or alter its angle from the camera's viewpoint, and the Scheimpflug 'point' moves with it, and your lens plane and film plane must then play catch-up to find the focus and therefore also a new intersection.

In practice, to be focus, planes AB and A'B' cannot intersect at the same point as in your sketch. One might be in focus but then the other will not. To put it another way, for your sketch to work you must also reposition the lens plane to accommodate A'B'. Or, The existence of the intersection does not make the focus.

Add the bellows to your sketch, and the expansion or contraction of the bellows will show how the intersection must change as the lens plane moves forwards or backwards to accomodate any new position of the objects.

But I know from experience that I need a different lens to film board angle to get both A and A' in focus

Yes, quite different, if that's what you meant to say.

Believe me, if I can help you on this I'll be helping myself with anything I might have missed.

For what it is worth: isn't this about the fact that the image is seen by the camera as inverted & back to front. Tilting, &/or swinging, the lens frame brings the further parts of the subject into the same focus as the foreground. The Scheimflug rule is just an explanation of this, which is normally done by simply viewing the focussing screen & playing with the focus. Or am I just naive? Dennis

dennis wrote:For what it is worth: isn't this about the fact that the image is seen by the camera as inverted & back to front. Tilting, &/or swinging, the lens frame brings the further parts of the subject into the same focus as the foreground. The Scheimflug rule is just an explanation of this, which is normally done by simply viewing the focussing screen & playing with the focus. Or am I just naive? Dennis

I think that's dead on the button. For photographers, Scheimpflug's discovery was little more than a rule to explain what is apparent.

Charles

In your sketch I doubt that either A-B or A'-B' would be in focus. From my understanding of Scheimpflug (and practical usage going back 30 years) the planes not only have to intersect, but the lens plane has to bisect the angle between the subject and film planes.

One of the first exercises at college was to photograph a chess board at an angle and get it all sharp at full aperture. This looked great – until you added a chess piece!



Richard

I don't actually see the difficulty,.....

both A and A' can be brought into a common plane of focus using tilt....

Both B and B' can also be focussed using tilt, albeit in the opposite direction...

As a broad guide, any two points are automatically in the same plane and can thus be brought into focus,...the problem with using tilt is when there is a third point which must be sharp but is far, or divergent, from the first two. The typical scenario is when focussing along a wall whic is easy using tilt/swing,....However, if a window is opened from the wall then this will present difficulties to get into focus since the edge of teh opened window is the third point and cannot be encompaed into the plane of the wall....

Sorry for not getting onto this for a while, I was ill...

To sum it up, in "logic speak": The requirement that the Film Plane, the Lens Plane and the Object Plane need to meet in one line ("point" in a 2D projection) is a necessary cnodition, but not a defining condition. There are additional conditions. Most photographic textbooks do not explain this very well.

For each arrangement between FP and LP, there is exactly one (real) solution for where the OP is. The main limit is given by the fact, that the intersection between the OP and the straight view out of the camera, is still defined by the distance that the camera is focussed to! Let's have a look at this in a (very poor) graphic representation:


On the left, we have the "classical" case with FP LP and OP all in parallel, resulting in an image distance of "i" and an object distance of "o". If we now tilt the lens by a few degrees, the OPdoes tilt as well, but it still retains the object distance "o" in a straight line, resulting in OP' being the plane of sharp focus and e.g. OP'' not being so.

This means that while bisection of the angle is often a good approximation, it is not necessarily completely accurate.

An interesting observation, that are not necesasarily obvious: Your "infinite plane of focus" is nowhere near infinite in real conditions. This originates from the viewing angle of the lens (image circle) and limits the expansion of the sharp object plane in space. For most practical issues this does not make a difference, but can become aproblem when requiring strong tilts/swings.

I hope this does clear Charles' question up a little, and I hope I haven't made some Huge obvious mistake somewhere

Marc

If you want a full definition of which one of the infinitely many planes that intersect the lens/film planes in a common line will be in focus, you are looking for something called "the Merklinger Hinge Rule".

Look at http://www.trenholm.org/hmmerk/ and read everything there. At the end you will know just about everything there is to know about focussing a view camera, and far more than you will ever need!

Hello all,
Sorry to hear you have not been well Marc, but hopefully you’re back on top form. I am glad we have some higher minded discussions going on. Thank you Ole too for the Merklinger thread: I actually knew about the site, but when I saw hinge rule, I just presumed he was using a fancy name for the Scheimpflug rule. Far from it: entirely my oversight. With the combination of the Scheimpflug and Carpentier rules – both necessary but not sufficient – a single object plane is defined. Great! I have gone away and done some maths to test your various ideas.
Richard Kelham says “From my understanding of Scheimpflug the planes not only have to intersect, but the lens plane has to bisect the angle between the subject and film planes.” This below is a plot of the angle of the object plane relative to the horizontal for different tilt angles on the front standard (lens board), assuming that the back standard (film plane) is vertical.

I have given several curves denoted by a number running from 1 to 0.7: this number corresponds to the relative extension of the bellows, ie the focal length of the lens divided by the bellows extension. As you can see, bellows extension (what Marc calls i) has comparatively little effect on the angle of the OP. You'll also notice that the OP angle for 0 degrees of tilt is 90 degrees, ie vertical, therefore the OP is parallel to the lens and film planes. The OP gradually flattens with the tilt. All is well. I have also plotted on the graph, Richard’s rule of thumb (curve RKRoT) and as you can see, it is a pretty rough estimate, being correct for only one point. Looking at the numbers I have devised another rule of thumb which is more accurate over the low tilt angles used in landscape photography. This RoThumb says that the OP is parallel to the lens board. Quite simply! It seems remarkable simple, so I invite all to check the maths, but I am pretty sure I got it right.
As well as the angle of the OP, it is important to consider how far from the camera, the line of the OP runs. I get the feeling that this has more impact than the angle. To calculate the distance from the centre of the lens board, divide the focal length by the sine of the tilt angle, that is d(lens) = f/sin(a). To calculate the distance from the centre of the film board, multiply the bellows extension by the tangent of the tilt angle, that is d(film) = i x tan(a). What is curious about these distances, is how remarkably similar they are. It’s easy enough to take the ratio of the two: ratio(film/lens) = (i/f) x cos(a). This is what it looks like, assuming i/f = 1 (ie focussed on infinity):

What bugs me is that a ratio close to 1 means that the OP is virtually flat (identical distances from both boards). As the angle of tilt increases, the ratio gets smaller, ie the OP gets more tilted. Which would be fine if that were a deviation from vertical rather than a deviation from horizontal. Anybody understand that?
The question is not just academic: Jo maintains that a very negligble amount of tilt yields greater depth of field (I hope I am not giving any secrets away). Anyway that would fit in with the ratio idea (which seems paradoxical), but not with the angle approach in the first figure (which seems far more sensible).
Finally the other comment by Marc is that “The main limit is given by the fact, that the intersection between the OP and the straight view out of the camera, is still defined by the distance that the camera is focussed to!”. Are you sure about this? The distance X from the image to the object (ie X = i + o) is X = i^2 / (i – f) for a camera with parallel lens and film boards. With tilt involved, X becomes far more complicated with a strong dependence on the angle of tilt. If you care to check it out, I find X = (i tan(b) cos(b)) / (sin(b) – f/i), with the angle b being the complementary of the tilt angle a (in degrees, b = 90 – a). The angle of tilt is an integral part of the problem and cannot be resolved out. Any opinions, Marc?
Sorry for the horrible length.
I look forward to at least one reply…
Thanks,
Charles

Charles Twist wrote:The question is not just academic: Jo maintains that a very negligble amount of tilt yields greater depth of field (I hope I am not giving any secrets away). Anyway that would fit in with the ratio idea (which seems paradoxical), but not with the angle approach in the first figure (which seems far more sensible).

Can I point you to an article on the Merklinger site that demonstrates my assertions on the angle issue ? http://www.trenholm.org/hmmerk/SHBG09.pdf. There are some tables at the end of the article that demonstrate the relationship between lens tilt, plane of sharp focus and the range of angles for acceptable definition.

I really love this little article http://www.trenholm.org/hmmerk/VuCamTxt+.pdf, it has some great little animations that demonstrate how the angles change as things like lensboard angle and bellows length.

Charles Twist wrote:Any opinions, Marc?

I'm still claiming illness...

seriously, I'll take a closer look at this this WE. I'm in no state to work out angles, etc.

I think this is also a candidate for discussion over a beer or 3 and a flipchart...

Marc

Thinking about it this morning, I realised I miscopied an equation when going to Excel... I must check more carefully tonight but I think the first graph actually looks like this:

The relative extension of 1 gives a weird curve, so I'll check some more tonight.
Thanks for the link, Jo: there's a lot there.
Sorry for the trouble.
Charles