Tilt trig

couldabin · Feb 10, 2012

I'm planning a photo using my 8x10; the scene is pretty mundane -- an auditorium stage, with risers. I'll be shooting from the back of the auditorium and would like to have the plane of focus follow the risers as closely as possible. So out of curiosity I tried to calculate how far the front lens board would be tilted forward in order to get a 45 degree plane of focus. Using a 12" lens, shooting from 100 feet away, I come up with a ridiculously small distance -- about 0.6 degrees, which would put the top of the lensboard less than 1/16" further away than the bottom.

Can that be correct?

Mark Crabtree · Feb 10, 2012

I can't do the trig, but that doesn't sound wrong. You're 100 ft away, so the angle of the risers isn't much.

David A. Goldfarb · Feb 10, 2012

It's usually a lot less than you would expect.

keithwms · Feb 10, 2012

Doesn't sound correct to me, offhand. Check that you sorted your degrees and radians

DanielStone · Feb 10, 2012

Personally, I'd bring a few lenses of various focal lengths, if possible. Depending on how you want to portray the subject, a 12" lens might be somewhat "short". If you're attempting to capture as much of the surroundings as possible(seating, etc...), a longer lens (such as a 360(14") or a 420(16.5") might be helpful as well.

Also, having a slightly wide lens(such as a 240mm, or a 210mm of sufficient coverage) will allow you full creative control, just "in case" a 12" is too long.

-Dan

couldabin · Feb 10, 2012

OK, I'm where I can measure my camera now, and I did make one miscalculation -- I should be measuring the size of the front lensboard frame, rather than just the lensboard. So the physical distance the top moves is greater, but not a lot. Using the revised size (8" frame, as opposed to 5" lensboard), I estimate the top of the frame will be 0.080" further away from the back than the bottom. I had no idea such a small misalignment (0.58 degrees) shifted the plane of focus 45 degrees. Your run-of-the-mill spirit level cannot resolve much less than 0.3 degrees; if you want the plane of focus to be within 10 degrees of parallel of the back, the front frame has to be within 0.1 degrees of parallel (assuming the same focusing distance and lens). I hope I have this math wrong ...

pgomena · Feb 11, 2012

I think you're overthinking this one. From the back of the auditorium, 100' away, I would think that you would be able to fit the risers into the depth of field of the lens with little or no trouble at a reasonable aperture. Find a depth of field table for your focal length before you bring out the calculators. If you do need tilt, it won't be much, and you can do it by eye.
Peter Gomena

Ian Grant · Feb 11, 2012

Greg Davis said:
Imagine an invisible line that extends downward from the film plane, one from the lens palme, and one from the subject plane. When all three intersect, the angled subject will be in focus. Since the lens and film planes are so close to each other, it doesn't take much to make them meet at a common point.

Have to agree totally. I've found that if you teach someone the principles in the drawings with a quick practical demonstration then imagining the intersection point quickly becomes second nature and it's very easy and fast to set up movements.

Ian

couldabin · Feb 11, 2012

Yup. That's the basis for doing the tilt calculation. I think that no matter what the distance is between the film and lens, if the film plane is perpendicular to the optical axis, those lines will never meet; if it is not perpendicular, they will.

couldabin · Feb 11, 2012

No, until now I've been entirely underthinking this. The exercise has demonstrated to me how remarkably sensitive the plane of focus is to lens board alignment. Not that alignment affects the plane of focus; how remarkably sensitive it is to that alignment. You note that "if you need tilt, it won't be much ..." I'll say. How much did you have in mind? I would never have guessed that having the top of the lensboard frame 1/32nd of an inch forward of perpendicular would (under the circumstances in question) make the plane of focus slope at almost 40 degrees. Certainly eyeballing the front and back isn't remotely sufficient for ensuring they are parallel. The depth of field table doesn't help me much -- everything in front of and behind the plane of focus becomes increasingly unfocused, and what I'd like to do is get as much of the performance group in focus. Sloping the plane would help achieve that.

David A. Goldfarb · Feb 12, 2012

For more than you wanted to know, read this: http://www.trenholm.org/hmmerk/

The reason you need so little tilt is that the subject is 100 feet away, which is actually beyond the hyperfocal distance for a 12" lens on 8x10" at f:16, which is probably a larger aperture than you will actually want to use unless your only lighting is on stage. You don't really need any tilt for this situation. If you set the focus at, say, 105 feet (say the middle of the second row, assuming the front of the first row is 100 feet away), the DOF range at f:16 for 8x10" is about 48 feet to infinity. If your entire group is between 100 and 125 feet, say, you'll be well within the DOF range even at f:8, but if the focal length of your lens is given in inches, it's probably old enough that you'll want to stop down more than that (f:16-32) to get the corners sharp. If you were much closer to the group, or if there were something important that you wanted to have in focus, say, 8 feet from the camera, then you would need more tilt.

pgomena · Feb 12, 2012

Bingo.

I don't know what the final size of your image will be, but a contact print will be totally sharp to the naked eye.

Peter Gomena

couldabin · Feb 12, 2012

David, thanks for the link. I am anticipating a fairly large final print (200+ people in the image, many of whom will want to see themselves), so I'm using a 4x - 6x enlargement factor. Also, while I'd like to use f16 or f22, I'm afraid that under the lighting conditions and using HP5, I'm going to be exposing at f11 for 1/2 second. I think 1 sec invites too much movement. Using those assumptions (6x and f11), and Stroebel's formuae for near/far sharp, I get a sharp zone from 62 to 179 feet if I manage to focus at 92 feet (I say "manage" bearing in mind Stroebl's droll observation that "photographers have a tendency over overestimate their ability to [place the ground glass in the exact position where it will produce the sharpest focus].")

So far, so good. Now, if I bump the rear standard back 1/32" putting the film holder in, my plane of focus drops to 75', and the sharp zone moves from 54 to 124. That's getting uncomfortably close to losing the rear area-of-interest on the stage.

Which raises my question: the sharp zone isn't a discrete (quantum-like?) area; it's a continuum of increasing and then decreasing sharpness that falls between two parameters. So assuming perfect focus and lensboard/film plane alignment, I understand that areas that lie 170' away should look acceptably sharp, but will they look as sharp as the area at 95'? Will there be a perceptible diminishing in sharpness toward the back of the sharp zone? Secondly, would tilting the plane of focus provide a greater likelihood of getting the stage occupants sharp? After playing with my miniature level, I think I can detect a tilt of roughly 0.3 degrees. I'm wondering if the safest route is setting the lensboard frame at the slightest detectable forward tilt (0.3 degrees translates in 25 deg of focus plane tilt under the circumstances). Thanks for your input.

polyglot · Feb 12, 2012

couldabin said:
David, thanks for the link. I am anticipating a fairly large final print (200+ people in the image, many of whom will want to see themselves), so I'm using a 4x - 6x enlargement factor. Also, while I'd like to use f16 or f22, I'm afraid that under the lighting conditions and using HP5, I'm going to be exposing at f11 for 1/2 second. I think 1 sec invites too much movement. Using those assumptions (6x and f11), and Stroebel's formuae for near/far sharp, I get a sharp zone from 62 to 179 feet if I manage to focus at 92 feet (I say "manage" bearing in mind Stroebl's droll observation that "photographers have a tendency over overestimate their ability to [place the ground glass in the exact position where it will produce the sharpest focus].")

So far, so good. Now, if I bump the rear standard back 1/32" putting the film holder in, my plane of focus drops to 75', and the sharp zone moves from 54 to 124. That's getting uncomfortably close to losing the rear area-of-interest on the stage.

Which raises my question: the sharp zone isn't a discrete (quantum-like?) area; it's a continuum of increasing and then decreasing sharpness that falls between two parameters. So assuming perfect focus and lensboard/film plane alignment, I understand that areas that lie 170' away should look acceptably sharp, but will they look as sharp as the area at 95'? Will there be a perceptible diminishing in sharpness toward the back of the sharp zone? Secondly, would tilting the plane of focus provide a greater likelihood of getting the stage occupants sharp? After playing with my miniature level, I think I can detect a tilt of roughly 0.3 degrees. I'm wondering if the safest route is setting the lensboard frame at the slightest detectable forward tilt (0.3 degrees translates in 25 deg of focus plane tilt under the circumstances). Thanks for your input.

This latter point regarding relative sharpness is important, especially when traded off against unsharpness from subject motion. Since you're considering shooting people at 1/2s (I'll assume f/11 ISO400), there's going to be noticeable motion blur. You might even find that you get a better result by opening up a long way; the front & back rows might not be "optimally" sharp but the lack of DOF may not be the limiting factor.

Which begs the question of "why 8x10?". The huge film means you have illumination/DOF issues and I would bet dollars to donuts that you can make a better overall image using a smaller format. Regardless of your print size, you're going to get softness/blur artefacts much much larger than the grain size, which means that there is no benefit to shooting such large film. You could, for example, shoot 4x5 TMY2 at f/5.6: that would get you the same DOF as f/11 on 8x10, you get two stops more light from the aperture and you get even smaller grain at final print size (HP5 grain is more than 2x larger than TMY2 grain IMHO). TMY2 will also do EI800 or 1600 more easily than HP5, so you could be shooting at 1/15s and I assert that that will likely be a much better overall image than 1/2s on 8x10 HP5.

Mark Crabtree · Feb 12, 2012

I thought this was just an exercise to see if you could calculate it. I've shot a lot of groups (with a Cirkut Camera). For actually taking the picture finding the tilt is very easy and doesn't require any calculation.

If you are not used to groups this size, it would be nice if you can set up in advance (but easy enough live). It is best to have two volunteers to focus on. Set up the camera - higher is better in general. Rough focus. Tilt the front a little. Put your two volunteers where the front and back row will be. Focus on the front person, then check focus on the one in back. See which direction you need to to change focus to bring the back person in; farther (less bellows) -means you need more tilt, or closer (more bellows - means you need less tilt). Adjust the tilt as needed, but you'll be very close the first time (you already have an idea how much tilt is needed). This won't require a lot of trial and error - it just isn't very fussy, though a practice session might be nice.

8x10 sounds good to me. A 40 - 60" group picture does require a lot of sharpness. F11 @ 1/2 sec isn't too scary, you do have to calm the group and get their attention focused for the exposure.

couldabin · Feb 13, 2012

Mark, in one important sense it is an exercise/practice session, and I'm glad I went through it. I never would have dreamed that the tilt would be so slight, so if I had simply tried to find the correct setting through trial and error it would have been all error. I simply would not have believed that the tilt would be on the order of 1/32". Simply locking the standard down could easily move it that much. I have no confidence whatsoever that in past usage the front/back alignment has ever been closer than that, since I never actually measured it. I know I cannot detect that closeness of alignment with my naked eye. What I plan on doing is using my level to find vertical on the back, then find the smallest discernible forward tilt of the lensboard frame that I can -- I experimented a little with the spirit level I use and the smallest angle it registers is about 0.3 degrees; 0.4 is the theoretical tilt I'm shooting for.

Mark Crabtree · Feb 13, 2012

Yes, the more you know beforehand the better. I do think you are being mislead somewhat by your calculations. It seems like you are interpreting the small amounts of tilt needed to mean that the tolerances are critical. My point was really that you do not require high precision of these adjustments on 8x10 (in the situation you descirbe).

Good luck with the shoot. Let us know how it works out.

Mark Layne · Feb 13, 2012

See 'Merklinger-Focusing the View Camera'
Mark

couldabin · Feb 13, 2012

Yes, David posted a link to it above. I looked at, and applied some of his alternative calculations. Same result. Do you agree?

couldabin · Feb 14, 2012

Not sure about the misled part. It's true I'm interested in knowing how misalignment affects plane of focus -- I started this thread out of a sense of disbelief that virtually undetectable amounts of misalignment can result in significant changes in the plane of focus, and so far I've not had anyone challenge the math. (If that's not the case, I do hope someone will set the record straight.) That said, I believe that in the end it's what the photo looks like that counts, and if the elements of interest in the image are sufficiently sharp -- entirely a judgment call -- then the process worked. This exercise has shown me that I was blissfully unaware of the way some pretty fundamental principles actually play out.

Mark Crabtree · Feb 14, 2012

Being mislead by thinking this is a very significant change in the plane of focus. It requires very little tilt because it is a very slight shift in the plane of focus. That is because of the distance.

You are at 100 feet distance IIRC. Move those risers closer (20 feet) and you'll need much more tilt (a little more like the groups I shoot, though still not an extreme shift in the plane of focus). Move the risers back to 300 feet and I think you'll realize without math that even though the risers have a 45 degree plane that makes effectively no difference to focus (or try 500 or 1000 feet if that isn't convincing). What you are calling the plane of focus hasn't changed in these situations., but the amount of tilt required does.

couldabin · Feb 14, 2012

I'm afraid I'm not tracking. In my mind, if a tilted plane of focus is what we want, that angle remains at 45 degrees regardless of whether I shoot from 20 ft. or 250 ft. What does change is the tilt of the front lensboard that creates a 45 degree plane of focus at the subject in those two situations -- considerably more tilt when I'm 20 ft away, virtually none when I'm 250 ft away. Yes?

Mark Crabtree · Feb 14, 2012

Edited - I apologize if I've made this more confusing.

E. von Hoegh · Feb 14, 2012

couldabin said:
I'm afraid I'm not tracking. In my mind, if a tilted plane of focus is what we want, that angle remains at 45 degrees regardless of whether I shoot from 20 ft. or 250 ft. What does change is the tilt of the front lensboard that creates a 45 degree plane of focus at the subject in those two situations -- considerably more tilt when I'm 20 ft away, virtually none when I'm 250 ft away. Yes?

Lets say the distance between the near and far points on your 45deg plane are 4 feet apart. How much lens displacement - not tilt, just movement of the focus rack - does it take to alter the focus 4 feet at 20 feet? At 250 feet? This is what you are missing.

mark · Feb 14, 2012

Let me get this straight
You are 100 feet away
There are 200 or so people
and you are going to make roughly a 48 x 60 inch print (6x enlargement) or 32 x 40 (4x)
I don't remember if you said what kind of film
And people are going to want to see themselves clearly?

I am going to assume this is NOT an optical analog printed in the darkroom enlargement, because even with an 8x10 people will begin to get muddy as the space between the grains will be amplified that much as well. If you are doing this in the darkroom I hope you have your equipment dialed in sharp enough to prick a finger.

JMO though.

Tilt trig

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Tilt trig

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