Why so little tilt needed?

[Bill_1856]

The best way to think of it is that the focal length of the lens is (let's say) 150mm which is approximatey 6". The distance from the camera sitting on the tripod to the ground is approximately 5 feet. Think of the little bitty triangle consicting of the short side equal to 6" (of .5 feet), and the long side of 5 feet. It's just a tiny little angle to make this long, narrow triangle. For a 12" lens, it's twice as "fat" but still only a tiny little angle to make the triangle.
It's really seldom needed -- just stop down to f:32-64, and you may never need to lilt the lens at all.

[Ben R]

Um, have to admit that my cars have seen 100mph many times though always by accident, you can hit it quite easily by mistake when you cruise at 90...

I suppose it's more common here in the UK when youre doing 90 in the fast lane and a 15 year old white transit van starts tailgating you and hurling abuse because you aren't going fast enough!

[Marko]

Um, have to admit that my cars have seen 100mph many times though always by accident, you can hit it quite easily by mistake when you cruise at 90...

I suppose it's more common here in the UK when youre doing 90 in the fast lane and a 15 year old white transit van starts tailgating you and hurling abuse because you aren't going fast enough!

I was always wondering what was it all about white vans in England...

It is mostly huge pickup trucks here (and I mean ridiculously oversized and elevated with grotesque set of tires kinda huge).

But depending on the car you drive and the road you travel, hitting or even stepping over 100 mph is not all that big of a deal, as long as you have good tires and very light foot on the brakes. I guess those commercials are meant to lure folks with old clunkers into buying new.

[Ben R]

One road I could have killed to put my foot down on was the Icelandic Route 1 along the south of the country. I was there shooting for a week and sleeping in the car, there is a stretch of road where you can see almost 100 miles of road in a straight line ahead of you and the speed limit is 50 mph! I got a speeding ticket there for going 80...

[Leonard Evens]

It is in fact true that the amount of tilt needed to produce a specified position for the subjtect plane is directly related to the focal length. I don't know if it will make any sense for you, but here is the explanation, which requires some mathematics. For small tilt angles, the tilt angle is given pretty closely by the formula

Tilt angle in radians ~ focal length divided by hinge distance.

The hinge distance is the vertical distance below the lens of the exact subject plane.

That means that, other things kept equal, the tilt angle is roughly proportional to the focal length. 90 mm is 3/7 of 210 mm, so the tilt angle for 90 mm will be 3/7 of that for 210 mm.

But the tilt angle also depends on the hinge distance. Thus if the lens is one meter above the subject plane, the tilt angle is radians would be about 90/1000 = .09 radians, which is a little over 5 degrees. If the lens is 1.5 meters over the subject plane, the tilt angle is about 3 1/2 degrees. For the best tilt angle to be as small as 1 degree, the hinge distance would have to be over 5 meters. That might happen if the exact subject plane is tilted upward, or, if the camera's vantage point is elevated. It wouldn't be the case if the exact subject plane is close to being horizontal along the ground next to the camera.

But there is another complication which might affect your judegment of what tilt angle to use. Other things (such as f-stop and subject plane) being equal, shorter focal length lenses have more depth of field. For a tilted lens, the DOF region is a wedge shaped volume in space, starting at the hinge line below the lens. Again, roughly speaking, the angular opening of the DOF wedge varies as the inverse of the square of the focal length. Thus the angular opening for a 90 mm lens might be (210/90)^2 ~ 5.4 times as large as that for a 210 mm lens. The large depth of field might mean that it is harder to place the exact subject plane just where you want it, and if you set it wrong, it would make less difference. Indeed, with a short focal length lens, you might need no tilt at all to get everything you want in focus.

Theoretically, if the position of the subject plane is crucial, you would be better off using a longer focal length lens to set the tilt anlge and then switch to the shorter focal length lens, but keep the same tilt.. But in most cases, there wouldn't be much point in doing that.

[65Galaxie]

I don't even focus on my Speed with 90 Optar. I marked my bed for infinity, 8 ft. and 4 ft. If I step down to f22 or f32 I put the focus on 8 ft. and everything from 4ft to infinity will be in focus. If you put the camera at head level and straight ahead I doubt if the nearest viewable point would be as close as 4 ft. I bet it's closer to 5-6 ft.

[Leonard Evens]

With a coc of diameter 0.1 mm, the hyperfocal distance of a 90 mm lens at f/22 is about 12 feet. Many people would consider even 0.1 mm too large, so I think that is a conservative choice. It is quite possible to have a scene where you want something to be in focus at less than 6 feet. You could avoid tilting in such a case by stopping down further than f/22, but then the necessary exposure time might be long enough to show subject motion.

[Ben R]

Firstly Leonard, thank you for all the details, I will have to read it a couple of times until I understand it mathematics never having been my strong point. What would you accept as a more realistic CoC for LF? What CoC would I be aiming for in general using the hansma method for example (I know that it isn't comparible but the sharpness should).

[Leonard Evens]

It seems generally agreed that people can resolve between 5 and 10 lp/mm when looking at an 8 x 10 print from about 10-12 inches. That corresponds to a coc of diameter between 0.2 and 0.1 mm. If you enlarge two times to produce the 8 x 10 print from your 4 x 5 film, that would correspond to between 0.1 mm and 0.05 mm at the level of the film. You have to make the choice based on what you see when you look at prints. Some DOF tables are based on an even coarser choice, larger than 0.1 mm, but I think one should not go below that.

How this relates to Hansma's tables is a bit complicated. DOF tables generally ignore diffraction and assume sharpness is governed simply by the coc. In principle, for a point in the exact plane of focus, the image is exactly a point. For a point on either side of the plane of focus, the corresponding image is a disc, called a circle of confusion (coc). Up to a certain size, the human eye can't distinguish that disc from a point, and that is what the choice of coc is for. It determines how much on either side of the exact plane of focus is adequately in focus according to the standard you set.

In reality of course, it is more complicated. Lens aberrations create some blur, so the image is never exactly a point. More important, diffraction means that any point is imaged as a small disc, the size of which is determined by the f-stop. The smaller the aperture, the larger the blur disc from diffraction. What Hansma did was to combine the defocus disc which results from the subject point not being in the exact plane of focus with the diffraction which would be there anyway. It is based on the focus spread on the rail between two points you want to be in adequate focus. He doesn't give you a specific size but he assures you that for the f-stop he recommends that the combined effects of defocus and diffraction at the desired limts of DOF will be as small as possible. This is independent of format, enlargement or anything else. If you use his estimate, your blur disc will often end up being much smaller than 0.1 mm, but it is not guaranteed to be. It will just be smaller at the recommended f-number than at any other choice.

Generally, the recommended f-number based just on defocus less than 0.1 mm, and ignoring diffraction, will be less than the Hansma recommended f-number by several stops. Personally, I think the Hansma recommendation is far too restrictive in most cases. What I do is determine the f-stop for the given focus spread, based on a defocus coc of diameter 0.1 mm and I also determine Hansma's recommendation from his table. I then choose an f-stop somewhere in between.

To determine the f-stop with a coc of size 0.1 mm is quite easy. You multiply the focus spread in mm by 10 and divide the result by 2. So if the focus spread is 4 mm, it would give 40/2 = 20. In that case I would take f/22 as the largest aperture I might use and then check also what Hansma recommends for focus spread 4 mm, which would be somewhat smaller. I then pick something in between depending on what the corresponding exposure times would be. Often the Hansma recommendation would result in an exposure time so long that subject movement would be a problem,

[Ben R]

About f40 actually for a 4mm spread according to Hansma. Leonard, that was exceptionally clear proof being that I understood it!

If we assume that CoC is based on the viewing distance for a 8X10" print then for a far larger print it should be less restrictive should it not? In that case, if I would want a level of resolution which is still sufficient for a large print that people will be viewing closely (who ever viewed detailed prints at the 'viewing distance'?) I should be safe.

Or did I just get that mixed up?