A comment on when to use a tilt

[Leonard Evens]

Generally, you use a tilt (or swing) to extend the depth of field from near to far along an appropriately chosen exact subject plane in situations where just stopping down far enough is not a viable option. But, you pay the price of limited depth of field on either side of that exact subject plane, most commonly in the foreground.

I've come up with a rule of thumb which quantifies this. I realize that most people won't want to bother with using such rule and will prefer just to try a tilt to see if it works. If you are such a person, please don't read any further. In addition, the rule requires knowing some quantities such as focus spread and tilt angle, which in practice you may not bother to determine. If you don't happen to know these anyway because of how you proceed, it may not be worth the extra trouble to measure them.

But for some, who are good a mental arithmetic, and ordinarily measure focus spread and tilt angle anyway, it may be helpful.

The idea is to compare the focus spread on the rail between near and far points you want in focus to the greatest height (width for swing) you want in focus on the ground glass at any given subject distance from the lens. The former is proportional to the f-number you would use without tilting and the latter is proportional to the f-number you would need with tilting. The ratio of the two f-numbers is given by the ratio of the focus spread to the height times the tilt angle in radians. If that numerical quantity is less than 1, there is an advantage in tilting, and the smaller it is, the greater the advantage.

Another way to state this for quick use in the field is as follows. Take the ratio of the focus spread to the height and multiply it by 60 (more accurately 57.3). That is where the mental arithmetic comes in. If this number is greater than the tilt angle in degrees, there may be an advantage in tilting. How much of an advantage depends on how much greater it is.

Let me give an example. Suppose the tilt angle is 5 degrees. Suppose the focus spread is 10 mm. Suppose also that there is a small shrub in the foreground you want in focus, which measured on the ground glass is 50 mm high, and no other vertical range at any another distance is greater than that. Then the ratio would be 10/50 = 0.2 and 60 times that would be 12, which is greater than 5. So that indicates that tilting would be worthwhile.

In using this rule, you can gauge how much you would gain by stopping down by seeing how much greater than the tilt angle the quantity is. Thus if you divide 60 times the ratio by the tilt angle in degrees, you get a rough estimate of 12/5 = 2.2 which suggests a tilt advantage in terms of f-numbers of more than 2, i.e., more than two stops. Depending on your criterion for sharpness, a focus spread of 10 mm would require (ignoring diffraction) stopping down to between f/45 and f/64, whereas using a tilt you could get by with something in the range f/22 to f/32.

On the other hand, suppose the height were 100 mm instead of 50. Then the ratio would be 10/100 = .1, and 60 times that would be 6 which is greater than 5 degrees. But 6/5 =1.2 which suggests perhaps half a stop gain by tilting. In that case, it is not clear it would be worth trying.

Usually the greatest height required in focus on the ground glass comes from a transverse section in the foreground, but that need not always be the case. You could just as well have, for example, a tree in the middle distance, or a large building in the background, which dominates on the ground glass.

[Ron Marshall]

Thanks Leonard. Is the 5 degrees in your example the actual tilt required? If so then I understand what you have written and this method will definately be of use to me.

[Leonard Evens]

Ron,

As I noted before, usually you set the tilt angle optically by trying to put a desired exact subject plane in focus, so you might not know the tilt angle unless your camera has a scale which shows it. There are a couple of ways to calculate it, but you probably wouldn't bother making those calculations in the field, so the whole approach assumes you do have some way of determining the tilt angle.

More important, the rule of thumb would normally be used before you tilted, to decide whether or not tilting would be worthwhile. So in any given particular situation, although in principle, you could calculate it---see below---, most likely you would just use your prior experience with similar situations to decide what the tilt angle would be. In my case, my tilt angle for my 150 mm lens is usually just about 1 radian, i.e.,slightly less than 6 degrees.. But it would be different for you.

Note that the rule is meant just as a rough guide. It can, for example, be used to keep you from trying to use a tilt in situations where it clearly won't do any good. But it wouldn't normally be used for precise calculations since you wouldn't be making precise measurements of the relevant quantities. In ambiguous situations, you would still have to set the tilt and see if it works.

5 degrees is a typical value for the tilt angle, but it could be anything from 2 to 10 (sometimes more) degrees. Just what it will be depends on the focal length of the lens and the distance to the exact subject plane. That in turn will depend on how tall you are since that will determine where the lens is.

The most common situation is that the exact subject plane passes beneath the lens at ground level. For a relatively short person like myself, the lens is usually about 1.5 meters above the ground, and for a 150 mm lens, the tilt angle would be about one radian or 5.7 degrees. For my 90 mm lens it would be about 3.4 degrees, and for my 300 mm lens it would be about 11.5 degrees. If you are tall and usually place the lens at 2 meters, the angles would be 3/4 ths of those values.

You can calculate the tilt angle as follows. For small angles, a good approximation for that angle( in radians) is the focal length of the lens divided by the distance from the lens to the exact subject plane. So for 150 mm lens and a 2 meter = 2,000 mm distance, it would be 150/2000 = 0.075 radians. To convert this to degrees, it is close enough to multiply by 60 to get 4.5 degrees. (The actual multiplier is closer to 57.3. If you used that instead, you would get about 4.3 degrees instead, which is the same to the nearest half degree.) If you tell me the height you usually put your lens above the ground and the focal lengths of your lenses, I would be happy to calculate the corresponding tilt angles in both degrees and radians. You don't have to give the measurements in metric units. I can convert from inches to mm easily enough. Of course, these calculations would only apply if the exact subject plane were at ground level. But if you know the angle for ground level, it is not hard to find the corresponding angle for another position of the exact subject plane. Just multiply by the ratio of the distance above the ground to the actual distance. So, suppose the distance above the ground is 1.5 meters, and the distance to the exact subject plane is 0.75 meters. You would multiply by 1.5/0.75 = 2.

As I noted, you would be unlikely to actually make such calculations in the field. You could of course make them in avance and prepare a table, but if you are like me, you would not be able to find the table when you needed it. Instead, you would just be able to guess from previous experience what the angle would be.