Bellows extension and exposure

[Hiro]

One more question, relates to Telephoto lens. Does the disk and 25% equal one half stop work there as well?

Just in case...actual bellows extension is shorter with a telephoto lens, by the difference between the focal length and the flange focal distance. You don't have to worry about it if you work with the magnification ratio using the Quick Disk or the Calumet's device.

[Leonard Evens]

The Quickdisc method or something similar will work, but it does require putting it in the scene at the proper position and then remembering to remove it before making the exposure.

I think everyone should understand the importance of the ratio of the total bellows extension to the focal length. Not only does it play a role in calculating exposure in close-ups, but it also plays a role in other area. The only problem with using it is that it may not be clear from where you should measure to find the total bellows extension, particularly for telephoto lenses. There is one way to avoid that problem. First focus on infinity, note where you are on the rail (or camera bed), refocus on your subject, and measure the extension from the infinity position. Add this to the focal length, and that will give you the total bellows extension for any lens.

I also think it is important to understand how to use it in modifying exposure, even if you use another method to do that. When you extend significantly further than the infinity position, you effectively change the f-number. The effective f-number is the marked f-number times the above ratio. For example, suppose you are using a 150 mm lens, and the total bellows extension is 200 mm. The ratio is 200/150 = 4/3 or about 1.3. If you set the aperture as marked to f/16, you are actually using an effective f-number of 16 x 4/3 ~ 21.3 or just about 22. That means by extending you have effectively stopped down one stop more than marked. You have to open up one stop or increase exposure by one stop to compensate.

The main trouble with using the ratio to determine exposure increase is translating from f-numbers or ratios of f-numbers, to number of stops, including fractions of a stop. There is a simple formulas for that relation which uses logarithms, but few of us are going to be using such a formula in the field. the most practical solution to this problem is to carry a table which gives you the correction in stops for selected ratios and then interpolate. Here is such a table, with the first number being the ratio and the second the correction: 1,0; 1.1, 0.28; 1.2, 0.53, 1.3, 0.76, 1.4, 1.0; 1.5, 1.2; 1.6, 1.4; 1.7, 1.5; 1.8, 1.7; 1.9, 1.9; 2, 2. (Anyone who regularly uses a magnification greater than 1:1 should know how to use exact calculations.)

But there is one simple way to estimate the number of stops increase in exposure without a calculator for those who are good a mental arithmetic.

Take the ratio and square it. For example in the above example 1.3 squared is 1.69 or about 1.7. If the square is between 1 and 2, subtract 1 and multiply the result by 1.5, i.e. increase it by 50 percent. In the example 0.7 x 1.5 = 1.05. This always gives a slight overestimate, so you can donwsize it to the next lowest fraction of a stop.

If the square of the ratio is larger than 2, just divide by 2. That accounts for 1 stop. Usually that will get you between 1 and 2, but if not, divide by 2 again, accounting for an additional, and so on. When you get a number between 1 and 2, calculate the increment in stops as above.

Let me do another example. Suppose the ratio of total bellows extension to focal length is 1.6. the square of that is 2.56 or about 2.6. Divide by 2 (one stop) to get 1.3. Subtract 1 to get 0.3 and multiply by 1.5 to get 0.45. That looks close to half a stop, but if we remember that it is an overestimate, it might actually be closer to 1/3 of a stop. So the totoal exposure correction would be between 1 and 1/3 and 1 and 1/2 stops. (The exact caluclation using logarithms is 1.36 stops or closer to 1 1/3 stops.) Using the larger estimate would at worst produce a sliight overexposure, and in most cases that would be innocuous. It is not possible to set the aperture that closely in any case.

You may wonder how I could possibly suggest using a method which requires squaring something in my head. Well, it turns out that it isn't that hard. First round-off to a 2 digit number such as 1.6. Many people in school learn all the squares up to 20: 10^2 = 100, 11^2 = 121, 12^2 = 144, 13^2 = 169, 14^2 = 196, 15^2 = 225, 16^2 = 256, 17^2 = 289, 19^2 = 361, 20^2 = 400. If you know that sequence, then it is just a matter of putting the decimal place in the right place and rounding off again to two digits.

As to what happens if you use movements, I can tell you what theoretically should happen, but I have to admit I haven't carefully checked it in the field. If you use a rise or fall, the only effect is that you are moving the frame within the image circle. Illumination drops as you approach the edges of the field by well knwn laws. If you are using a wide angle lens, even if you can get by without a center filter without a rise, you may need one if you use an extensive movement of this kind. But this is an entirely separate issue from that of bellows extension. You would still calculate the necessary extra exposure the same way. As to fall off of illumination, it seems to me you would actually be better off with significant bellows extension. The angle covered by the lens stays fixed, but the image circle at the film plane increases with distance from the lens. So the same rise of fall is less likely to get you outside the range where fall off of illumination is significant.

If you tilt, the situation is quite a bit more complicated, and I don't know yet just what happens. The film plane may be shifted further back when you tilt, and that should require aditional exposure to compensate. But for modest tilts, the difference is quite small. For example for 10 degrees, it is about 1.5 percent and for 20 degrees, it is about 6.4 percent. In any case, if you measure the total bellows extension after tilting, any such adjustments should already be incorporated. The more interesting question is whether or not the fact that subject points at vastly different distances from the lens all come to focus in the same film plane makes any difference. My guess is that it doesn't, but I could be wrong. I have to think about it.