Aperture: diameter for given focal length

I have just assembled a 600mm Nikon ED telephoto from separately acquired front and rear elements to which I am fitting a new Copal 3 shutter. The shutter comes with shutter speed stops and scale but no aperture scale. The problem is to determine the locations of the aperture stops (and mark them with tape, or whatever).

From pictures of the same shutter calibrated by Nikon and provided with the complete new lens as part of the 600-800-1200mm set, it is clear that the diameter of the opening is a function of focal length. For a given aperture setting (say, f/64 in my picture), f/64 is a stop more open for the 800mm than for the 600mm, and two stops more open for the 1200mm than for the 600mm. My light meter has no setting for focal length, and the exposure it gives for a given subject is the same for any lens of any focal length. So each individual lens must be calibrated in such a way that f/64 corresponds to shutter openings of varying diameter depending on the focal length.

I put two lenses with calibrated shutters, a 300 and 450, on my 8x10, set each at f/11, focused, and took a meter reading of the same part of the subject off the ground glass from underneath the dark cloth. Pretty near the same reading. But when I measured as best I could with a ruler the width of the shutter opening at f/11, I got 2.5mm for the 300 and 3.5mm for the 450.

After all these years, none of this dawned on me until this morning. Could someone help with some basic optics? And an equation or two? There’s also the practical matter of positioning the shutter stops on my blank Copal 3. I suppose I could work with the light meter, opening and closing the shutter of the 600mm until I get the same exposure reading that I get on the 300 or 450 at a known aperture, then correcting for focal length. But for that I need a formula for making the correction. Thanks in advance for any help in clearing up my confusion.

Nicholas

Your suggestion to use a light metering technique might work but there might be several biasing effects very difficult to master.

The practical method I would attempt is based on the definition of the numerical aperture in a thick compound lens and hopefully can easily be implemented in the real world.

For some reasons a bit difficult to explain, (I have the maths handy if you wish but this is not the priority in our problem) the numerical aperture N or f-stop number N in a thick compound lens is defined with respect to the diameter of the entrance pupil, a_EP as :

N = f / a_EP
a_EP = f / N

where f is the focal length.

If f = 600mm and N=22, a_EP = 600 / 22 = 27mm

The entrance pupil is the image of the iris as viewed from the front of the lens. We'll see below how to measure it since it is not physically accessible. And this diameter is different from the actual diameter of the iris, there is an optical magnification factor by the front lens element.

The Nikon system of convertible telephotos interchanges the rear lens element, so once you have calibrated the lens for one configuration, the f-stop scale will be easy to re-compute when you swap to another rear element since the entrance pupil diameter is the same. the focal length however changes but you know it : 600, 800 and 1200.

In other words, set the lens in the 600 mm configuration, stop down to f/16, swap to the 1200 config, since the focal length has doubled, when the 600 is set to f/16, the 1200 will be set to f/32 if you keep the lever in place, since f has doubled.

Now the problem is to measure a_EP.
A reader of the French LF forum, André Gély, has found in a vintage brochure from the 1920's a precise description of a protocol that I had imagined myself except for the last step (use photographic paper to measure the diameter). So we should always read and re-read vintage brochures ;)

http://www.galerie-photo.info/forum/...70#reply_57085

The idea is as follows.
Place a very small light source in the focal plane, e.g. a small LED or simply a small battery-operated flashlight. The focal plane is where the image of a distant object focuses, you can find this easily. Note that in a telephoto the focal point is not located at one focal length behind the last lens element, this is the main advantage of telephotos !
Tighten the controls and place the light source where the ground glass has been secured. Illuminate the lens backwards and check that all the rear lens element is illuminated. Place some translucent paper in front of the lens, you'll see an iluminated circle which diameter is equal to the entrance pupil diameter a_EP. Why ? because if the light source is very small, the rays propagating from the focal plane backwards will be almost parallel when they come out of the lens, in front. Hence you get a parallel projection of the entrance pupil. the beam diameter is the diameter you want to measure. So what you get is not exactly a circle but a kind of a polygon, depending on the number of blades in the iris. This is not a serious issue, you'll easily estimate a mean value for the diameter of a circle of same surface.

The old brochure of 1920 suggets to put a piece of photographic paper close to the entrance of the lens, expose, develop and measure the diameter of the black circle printed on the paper.
Well I'm quite sure that with a pencil and a piece of translucent paper you can get a reasonable measurement of this diameter. The advantage of recording on paper is that it will ne easier to estimate the equivalent diameter when the iris has a small number of blades.

The measurement need not be very accurate.
Let 1/6-th of f-stop be the required precision, this corresponds to a relative error of 12% (2 ^(1/6) = 1.12) on the total area of the circle, about 6% on the measurement of the diameter. In a 600mm lens opened at f/16 this diameter is 37.5mm, 6% thereof is 2 mm.
Easy. No need for some expensive measuring tool !

Now you have to re-do it for all required f-stops.
Modern shutters have equidistant markings it means that the distance that the lever travels between f/16 and f/22 is the same when travelling between f/22 and g/32, etc..

Once the scale for the 600 is made, the scale for the 1200 is made by translating it by one f-stop.
The scale for the 800 is somewhat in between, not exactly a half f-stop.
For a half f-stop the ratio of focal lengths should be 1.41, here 800/600 equals 1.33.
But anyway once the 600 has a scale, the rest will follow easily.

I hope that this will work for you as is worked for the people reading the 1920 brochure !!
Keep us informed about the project !

It's obvious I have some work to do, Emmanuel. Meanwhile I'll simply use my spot meter on the ground glass as I described, work up some rough-and-ready working aperture positions for the new lens, then do some test shooting. P.S. In my next to last paragraph, I of course meant to write 25mm and 35mm.

Well Nicholas your measurements are perfectly correct as far as the influence on focal length is concerned. And I made a terrible mistake ! Shame on me :(
For a given aperture setting (say, f/64 in my picture), f/64 is a stop more open for the 800mm than for the 600mm, and two stops more open for the 1200mm than for the 600mm.
This perfectly matches the formulae, my text above is incorrect and should read :
- Once the scale for the 600 is made, the scale for the 1200 is made by translating it by TWO f-stops. N is multiplied by a factor 2, this means 2 f-stops of course !! One f-stop : multiply N by 1.41.
- The scale for the 800 is somewhat in between, not exactly ONE f-stop.
- For ONE f-stop the ratio of focal lengths should be 1.41, here 800/600 equals 1.33.

So go ahead with your procedure, there are probably less biases than I thought, if you know the maximum aperture for the 600 mm, you'll be able to find f-stops with the spotmeter.
The idea to measure on the GG is perfect since you do not have to precisely aim the spotmeter at the exit pupil of the lens (image of the iris seen from the back). And you just need relative measurements with respect to a certain reference, this is always easier.

An update for this discussion
A French photographer is selling (January 2008) a complete Nikkor T-ED kit (600,800 and 1200mm)
http://www.galerie-photo.info/forum/...=30963&t=30963
and in one of his photos you can easily see the engravings for the 3 focal length on the shutter
This solves the problem !! (the link will expire in a few weeks but I'll make a copy for reference)
http://cjoint.com/data/bBv7R8LOA0_IMGP0210.jpg

The summary is simple : for the 800 the manufacturer's engravings are plus one f-stop (e.g. 16 for the 600 becomes 22 for the 800) and for the 1200 plus 2 f-stops...
Max aperture f/9 for the 600 becomes f/12 for the 800 and f/18 for the 1200.


DISCLAIMER : I'm not affiliated with this photographer and have no interest whatsoever, etc..etc... ;)