Calculating, NOT measuring, aperture of compound lenses

[Jockos]

Hello everyone!

I'm thinking of making my own lens, as a hobby project. However I've struck a wall, since I can't find the equation for calculating the max aperture of a multiple element lens.
When using a single element, it's simple: focal length divided by diameter. For compound lenses though, the only instruction I can find is to measure the entrance pupil.

Now this presents a problem as I don't have the lenses to measure, and I want to build the lens to spec. instead of just putting things together and measure the end result.

For the curious, I'm looking to build a ~f2.8 ~180mm, no shutter, no aperture, probably 3d printed barrel for wide open portraits.


I hope this is intelligible, English is not my first language

[Tim Meisburger]

Its the same calculation. Since it will be in barrel the diameter will be the internal diameter of the barrel. If you had a cone shaped lens the entrance pupil would be the narrowest part of the cone. You need a 65mm barrel.

[Jockos]

So it's total focal length divided by the smallest element size?

[Dan Fromm]

So it's total focal length divided by the smallest element size?

no

[Jockos]

no

Why not? That would be the smallest part of the barrel, and the barrel will effectively be the "aperture" if Tim's correct.

[ic-racer]

Depending on the software you are using, you would specify your aperture in the design.

[Dan Fromm]

Why not? That would be the smallest part of the barrel, and the barrel will effectively be the "aperture" if Tim's correct.

It isn't the entrance pupil (image of the aperture as seen through the front of the lens).

[Jockos]

Depending on the software you are using, you would specify your aperture in the design.

That'd be pen and paper thus far..

It isn't the entrance pupil (image of the aperture as seen through the front of the lens).

Right, got it.

[Emmanuel BIGLER]

Hello from France !

To continue with the entrance pupil issue, if you wish to calculate anything, you need to know a minimum of data. No entrance data, no possibility of computing .

For the f-number you need to know the focal lenght of the compound lens, and the position (and diameter) of the iris. Plus, in principle, all the characteristics of your glasses : radii, refractice indices, spaces between lens elements.

But imagine that your future compound lens is made from individual thin lens elements.
In this situation, you can compute what is called "paraxial lens data" by hand, on the back of an envelope with a pocket calculator equiped with the following functions : + - / *

Using some good old formulae well-known to college students, if you know the focal lengths of your individual thin lens elements and the distances between them, you can compute the paraxial focal length of the compound lens and the location of the image of the iris as seen from the front of the lens.

This will give you a pretty good estimation of the focal length and f-number of your future lens.

Now if you want to be more precise, and more professional.
If the number of lens elements is smaller than 4 - 5 elements (depending on the actual design and actual number of independant lens surfaces), you can make a complete simulation, with a professional software like Oslo-edu, which is free; it is the education version of the professional lens design software Oslo, it is in principle limited to 10 surfaces, I was able to run a simulation for the Heliar design (5/3) = 1 object plane, 1 image plane, 1 iris plane plus 8 lens dioptre surfaces.
The triplet, tessar and heliar designs can be simulated with Oslo-edu, and, may be, the dialyte (4/4 air-spaced) which requires 8 independant lens surfaces like the heliar.

For example, you'll find at the end of this article (sorry, it is in French) the output of Oslo-edu for the original Voigtländer Heliar design by Hans Harting (thanks to Richard Knoppow for sending me the data file, taken from the original 1902 patent). Simulation for a focal length of 100 mm.

The section of the article, is named : "finding the entrance pupil with a simuation software".
http://www.galerie-photo.com/pupille...que.html#sec35 gives you an example of paraxial computation with Oslo-edu.

The more difficult task using Oslo is to enter all the lens data.
Once this is done, you select "paraxial analysis" and the program gives you in a snap a listing with everything needed, see the example listing for the heliar.
The listing for the paraxial setup tels us, for the heliar that when the iris diameter is equal to 7.5 mm, the diameter of the entrance pupil is about 9 mm. The f-number, hence, is equal to 100 mm / 9 mm = 11. The listing gives ou the position of the principal planes H and H' and the position for the pupils.


And do not hesitate to ask all questions you would have!

[Struan Gray]

Hej Jockos

There is a halfway house between using Oslo and guessing.

As Dan said, the entrance pupil is the aperture as seen from the front of the lens. When you have no explicit aperture stop, the aperture is set by whichever element appears to be smallest when viewed through all the elements between it and the object space out in front of the lens. Provided you don't have too many elements and they are not too far apart, you can step through the lens, finding the virtual images of the mounts for each element, and choosing the smallest of them for the final figure.

If that doesn't seem obvious to you, it might be better to spend your time learning Oslo. Or tinker and measure.