# Measuring focal length of complex lens

I'm trying to accurately measure the focal length of a lens.

I have a complex computerised system lens measuring system that I don't entirely trust (I worked with Hubble) so I want to confirm the focal length - to an accuracy of 1% or better.

The complications:

• This is a multi-element lens so I don't know precisely where the principle planes are.
• It is pre-focussed at 1m (approx f=0.01m) and I can't re-focus to infinity to test

The plan was to image a precision USAF target at precise stepped distances $\Delta d$ from the lens and measure the image size to get a pixel scale at each increment of distance. Plot image scale against $d+\Delta d$ and iteratively fit an f to minimise variation.

(I don't know absolute $d$ of course because I don't know the principle plane location in the lens)

• Your answer basically contains the suggestion that I would have made. Is this for a production test system, i.e. are you trying to test products for being within specs, or is this for a one-off use of one or a few particular lenses? In the latter case I would probably try to experimentally optimize the real goal function (best possible image quality, correct image scale etc.) in the final product rather than extract an intermediate engineering parameter like the focal length. Sep 10, 2015 at 16:12
• @CuriousOne - the experiment is a one off to verify the complex system which tests production units. So it is the number I need. Sep 10, 2015 at 16:19
• In that case I would probably have done what you are suggesting, probably with additional controls like sticking a simple lens with well defined principle planes in the same setup to verify that my understanding of what is going on is correct. In general the instance that I trust the least in my work is myself and my understanding of what I am really doing vs. what I think I am doing. Sep 10, 2015 at 16:26
• @CuriousOne. In this case the complex computerised measurement system was also built by me. So I distrust; me , software, and software built by me! Sep 10, 2015 at 16:57
• Welcome to the world of the experimentalist... utter distrust and lack of self-respect - usually based in the insight that everybody makes mistakes all the time! :-) Sep 10, 2015 at 16:59

A classic method of measuring focal length is with an interferometer rather than by imaging. This is because you can determine movement in conjugate points very precisely.

For example, using the interferometer you can:

1. Locate the front and back surfaces of the lens and measure their optical thickness by measuring the translation of the interferometer that results in Cat's Eye returns from the front and back surface.
2. Back off the interfometer to a known distance from the lens by measuring the distance it moves from Cat's Eye to your test distance (measurement can be done with a laser tracker or laser distance interferometer or optical encoder scale)
3. You can place a concave or convex mirror on the opposite side of the lens to create a retroreflection. You can measure its movement again with similar tools as above.
4. You can try to move one conjugate and determine the movement of the other conjugate with similar methods in the same way you proposed to do it by imaging.

I suggest an interferometer because the focal point will be extremely well known without relying on image processing to tell the magnification.

Ask me more questions and I'll provide more details...

• Interesting. I don't have the lab setup to immediately try this but it is worth considering. Sep 17, 2015 at 15:13