Determining Pupil Ratio?

[Jim Ford]

Is there a simple way of determining the pupil ratio of a variety of lens set-ups eg with extension tubes/bellows, reversed prime, tele with reversed prime on front etc., sufficiently 'near enough' for macro work?

As I've mentioned in the description of my focus stacking rail, I've allowed for entering the pupil ratio in the calculations, but I'm just calling it '1' for now. I feel I'll need to do better than this with more ambitious work.

Jim

[rjlittlefield]

See FAQ: What is "pupil ratio" and why would I care?. Be aware that determining pupil sizes can be very difficult with some combos because they approach telecentric -- the pupils are very large and located very far from the lens.

I see you've been referred to that article before (on Aug 17, 2011), but I'm mentioning it again because it's the best reference I know.

By the way, my standard recommendation is to avoid optics computations as much as possible. This is perhaps ironic, since I do a lot of math -- I have a college degree in numerical analysis, I've spent most of my life computing stuff, and I've taught at the college level also. The reason is simple: in most cases accurate computations are unnecessary, and they are very easy to foul up. The only way to be sure you've done the right computation is to also do the experimental measurements to confirm it. But then in most cases it would have been more efficient to just do the measurements and stop. Formulas are great for getting you in the right ballpark. Beyond that they're generally more trouble than they're worth.

--Rik

[Jim Ford]

See FAQ: What is "pupil ratio" and why would I care?. Be aware that determining pupil sizes can be very difficult with some combos because they approach telecentric -- the pupils are very large and located very far from the lens.

I see you've been referred to that article before (on Aug 17, 2011), but I'm mentioning it again because it's the best reference I know.

Thanks for the reply.

Yes, I did read the article in August (and have 2 copies printed out!).

It left me with the uneasy feeling that the Pupil Ratio is very important and ought to be known for a particular lens set-up, but ended by saying that it's very difficult to determine, and in the case of telecentric lenses near impossible.

I was kind of hoping that I'd get a reply of the form: 'Project the image of a candle onto a screen and measure .....'!

;^)

Formulas are great for getting you in the right ballpark.

Ahh, this is what I was hoping for - a 'ballpark' formula. Currently my ballpark formula is PR=1!

Jim

[rjlittlefield]

It left me with the uneasy feeling that the Pupil Ratio is very important and ought to be known for a particular lens set-up, but ended by saying that it's very difficult to determine, and in the case of telecentric lenses near impossible.

Pupil ratio is very important to know if you want to do computations that accurately match reality. It's not very important if you just want to get in the right ballpark to make a measurement.

The reason I've spent so much time studying pupil ratio et.al. is because I have a personal compulsion to match theory and experiment. It drives me nuts when somebody hauls out a formula, plugs in some numbers, and makes a conclusion, without ever knowing that they've used a formula that doesn't apply, and plugged in the wrong numbers anyway. I've made those same mistakes often enough myself to be very leery of the process. That's why I always look for some independent confirmation of my own computations, preferably a physical measurement, and it's why I encourage other people to rely on measurements and use the formulas only for rough guidance.

In the spirit of "rough guidance", P=1 is not that bad for most setups. Measurements made using the arm's length method are better, and are probably good enough for your purposes. In the same spirit, but much more accurate, are the measurements that you get from pointing another camera into the front and rear of the stopped-down optics under test. Many combos remain a problem because they're near telecentric, but for a lot of those the computation works out OK if you just recognize the situation and plug in PR=big or PR=0, as appropriate. However, it's still tricky to figure out just what to plug in for nominal aperture, because that depends on where and how you stop down.

I was kind of hoping that I'd get a reply of the form: 'Project the image of a candle onto a screen and measure .....'!

Funny you should mention that. I recently received an email from a fellow who's playing around with combos, in particular a 100 mm macro lens on camera, with a reversed 17-40 mm lens in front of it. His email included the following snippet:

I also noticed a strange phenomenon: if I set the combo macro focus at infinity and zoom the wide angle to 17, my width of field depends on whether I use extension as follows:

Extension (mm) field width(mm)
64 4.25
0 4

That is, adding extension *decreases* magnification for this configuration. I checked this a second time.

My first thought was that he'd messed up the measurement, despite his assurance of checking it. So I set up a similar combo of my own, using Canon's EF 100mm f/2.8L Macro IS USM lens in combination with the 18-55 mm kit lens that came with my Digital Rebel some years back. Lo and behold, it did basically the same thing. Hhmm...

As mentioned, I'm pretty obsessive about matching up theory and experiment, so of course I had to investigate what the heck is going on.

The first part of that investigation was to locate the principal planes of both lenses, and that process involves projecting an image from infinity onto a screen. (Maybe you wondered where I was going with this story. )

Well, it turns out that the reversed wideangle won't project an image at all, because one principal plane is buried too far inside the lens. I had to determine that location by other means -- computation based on other measurements, as it happens.

Once I knew where the planes were, it wasn't too much trouble to model the combo in my favorite ray-tracing package. Here's the schematic diagram:



Now, if that doesn't immediately strike you as a bit bizarre, then consider this other diagram that corresponds to naive application of the well known thin lens equation:



Notice that in the too-simple model, cones of light are predicted to emerge from the center of the lens and get farther apart as they approach the sensor. In this model, the lens would be expected to have traditional behavior: effective focal length = 1/(1/18+1/100) = 15.3 mm, with magnification increasing as you add extension. But in the more accurate model, and in the real world, the combo has unexpected behavior. Its "effective focal length" is around -75 mm --- yes, negative, despite that in certain focal arrangements it forms real images just fine -- and this negative EFL nicely explains why adding extension reduces the magnification. It should come as no surprise that the pupils are a bit tricky to measure also.

This illustrates the problem with combos: they're a lot more complicated than you might think. Everything works out when you get enough details into sufficiently complex formulas. But before you get to that point, the formulas may not come even close to predicting actual behavior.

I apologize for delivering the bad news, but that's just the way things are!

--Rik

[Jim Ford]

Hmm, a lot to think about and digest, but none of it good news!

The 'What is pupil ratio etc.' article mentions the 'arm's length' method, but doesn't go into any details. I'd be interested to get more information on this.

Jim

[rjlittlefield]

It's nothing fancy -- you just hold the lens at arm's length with a ruler or calipers directly in front of it, and eyeball the diameter of the pupil. With most lenses this works pretty well because the pupil is within a few centimeters of the ruler so the parallax error is small. You're not going to get 1% accuracy this way, but 10% or so should be doable.

--Rik

[Jim Ford]

Fine - thanks 'Rik'. As a 'nut strangling' mechanical engineer I can just about cope with that!

;^)

Jim