effect of reversing lens on resolution?

[dh003i]

I've read many places that normal lenses for 35mm, optimized for say 1:20 front-forward, are optimized for 20:1 reversed. If a lens is diffraction limited at f/10 at 1:20, is it also diffraction limited when reversed at f/10 at 20:1?

e.g., if a symmetrical lens is diffraction limited at f/10 stated at 1:20, effective f-stop is f/10.5 and resolution is 1500/10.5 = 142.86 lp/mm. So, when reversed and used at f/10 stated at 20:1, the effective f-stop is f/210 (strictly speaking, a symmetrical lens doesn't have to be reversed for this example, but a asymmetrical one would need to be). Is the resolution then diffraction limited to 7.14 lp/mm? (note that this would be the resolution at 1:20 divided by 20).

More generalized, say resolution at f/10 stated at 1:20 is 71.43 lp/mm (50% of the diffraction limited). When reversed and used at f/10 stated at 20:1, would the resolution then be 3.5715 lp/mm (also 50% of the diffraction limit)?

e.g., for f = stated f/stop, m = magnification, R = resolution at m,


R = 1500 / f(1 + m)

Assuming r = resolution at 1/m


r = 1500/ f(1 + 1/m)

We can equate these two to eachother


1500 = R × f(1 + m)
1500 = r × f × (1 + 1/m)
R x f(1 + m) = r × f(1 + 1/m)
r = R × (1 + m) / (1 + 1/m)
r = R × (1 + m) / (m/m + 1/m)
r = R × (1 + m) / ([m + 1]/m)
r = R × (1 + m) × m / (1 + m)
r = R × m

Ergo, for any given stated f-stop, if the resolution at 1:10 is say 500 lp/mm, the resolution at 10:1 with the same stated f-stop would be 70 × 1/10 = 50 lp/mm. This makes sense based on what I've read; lenses optimized and very sharp at 1:10 make good macro lenses at 10:1.

Am I correct in my assumption here? Fundamentally, that a diffraction limited lens at stated f/10 at 1:20 is also diffraction limited at stated f/10 at 20:1 when reversed?...or that a lens limited to 50% the diffraction limit at 1:20 f/10 stated is limited to 50% the diffraction limit at 20:1 f/10 stated?

[Dan Fromm]

When you're not sure whether a calculation gave the right answer, run the experiment.

Visit Edmund Industrial Optics' site, look at their USAF 1951 targets on glass. You'll need one of them to test resolution at high magnification.

[Jack Dahlgren]

I've read many places that normal lenses for 35mm, optimized for say 1:20 front-forward, are optimized for 20:1 reversed. If a lens is diffraction limited at f/10 at 1:20, is it also diffraction limited when reversed at f/10 at 20:1?

e.g., if a symmetrical lens is diffraction limited at f/10 stated at 1:20, effective f-stop is f/10.5 and resolution is 1500/10.5 = 142.86 lp/mm. So, when reversed and used at f/10 stated at 20:1, the effective f-stop is f/210 (strictly speaking, a symmetrical lens doesn't have to be reversed for this example, but a asymmetrical one would need to be). Is the resolution then diffraction limited to 7.14 lp/mm? (note that this would be the resolution at 1:20 divided by 20).

More generalized, say resolution at f/10 stated at 1:20 is 71.43 lp/mm (50% of the diffraction limited). When reversed and used at f/10 stated at 20:1, would the resolution then be 3.5715 lp/mm (also 50% of the diffraction limit)?

e.g., for f = stated f/stop, m = magnification, R = resolution at m,


R = 1500 / f(1 + m)

Assuming r = resolution at 1/m


r = 1500/ f(1 + 1/m)

We can equate these two to eachother


1500 = R × f(1 + m)
1500 = r × f × (1 + 1/m)
R x f(1 + m) = r × f(1 + 1/m)
r = R × (1 + m) / (1 + 1/m)
r = R × (1 + m) / (m/m + 1/m)
r = R × (1 + m) / ([m + 1]/m)
r = R × (1 + m) × m / (1 + m)
r = R × m

Ergo, for any given stated f-stop, if the resolution at 1:10 is say 500 lp/mm, the resolution at 10:1 with the same stated f-stop would be 70 × 1/10 = 50 lp/mm. This makes sense based on what I've read; lenses optimized and very sharp at 1:10 make good macro lenses at 10:1.

Am I correct in my assumption here? Fundamentally, that a diffraction limited lens at stated f/10 at 1:20 is also diffraction limited at stated f/10 at 20:1 when reversed?...or that a lens limited to 50% the diffraction limit at 1:20 f/10 stated is limited to 50% the diffraction limit at 20:1 f/10 stated?

This all seems to hinge on your concept of "optimized". Most lenses generally work at almost all normal reproduction ratios losing perhaps a small fraction of their resolution when used outside the distance they are optimized for. For example you can use most 35mm macro lenses at infinity with perfectly fine results. Same with large format lenses, there are any number of process lenses that people have put to use for landscapes and other long subject distances.

The degradation of their performance from "optimum" is certainly NOT linear with reproduction ratio/subject distance etc. so you can't use those ratios in your formula the way you have.

As Dan said, testing is going to be your best way to understand what a particular lens does in a particular situation.

[ic-racer]

I lost you in the first paragraph. You need to define what you mean by "Diffraction Limited"

I use that term for slow lenses that decrease the resolution across the field the moment you start stopping down. In a "Diffraction Limited Lens" the limit is at the widest aperture.

As far as I am concerned, If a lens is "Diffraction Limited" it really has nothing to do with the aperture. It just means the spherical and chromatic and other aberrations are fully corrected when wide open. So when you stop down you gain no more resolution and just increase diffraction at the first click.

When you stop down ANY lens the "Limit" of the degree of acceptable diffraction is going to be USER DEFINED.

[Nathan Potter]

I have always assumed that reversing any lens does not appreciably change the optical performance in terms of resolution - it simply reverses the side of the lens where the finest detail occurs. Or put another way reversing just reverses the conjugate. This is probably not strictly true but as Dan says careful resolving power tests would need to be done to determine this. So I think your final assumption is essentially correct as long as the optimum design ratio of the lens is maintained.

Nate Potter, Austin TX.

[dh003i]

When you're not sure whether a calculation gave the right answer, run the experiment.

Visit Edmund Industrial Optics' site, look at their USAF 1951 targets on glass. You'll need one of them to test resolution at high magnification.

Yea, I'm certainly not sure this calculating gives the right answer. In fact, the derivation is correct, but is really merely tautological. It derives the consequences of what happens when a lens is diffraction-limited at a given stated f-stop at 1:x, assuming it is also diffraction limited therefore when reversed at x:1.

Sometime I'll think about the experiment on my Oly E3.

[dh003i]

This all seems to hinge on your concept of "optimized". Most lenses generally work at almost all normal reproduction ratios losing perhaps a small fraction of their resolution when used outside the distance they are optimized for. For example you can use most 35mm macro lenses at infinity with perfectly fine results. Same with large format lenses, there are any number of process lenses that people have put to use for landscapes and other long subject distances.

The degradation of their performance from "optimum" is certainly NOT linear with reproduction ratio/subject distance etc. so you can't use those ratios in your formula the way you have.

Maybe my notation was confusing, I'm not saying the degredation of performance from optimum is linear with reproduction ratio. What I was saying is that -- and I've also read this online from a poster, trying to find the source -- it seems like if a lens performs at the diffraction limit at 1:10, it would also perform at the diffraction limit when reversed and used at the same stated f-stop at 10:1...so the resolution when reversed and used at the reciprical magnification ratio would be "Resolution front forward @ 1:10 / 10".


As Dan said, testing is going to be your best way to understand what a particular lens does in a particular situation.

[dh003i]

I lost you in the first paragraph. You need to define what you mean by "Diffraction Limited"

I use that term for slow lenses that decrease the resolution across the field the moment you start stopping down. In a "Diffraction Limited Lens" the limit is at the widest aperture.

As far as I am concerned, If a lens is "Diffraction Limited" it really has nothing to do with the aperture. It just means the spherical and chromatic and other aberrations are fully corrected when wide open. So when you stop down you gain no more resolution and just increase diffraction at the first click.

I've seen the term used that way in many articles, it seems bizarre to me. But "diffraction limited lens" is a stupid way to say it to begin with, since all lenses (outside of possible ones with negative indexes) are limited by the diffraction limit and can't exceed it.

What I meant to say was "a perfect lens" that performs "at the diffraction limit". Just because the resolution of a lens decreases as you stop down doesn't mean it is performing at the diffraction limit...e..g., look at the resolution of the Kodak 203/7.7 lens at 0 degrees from axis (http://www.hevanet.com/cperez/testing.html) (scroll to bottom of page). Using 1600/N to determine max possible resolution and assuming that the data linked to is actually lp/mm (not lines/mm):

fstop : measured resolution : theoretical max resolution : % of diffraction limit
7.7 : 100 : 208 : 48%
11 : 120 : 145 : 83%
16 : 90 : 100 : 90%
22 : 60 : 73 : 82%
32 : 50 : 50 : 100%
45 : 30 : 36 : 83%

Starting at f/11 and above, it resolution decreases as you stop it down...some would call this "diffraction limited". But it certainly isn't performing at the maximum possible resolution (and oddly the % of the theoretical diffraction limit isn't always increasing as the lens is stopped down).

[Lynn Jones]

I've never seen a diffraction limited refracting optic, the only thing close to it is a Schmidt Camera with approaches theoretical perfection. When we designed Computar DL lenses, we were going to advetise them as diffraction limited and people in optical physics said that this was theoretically impossible, so we just called them DL.

Besides that the optical resolution is way higher than the film resolution, far beyond what we would like from film.

Lynn