Why do asymmetric lenses have less DOF in front-forward position?

[dh003i]

Looking at Appendix B of The Manual of Close-Up Photography by Lester Lefkowitz, he provides the following equations for the effective aperture (and hence depth of field) of symmetric, asymmetric (front-forward) and asymmetric (reversed) lenses:

m = magnification
P = pupillary magnification factor = exit pupil diameter / entrance pupil diameter

Symmetric lens:
Effective f-stop = Stated f-stop × (m + 1)

Asymmetrical lens (front forward):
Effective f-stop = Stated f-stop × (m/P + 1)

Asymmetrical lens (reversed):
Effective f-stop = Stated f-stop × (1 + P × m) / P

Assuming a stated f-stop of f/4 and a magnification of 3×, the effective f-stops are:

Symmetric lens effective f-stop = 4 × (3 + 1) = f/16

Asymmetrical lenses with pupillary magnification factor of 0.8:
Asymmetrical lens (front forward) effective f-stop = 4 × (3/0.8 + 1) = f/19
Asymmetrical lens (reversed) effective f-stop = 4 × (1 + 0.8 × 3) / 0.8 = f/17

Why is this? I would expect that the effective f-stop an asymmetric lens would be larger when reversed than when front-forward, as the smaller exit-pupil is facing the subject. Also, why is the effective f-stop for the front-forward asymmetrical lens different from that for the symmetric lens?

[Emmanuel BIGLER]

Hello from France !

Congratulations far having found one of the rare references printed on paper dealing with the effective f-number of asymmetric lenses in close-up photography !
The other reference on the web is the Lens Tutorial by David Jacobson
http://photo.net/photo/optics/lensTutorial
But Jacobson only gives the effective f-number when the lens is used in its "normal" (forward, not reversed) position.

Lefkowitz's book is among the best books on close-up photography. I have bought one copy after reading the recommendation posted here by a friend living in New Jersey and I really recommend this book without restriction.

I have re-computed the formulae from scratch on my side and I can testify that those formulae either in Lefkowitz's book or Jacobson's tutorial are the same as mine. This does not prove that we are correct all three, but at least I can feel comfortable about it
Those formulae are somewhat diabolic because it is extremely easy to be confused and make mistakes when typesetting them... the derivation of the effective f-number when the lens is reversed, although not "rocket science", is really tricky...

Now to answer your question :
Why is this? I would expect that the effective f-stop an asymmetric lens would be larger when reversed than when front-forward, as the smaller exit-pupil is facing the subject. Also, why is the effective f-stop for the front-forward asymmetrical lens different from that for the symmetric lens?

First, we should identify what kind of lenses have a pupillar magnification ratio P (following Lefkowitz's convention) of 0.8.
"P<1" : this is a kind of a telephoto lens. The other case, where P is greater than unity is the case of retrofocus lenses.

P = 0.8 means that the exit pupil is smaller than the entrance pupil.
The f-number is always defined with respect to the entrance pupil. This property is really not easy to explain, but can be derived as well.

When used forward, the entrance pupil of a "P=0.8" lens, a telephoto lens, is bigger than when used reversed. The focal length does not change when reversing the lens : this is an important point !!
Hence the f-number in the infinity-focus position is greater for a telephoto when used forward (infinity to focal point F') than when used reversed (infinity to the reverse focal point F).

BUT....
A telephoto lens is designed to be used forward for far distant objects. It is not designed to be used at 1:1 ratio, not even at 1:3.
When reversed, used at 3:1, the image quality will not be that good and at 1:1, either side, it will be terrible.

Hence, the general formulae explain, for sure, what really happens, but in strange situations that actually nobody uses when looking for the best possible image quality

Now regarding the situation of a "P>1" lens.
This is a retrofocus lens. To the best of my knowledge, no such lens exists for the large format. Even the most recent "digital" wide angle lenses for small precision view cameras have a P-factor very close to unity. Not at all like retrofocus lenses used for reflex cameras in for 35-mm or medium format cameras.

For example, the classical f/4 - 50mm Zeiss Distagon, the first version with no floating elements, has a P-factor equal to 1.8.
If you intend to use it reversed, in the reversed infinity-focus position you get, in theory, a 50 mm lens with a maximum aperture of 4/1.8 = 2.2 .... but forget it in infinity-focus-reversed, since the reversed focal point F lies somewhere within the glass... However since the lens can deliver good images for far distant objects, and in the close-up range down to its minimum focusing distance as desiged by Zeiss of 0.5 metre, i.e. an image magnification of about 1:10, may be you could use it reversed. But only for extreme close-up, image magnification 10:1 or above, and apply Lefkowitz's formulae for reversed lens, f/N=4, P=1.8, m = 10 or more.

[Dan Fromm]

Hmm. The formulae for calculating effective aperture for lenses with pupillary magnification <> 1 have been known to Nikon for quite some time. The PB-4 bellows I bought in 1970 came with a set of charts showing exposure adjustment given magnification for quite a number -- sorry, I can't specify them now, the PB-4 is at home and I'm in the office -- of F-mount Nikkors. The curves for the 24/2.8, a retrofocus lens, are, um, scary.

Emmanuel, if you'll look at the spreadsheet I use for designing macro flash rigs -- I sent it to you some time ago -- you'll see that it takes account of pupillary magnification.

[dh003i]

Hi Emmanuel, thank you very much for your response...

Looking at for example my Minolta Rokkor 50/1.4 lens, which has a larger exit diameter than entrance diameter, now I understand. The exit diameter is ~1.0625 in, while the entrance diameter is ~0.875 in, for a pupillary magnification factor of ~1.21.

Looking at it (i.e., from the "film perspective"), the iris at the same marked f-stop is larger when the lens is front-forward, hence I expect a smaller effective f-stop in the front-forward orientation; looking at it in the reversed orientation, the iris is smaller, hence I expect a larger effective f-stop in the reversed orientation. This is born out by the math at say 20x at fr/4:

Effective f-stop at f/4 marked, Front-forward = 4 × (20/1.21 + 1) = f/70.1
Effective f-stop at f/4 marked, Reversed = 4 × (1 + 1.21 × 20) / 1.21 = f/83.3

Hence, there is a larger effective f-stop (smaller effective aperture) at the same marked f-stop when the lens is reversed (and when the iris looks smaller from the film pov). This makes sense.

But why does the front-forward asymmetrical lens have any difference from the symmetrical lens at the same marked f-stop and magnification?

[Kirk Gittings]

Sometimes I am truly amazed at the knowledge base of some of the members here.....

[dh003i]

In relation to the topic of this thread, and using the formulas in Lefkowitz' book and elsewhere, I've made a spreadsheet determining effective apertures at relative (marked) apertures, maximum resolution possible (1500/f) at those effective apertures, minimum circles of confusion possible, maximum enlargement for final print, EIF, and Total DoF.

Cells with Blue text are cells that are input cells and can be changed depending on your specifications.

I've attached the spreadsheet in MS Excel and OpenOffice.org Calc format. I created the spreadsheet in OO.org, so hope it comes out ok for those of you who only use Excel (saved an Excel version of the file).

Attachment 44574

[Martin Miksch]

Sometimes I am truly amazed at the knowledge base of some of the members here.....

We could send a copy of this thread to Stockholm^^

[Dan Fromm]

Sometimes I am truly amazed at the knowledge base of some of the members here.....

Um, Kirk, you can find Emmanuel's campaign biography here http://www.galerie-photo.com/film-co...esolution.html. If you can't read it, run it through Google Translate. Not to put anyone down, but in some respects he's far above most of us.