Calculating Bellows Extension from Magnification Factors? Anyone?

Sparky · Feb 24, 2013

It's embarrassing to ask such a basic question for me but.. I just spent a good amount of time wading through the 'net trying to find what I'm looking for but can't seem to locate it (here either!) - Does ANYONE know a simple formula for deriving the effective focal length (bellows draw) from magnification and nominal focal length ALONE?

So here's the deal - Let's say I'm trying to make a photograph of an object I know I need a magnification of 10x on in terms of what I want the aerial image height (fancy talk for image size) on the negative to be. One of the lenses I have at my disposal is a 105mm componon - but I think that's going to be way too long. Basic rule of thumb tells me that at 1:1, the focal length will be 210mm, and at 2:1 twice that, it will be 420mm, at 4:1, 840mm, 8:1 it will be 1680mm... and 10:1 would be SOMEWHERE in the region of 2400mm (7.5 feet) I'm guessing. So in that case I would try to find myself a 50mm lens to keep the bellows extension around 1.2m since it's more convenient...

So fine - I can work through this manually as above... but I have a dozens of such scenarios to work out so I'm wondering if there's a good simple formula that can help me automate my shot planning... (?)

Thanks if anyone can help...

cliveh · Feb 24, 2013

Why would you wish to do this?

Sparky · Feb 24, 2013

making photographs of small objects...

jeffreyg · Feb 24, 2013

Bellows extensions when using various lenses may require exposure compensation. There is a formula for figuring it out (forgot the formula) but when I started with LF, I sat down with a calculator and figured it out from F stops to length and marked a small retractable ruler that I keep with my light meter. I just measure the distance from the lensboard to the film plane and see what increase is needed. You should be able to see how the image will appear on the ground glass. Lens selection will be governed by the maximum length of your bellows. How small are the objects?

http://www.jeffreyglasser.com/

polyglot · Feb 24, 2013

In direct answer to your question, you can almost certainly find the formula on the front of the LFPF homepage or with a second of googling.

You'll find that most lenses have huge aberrations when focused that close. Getting to 1x with good quality requires a macro lens and even then it's going to start looking bad probably by 4x. At 10x, you're going to have mush from any lens not designed for use at that range, i.e. microscope objective lenses. If you're using normal lenses for very high magnification, you can somewhat avoid this problem by using the lenses reversed because they are generally well-corrected for the rear image plane being very close and the front image plane being further away. If you want a 10x shot, set it up like a 0.1x shot but swap the film and subject locations.

Don't forget also that diffraction gets worse: a 2x bellows extension to reach 1x magnification will double the effective focal length and add two stops to your effective aperture. Go to 5x or 10x and you'll find that diffraction means you need to be shooting at much larger apertures than you're used to so the DOF will be practically nil.

If you want to do ultra-macro and despite this being APUG, I strongly suggest looking into the newer digital techniques like focus-stacking. It also helps that there are lenses available for 35mm that are specifically designed to reach about 6x magnification. Right tool(s) for the job and all that.

Dan Fromm · Feb 24, 2013

The lens' focal length is independent of its position between film and subject.

Extension can be thought as starting from two different positions: the film plane and the lens' infinity position.

The distance from the film plane to the lens' rear node when the lens is focused at infinity is the lens' focal length.

The distance from the film plane to the lens' rear node when magnification (m) > 0 (m = 0 means the subject is really, really far away) is f * (1 + m). By subtraction, extension from the infinity position is f * m. f is the lens focal length.

For lenses commonly used on LF cameras (not retrofocus, not telephoto) both nodes (front and rear) are close to the diaphragm.

Sparky · Feb 24, 2013

well thanks for the responses but I dare say few people have read the question. I'm really not concerned with exposure compensation or subject/object distances. Those (subject/object distances cancel out to become magnification in certain formulae) - but I've been googling for some time and can't find the correct formulae - though I know they exist since I've used them before but it must be 15 years since I have.

I wouldn't really call it 'ultra macro' or anything of the sort. It's just regular 'macro' photography. I figure a micro nikkor would probably work the best... maybe i'll just stick with one of those for everything... but I was just hoping there was a quick formula i could use to derive the extension from the F.L. and the magnification - but I guess it's not too well known...

Sparky · Feb 24, 2013

Here's an example of a page where someone's comparing enlarger vs macro lenses... so I think it should work just fine... I've been doing LOTS of 1:1 work on 4x5 with old sironars etc and the results have been quite outstanding (40x50 prints with TONS of detail)... I would encourage others to try...

http://savazzi.freehostia.com/photography/enlargerlensespm.htm

Prof_Pixel · Feb 24, 2013

The Kodak Professional Photoguide says: Lens-to-film Distance = (Magnification + 1) X Focal Length and Effective Aperture = f-number X (Magnification + 1)

Sparky · Feb 24, 2013

Prof_Pixel said:
The Kodak Professional Photoguide says: Lens-to-film Distance = (Magnification + 1) X Focal Length and Effective Aperture = f-number X (Magnification + 1)

hmmm... okay that sounds more fruitful... maybe I should look it up - I think i even have one of those somewhere! only question - what do you mean by 'and' as in FL and eff. aperture?

I'm pretty sure you can cancel out the aperture somehow - i.e. - it really shouldn't come into play (?) except where exposure compensation is needed I think?

Prof_Pixel · Feb 24, 2013

There are two different equations:

Lens-to-film Distance = (Magnification + 1) X Focal Length

and

Effective Aperture = f-number X (Magnification + 1)

Sparky · Feb 24, 2013

ahhh okay. so for a 55mm lens in the case of a micro nikkor if i chose to go that way - i'd be looking at (10 +1)x55mm = 605mm

and in the case of an 80mm rodagon:

(10+1)x80mm= 880mm

wow that was easy cheesy.

Although what confuses me about that is - I always understood that ever doubling of a bellows length implied a doubling of image size (and quadrupling of exposure of course)... but in the case of a 55mm lens - 1:1 gives you 110mm and therefore 2:1 gives you 220mm 4:1 is 440mm etc... which doesn't seem to jive with the above formula!

which is wrong here? (not meaning to complicate things - I'm thankful for the formula though)

Prof_Pixel · Feb 24, 2013

To reproduce something at full size (Magnification = 1), the lens-to-film distance would be ( 1 + 1) X focal-length which is 2 X focal-length (known as double extension). For a 55mm lens, this would be 110mm

To reproduce something at twice full size (Magnification = 2, the lens-to-film distance would be ( 2 + 1) X focal length which is 3 X focal-length. For a 55mm lens, this would be 165mm

Prof_Pixel · Feb 24, 2013

Sparky said:
Although what confuses me about that is - I always understood that ever doubling of a bellows length implied a doubling of image size (and quadrupling of exposure of course)... but in the case of a 55mm lens - 1:1 gives you 110mm and therefore 2:1 gives you 220mm 4:1 is 440mm etc... which doesn't seem to jive with the above formula!

Doubling the focal-length only applies to a magnification of 1

Sparky · Feb 24, 2013

Prof_Pixel said:
To reproduce something at full size (Magnification = 1), the lens-to-film distance would be ( 1 + 1) X focal-length which is 2 X focal-length (known as double extension). For a 55mm lens, this would be 110mm

To reproduce something at twice full size (Magnification = 2, the lens-to-film distance would be ( 2 + 1) X focal length which is 3 X focal-length. For a 55mm lens, this would be 165mm

Yep - well that makes good sense... thanks professor...

Dan Fromm · Feb 25, 2013

Sparky said:
well thanks for the responses but I dare say few people have read the question. I'm really not concerned with exposure compensation or subject/object distances. Those (subject/object distances cancel out to become magnification in certain formulae) - but I've been googling for some time and can't find the correct formulae - though I know they exist since I've used them before but it must be 15 years since I have.

I wouldn't really call it 'ultra macro' or anything of the sort. It's just regular 'macro' photography. I figure a micro nikkor would probably work the best... maybe i'll just stick with one of those for everything... but I was just hoping there was a quick formula i could use to derive the extension from the F.L. and the magnification - but I guess it's not too well known...

Knothead, see post #6 in this thread.

What format are you shooting? I ask because the MicroNikkors sold for 35 mm cameras don't cover 4x5 at magnifications much below 4:1.

Oh, and by the way, if you're going to use a MicroNikkor at magnifications > 1:1, it should be reversed. My tests of my 55/2.8 MicroNikkor AIS found that it is best at f/4 above 1:1 and that image quality rapidly vanishes as it is stopped down farther.

You and most of the participants in this thread should read a book. Two books, in fact, and the last time I looked the usual places (abebooks.com, alibris.com, amazon.com, ...) showed copies of both at reasonable prices.

Lefkowitz, Lester. 1979. The Manual of Close-Up Photography. Amphoto. Garden City, NY. 272 pp. ISBN 0-8174-2456-3 (hardbound) and 0-8174-2130-0 (softbound).

A thorough discussion of getting the magnification, lighting, and exposure. Especially good on working above 1:1. Extensive bibliography.

Gibson, H. Lou. Close-Up Photography and Photomacrography. 1970. Publication N-16. Eastman Kodak Co. Rochester, NY. 98+95+6 pp. The two sections were published separately as Kodak Publications N-12A and N-12B respectively. Republished in 1977 with changes and without the 6 page analytic supplement, which was published separately as Kodak Publication N-15. 1977 edition is ISBN 0-87985-206-2.

Gibson is very strong on lighting, exposure, and on what can and cannot be accomplished. His books, although relatively weak on getting the magnification with lenses made for modern SLR cameras, provide a very useful foundation for thinking about working at magnifications above 1:10 and especially above 1:1. Extensive bibliography.

Prof_Pixel · Feb 25, 2013

Dan Fromm said:
Knothead, see post #6 in this thread.

Yup, you were first with the correct answer. Congratulations. However, you've got to admit that the answer was well hidden in a lot of extra words.

Dan Fromm · Feb 25, 2013

P_P, I won't accept responsibility for the OP's inability to read. I hope he/she/it gets the books, reads them, and learns to think for himself/herself/itself.

Prof_Pixel · Feb 25, 2013

Dan Fromm said:
I won't accept responsibility for the OP's inability to read.

If a person asking for help doesn't understand our reply, we really haven't helped that person, have we?

I thought the object here was to help people.

cliveh · Feb 25, 2013

Sparky said:
making photographs of small objects...

Why don't you just meter at the focal plane?

Mainecoonmaniac · Feb 25, 2013

Ralph Lambrecht author of Way Beyond Monochrome has a generous heart and has posted a templates online. There's one for calculating bellows extension and magnification. It's highly accurate and It's simple. Just print out the template, place the square target on your subject and measure fstop compensation with a ruler on the ground glass. I'm not good at math, so I use the template.

http://www.waybeyondmonochrome.com/WBM2/Library_files/TemplatesEd2.pdf

I also recommend buying the book. It's helped me out a bunch. Cheers!

Sparky · Feb 25, 2013

cliveh said:
Why don't you just meter at the focal plane?

why? when i can easily calculate the exposure based on the bellows draw (i always do it that way) - new F.L. squared over nominal FL squared...

cliveh · Feb 25, 2013

Sparky said:
why? when i can easily calculate the exposure based on the bellows draw (i always do it that way) - new F.L. squared over nominal FL squared...

But is it not more likely that you could make an error in your calculations as opposed to reading the luminance at the focal plane? Or even do this to check you are correct?

Sparky · Feb 25, 2013

Dan Fromm said:
Knothead, see post #6 in this thread.

Thanks - if you're referring to polyglot's post - I didn't see what I was looking for there. If you're referring to your OWN post - it wasn't at all clear to me that you were understanding what I was looking for. But only after seeing PP's post on the subject with the formulae I recognize the fxM constant... so - well.. thanks

Dan Fromm said:
What format are you shooting? I ask because the MicroNikkors sold for 35 mm cameras don't cover 4x5 at magnifications much below 4:1.

4x5. Should cover it just fine. I see no problems here.

Dan Fromm said:
Oh, and by the way, if you're going to use a MicroNikkor at magnifications > 1:1, it should be reversed. My tests of my 55/2.8 MicroNikkor AIS found that it is best at f/4 above 1:1 and that image quality rapidly vanishes as it is stopped down farther.

yes of course. I may be an idiot but I'm no fool! I've written and taught LOTS on technical photography over the years...

Personally, and through the findings of others (web pages with experiments and the like) I'm not so sure the practice holds up to the theory. I would go to a Zeiss Luminar directly ordinarily but it looks like others have found the Micro Nikkor superior for this application. I've also had ASTOUNDING successes with my own 1960s 180mm Sironar at 1:1 and beyond (as mentioned - enough for 40x50 prints - I get asked frequently if I've shot on 8x10 film! so that's good right?)

Dan Fromm said:
You and most of the participants in this thread should read a book. Two books, in fact, and the last time I looked the usual places (abebooks.com, alibris.com, amazon.com, ...) showed copies of both at reasonable prices.

Lefkowitz, Lester. 1979. The Manual of Close-Up Photography. Amphoto. Garden City, NY. 272 pp. ISBN 0-8174-2456-3 (hardbound) and 0-8174-2130-0 (softbound).

A thorough discussion of getting the magnification, lighting, and exposure. Especially good on working above 1:1. Extensive bibliography.

Gibson, H. Lou. Close-Up Photography and Photomacrography. 1970. Publication N-16. Eastman Kodak Co. Rochester, NY. 98+95+6 pp. The two sections were published separately as Kodak Publications N-12A and N-12B respectively. Republished in 1977 with changes and without the 6 page analytic supplement, which was published separately as Kodak Publication N-15. 1977 edition is ISBN 0-87985-206-2.

Gibson is very strong on lighting, exposure, and on what can and cannot be accomplished. His books, although relatively weak on getting the magnification with lenses made for modern SLR cameras, provide a very useful foundation for thinking about working at magnifications above 1:10 and especially above 1:1. Extensive bibliography.

Thanks for the suggestions - I've probably read far too many books on the subject as it is!! But I just don't have anything handy right now (they're all in storage) - Langford and LP Clerc are my go-to enclyclopaediae normally.

Sparky · Feb 25, 2013

cliveh said:
But is it not more likely that you could make an error in your calculations as opposed to reading the luminance at the focal plane? Or even do this to check you are correct?

not really. that's why you do exposure tests. Shoot film and see where you're at. with such bellows extensions it's pretty easy to be close to dead on in my experience (you can be out by several mm and it really doesn't make a difference). I'm far more likely to have variations in strobe power or development etc than be off in my measuring...

Calculating Bellows Extension from Magnification Factors? Anyone?

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