Calculating magnification, etc., using extension tubes on a macro lens?

[larry h.]

<p>Sorry in advance for the length of this question. The issues are harder than they seem at first glance.</p>

<p>On Thursday, I posted a photo of a flower called <em>Diamorpha smallii</em> that is between 5 - 6 mm from tip-to-tip, taken with a 100mm/2.8L IS lens plus 65mm of extension tubes.</p>

<p>Just before I left the site, I suddenly thought to ask the ranger accompanying me if she had a metric scale of any kind with her -- Leatherman tools are great! By photographing that, I calculated that I was working at about 1.67x (13.5mm field across a 22.5mm -- long side -- sensor). I have never worked beyond 1:1 before, nor really done much macro work at all.</p>

<p>My questions are:<br>

1) I tried to figure out ahead of time what the maximum magnification was that I could achieve, but couldn't. How would I do that?<br>

2) How do I calculate the **actual** working f/stop of a floating element macro lens, especially when working with additional extension?<br>

3) What is the best way to get beyond 1:1 (1.0x), other than the obvious 65mm 1x - 5x lens, which just ain't going to happen for me.</p>

<p>My crack at answering my own questions:<br>

1) In the old days, to reach 1.0x with a 100mm macro lens, you needed 100mm of extension. But now, with floating optical systems, you need to know what the **actual** focal length of this lens is at 1.0x, something I could not find after about an hour searching photo.net and the internet. Anyone know? After the fact, I calculated that the **actual** focal length of the 100mm/2.8L at 1.0x was in fact 100mm -- which I frankly don't believe. (I'm actually pretty decent at math.)<br>

2) Again in the old days, a lens at 1.0x was actually working at an aperture 2.0 stops smaller than reported (i.e., f/11 was actually f/22). I've heard that Nikon bodies automatically account for this, but don't know for sure. Does that still hold true with floating focus macro lenses? How about with further magnification discussed below? This question is of course important when trying to balance depth-of-field with diffraction.<br>

3) Options are a) extension tubes, b) teleconverters, c) screw-in high quality diopters (Canon or Nikon), and d) reversing another lens in front of the macro.</p>

<p>But each of these introduces problems. In reverse order:<br>

d) This is just plain too cumbersome. It also raises issues with questions #1 & #2, quality issues, magnification issues (I’d need to attach a 200mm lens in front to **limit** mag to 1.5x), optimizing f/stop on the front lens, etc.<br>

c) I think this option would have been the best except that I’ve heard that the diopters are designed to create a flat field of focus from lenses (like a 50mm/1.4) that normally don’t have one. Because macro lenses are designed inherently for a flat field, the diopters overcompensate for this problem.<br>

b) Teleconverters (1.4x) immediately rob one stop of light, add glass that can cause optical degradation, in the case of the Canon requires a short extension tube to even fit (and Canon presumably designed the lens not to be compatible with teleconverters for a reason), and in the case of the Kenko Pro or Tamron SP TCs, don’t even try to use autofocus to chase butterflies (although not really pertinent to this question).<br>

a) Extension tubes are also cumbersome when trying to get just the right magnification (admittedly easier with a wide-focus-range macro lens than with conventional lenses). I have a no-name set (not even Kenko) with 13mm, 21mm and 31mm tubes. On some lenses, I am limited to using just one to maintain electronic compatibility. On the 100L, using all three at once seemed to work, except for when I did not tighten EVERYTHING down (which also could have been disastrous). Same as d), I am not sure how to calculate Qs #1 & #2.</p>

<p>Again, sorry for the length of this post. I guess I get anal about explaining everything I’ve considered. Thanks a million for reading and for any help you can offer.<br>

Larry</p>

[zml]

<p>For calculations, a good start would be the instruction booklet that came with your macro lens/tubes and, say, among thousands on the web, <a href="http://www.cambridgeincolour.com/tutorials/macro-extension-tubes-closeup.htm">here</a>. There also are several photography books (macro, LF shooting) which cover "photographer's math."</p>

<p>Oh, can't help it: in the old times almost all serious photographers carried some sort of a tape measure for use with their MF/LF/GF (gigantic format...) rigs sans range finders :-)</p>

 

[scott_ferris]

<p>A workable rule of thumb is that at 1:1 the working distance is twice the focal length. So for your Canon 100mm IS macro, at 1:1 it has a working distance of 146mm, so focal length is approximately 73mm.</p>

<p> Alternatively you can use a truer formula, the focus distance, the distance from sensor to subject, is four times focal length at 1:1. </p>

[scott_ferris]

<p>Sorry, to finish off the second section, focus distance at 1:1 with the Canon 100mm IS Macro is 300mm, therefore 300/4 = 75, so the focal length at 1:1 is 75mm.</p>

[scott_ferris]

<p><a href="http://www.cambridgeincolour.com/tutorials/macro-lenses.htm">This link</a> is a good one and gives some equations and calculators.</p>

[bobatkins]

<blockquote>

<p>A workable rule of thumb is that at 1:1 the working distance is twice the focal length. So for your Canon 100mm IS macro, at 1:1 it has a working distance of 146mm, so focal length is approximately 73mm.<br>

Alternatively you can use a truer formula, the focus distance, the distance from sensor to subject, is four times focal length at 1:1.</p>

 

</blockquote>

<p>Both good rules of thumb but they assume the thin lens approximation, i.e replacing the actual lens with a thin single element lens of the same focal length. In the real case you have to know where the cardinal points are within a complex lens structure (principle points, nodal points etc). The distance from subject to sensor at 1:1 is 4x the focal length plus the separation of the nodal points. In many cases that's not a trivial correction</p>

<p>All of these things are actually much easier to MEASURE than calculate. For example the f-stop can be measured by taking an exposure reading from a uniform target with the lens set to infinity. The target won't be in focus, but that's OK. You might want to stop down from wide open to eliminate vignetting effects, or use a spot meter. Then you refocus, add extension etc. etc. and take another reading. The difference is your light less due to any effects from extension and floating elements.</p>

<p>Measuring magnification is easy. Just take a picture of a ruler.</p>

<p>In general close focusing zooms are much more likely to change focal length on focusing than are primes. I don't know that the 100mm macro stays at 100mm all the way through the focusing range, but I wouldn't be amazed if it was pretty close to that. Floating elements do not necessarily indicate a focal length change.</p>

[larry h.]

<p>"Oh, can't help it: in the old times almost all serious photographers carried some sort of a tape measure for use with their MF/LF/GF (gigantic format...) rigs sans range finders :-)"</p>

<p>Michael: Thanks! I deserved that! Actually, the mm scale was sitting on my desk but never made it to the camera bag because I was trying to sneak out of the house without waking up my wife. ;-) Also, thanks for the link. I saw that during my Google search but skipped it. Considering your memory of the 'old times', you might recall the days when the word 'Cambridge' related to photography connoted things like 650-1300mm f/16 lenses and spider's-eye filters advertised in the back of Pop & Mod Photo mags. It turns out that the site's decent, although it is at least misleading if not downright wrong at points, such as when it states that a lens's focal length increases when it is extended farther from the sensor. Finally, both the lens and the tubes were bought used with no manual. In the case of the no-name tubes, if they even came with instructions, I wouldn't have been able to read them. I WILL give a mea culpa for not looking up the lens manual online, but after just looking at it, the magnification it suggests for the 25mm tube does not jibe with what I measured for the 65mm of extension I used.</p>

<p>Scott: Thanks. Now that you mentioned it, I think I had once heard them but completely forgot those rules of thumb. They seem to make some pretty decent sense in this case.</p>

<p>Bob: I was hoping you'd chime in. Especially the part about these things being easier to measure than calculate. I've got a BS in engineering, have taught high school honors physics and astronomy classes and have always been a physics geek in general, but I'll always happily defer to someone with a PhD in optics. I'll admit you lost me about cardinal points, principle points and nodal points. But now maybe I'll force myself to read and try to comprehend your online technical articles about lenses. ;-) Thanks as always.</p>