A technical photography question: discrepancies between zoom lenses

I haven’t written about photography here before, but I have a technical issue and I thought this would be a good place to raise it…

I use two lenses with my DSLR: an 18-50mm zoom and a 55-200mm zoom, both Sigma. Before I went on holiday in June, I bought one lens to cover the same range – another Sigma, 18-200mm.

When I got home, I wanted to compare the new lens quality to my old lenses. I set it to 200mm and took a picture; then did the same with my 55-200mm.

The quality wasn’t an issue; but the two pictures had quite different fields of view – despite both being “200” mm. I estimated that at its full extent, the new lens was equivalent to c. 130mm on the older lens.

I wasn’t happy about this – having just forked out a couple of hundred quid, I had failed to duplicate the full range. I took the lens back to the shop, where we duplicated the test, and the salesman agreed that the field of view was significantly less than I had expected. He explained that this was because the 10-200mm lens was not a zoom but a “versatile” lens. This sounded like saleman’s flannel – surely 200mm should be 200mm? (He was good enough to refund my money, and I would recommend them for good service and prices.)

My brother was visiting this weekend, and he has a Nikon 18-200mm zoom, so we repeated the experiment – with exactly the same results. The image from the Nikon lens had a much wider field of view, equivalent to about 130mm on the Sigma.

Here’s the image from my original lens, set at 200mm:

DSC_8617

Here’s that from the Nikon 18-200mm, set to 200mm:

DSC_8618

Here are the two overlaid, the Sigma image resized (not a perfect fit):

DSC_8618 v 8617

And here are the outlines of the two, for comparison – the Nikon 18-200mm in red, the Sigma 55-200 in blue:

200 comparison

The metadata recorded by the camera says that both lenses were shooting at 200mm.

Clearly, 200mm is not always 200mm. I don’t know which lens is truer to 200mm: I don’t have access to a fixed 200mm lens.

Does anyone have an explanation for the difference between the lenses?

Any views appreciated!

(crossposted)

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15 thoughts on “A technical photography question: discrepancies between zoom lenses

  1. Gideon

    130mm x 1.6 is about 200mm – could there be some naming weirdness relating to lenses made for 1.6x crop cameras?

    Reply
    1. patrickhadfield Post author

      Possibly – that was my brother’s thought, as well – but if one lens was “200 for DSLR” and the other “200 for full frame”, would they both show 200 in the image metadata?

      Also, the Sigma 55-200mm clearly states “made for digital” on its box (yes, I keep the boxes…), which is not what I’d have expected in that case.

      Reply
  2. Jos

    I had a quick peek at the specs, and Sigma seem to be using proper focal lengths rather than “35 mm equivalent focal lenght assuming a certain crop factor”.

    For both the 18-200 f3.5-6.3 DC and the 50-200 f4-5.6 DC OS HSM (to pick two current models; the 55-200 is discontinued, I suspect) Sigma’s website lists the field of view as 7.1° at full zoom, with their SD camera format.

    I’d need diagrams to fully illustrate, but I currently suspect it’s because they are different designs, and you’re not comparing them at infinity.

    The focal length of the lens is defined when it’s focussed at infinity, and it is the distance from the rear principal plane to the camera’s sensor. As an aside: for telephoto lenses, the rear principal plane is very often outside the actual objective, somewhere in front of it (just think, your lens is about 10 cm long, the flange focal length for a Nikon mount is about 4.5 cm, but your lens has an effective focal length of 200 mm!).

    When you focus on something that’s not at infinity but much closer, say 3m, the effective focal length of your lens will change. It has to, otherwise you wouldn’t be in focus! Lens elements move around, the various cardinal points and planes shift.

    How things change depends on the design of the objective. I’ve quickly whipped up two dummy model objectives in optical modelling software. One has a length of 100 mm, the other of 70 mm, but they are both 200mm focal length objectives when focussed at infinity, consisting of three idealised lenses.

    When I focus them at 3m, their EFLs change to 177mm and 167mm respectively. That immediately translates to quite different fields-of-view.

    Reply
    1. patrickhadfield Post author

      Thanks for doing so much work! I appreciate it.

      At first glance, that makes sense, but I’ll need to think about it a but to fully understand.

      Reply
  3. Tom Nicholls

    200mm has got to produce the same field of view in all cases, by simple geometry:

    x(o)/x(i) = d/f

    where
    x(o) is the field of view (=the size of object that will be projected on the sensor)
    x(i) is the size of the image on the sensor
    f is the focal length
    d is the distance of the object from the lens

    f,d and x(i) are fixed – the same in all cases.
    So x(o) must also always be the same.

    Unless you walked closer to the bookcase in one instance :)

    Reply
    1. patrickhadfield Post author

      Thanks, Tom! Essentially I think you are saying that 200mm *ought* to be 200mm regardless – my initial gut reaction.

      I definitely didn’t move closer to the bookcase! ;)

      Reply
    2. patrickhadfield Post author

      For other’s who may have read Tom’s comment, he just posted this link via Twitter, including a diagram detailing the geometry…

      Reply
    3. Jos

      Yes, but no.

      200m is the focal length when focussed at infinity. The bookcase is at about 3m, and the focal length of the lenses can change differently when focussing, depending on the design. Different focal lengths giving different fields-of-view.

      Reply
      1. Tom Nicholls

        I take your point that complex lenses will behave slightly differently, but the specifications are highly devious if they can produce a discrepancy of 60% in the real world, otherwise the 200mm figure is meaningless. Who ever focuses their lens at infinity (apart from astronomers)?

        Also, I would question the quality of the optical design if it can produce what is effectively an optical aberration that size!

        Reply
        1. Jos

          Everybody who takes photos of mountains, the horizon, etcetera, focuses at infinity (ignoring hyperfocal etcetera).

          There’s nothing devious about it: if you want to capture the properties of a lens in a single number, you do it with for a well-controlled situation. Infinity-focus is the obvious choice.

          [Ah soddit, Firefox has crashed three times already and eaten my comment every time. In bullet points:]

          It’s not an aberration, unit focussing lenses like this isn’t generally sensible.

          Therefore, to focus you need to change the effective focal length (EFL).

          The relation between EFL and back focal length (BFL) (or more accurately flange focal length) depends very strongly on the design of the lens.

          The design of the lens depends strongly on a multitude of factors: zoom range, quality, price point, aperture size, etc.

          It doesn’t surprise me at all that an 18-200 at 200 mm differs significantly from a 55-200 at 200 mm, when both are focussed at 3m.

          Even the difference between two 18-200s from different manufacturers doesn’t really surprise me. Lens design is a game of compromises and design choices in a very big multi-dimensional space.

          So, not an aberration, but a consequence of design choice and overall lens specs.

          Reply
          1. Tom Nicholls

            Fair enough, you’re entirely right – I’d just not thought deeply enough about this stuff for years. Bit of a nasty shock to discover that your zoom lens doesn’t “zoom” though! I guess that’s part of what you pay for in price.

            Reply
            1. patrickhadfield Post author

              Thanks, Tom and Jos – very informative.

              I’ll give it a go with more distant objects when I next can – I’ll let you know!

              Reply
    1. Jos

      With interchangeable lenses, you can’t. You don’t know what sensor size the lens is going to be used with, so you can’t convert the focal length to a “35mm equivalent” (which typically means equivalent field-of-view).

      The best you can do is specify the actual focal length, which is a measurable physical property of a lens. Then, when you know the sensor size, you can do all the calculations & conversions you like.

      Reply
  4. Little Richardjohn

    I know I know. It’s exactly the same confusion that would have happened if you’d been able to mount medium format lenses on 35mm bodies – which never arose.
    But nevertheless, the standard specs now seem to avoid giving real or 35mm equivalents under any circumstances, just to be pedantic and annoying.

    Reply

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