Equivalent crop sensor lenses

Discussion in 'Digital Photography' started by Peabody, Dec 16, 2009.

  1. Peabody

    Peabody Guest

    Every time I think I understand this, another thought experiment
    comes up, and I realize I may not.

    So lets say you have a full-frame 35mm DSLR camera (D700, or
    whatever) with a fixed 50mm lens, and you take a landscape picture.

    Now you move a 1.5X crop-sensor camera (D300) into the same place,
    and you want to take a picture with that camera which you want to
    have exactly the same field of view as the previous picture - it
    shows exactly the same scene.

    If the lens on the smaller camera was designed for that size camera
    (it's a "DX" lens), what focal length is it?

    Does it make any difference that it's a DX lens - would a full-frame
    lens produce the same picture in the smaller camera as the DX lens?

    My guesses are: To produce the same field of view, the DX lens on
    the smaller camera would need to be 33.33mm. And it doesn't make
    any difference on the crop-sensor camera whether it's a DX lens or
    an "FX" lens, so long as they are both 33.33mm.
    Peabody, Dec 16, 2009
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  2. Peabody

    Ray Fischer Guest

    50mm / 1.5x = 33mm
    Lenses for dSLRs are almost universally specified in 35mm equivalent
    focal length.
    Ray Fischer, Dec 17, 2009
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  3. Peabody

    Paul Furman Guest

    Yep. It's exactly like cropping (with the pixels jammed in the smaller
    space). The DX designation means you'd have dark corners on full frame
    because it's only designed to accommodate the smaller cropped view.

    The other result is less depth of field, a narrower focus range for the
    same lens when it's image finally ends up on a print of the same size.
    Cropping obviously doesn't change the absolute DOF but when you print
    the same size as the uncropped version it does. That is confusing and
    contradictory because you normally would use a wider lens to get the
    same view and then the goalposts have moved and you get *more* depth of
    field for the same view with a smaller sensor.

    Paul Furman

    all google groups messages filtered due to spam
    Paul Furman, Dec 17, 2009
  4. Agreed. However, if the full-frame (FX) camera had an f/4 lens used at
    f/4, what aperture lens would be required:

    - for the same depth-of-field
    - for the same light gathering - i.e. same exposure at same ISO?

    David J Taylor, Dec 17, 2009
  5. Peabody

    Martin Brown Guest

    However, it is quite likely to be marked as 50mm DX :(
    Which is confusing for anyone who uses other formats than 35mm where the
    lens focal lengths are specified correctly in real millimetres. This DX
    lens specified in "equivalent 35mm full frame" effective focal length
    serves only to confuse people and treats 35mm users like morons.

    For every other photographic film format the lens focal length is
    specified in real units of length. It was a terrible mistake to scale
    DSLR lenses to notional equivalent focal lengths by sensor size when a
    convention already existed for other film formats.

    Telling people that on the smaller DX format the camera gives a field of
    view 1.4x or 1.5x smaller for the same focal length lens makes it a lot
    clearer. Just like using a teleconverter on a full frame camera.
    Putting the DX lens on the full frame camera will show significant
    vignetting but vice versa the FOV will be fine. In fact the FX lens
    designed for full 35mm frame illumination and cropped to the smaller DX
    sensor size might have appreciably less vignetting at wide apertures
    than the physically smaller DX lens. But it may have other internal
    reflection problems when facing a CCD though so it is worth experimenting.

    The 1.5x factor makes fisheye a lot harder to do on a DSLR a 16mm FX
    full frame fish eye lens is barely wider than the wide end of standard
    DX zoom lens. I eventually got an 8mm Sigma for this task.

    Martin Brown
    Martin Brown, Dec 17, 2009
  6. Peabody

    Ofnuts Guest

    Of course not. Lenses for DSLRs are always specified in absolute focal
    length. The Canon 300mm f/4 is a real 300mm (that gives the same field
    as a 480mm on the APS-C bodies).

    On the P&S, however, specs (especially the ones displayed in the store)
    are usually 35mm equivalent (because it gives bigger numbers) and the
    bridge camera sporting a 28-420mm zoom has actully got a 5-72mm lens.
    Ofnuts, Dec 17, 2009
  7. Ah! So you've never actually ever held a DSLR! That explains a lot!
    Chris Malcolm, Dec 17, 2009
  8. Peabody

    Chris H Guest

    What do you mean?

    I am just now buying the Nikon 35mm F1.8 DX and according to Nikon it
    gives the same picture on a DX camera as a 52.5 mm lens on a 35mm film
    camera or FX DSLR)

    So Ray is correct. Even the DX lenses are specified as 35mm/FX lenses.

    The point is if ALL lenses use the same system you know where you stand.
    The change occurs when you fit it to a camera body. There are AFAIK
    various sizes of sensor and 1.2 to 1.6 (?) as well as FX.

    As in the future FX is likely to be the standard and the DX will
    disappear over the next decade (as new products and the old ones will be
    discontented even if people use them for the next 20 years) we will all
    forget this temporary DX "blip"

    Just as 8 track cartridges, Cassette tapes, Vinyl LP's, flash bulbs,
    glass plates, dot matrix printers, 14" CRT computer monitors, all came
    and went.
    Chris H, Dec 17, 2009
  9. Peabody

    True Info Guest

    They are not given in 35mm equivalents for P&S cameras as any kind of
    marketing ploy. I.e. "because it gives bigger numbers". They are stated
    that way in store/advert/review-site specifications to give people an idea
    of how that camera's FOV range will perform compared to all cameras and
    lenses that have come before. Most people who are buying such cameras are
    well aware of this. I know what kind of scenes are best shot in 28mm, and I
    know I need 200mm to 300mm and more for much of wildlife photography. I
    welcome when they show the 35mm equivalent in the advertised specs. All of
    my P&S cameras list the true focal-lengths on the lens barrels. As well as
    in the manual's specifications. The 35mm equivalent are listed in
    fine-print in parentheses in the manuals, and appear nowhere on the
    lens-barrels or cameras themselves. They are not trying to artificially
    inflate focal-length numbers or they'd be sure to do so in all aspects of
    information presented with the camera. The 35mm equivalents are provided as
    a nice courtesy feature for those that already know about cameras and
    lenses to make their educated and experienced buying decisions. To someone
    who has never held a camera before, a listing of 28-420mm will mean
    nothing. An arbitrary range. To someone who has used cameras before and
    knows what they are doing, that is important information to present up

    With the wide range of sensor sizes available today it makes sense to give
    the buyer a common denominator so they don't have to sit there doing the
    math trying to figure out if a 1/2.5" sensor has to have the lens' true FL
    multiplied by 6.0, or a P&S camera's 2/3" sensor has to have the lens' FL
    multiplied by 3.92 to give them an idea of how that camera's lens will
    perform compared to all 35mm cameras they've used in the past.

    If one day they perfect a 1/8" sensor size to give equivalent or better
    images than your APS-C sized sensor, are you going to claim they are
    artificially bumping up the 35mm equivalent focal-length FOVs presented
    with that sensor so it looks better on paper? Or will you welcome that as
    valuable buying-decision information? With so many variables today it makes
    perfect sense to provide a common denominator to the educated and
    experienced buyer.
    True Info, Dec 17, 2009
  10. Er, no. The average photog doesn't use/understand field of view. He
    (impersonal pronoun) is likely to think in terms of the 1.5 or 1.6
    factor as a mulitplier. Gets to the same place, and it's also simpler to
    multiply than divide.
    John McWilliams, Dec 17, 2009
  11. Peabody

    Ray Fischer Guest

    Which amounts to exactly the same thing.
    Ray Fischer, Dec 17, 2009
  12. Peabody

    Rich Guest

    It's not going to happen, no matter how many octogenarians want the
    ancient 35mm FILM format to be the standard in digital.
    Rich, Dec 17, 2009
  13. Peabody

    Peabody Guest

    Chris H says...
    Well, Nikon does indeed include the full-frame equivalent
    information, but Nikon's website, and Amazon, and I suspect
    everybody else, refers to this lens as a 35mm lens. That's
    what it appears to be called when you order it.

    But I've yet to buy an DSLR, so I may be wrong.
    Peabody, Dec 17, 2009
  14. Peabody

    Peabody Guest

    Ofnuts says...
    Well, this must vary a good bit. My Canon A590 P&S shows
    5.8-23.2mm on the lens, and you have to go to the Specs
    page at the back of the manual to find the 35mm equivalent
    Peabody, Dec 17, 2009
  15. Peabody

    Peabody Guest

    David J Taylor says...
    Show off. :)

    Well, I wish I could answer those questions, but I can't. I
    assume you mean if the FX lens is 50mm shooting at f/4 and
    the DX lens is 33.33mm and shooting at [?].

    So to get the same depth of field, you need to go wider
    aperture on the DX camera, but I don't know what the
    calculation is.

    You know, someone here explained a few months ago why depth
    of field increases as sensors get smaller and focal lengths
    get shorter (i.e. - from 50mm full frame to 33.33mm crop
    frame. It went something like this:

    Assuming distance to the subject is fixed, depth of field is
    inversely proportional to the square of the focal length,
    just because of how lenses create images. So a shorter true
    focal length produces a larger depth of field if focused at
    the same distance.

    However, when you also go to a smaller sensor, you reduce
    the depth of field in a linear relationship. This is
    because with smaller pixel sites the same circle of
    confusion produces more blurring.

    So you have the focal length going in one direction
    exponentially, but the sensor size going in the other
    direction linearly, and the net result is a kinda linear
    increase in depth of field as sensors get smaller with
    corresponding reductions in lens focal length.

    I don't know if this is right, or even if I described it
    correctly, but it sounded pretty good to me.

    As for light gathering, I don't know, but would like to.

    Can you please give the answers to these questions? And
    please show your work.
    Peabody, Dec 17, 2009
  16. Peabody

    MikeWhy Guest

    Millimeter is millimeter, be they Metric millimeters or Imperial

    35mm equivalent can be confusing for those not coming from a 35mm
    background. I still think in 35mm equivalents even after 7 years with a
    DSLR. 17mm on an APS-C is meaningless to me, other than I know it to mean
    "medium wideangle". It makes much more intuitive sense once I translate that
    to 28mm, its 35mm equivalent, which I now have committed to memory. (Oddly,
    though, as seldom as I use it these days, 90mm Grandagon still means 90mm
    Grandagon. Oh well.) Apparently, for better or worse, the industry has
    chosen 35mm equivalent to describe the wideness or reach of a lens, rather
    than something neutral like angle of view. If they had done that, we could
    all be equally in the dark.
    MikeWhy, Dec 17, 2009
  17. Peabody

    MikeWhy Guest

    Depth of field is linear with respect to working aperture size.

    f/N = d, the diameter of the working aperture.
    50mm / 4 = 12.5mm working aperture diameter.
    35mm / 12.5mm = f/d = N = 2.8

    f/2.8 for 35mm gives the same depth of field as f/4 for 50mm. Shoot it and
    prove it to yourself.

    Forget about CoC, sensor feature size, and exponentials or squared
    relationships for the time being. Keep firmly in mind that f/4 really means
    1/4 the focal length, f/8 is 1/8 the focal length, and so on. This is the
    size of the working aperture. Since DoF relates to aperture diameter, you
    can very easily relate DoF for different focal lengths.

    Coming back to 35mm equivalents, there's something almost mystical about the
    progression of 50mm, 35mm, and 24mm. At each step, opening (or closing) the
    aperture one stop maintains the same apparent DoF as you step down (or up)
    in focal length.
    Rather than answer the question, I'll ask one of my own. What type of meter
    do you use, and where is its setting to tell it the lens focal length?

    As an aside, 1.4, as in f/1.4, really means 1.4142, the square root of 2. I
    guess you can't completely get aways from squares and exponentials. In any
    case, when you decrease the working aperture diameter from f/1 to f/1.4, you
    decreased the area of the opening by 2, or by one EV or f-stop. Light
    gathering relates to area.

    Now the followup question: We already know that angle of view relates to
    focal length. Why does constant f/N aperture size maintain the same exposure
    value regardless of focal length?
    MikeWhy, Dec 18, 2009
  18. []
    You could look at it as - if all the lens dimensions were simply scaled,
    one with 50mm focal length and one of 35mm f.l., the smaller f.l. lens has
    half the input area, gathers half the light, and spreads it over half the

    So the next part of the question is - does the smaller sensor in the
    "crop" camera deliver the same image quality as the "full-frame" camera?
    Some would answer "no", because if the sensors are both quantum-noise
    limited, the smaller sensor receives only half the number of photons, and
    hence will have a poorer signal to noise ratio.

    You note that f/2.8 on the 35mm lens gives the same DoF as f/4.0 on the
    50mm lens, equally for the same signal-to-noise, and hence the same image
    quality, an f/2.8 opening is also required in terms of light level. I.e.
    you would need to operate the "crop" sensor at half the ISO as the
    "full-frame" one to gather the same light, for the same image quality.

    BTW: all my DSLR lenses are marked with their true focal length - not any
    "35mm equivalent" - so my 300mm telephoto in a crop-frame camera actually
    has an FoV the same as 450mm lens on a full-frame camera.

    All figures rounded - and lens defects ignored.

    David J Taylor, Dec 18, 2009
  19. Peabody

    Chris H Guest

    Of what? The lens on an FX body or a DX body and what happens if you
    swap them over?
    Chris H, Dec 18, 2009
  20. The focal length is a simple distance you can measure. If you take a
    simple single element lens like a magnfifying glass simply focus
    something a long distance away onto a sheet of paper and move things
    about until the image is sharp. The focal length is the distance
    between the lens centre and the sheet of paper, which is at the
    position of the sharp image plane.

    It has absolutely nothing to do with image size or sensor size. You
    can measure it for any DSLR camera lens by taking it off the camera
    and doing the same thing, focussing a sharp image on a bit of
    paper. But you'll need to know where the virtual centre of the lens
    is. As a fair approximation you can take it to be where the iris is.

    If you want to know what happens when you change sensor sizes simply
    cut out two bits of paper of two different sensor sizes and focus the
    image on each. The smaller one doesn't see as much of the image. Same
    effect as trimming off the edges of a photograph. That's why the
    effect of a smaller sensor is sometimes expressed as the crop factor
    -- how much it crops off the edges. That's all that happens.
    Chris Malcolm, Dec 18, 2009
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