Math question - sort of

Discussion in '35mm Cameras' started by Eric Miller, Sep 23, 2009.

  1. Eric Miller

    Eric Miller Guest

    I went from the 10D to the 5D. When I had my 10D, I learned to like the
    1.6x way of fooling myself into thinking my 400mm lens was a 560mm lens.
    Now I am thinking of getting myself another birding camera and am trying
    to figure out if there is a way to think of resolution as effective
    focal length versus the 10D. So, for example, if I were to get a 7D at
    18 megapixels how would that compare to 10D resolution wise in terms of
    what focal length lens would I have had to put on the 10D to get a 5
    inch tall bird at 20 meters (or any distance) to be rendered by the same
    number of pixels (one dimension only or my head will hurt too much) on
    the 10D that it would be rendered on the 7D using the 400mm lens.

    Eric Miller
    Eric Miller, Sep 23, 2009
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  2. Eric Miller

    Paul Furman Guest

    It's all relative, the noise level matters too for how much you can
    enlarge but yes it would be useful to have a common terminology for
    describing pixel magnification rather than 35mm equivalent FOV. Hmm, I
    was thinking macro when I wrote "pixel magnification" but at infinity I
    guess it would be pixels/field of view in degrees?

    Set the number relative to a 'normal' lens, which coincidentally is very
    close to 50 degrees for the diagonal FOV of a 50mm lens on a 35mm
    camera. Then let's use 300dpi as a standard metric for enlargement, on
    an 8x10 print that's 2400x3000 or 7.2MP. So, a full frame 7.2MP camera
    making an acceptable 8x10 print with a normal lens of 50 degrees
    diagonal field of view represents the basepoint. Damn, now I've exceeded
    my mathematical skills and/or patience and cannot figure out how to set
    up a formula to calculate/express this. It would look something like if
    you doubled the focal length, the number would be 2 and the number is 1
    with the default setup. A 500mm lens on FX would be a 10 and a 10mm FX
    fisheye would be -5. I'm not certain what doubling the megapixel count
    would do to the number, probably not double it. Can anyone finish my
    logic? A chart would be nice <g>.

    Paul Furman

    all google groups messages filtered due to spam
    Paul Furman, Sep 23, 2009
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  3. My take is that while you can come up with an approximation of what the
    comparables are, so what? You'll still want to maximize sharpness and
    detail on each shot, and won't be telling yourself, well, I can stay
    back and crop later to get an image I would have had on a previous set up.

    Besides the math part, there're different curves for each ISO setting,
    as well as available light and so on.

    I am thinking of picking up a 7D, and still shoot with my 20 D and 5D.....
    John McWilliams, Sep 23, 2009
  4. Eric Miller

    ray Guest

    400*1.6 = 640
    Dunno - what's the resolution of the 10d? But your question will be
    answered by taking the square root of the ratio.
    ray, Sep 23, 2009
  5. Eric Miller

    Eric Miller Guest

    Yep, caught that after posting. I mixed up my 1.4x converter with the 1.6x

    Eric Miller
    Eric Miller, Sep 23, 2009
  6. Eric Miller

    Eric Miller Guest

    I don't think that my 10D was pushing up against the resolution limit of my
    400 f/5.6L and while I may not realize the all the resolving potential with
    that lens on the 7D, I was more interested in the difference in potential
    resolution, the conversion puzzle and not so much the practicality, i.e.,
    don't spoil my fun!

    Eric Miller
    Eric Miller, Sep 23, 2009
  7. Eric Miller

    No One Guest

    Both the 10D and the 7D are APS-C sized sensors, so your 400mm lens will
    have a 1.6 FOV crop, so both will be similar to a 640mm (not 560mm). I never
    work in pixel pitch in photography.
    No One, Sep 23, 2009
  8. If we assume that sensors in both cameras have the same physical size
    (and they basically do), then all we need to know is the size of each
    sensor in physical pixels. I don't know the numbers for 7D, but we can
    just assume a square pixel (for both sensors) and use the square root of
    the total physical pixel count instead

    10D has a 6.5Mpix sensor. Sqrt(6.5) = 2.55
    7D has a 19Mpix sensor, Sqrt(19) = 4.36

    The above immediately means that given the same bird and fixed distance
    to the bird (as you requested in your message), you'd have to increase
    the focal length of 10D lens by a factor of 4.36/2.55 = 1.7. If you are
    using a 400mm lens on 7D, the 10D would require a 680mm lens.
    Andrey Tarasevich, Sep 23, 2009
  9. It's not just about the maths. Way too many other factors affecting IQ,
    and I suspect most photographers will soon forget about how equivalent
    one framing on one camera is to another body he's used. He'll go for the
    highest IQ he can in the moment.
    John McWilliams, Sep 23, 2009
  10. IQ is IQ. But the question the OP posted is about the _math_, as he
    stated in the subject. Also, the way it is formulated in the message
    body, it is about the math and math alone.

    I think the OP knows perfectly well that the IQ is not just about the
    math, which is why he made a specific effort to extract and isolate just
    the math part of the problem in his question.
    Andrey Tarasevich, Sep 23, 2009
  11. Eric Miller

    Guest Guest

    nonsense. there is a very clear and visible difference between an 8 mp
    camera such as a canon 20d and an 18 mp camera such as a canon 7d.

    dpreview measured the resolution of the 8mp 20d at 1850/1650 lines and
    the 15 mp 500d at 2400/2350 lines (the 7d has not yet been reviewed).
    moving up to the 24 megapixel nikon d3x, it's 2700/2600 lines. if the
    excess megapixels beyond 8 were wasted there would be no difference,
    yet there is.

    Guest, Sep 23, 2009
  12. Eric Miller

    Eric Miller Guest

    You read me well.

    Eric Miller

    "When the only tool you have is a hammer, every problem begins to resemble a
    nail." - Abraham Maslow
    Eric Miller, Sep 23, 2009
  13. Eric Miller

    John Sheehy Guest

    Aliased imaging ... shift everything 1/2 pixel horizontally and vertically,
    and what do you get? Gray nothing.

    It takes *SIX* pixels, exclusive, to properly sample a line pair.

    And there is usable contrast at much higher than 80 LP/mm with a lens like
    the 400mm f/5.6, especially if the noise is low and you can sharpen
    John Sheehy, Sep 24, 2009
  14. Eric Miller

    John Sheehy Guest

    I don't find that a very useful way of looking at things.

    A lens is the focal length that it really is. The *sensor* captures a
    certain area of the focal plane, with certain potential MTF curves,
    depending on sensel spacing, effective fill factor (photosite or
    microlens, whichever is wider), and AA filter strength. The size of the
    sensor, combined with the focal length, determine the *breadth* of the
    capture, IMO, and the term "reach" (which, also IMO, is poorly
    selected), if used at all, should be related to the pixel spacing and
    pixel qualities rather than the "crop factor". A 5D2 with the same lens
    has more "reach" than a 10D, in the sense that it puts the subject over
    more pixels. Going by crop factors, one might erroneously assume that
    the 10D will get you more subject detail.
    I would just think of it as 400mm, same FOV, but with higher subject
    resolution and less subject noise.
    John Sheehy, Sep 24, 2009
  15. Eric Miller

    Guest Guest

    "assume a top (not cheap) non-zoom telephoto lens"
    Guest, Sep 24, 2009
  16. Eric Miller

    Charles Guest

    Charles, Sep 25, 2009
  17. If it is just about the math then you need to quantify the lens quality
    contribution as well - your math is less than half the story, dealing
    only with pixel geometry.

    To include the lens contribution you need to use significantly more
    complex math, convolving pixel geometry with lens aberration geometry,
    or a completely different type of math using pixel MTF and lens MTF to
    scale resolved spatial resolutions at equal contrast. That is what the
    discussion on the LL site is trying to explain.
    Kennedy McEwen, Sep 25, 2009
  18. Eric Miller

    Eric Miller Guest

    No, the question posed in the original post had nothing to do with that.
    That would actually be the whole story, since the original question
    strictly concerned the pixels.
    Pertinence to this thread?

    Eric Miller
    Eric Miller, Sep 26, 2009
  19. I suggest you read what you wrote in your question again and, in future
    ask what you mean or mean what you ask! You specifically refer to
    resolution and that is a lot more than just pixel density!
    No, you stated: "if there is a way to think of resolution as effective
    focal length versus the 10D".

    Pixels are only one component of resolution: optics contribute
    significantly and, in this particular case, dominate.

    Others have tried to explain this to you in the thread, but it is
    clearly making your "head hurt too much"!
    If you have to ask that question then the answer is clearly beyond you,
    but it is pertinent on at least three counts:
    1. It is the full answer to your question, which you clearly seem unable
    to understand. Even perfect optics have a finite resolution, and when
    the sensor resolution approaches that, which is certainly the case in
    the 7D, that needs to be included in any scaling comparison, as
    explained in the LL article. The optical resolution is limited in terms
    of the minimum blur spot, while the sensor is limited in resolution by
    the pixel area. The cameras limits are determined by convolution of
    optical blur spot and pixel area. Convolution is a fairly complicated
    mathematical procedure and it is simpler to represent these parameters
    in terms of MTF curves simplifying the calculation of the camera
    resolution as it is just the product of the MTFs. The effective focal
    length scaling, in terms of reach, is simply then the ratio of the
    spatial resolutions at which the limiting contrast is achieved. That is
    the COMPLETE answer to your question. Whether you understand it or not,
    pixel scaling is only part of the issue and, in the case of comparing
    anything to the high pixel density of the 7D, will yield highly
    optimistic scaling on its own.

    2. It has already been linked to in this thread, but obviously ignored
    by you. I suggest you read it again and make some effort to understand
    it before claiming it is irrelevant, since optics dominate the question
    you have asked, NOT pixels.

    3. Others who read this thread in future, which will be archived
    forever, may be less mentally challenged than you and be looking for a
    more complete answer, not a simple pixel scaling answer which is trivial
    to calculate but optimistic at best and wrong in general.
    Kennedy McEwen, Sep 26, 2009
  20. Eric Miller

    Eric Miller Guest

    Which is a selective quote designed to explain your need to pontificate
    about something other than what was really asked (and as argument that
    the most direct and succinct response to the question posed really
    missed the point), which was:

    "So, for example, if I were to get a 7D at 18 megapixels how would that
    compare to 10D resolution wise in terms of what focal length lens would
    I have had to put on the 10D to get a 5 inch tall bird at 20 meters (or
    any distance) to be rendered by the same number of pixels (one dimension
    only or my head will hurt too much) on the 10D that it would be rendered
    on the 7D using the 400mm lens."

    It isn't surprising that, on the usenet, posters will feel the necessity
    to take every question as an opportunity to educate those lesser minds
    about what they really should have asked. But why hide from that conceit
    by quoting a selected part of the preamble to my math question to
    suggest that I really asked about that which you want to talk about?
    Seriously, why not just say what your thinking? You're smarter than
    everyone else and we should all worship you, right?

    Oh wait, let me mimic that little voice you just heard, "Remember, this
    post is an opportunity to tell them more of what we know about what they
    should have been asking, but were too ignorant to, hee hee hee . . . God
    we are smart."

    Eric Miller
    Eric Miller, Sep 26, 2009
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