# Math question - sort of

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

1. ### Eric MillerGuest

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
www.dyesscreek.com

Eric Miller, Sep 23, 2009

2. ### Paul FurmanGuest

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
www.edgehill.net
www.baynatives.com

all google groups messages filtered due to spam

Paul Furman, Sep 23, 2009

3. ### John McWilliamsGuest

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. ### rayGuest

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 MillerGuest

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

Eric Miller
www.colibrihotsauce.com

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

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
www.colibrihotsauce.com

Eric Miller, Sep 23, 2009
7. ### No OneGuest

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. ### Andrey TarasevichGuest

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. ### John McWilliamsGuest

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. ### Andrey TarasevichGuest

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. ### GuestGuest

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.

<http://www.dpreview.com/reviews/canoneos20d/page27.asp>
<http://www.dpreview.com/reviews/canoneos500d/page28.asp>
<http://www.dpreview.com/reviews/nikond3x/page32.asp>

Guest, Sep 23, 2009
12. ### Eric MillerGuest

Eric Miller
www.dyesscreek.com

"When the only tool you have is a hammer, every problem begins to resemble a
nail." - Abraham Maslow

Eric Miller, Sep 23, 2009
13. ### John SheehyGuest

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
aggressively.

John Sheehy, Sep 24, 2009
14. ### John SheehyGuest

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. ### GuestGuest

"assume a top (not cheap) non-zoom telephoto lens"
likewise.

Guest, Sep 24, 2009
16. ### CharlesGuest

Charles, Sep 25, 2009
17. ### Kennedy McEwenGuest

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 MillerGuest

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.

Eric Miller
www.dyesscreek.com

Eric Miller, Sep 26, 2009
19. ### Kennedy McEwenGuest

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
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.

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

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 MillerGuest

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
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
www.dyesscreek.com

Eric Miller, Sep 26, 2009