Field of view
Alfred Molon
view out of focal length, crop factor and aspect ratio of the sensor?
--
Alfred Molon
------------------------
Olympus 50X0, 8080, E3X0, E4X0, E5X0, E620, E30, E3 forum at
http://tech.groups.yahoo.com/group/MyOlympus/
http://myolympus.org/ photo sharing site
Nicko
> What is the formula for calculating horizontal and vertical field of
> view out of focal length, crop factor and aspect ratio of the sensor?
You can find all of that information here:
or more specifically, here:
http://kriho.com/fun_stuff.html
HTH.
HABD.
--
YOP...
David J Taylor
> What is the formula for calculating horizontal and vertical field of
> view out of focal length, crop factor and aspect ratio of the sensor?
Tangent is your friend here. IIRC:
FoV (H) = 2 * ArcTan (sensor-semi-width / focal-length)
FoV (V) = 2 * ArcTan (sensor-semi-height / focal-length)
FoV (diag) = 2 * ArcTan (sensor-semi-diagonal / focal-length)
Ignore crop factor, and use the actual active area dimensions of the
sensor.
David
Don Stauffer
However, if you do not have the actual dimensions, they are 24mm divided
by the crop factor, and 36mm divided by the crop factor. Those are the
full height and width, you then need to divide by two to get the
semi-(values).
David J Taylor
Thanks, Don. My reservation is that the usually quoted crop factors are
not all that accurate!
Cheers,
David
Alfred Molon
Taylor says...
> Tangent is your friend here. IIRC:
>
> FoV (H) = 2 * ArcTan (sensor-semi-width / focal-length)
>
> FoV (V) = 2 * ArcTan (sensor-semi-height / focal-length)
>
> FoV (diag) = 2 * ArcTan (sensor-semi-diagonal / focal-length)
Long live the arctan ;-)
Let's calculate an example.
APS-C sized sensor 23.5 x 15.7 mm
At 10mm:
Hor. fov = 99.2°
Ver. fov = 76.3°
At 16mm:
Hor. fov = 72.5°
Ver. fov = 52.3°
At 80mm:
Hor. fov = 16.7°
Ver. fov = 11.2°
At 300mm:
Hor. fov = 4.5°
Ver. fov = 3°
David J Taylor
[]
> Long live the arctan ;-)
>
> Let's calculate an example.
>
> APS-C sized sensor 23.5 x 15.7 mm
[]
> Hor. fov = 4.5°
> Ver. fov = 3°
.. and my Nikon 300mm says "5 degrees 20 minutes FoV" in the manual, which
is 5.333 degrees diagonal. Your calculation gives 5.4 degrees. Probably
within the limits of the approximations in the data.
Cheers,
David
Paul Furman
> What is the formula for calculating horizontal and vertical field of
> view out of focal length, crop factor and aspect ratio of the sensor?
In addition to the suggestions given, the distance you are focusing on
can change the fov, especially when doing closeups & macro work. The
focal length is stated for infinity *and* often rounded to some industry
standard like 50mm, 135mm, 300mm but might actually be 52mm, 138mm, 290mm...
--
Paul Furman
www.edgehill.net
www.baynatives.com
all google groups messages filtered due to spam
Alfred Molon
says...
> In addition to the suggestions given, the distance you are focusing on
> can change the fov, especially when doing closeups & macro work. The
> focal length is stated for infinity *and* often rounded to some industry
> standard like 50mm, 135mm, 300mm but might actually be 52mm, 138mm, 290mm...
Sorry, I don't follow you here. Are you saying that the focal length in
the exif data is not accurate?
Matt Ion
> In article <dPWsl.15271$as4....@nlpi069.nbdc.sbc.com>, Paul Furman
> says...
>
>> In addition to the suggestions given, the distance you are focusing on
>> can change the fov, especially when doing closeups & macro work. The
>> focal length is stated for infinity *and* often rounded to some industry
>> standard like 50mm, 135mm, 300mm but might actually be 52mm, 138mm, 290mm...
>
> Sorry, I don't follow you here. Are you saying that the focal length in
> the exif data is not accurate?
I dunno about accuracy, but with my cameras and lenses, it's always
listed to the nearest millimeter; rounding isn't any rougher than that.
Chris Malcolm
> In article <dPWsl.15271$as4....@nlpi069.nbdc.sbc.com>, Paul Furman
> says...
>> In addition to the suggestions given, the distance you are focusing on
>> can change the fov, especially when doing closeups & macro work. The
>> focal length is stated for infinity *and* often rounded to some industry
>> standard like 50mm, 135mm, 300mm but might actually be 52mm, 138mm, 290mm...
> Sorry, I don't follow you here. Are you saying that the focal length in
> the exif data is not accurate?
It wouldn't suprise me if at least some of the fixed focus "prime"
lenses which change their effective focal length as they focus close
didn't bother with calibrating and reporting that, but simply reported
the canonical fixed focal length of the lens.
--
Chris Malcolm
Alfred Molon
> It wouldn't suprise me if at least some of the fixed focus "prime"
> lenses which change their effective focal length as they focus close
> didn't bother with calibrating and reporting that, but simply reported
> the canonical fixed focal length of the lens.
By the way, how do zoom lenses in a camera measure the focal length and
report it back to the image processor, so that it can write it in the
exif?
David J Taylor
> In article <71klq2F...@mid.individual.net>, Chris Malcolm says...
>
>> It wouldn't suprise me if at least some of the fixed focus "prime"
>> lenses which change their effective focal length as they focus close
>> didn't bother with calibrating and reporting that, but simply
>> reported the canonical fixed focal length of the lens.
>
> By the way, how do zoom lenses in a camera measure the focal length
> and report it back to the image processor, so that it can write it in
> the exif?
Most likely a mechanical position sensor, and a simple look-up table.
Some compact cameras only have a limited number of zoom positions, so it
may be counting steps to a stepper motor.
David
Paul Furman
I think that's normal expected behavior for the real focal length to
change while focusing. Some macro lenses give corrected exif data for
the aperture but none attempt to calculate the focal length, I guess
because the definition of focal length is 'at infinity'. Lord only knows
how the focal lengths of microscopes are figured <g>. Obviously I'm in
over my head at this point!
I've heard it's common to round off the actual focal length also.
You never see 27.63mm lenses... just 28mm. Perhaps zooms are calibrated
more carefully... I doubt it. Also consider fisheye lenses or those with
noticeable barrel distortion: the center is a whole different
magnification than the corners... it's all somewhat arbitrary, or a
matter of accepted benchmarks.
Bob Larter
>> the exif data is not accurate?
>
> It wouldn't suprise me if at least some of the fixed focus "prime"
> lenses which change their effective focal length as they focus close
> didn't bother with calibrating and reporting that, but simply reported
> the canonical fixed focal length of the lens.
That's correct (at least with Canons). I've also noticed that Canon
zooms only report back the shot FL in quite large steps.
--
W
. | ,. w , "Some people are alive only because
\|/ \|/ it is illegal to kill them." Perna condita delenda est
---^----^---------------------------------------------------------------
ASAAR
>> However, if you do not have the actual dimensions, they are 24mm
>> divided by the crop factor, and 36mm divided by the crop factor. Those
>> are the full height and width, you then need to divide by two
>> to get the semi-(values).
>
> Thanks, Don. My reservation is that the usually quoted crop factors are
> not all that accurate!
Nikon's is supposed to be pretty close to 1.52, but even if you
use 1.5 the calculated error may be less than the actual error when
focused closer than infinity with many zoom lenses. That's probably
no big deal if the concern about FOV is for landscapes when the lens
*is* focused near infinity. I assume that the 2x crop factor for
4/3 systems is accurate, but I don't know how accurate Canon's 1.6x
and 1.3x crop factors are.
David J Taylor
Just why I said use the sensor dimensions rather than some nominal
"crop-factor". Ideally use the actual focal length of the lens, rather
than the sanitised marketing value (i.e. 28.4mm and not "28mm").
The change of focal length at finite subject distances is a very good
point. I wonder if graphs are published anywhere, or if it's something we
should expect to see in reviews?
David
ASAAR
>> Nikon's is supposed to be pretty close to 1.52, but even if you
>> use 1.5 the calculated error may be less than the actual error when
>> focused closer than infinity with many zoom lenses. That's probably
>> no big deal if the concern about FOV is for landscapes when the lens
>> *is* focused near infinity. I assume that the 2x crop factor for
>> 4/3 systems is accurate, but I don't know how accurate Canon's 1.6x
>> and 1.3x crop factors are.
>
> Just why I said use the sensor dimensions rather than some nominal
> "crop-factor".
That may be acceptable for you or me, but most people have no idea
what their camera sensor's dimensions are. Crop factor is far more
well known, even for the camera-semi-literate. Aston Kutscher (in
Nikon's DSLR commercials) looks like he wouldn't know FX from DX.
Waving the camera in the air, nowhere in particular, he says that
the camera is properly set because he's able to fire a quick AF-C
burst while holding it only in one hand. Bleah.
> Ideally use the actual focal length of the lens, rather than the
> sanitised marketing value (i.e. 28.4mm and not "28mm").
Does it matter with less than 100% accurate viewfinders? Most
cameras are used for taking pictures, not for surveying. :)
David J Taylor
I rather suspect that anyone who wants to calculate the FoV has more idea
than "most people". I am grateful that we do not get the same advertising
as you, it would likely put me off buying /anything/! For the sensor
sizes, DP Review is one sourse:
http://www.dpreview.com/reviews/nikond60/page2.asp
where the D60 is given as 23.6 x 15.8 mm, so it's not that difficult to
find out. It's what appears on the final image, not in the viewfinder
which matters.
Anyway, the formulae are there for those who want them. Whether the data
on the lenses is, is another matter.
Cheers,
David
David J Taylor
[]
> For the sensor sizes, DP Review is one sourse:
Argh: s/sourse/source/
David
ASAAR
>> Does it matter with less than 100% accurate viewfinders? Most
>> cameras are used for taking pictures, not for surveying. :)
>
> I rather suspect that anyone who wants to calculate the FoV has more idea
> than "most people". I am grateful that we do not get the same advertising
> as you, it would likely put me off buying /anything/! For the sensor
> sizes, DP Review is one sourse:
>
> http://www.dpreview.com/reviews/nikond60/page2.asp
>
> where the D60 is given as 23.6 x 15.8 mm, so it's not that difficult to
> find out. It's what appears on the final image, not in the viewfinder
> which matters.
We seem to be talking past each other. Sure, those that are
*really* interested in photography are likely to be able to find
sensor dimensions with little effort. Your last sentence above
seems little more than a non sequitur truism. If what you see in
the viewfinder is less than what you get (for most DSLRs), and isn't
a concern, then why be concerned about the inaccuracy of using 1.5
as the crop factor for Nikon's DSLRs? It also promises a little
less than you actually get, and the difference is trivially small.
The advantage of using crop factors is that they only require simple
math. Telling photographers that they should use arctangents
instead violates the KISS principle but might be useful in that it's
likely to convince many to avoid asking you for further help. :)
Alfred Molon
Taylor says...
> David J Taylor wrote:
> []
> > For the sensor sizes, DP Review is one sourse:
>
> Argh: s/sourse/source/
presentation. He replaced "licence" with "lisence", not just on one
page, but on several pages. I sent him a link to an online dictionary.
J. Clarke
> In article <8Zqul.6383$Lc7...@text.news.virginmedia.com>, David J
> Taylor says...
>> David J Taylor wrote:
>> []
>>> For the sensor sizes, DP Review is one sourse:
>>
>> Argh: s/sourse/source/
>
> Never mind. Today a colleague "corrected" one of my slides in a ppt
> presentation. He replaced "licence" with "lisence", not just on one
> page, but on several pages. I sent him a link to an online dictionary.
What's truly sad is that Google has more than 4 million hits on "lisence".
David J Taylor
[]
> We seem to be talking past each other. Sure, those that are
> *really* interested in photography are likely to be able to find
> sensor dimensions with little effort. Your last sentence above
> seems little more than a non sequitur truism. If what you see in
> the viewfinder is less than what you get (for most DSLRs), and isn't
> a concern, then why be concerned about the inaccuracy of using 1.5
> as the crop factor for Nikon's DSLRs? It also promises a little
> less than you actually get, and the difference is trivially small.
> The advantage of using crop factors is that they only require simple
> math. Telling photographers that they should use arctangents
> instead violates the KISS principle but might be useful in that it's
> likely to convince many to avoid asking you for further help. :)
My feeling is that someone who wants to calculate the FoV wants an exact,
and not an approximate, answer. Calculation was the OP's requirement.
David
ASAAR
That "feeling" is only that, omniscience need not intrude, and it
should be pointed out that not only does using crop factors also
involve calculations, the OP's exact request was :
> What is the formula for calculating horizontal and vertical field of
> view out of focal length, crop factor and aspect ratio of the sensor?
which specifically asked for a formula using the crop factor, which
if the one for 4/3 sensors is used wouldn't have the greater
inaccuracy of Nikon's crop factor. Perhaps you also have a feeling
that the OP didn't really mean to phrase his question in terms of
crop factors? My "feeling" is that you will again attempt to
sidestep the issue, but it would be nice if I'm mistaken. :)
David J Taylor
[]
>> What is the formula for calculating horizontal and vertical field of
>> view out of focal length, crop factor and aspect ratio of the sensor?
>
> which specifically asked for a formula using the crop factor, which
> if the one for 4/3 sensors is used wouldn't have the greater
> inaccuracy of Nikon's crop factor. Perhaps you also have a feeling
> that the OP didn't really mean to phrase his question in terms of
> crop factors? My "feeling" is that you will again attempt to
> sidestep the issue, but it would be nice if I'm mistaken. :)
To know the "crop factor" exactly, you need to know the exact size of the
sensor. I don't see what your problem is with that.
If you insist on muddying the issue with 4/3 sensors, then you have two
"crop factors", one for vertical and one for horizontal.
horizontal: 36/18 = 2
vertical: 24/13.5 = 1.777....
Easier to use 18 x 13.5mm, isn't it?
David
Alfred Molon
> What's truly sad is that Google has more than 4 million hits on "lisence".
A million flies can't err.
ASAAR
wrote:
> ASAAR wrote:
> []
>>> What is the formula for calculating horizontal and vertical field of
>>> view out of focal length, crop factor and aspect ratio of the sensor?
>>
>> which specifically asked for a formula using the crop factor, which
>> if the one for 4/3 sensors is used wouldn't have the greater
>> inaccuracy of Nikon's crop factor. Perhaps you also have a feeling
>> that the OP didn't really mean to phrase his question in terms of
>> crop factors? My "feeling" is that you will again attempt to
>> sidestep the issue, but it would be nice if I'm mistaken. :)
>
> To know the "crop factor" exactly, you need to know the exact size of the
> sensor. I don't see what your problem is with that.
You've reverted to the classic David. This has never been about
knowing the crop factor "exactly". The "usually quoted crop
factors" (your words) are more than good enough for most people,
most of the time. You'll argue all day rather than be reasonable,
if it means you'd have to back down from unreasonable positions.
Since you've accused me of having a "problem", it's only fair to
note that the problem here isn't what you think it is. But then,
when have you ever acknowledged your own "problems"?
> If you insist on muddying the issue with 4/3 sensors, then you have two
> "crop factors", one for vertical and one for horizontal.
>
> horizontal: 36/18 = 2
>
> vertical: 24/13.5 = 1.777....
>
> Easier to use 18 x 13.5mm, isn't it?
Speak of muddying the waters . . . This is a good example of the
lengths you'll go to avoid being reasonable. Based on your way of
thinking, all of the photographers (and DPReview, et. al.) that
recognize the 4/3 system's generally accepted crop factor must have
problems of their own, and have no good reason to speak of crop
factors for 4/3 cameras because their image's dimensions don't share
the same 3:2 ratio. How foolish the photographic world must be when
they dare speak of crop factors for so many of the P&S cameras, such
as one of Panasonic's that lets you choose from among 4:3, 3:2 and
16:9 ratios. You'll probably want to expand on this to show why
it's so overwhelmingly important to be able to know the several crop
factors and FOVs for each of these different formats, but I and most
people don't really care. That's your problem, not ours.
David J Taylor
[]
> You've reverted to the classic David. This has never been about
> knowing the crop factor "exactly". The "usually quoted crop
> factors" (your words) are more than good enough for most people,
> most of the time. You'll argue all day rather than be reasonable,
> if it means you'd have to back down from unreasonable positions.
> Since you've accused me of having a "problem", it's only fair to
> note that the problem here isn't what you think it is. But then,
> when have you ever acknowledged your own "problems"?
> Speak of muddying the waters . . . This is a good example of the
> lengths you'll go to avoid being reasonable. Based on your way of
> thinking, all of the photographers (and DPReview, et. al.) that
> recognize the 4/3 system's generally accepted crop factor must have
> problems of their own, and have no good reason to speak of crop
> factors for 4/3 cameras because their image's dimensions don't share
> the same 3:2 ratio. How foolish the photographic world must be when
> they dare speak of crop factors for so many of the P&S cameras, such
> as one of Panasonic's that lets you choose from among 4:3, 3:2 and
> 16:9 ratios. You'll probably want to expand on this to show why
> it's so overwhelmingly important to be able to know the several crop
> factors and FOVs for each of these different formats, but I and most
> people don't really care. That's your problem, not ours.
ASAAR,
I've actually had to use the formulae I quoted to work out FoV, and I'm
quite happy to do so. No problem. If others want to use less accurate
ways, that's fine if the results are good enough for their purpose. I
have no problems with this.
I also tended to think in 35mm focal lengths (although when I started 35mm
was "wide", not it's 28 or even 24), and that can be a helpful way of
comparing lenses and systems, to a first approximation. Today I tend to
think more: "Is the 18-200mm enough or do I need the range of my 16mm and
300mm"? You might like to consider how a 24mm lens on a 4:3 and a 28mm
lens on a 16:9 aspect ratio sensor compare....
David
ASAAR
>> Speak of muddying the waters . . . This is a good example of the
>> lengths you'll go to avoid being reasonable. Based on your way of
>> thinking, all of the photographers (and DPReview, et. al.) that
>> recognize the 4/3 system's generally accepted crop factor must have
>> problems of their own, and have no good reason to speak of crop
>> factors for 4/3 cameras because their image's dimensions don't share
>> the same 3:2 ratio. How foolish the photographic world must be when
>> they dare speak of crop factors for so many of the P&S cameras, such
>> as one of Panasonic's that lets you choose from among 4:3, 3:2 and
>> 16:9 ratios. You'll probably want to expand on this to show why
>> it's so overwhelmingly important to be able to know the several crop
>> factors and FOVs for each of these different formats, but I and most
>> people don't really care. That's your problem, not ours.
> . . .
>
> I've actually had to use the formulae I quoted to work out FoV, and I'm
> quite happy to do so. No problem. If others want to use less accurate
> ways, that's fine if the results are good enough for their purpose. I
> have no problems with this.
I'm sure that you have used those formulas, but really, what kind
of accuracy is really needed by casual photographers, as opposed to
engineers or those doing scientific research. How many digits of
precision did you require. How many do you think the OP needed? Of
course you can't yet know the answer to that yet, and while you
could use this to justify your "solution", so could someone else
assume that double precision float might be warranted. It's often
noticed that when some in these newsgroups write, in effect "your
reasonable solution isn't good enough, mine is better . . ." it's
often done not to help answer and OP's question so much as it is to
strut one's superior knowledge in front of others. The ng is too
often used as a vanity forum.
> I also tended to think in 35mm focal lengths (although when I started 35mm
> was "wide", not it's 28 or even 24), and that can be a helpful way of
> comparing lenses and systems, to a first approximation. Today I tend to
> think more: "Is the 18-200mm enough or do I need the range of my 16mm and
> 300mm"?
Yes, that's also how I see it. And when others answered the OP,
using the terms he requested (crop factor included), it would have
been helpful and more accurate than this "first approximation".
> You might like to consider how a 24mm lens on a 4:3 and a 28mm
> lens on a 16:9 aspect ratio sensor compare....
Umm ... are you suggesting that you know something that I don't,
or that I might not have considered? See "superior knowledge",
above. When discussing FOV earlier you mentioned only two of the
sensor's dimensions. You might like to also consider its diagonal,
as some occasionally do.
David J Taylor
All I'm saying is that sometimes vertical FoV matters, sometimes
horizontal FoV, depending what you are trying to photograph. The
different aspect ratio will also affect the appearance of the final image.
David
ASAAR
>>> You might like to consider how a 24mm lens on a 4:3 and a 28mm
>>> lens on a 16:9 aspect ratio sensor compare....
>>
>> Umm ... are you suggesting that you know something that I don't,
>> or that I might not have considered? See "superior knowledge",
>> above. When discussing FOV earlier you mentioned only two of the
>> sensor's dimensions. You might like to also consider its diagonal,
>> as some occasionally do.
>
> All I'm saying is that sometimes vertical FoV matters, sometimes
> horizontal FoV, depending what you are trying to photograph. The
> different aspect ratio will also affect the appearance of the final image.
Yes, sometimes it does and more often than not, landscape
photographers are more interested in the horizontal FOV and
architectural photographers may be more evenly split. And all I was
saying (well, we both were saying more) was that this wasn't
sufficient reason to disparage calculations using crop factors,
especially when there was no good reason to assume extreme accuracy
was desired by the OP as shown by his modest request. After all,
you didn't just say "This is another way to calculate FOV that may
be preferable if you need great accuracy", you said instead,
suggesting more omniscience than was warranted, "Ignore crop factor,
and use the actual active area dimensions of the sensor.".
Alfred Molon
> I'm sure that you have used those formulas, but really, what kind
> of accuracy is really needed by casual photographers, as opposed to
> engineers or those doing scientific research. How many digits of
> precision did you require. How many do you think the OP needed?
Sorry, what exactly is the problem in using the simple formulas which
David kindly posted?
FoV (H) = 2 * ArcTan (sensor-semi-width / focal-length)
FoV (V) = 2 * ArcTan (sensor-semi-height / focal-length)
These are simple formulas which give accurate results, which anybody who
has been at school easily understands.
Using the crop factor is unnecessary and less accurate than these simple
formulas.
If the accurate formulas were complex and required a significant
computational effort, I'd be in favour of using the crop factor
approximation, but these formulas are plain simple.
ASAAR
> Sorry, what exactly is the problem in using the simple formulas which
> David kindly posted?
Nothing at all. Much gets by you as usual, Alfie*. To recap, you
asked for a formula (yes, *you* asked, remember?) using crop
factors. David answered your request as I mentioned in my last
reply, telling you to "ignore" crop factors. Do you agree with his
position, that crop factors don't provide enough accuracy? If you
do, then it's good that you've finally learned that crop factors are
so inaccurate as to be nearly useless, and are to be ignored.
* Cilla Black, Dionne Warwick, Cher, et. al. offered clues.
Alfred Molon
> Nothing at all. Much gets by you as usual, Alfie*. To recap, you
> asked for a formula (yes, *you* asked, remember?) using crop
> factors.
I asked for a formula to calculate the FoV. That I mentioned crop
factors is irrelevant (just ignore that). But frankly I don't understand
what we are disagreeing about
ASAAR
>> Nothing at all. Much gets by you as usual, Alfie*. To recap, you
>> asked for a formula (yes, *you* asked, remember?) using crop
>> factors.
>
> I asked for a formula to calculate the FoV. That I mentioned crop
> factors is irrelevant (just ignore that). But frankly I don't understand
> what we are disagreeing about
Yes, that's very clear. In the future it might be useful to
provide clues as to which parts of your posts are irrelevant. For
all anyone knew, the "formula" that you requested might have been
the irrelevant word, when what you really wanted was a table of
values. Except for those living in some far off land, words and
their usages aren't as elastic as you seem to think.
> "Words mean exactly what I want them to mean,"
> the Red Queen informed Alice in Wonderland.
> "It's too late to correct it," said the Red Queen: "when you've once
> said a thing, that fixes it, and you must take the consequences."