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Re: Field of view

 
 
David J Taylor
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      03-08-2009
Alfred Molon 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?


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

 
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Don Stauffer
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      03-08-2009
David J Taylor wrote:
> Alfred Molon 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?

>
> 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



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).
 
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David J Taylor
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      03-08-2009
Don Stauffer wrote:
> David J Taylor wrote:
>> Alfred Molon 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?

>>
>> 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

>
>
> 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!

Cheers,
David

 
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David J Taylor
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      03-08-2009
Alfred Molon wrote:
[]
> Long live the arctan
>
> Let's calculate an example.
>
> APS-C sized sensor 23.5 x 15.7 mm

[]
> At 300mm:
> 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

 
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ASAAR
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      03-13-2009
On Sun, 08 Mar 2009 16:21:48 GMT, David J Taylor wrote:

>> 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.

 
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David J Taylor
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      03-13-2009
ASAAR wrote:
> On Sun, 08 Mar 2009 16:21:48 GMT, David J Taylor wrote:
>
>>> 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.


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

 
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ASAAR
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      03-13-2009
On Fri, 13 Mar 2009 08:17:26 GMT, David J Taylor wrote:

>> 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.

 
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David J Taylor
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      03-13-2009
ASAAR wrote:
> On Fri, 13 Mar 2009 08:17:26 GMT, David J Taylor wrote:
>
>>> 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.


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

 
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David J Taylor
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      03-13-2009
David J Taylor wrote:
[]
> For the sensor sizes, DP Review is one sourse:


Argh: s/sourse/source/

David
 
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ASAAR
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      03-13-2009
On Fri, 13 Mar 2009 10:49:51 GMT, David J Taylor wrote:

>> 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.

 
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