# aperture angle

Discussion in 'Digital Photography' started by logiclips@yahoo.com, May 29, 2005.

1. ### Guest

Hi,

How can I obtain the aperture angle (in degrees) of a camera when I
have the aperture (e.g. f/3.2) and the focal length?

BTW: What is the meaning of this spec?
Focal Length: 4.5mm (35mm equivalent 37mm)

Peter

, May 29, 2005

2. ### JimGuest

<> wrote in message
news:...
> Hi,
>
> How can I obtain the aperture angle (in degrees) of a camera when I
> have the aperture (e.g. f/3.2) and the focal length?

You also need the sensor size, but the aperature is not needed. After that,
it is a matter of trigonometry.
>
> BTW: What is the meaning of this spec?
> Focal Length: 4.5mm (35mm equivalent 37mm)

The actual focal length is 4.5mm. The angle of view corresponds to that of
a 37mm lens on a 35mm image (which is 24x36 mm).
Jim

Jim, May 29, 2005

3. ### David J TaylorGuest

Jim wrote:
> <> wrote in message
> news:...
>> Hi,
>>
>> How can I obtain the aperture angle (in degrees) of a camera when I
>> have the aperture (e.g. f/3.2) and the focal length?

> You also need the sensor size, but the aperature is not needed.
> After that, it is a matter of trigonometry.
>>
>> BTW: What is the meaning of this spec?
>> Focal Length: 4.5mm (35mm equivalent 37mm)

> The actual focal length is 4.5mm. The angle of view corresponds to
> that of a 37mm lens on a 35mm image (which is 24x36 mm).
> Jim

Except that the sensor is (most likely) 4:3 aspect ratio rather than 3:2
aspect ratio...

David

David J Taylor, May 29, 2005
4. ### Guest

The sensor has a max resolution of 1280 x 960 (1.3 Mio). Is it possible
to get the sensor size of this information or can I work with 37mm lens
and 24x36 mm image?
Furthermore I'm a little bit confused: The aperture angle depends on
the aperture size, isn't it?

Thanks,

Peter

, May 29, 2005
5. ### David J TaylorGuest

wrote:
> The sensor has a max resolution of 1280 x 960 (1.3 Mio). Is it
> possible to get the sensor size of this information or can I work
> with 37mm lens and 24x36 mm image?
> Furthermore I'm a little bit confused: The aperture angle depends on
> the aperture size, isn't it?

Sensor sizes are described here:

http://www.dpreview.com/learn/?/Glossary/Camera_System/Sensor_Sizes_01.htm

Find out which of these is in your camera.

I would not use the term "aperture angle", it means nothing to me. You
can talk about focal length, field of view, and f/number.

David

David J Taylor, May 29, 2005
6. ### ASAARGuest

On 29 May 2005 09:00:27 -0700, wrote:

> BTW: What is the meaning of this spec?
> Focal Length: 4.5mm (35mm equivalent 37mm)

It means that the size of the sensor in the camera with the 4.5mm
lens is far smaller than the size of the film frame in the 35mm
camera. If both lenses (37mm and 4.5mm) could be fitted to the same
35mm camera (assuming that the 4.5mm lens could fill the frame,
which it probably couldn't), the 4.5mm would resemble a super-wide
lens. If a picture of an object was taken (at the same distance)
with both cameras and the film was developed, you could hack at the
negative produced by the 4.5mm with a pair of scissors. If you cut
out a rectangular piece of film that shows the same image that is
contained in the full frame taken by the 37mm lens, that small
rectangular piece you cut out would be the size of the sensor in the
camera using the 4.5mm lens. In other words, with that camera, a
4.5mm lens is equivalent to a 37mm lens in a 35mm camera, because
uncropped prints from both would show approximately the same image.

ASAAR, May 29, 2005
7. ### Joseph MeehanGuest

wrote:
> Hi,
>
> How can I obtain the aperture angle (in degrees) of a camera when I
> have the aperture (e.g. f/3.2) and the focal length?
>
> BTW: What is the meaning of this spec?
> Focal Length: 4.5mm (35mm equivalent 37mm)
>
>
>
> Peter

What is an "aperture angle?" I have never heard the term and I can't
imagine what it refers to.

--
Joseph Meehan

Dia duit

Joseph Meehan, May 29, 2005
8. ### Gisle HannemyrGuest

writes:

> The sensor has a max resolution of 1280 x 960 (1.3 Mio). Is it
> possible to get the sensor size of this information [...] ?

No, this is no use in computing the physical area of the sensor

But earlier, you wrote:

>>> Focal Length: 4.5mm (35mm equivalent 37mm)

This is the data you need to compute sensor size. By dividing 37 by
4.5, we find a crop factor equal to 8.2 - so the diameter of your
camera's sensor is 5.3 mm - which means the imager's dimensions is
something like 4.24 mm x 3.18 mm.

> Furthermore I'm a little bit confused: The aperture angle depends on
> the aperture size, isn't it?

I've never heard the term "aperture angle", so I am not sure what sort
of formula this would be.

But if you want to know the angle "seen" by your camera's - that
particular datum is usually called "field of view" (FOV) and depends
on focal length and sensor diameter (but not on aperture). You'll
find the formula explained on this webpage:
http://folk.uio.no/gisle/photo/crop.html

For your camera, the FOV a f=4.5mm is atan(5.3/2/4.5), which is
1.064 radians or ~ 61 degrees. It is the same FOV that a lens
with f=35mm lens would have with a 24x36 mm imager.
--
- gisle hannemyr [ gisle{at}hannemyr.no - http://folk.uio.no/gisle/ ]
------------------------------------------------------------------------
Kodak DCS460, Canon Powershot G5, Olympus 2020Z
------------------------------------------------------------------------

Gisle Hannemyr, May 29, 2005
9. ### Neil EllwoodGuest

wrote:

>
> BTW: What is the meaning of this spec?
> Focal Length: 4.5mm (35mm equivalent 37mm)

Exactly what it says. The focal length of the lens is 4.5mm which is
the equivalent to a 35mm camera with a lens of 37mm.
--
neil

Neil Ellwood, May 29, 2005
10. ### Neil EllwoodGuest

Joseph Meehan wrote:

>
> What is an "aperture angle?" I have never heard the term and I
> can't
> imagine what it refers to.
>
>

Don't tell him but there is no such animal.....
--
neil

Neil Ellwood, May 29, 2005
11. ### Guest

Thanks a lot for these answers.

With aperture angle I meant the field of view. Sorry for that
confusion.

When you compute the FOV with the formula mentioned here
http://folk.uio.no/gisle/photo/crop.html#fov
one has to multiply the result with 2, right? Is it because of the 2
directions from the center of the lense to the edge?
Is there only one FOV? I thought maybe there are two: for the
horizontal and vertical direction because of the unsymetric size of the
sensor? Why not, apparently?

Peter

, May 29, 2005
12. ### SheldonGuest

<> wrote in message
news:...
> Thanks a lot for these answers.
>
> With aperture angle I meant the field of view. Sorry for that
> confusion.
>
> When you compute the FOV with the formula mentioned here
> http://folk.uio.no/gisle/photo/crop.html#fov
> one has to multiply the result with 2, right? Is it because of the 2
> directions from the center of the lense to the edge?
> Is there only one FOV? I thought maybe there are two: for the
> horizontal and vertical direction because of the unsymetric size of the
> sensor? Why not, apparently?
>
> Peter

I guess my question is why do you need all this FOV info? Just look through
the viewfinder or at the LCD and that's your field of view. It sounds like
your camera does not have interchangeable lenses, so what you see is what
you get. Are you going to get the data on the FOV for a particular focal
length and then run out and measure how much area your camera will capture?

Most photogs with any experience will simply use the 35mm equivalent of the
zoom lens on a point and shoot camera and have a rough idea of what the FOV
will be (as a mental image, not an exact formula).

Sheldon, May 29, 2005
13. ### JimGuest

<> wrote in message
news:...
> Thanks a lot for these answers.
>
> With aperture angle I meant the field of view. Sorry for that
> confusion.

And, just to remind you, the lens aperature has no influence on field of
view.
Jim

Jim, May 30, 2005
14. ### ASAARGuest

On 29 May 2005 14:36:01 -0700, wrote:

> Is there only one FOV? I thought maybe there are two: for the
> horizontal and vertical direction because of the unsymetric size of the
> sensor? Why not, apparently?

Most photographers care primarily about one direction when they're
concerned about FOV, but it could be either one. It's usually
horizontal for landscapes, sometimes vertical for architectural
shots. You could have a third FOV. The minimum FOV is the shorter
of the horizontal or vertical distance, so that's already accounted
for. The maximum FOV would be based on the diagonal. Find a use
for it, but don't expect it to bring you fame.

ASAAR, May 30, 2005
15. ### Gisle HannemyrGuest

writes:
> Thanks a lot for these answers.
>
> When you compute the FOV with the formula mentioned here
> http://folk.uio.no/gisle/photo/crop.html#fov
> one has to multiply the result with 2, right?

Wrong. The formula is:

FOV = atan(D/2/f)

where "D" is sensor dimension and "f" is focal length of the lens.

The normal way to use this formula is to use the diagonal (the
distance in mm from the lower left corner of sensor to the upper
right corner of the sensor measured in millimeters) for the letter
"D". Because the diagonal stretches across the entire sensor,
the resulting angle is also for the entire sensor, so you don't
multiply with two.

> Is it because of the 2 directions from the center of the lense to
> the edge?

Again: this has /nothing/ to do with the width of the lens'
aperture. It is the dimension of the camera's /sensor/ you
subsitute for "D" in the formula:

> Is there only one FOV?

No - there are three: Across (diagonal), width (horizontal) and
height (vertical)

> I thought maybe there are two: for the horizontal and vertical
> direction because of the unsymmetric size of the sensor?

I computed FOV for the diagonal in my example, because I think that
is the most interesting datum. It also makes it simple to compare
the FOV of sensors with different aspect ratios.

If you want to compute the FOV across the sensor (horizontal
direction), substitute the /width/ of the sensor for the letter
"D" in the formula.

If you want to compute the FOV from top to bottom of the frame
(vertical direction), substitute the /height/ of the sensor for
the letter "D" in the formula given above.
--
- gisle hannemyr [ gisle{at}hannemyr.no - http://folk.uio.no/gisle/ ]
------------------------------------------------------------------------
Kodak DCS460, Canon Powershot G5, Olympus 2020Z
------------------------------------------------------------------------

Gisle Hannemyr, May 30, 2005
16. ### Dave MartindaleGuest

lid writes:
>On 29 May 2005 14:36:01 -0700, wrote:

>> Is there only one FOV? I thought maybe there are two: for the
>> horizontal and vertical direction because of the unsymetric size of the
>> sensor? Why not, apparently?

> Most photographers care primarily about one direction when they're
>concerned about FOV, but it could be either one. It's usually
>horizontal for landscapes, sometimes vertical for architectural
>shots. You could have a third FOV. The minimum FOV is the shorter
>of the horizontal or vertical distance, so that's already accounted
>for. The maximum FOV would be based on the diagonal. Find a use
>for it, but don't expect it to bring you fame.

Actually, the diagonal field of view is what interests a lens designer.
That's the field over which the lens has to deliver a decent quality
image.

Dave

Dave Martindale, May 30, 2005
17. ### StaceyGuest

wrote:

> Thanks a lot for these answers.
>
> With aperture angle I meant the field of view.

Then do a search for the FOV of a 35mm lens on a 35mm camera and you'll be
REAL close..

--

Stacey

Stacey, May 30, 2005
18. ### ASAARGuest

On Mon, 30 May 2005 03:58:04 +0000 (UTC), Dave Martindale wrote:

> Actually, the diagonal field of view is what interests a lens designer.
> That's the field over which the lens has to deliver a decent quality
> image.

Right, but because of that (lowest quality, usually) it's the
least desirable part of the image. Poor performance in the corners
would get a lens and its designers raked over the coals, so it is
important, but I was trying to think of cases where the average
photographer would be concerned with getting subjects placed near
the corners of the frame. Maybe sensors could ease the designer's
burden by being chamfered, producing an effect like that produced by
gummed corner mounts that used to hold snapshots in photo albums.

ASAAR, May 30, 2005
19. ### Guest

, May 30, 2005
20. ### Gisle HannemyrGuest

writes:
> IMHO I think one computes FOV/2 with your formula such that tan(FOV/2)
> = D/2/f.
> atan(5.3/2/4.5) -> atan(0.589) = 0.532 which is exactly the half of
>
> Here are some references which do the same, I think:
> http://www.cinematography.com/forum2004/lofiversion/index.php?t5207.html
> http://www.colloquial.com/photo/formats.html
> http://www.worldserver.com/turk/quicktimevr/calculators.html
>
> Or do I have an error or reasoning?

No - you are right.

The correct formula is: FOV = 2 x ATAN (D/2/f).

I do have the correct formula in the spreadsheet I use to compute
these things - but by error omitted the initial multiply by 2 when
I copied it from the spreadsheet into the news article.

Thanks for pointing this out.
--
- gisle hannemyr [ gisle{at}hannemyr.no - http://folk.uio.no/gisle/ ]
------------------------------------------------------------------------
Kodak DCS460, Canon Powershot G5, Olympus 2020Z
------------------------------------------------------------------------

Gisle Hannemyr, May 31, 2005