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06-09-2012, 03:56 PM   #76
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From the optical formulas page already linked above:

Angle of view
The angle of view of a lens depends on its focal length and the size of the image. The formula to calculate the angle of view is:
α=2arctan B/2f
Where α = Angle of view, B = Image size, and f = Focal length

Field of view
The field of view is the size (e. g. the width) of an object, filling a frame when photographed from a certain distance. The formula to calculate the field of view is:
G=dtan α/2
Where G = Field of view, d = Distance, and α = Angle of view


As you can see, the AOV formula does not have a variable for distance while the FOV formula does. I could be missing something but I don't think these are two sides to the same equation.

06-09-2012, 04:40 PM   #77
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QuoteOriginally posted by TomTextura Quote
From the optical formulas page already linked above:

Angle of view
The angle of view of a lens depends on its focal length and the size of the image. The formula to calculate the angle of view is:
α=2arctan B/2f
Where α = Angle of view, B = Image size, and f = Focal length

Field of view
The field of view is the size (e. g. the width) of an object, filling a frame when photographed from a certain distance. The formula to calculate the field of view is:
G=dtan α/2
Where G = Field of view, d = Distance, and α = Angle of view


As you can see, the AOV formula does not have a variable for distance while the FOV formula does. I could be missing something but I don't think these are two sides to the same equation.
They both have 2 variables for distance and one for angle. FOV contains G & d and Tan (angle), AOV uses B & f as well as the inverse of Tan(angle). If you like, the Angle of View formula can also be written in terms of G & d; substitute G for B and d for f.
06-09-2012, 06:45 PM   #78
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Which is just what I've said: AOV is a function of focal length and frame size. FOV is a function of focal length and frame size and distance. That's not difficult.
06-09-2012, 11:29 PM   #79
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QuoteOriginally posted by newarts Quote
They both have 2 variables for distance and one for angle. FOV contains G & d and Tan (angle), AOV uses B & f as well as the inverse of Tan(angle). If you like, the Angle of View formula can also be written in terms of G & d; substitute G for B and d for f.
Ah, yes, you are right. Wasn't really thinking of it that way but, yeah, it makes sense. I think you meant it the other way around though: substitute B for G and f for d. With that, rewriting the AOV formula does indeed work. There's still not a way to rewrite the FOV formula without distance though, right?

There's a couple of calculators here that work well. They distinguish the two by calling them Angular Field of View and Dimensional Field of View.

06-10-2012, 11:14 AM   #80
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QuoteOriginally posted by TomTextura Quote
Ah, yes, you are right. Wasn't really thinking of it that way but, yeah, it makes sense. I think you meant it the other way around though: substitute B for G and f for d. With that, rewriting the AOV formula does indeed work. There's still not a way to rewrite the FOV formula without distance though, right?
......
.
QuoteQuote:
Field of view
The field of view is the size (e. g. the width) of an object, filling a frame when photographed from a certain distance. The formula to calculate the field of view is:
G=dtan α/2 [nb should be G=d*2Tan(a/2)]
Where G = Field of view, d = Distance, and α = Angle of view
Distances are "hidden" in the Tan function. The definition of the Tan function is Tan(a/2) = (G/2)/d which is also Tan(a/2)=(B/2)/f by similar triangles.

I think the most useful relationship for estimation purposes is the one that follows from similar triangles:

d/G = f/B

For APS-C this is about d/G ~ f/25

Dave
06-10-2012, 02:22 PM   #81
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@Newarts Thanks for the lesson! I like that simple formula for making estimates. And this brings us back full circle to the solution provided by Lowell Goudge in post #14 but referring to subject height as FOV instead.
06-10-2012, 03:48 PM   #82
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QuoteOriginally posted by Asha Quote
Don't see how FOV is an exception, by the way. How can it be an exception when all the astronomers and optics professionals use FOV, but only in photography it is something else?
Yes it is, i clearly said that photography is the sole exception to this.
It's because like you say often it's the angular that's important but because with photography you also have a clearly defined focus distance it makes it posiable you can calculate the height of the field that is focus for example.
You can probably figure out yourself why that might be important for photography.

For astronomy and for biology this is of no interests at all and so no clear diffiration is make because it's never used while with photography both are actually used in practice and so we use AOV for angular and FOV for dimension just to make our speech clear.

You don't have to agree with this but this is how it is though, so if you use FOV for angular on photography discussion you know where the confusion might come from.


Last edited by Anvh; 06-10-2012 at 03:56 PM.
06-12-2012, 08:30 PM   #83
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QuoteOriginally posted by newarts Quote
Since you need a key that varies the result to translate from one to the other they are not equal. A angle is not equal to a length. Not in this world anyhow.

To translate from an angle to a length another length is needed; similarly to translate from a length to an angle another length is needed.

Fundamentally, an angle is a ratio and has no dimensions, unlike a length.
As you already stated in another post, the tangent of the angle is a ratio of dimensions. Also, the tangent of the angle can be approximated by the angle when angles are small. The equation for FOV that I was taught, and that is cited in Grievenkamp, has an infinite number of solutions, depending on what parameters you vary. You (or anybody else here) can argue that two sides of an equation are not the same, but I'm not going to buy it...LOL.

I think the heartburn people are feeling has to do with the fact that there are differences in the result when different calculations are made. I'm looking at it from a physics/mathematics perspective, so I really don't care about the calculation itself except when I need a number.

The other nit has to do with terminology. Again, I really don't care. The FOV equation and various other geometry/trigonometry rules allow for sufficient algebraic substitution that anybody can use the "knowns" to figure out the "unknowns".
06-12-2012, 10:01 PM   #84
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I think the terminology heartburn relates to conflating AOV and FOV in real-world photography. At astronomical distances, areal FOV doesn't change -- the subject field is always at infinity (or close enough). Calling what is seen either an Angle or a Field doesn't matter much. Sloppy terminology causes no pain there. But for walking-around photography, these are quite different. FOV is then a function of both AOV and lens-subject distance. See my previous brick-wall example. If astronomers want to call an angle a field, fine. I don't have that luxury.
06-13-2012, 03:56 AM   #85
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Maybe we should take a page from the specification of binoculars

They quote field of view in feet at 1000 feet
06-13-2012, 06:33 AM   #86
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QuoteOriginally posted by RioRico Quote
I think the terminology heartburn relates to conflating AOV and FOV in real-world photography. At astronomical distances, areal FOV doesn't change -- the subject field is always at infinity (or close enough). Calling what is seen either an Angle or a Field doesn't matter much. Sloppy terminology causes no pain there. But for walking-around photography, these are quite different. FOV is then a function of both AOV and lens-subject distance. See my previous brick-wall example. If astronomers want to call an angle a field, fine. I don't have that luxury.
Rio, to be honest, the only thing that prevents you from using angle is pure practicality and whatever experience you have. Sure, it is easier for most people to think in units of length when an object is up close, and it is certainly very pragmatic to do so. However, that does not preclude the use of angular subtense at any range.

ETA: One useful example of angular subtense for multiple ranges is in describing MTF (image quality). Whenever you see an MTF chart that is in units of "cycles/rad" or "cycles/deg", that is angular subtense.

Last edited by Asha; 06-13-2012 at 06:54 AM.
06-13-2012, 06:56 AM   #87
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QuoteOriginally posted by Lowell Goudge Quote
Maybe we should take a page from the specification of binoculars

They quote field of view in feet at 1000 feet
That's an interesting one since binoculars are basically two telescopes attached. The FOV formula doesn't actually work for binoculars since they are afocal. The image forming all happens in your eye, so you would have to add your eye to the optical system

ETA: I think you may have already mentioned this...but the more useful equation for binoculars and telescopes is magnification ratio. Usually it is angular (ie, ratio of angle in and angle out), but it can certainly be converted to linear units for any given distance.

Last edited by Asha; 06-13-2012 at 07:09 AM.
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