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03-31-2008, 05:15 PM   #1
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Field of view chart

Hello,
I had a few minutes to kill today, so I created a little chart. I think that you will find it interesting.

Dave


Last edited by Big Dave; 08-10-2008 at 03:44 PM.
03-31-2008, 07:03 PM   #2
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Neat! Hey, just thought I'd offer my QC input. Data for 430mm is cloned across both fields. Data for 640 has an extra 4 (in 44) for FF.

Best Regards,


Kelly.
03-31-2008, 09:29 PM   #3
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Original Poster
Kelly,
Your right. That must have been when I ran out of time. I made the corrections for those 430mm fans.

Dave

Last edited by Big Dave; 03-31-2008 at 09:37 PM.
04-01-2008, 05:29 AM   #4
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Typo, should be APS-C.

04-01-2008, 05:34 AM   #5
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Thanks Dave - this should be usefull.
04-01-2008, 12:50 PM   #6
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i love numbers..


i decided to plot your numbers, you will see how as the focal length increases the discreprency between the angle of view shrinks

meaning that anyone shooting more than 55-60 mm isnt gaining much by demanding FF coverage.

which begs the question of why people are so upset

infact it would seem that in this case the only people that should be upset are the architectural shooters, but thanks to stiching capabilities and softwares, this is becoming more of a moot point. since you can shoot distortionless images and then put them together to make something more crazy that you ever could using 35mm film, for 1/1000th of the effort!

Y AXIS : FIELD OF VIEW IN DEGREES
X AXIS: FOCAL LENGTH IN mm
Attached Images
 
04-01-2008, 01:01 PM   #7
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QuoteOriginally posted by Gooshin Quote
anyone shooting more than 55-60 mm isnt gaining much by demanding FF coverage.
Actually, you never gain more than 50% field of view by going to full frame, regardless of focal length.

Your plot is misleading if you don't know the math behind it. It seems to show the angle of view converging for long focal lengths. The discrepancy actually increases from what it is at wide-angle, but will never exceed 1.5X (the crop factor). The asymptotic formula for angle of view, in the limit of very long focal length, is:

FOV = d/f radians = (180/pi) * d/f degrees

So in the limit of long focal length, the FOV with a FF sensor is 1.5X that with an APS-C sensor.

On the other hand, at small focal lengths, the FOV discrepancy is less than 1.5X, since the exact formula is:

FOV = 2 arctan (d/2f) radians = (360/pi) * arctan (d/2f) radians

QuoteOriginally posted by Gooshin Quote
which begs the question of why people are so upset
Well, as you point out... it makes it harder to achieve wide-angle lenses with DSLRs, and easier to achieve telephoto lenses. So, yeah, the people who are upset are those who have an investment in nice wide-angle lenses already

Last edited by moxfyre; 04-01-2008 at 01:21 PM.
04-01-2008, 01:10 PM   #8
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QuoteOriginally posted by moxfyre Quote
Actually, you always gaining at least 50% field of view by going to full frame, regardless of focal length.

Your plot is misleading if you don't know the math behind it.
my plot is not misleading

you can even forget the plot

just look at the numbers

which i simply took from the OP thread

unless the OP's number are WRONG

because to support your claim at 14mm the FF camera should produce a FOV of 180 degrees, or, conversly, a 14mm on an APC should produce around 57* FOV

04-01-2008, 01:28 PM   #9
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QuoteOriginally posted by Gooshin Quote
my plot is not misleading

you can even forget the plot

just look at the numbers

which i simply took from the OP thread

unless the OP's number are WRONG
Your plot is correct, and the OP's numbers are numerically correct. What is misleading is the trend that you draw from it... that the FOV converges at long focal lengths.

What actually happens is the REVERSE. The FOV discrepancy is *worse* at long focal lengths. For example, look at the OP's numbers: at 14mm, the FF FOV is only 26% greater than the APS-C FOV. Whereas at 200mm+, the FF FOV is just about 50% greater than the APS-C FOV.

To see this relationship more clearly, you should make a plot with the y-axis on a logarithmic scale. You will then see the curves getting further apart, not closer, at long focal lengths.

The difference between the FOVs (A-B) is not significant, it is the ratio (A/B) that matters when comparing field of view.

QuoteQuote:
because to support your claim at 14mm the FF camera should produce a FOV of 180 degrees, or, conversly, a 14mm on an APC should produce around 57* FOV
Hmmm... you're multiplying by 2 here, when I said the limit was actually 1.5.

But in any case, you're applying the asymptotic formula, which is only valid in the case where the focal length is much greater than the sensor dimension, as I said above. In the case of short focal length / wide-angle, you need to use the exact formula:

FOV = 2 arctan (d/2f)

---------

EDIT: Here's a couple charts that shows the relationship more clearly.





EDIT: And the Scientific Python code to produce them:

Code:
f = array([14,19,24,35,55,90,105,150,200,220,320,430])
AOV_ff = (360/pi)*arctan(43.3/(2*f))
AOV_apsc = (360/pi)*arctan(28.8/(2*f))

figure(1)
semilogy(f, AOV_ff, '.-', label="Full frame")
semilogy(f, AOV_apsc, '.-', label="APS-C")
ylabel("Diagonal field of view (degrees)")
xlabel("Focal length (mm)")
legend(loc='upper right')
axis([0,450,1,200])
grid(True)
savefig("FOV_comparison.png")

figure(2)
plot(f, AOV_ff/AOV_apsc, '.-')
xlabel("Focal length (mm)")
ylabel("Ratio of FF-diag-FOV to APSC-diag-FOV")
savefig("FOV_comparison_2.png")

Last edited by moxfyre; 04-01-2008 at 01:46 PM.
04-01-2008, 02:04 PM   #10
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i get ya now,

yeah, you are right, % wise it increases


i was stuck in utilitarian mode, ie, what actualy matters (FOV as an image tool)
04-01-2008, 02:18 PM   #11
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QuoteOriginally posted by Gooshin Quote
i get ya now,

yeah, you are right, % wise it increases


i was stuck in utilitarian mode, ie, what actualy matters (FOV as an image tool)
You got it. Though I would say that the multiplicative difference (percentage-wise change) is actually the "utilitarian" conception of FOV

The thing that most interesting to me is that the FOV difference is *smaller* for wide-angle lenses. And yet it's the wide-angle users who are most unhappy with DSLRs.

It's because the crop factor is essentially making telephoto lenses "better". A 200mm lens effectively becomes a 300mm lens, which would be much more expensive with full frame... and is probably MORE useful if you're trying to take photos of distant objects/animals.

Whereas the crop factor makes a wide-angle lens "worse". An ultra-wide 14mm full frame lens becomes equivalent to roughly an 18mm lens, which is not as useful for architecture and such.
04-01-2008, 02:31 PM   #12
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It's actually more an illusion of "better" for telephoto. A 200mm will have the FOV of a 300mm, but the reach and perspective stay the same. If i buy the 300mm, it's more because i need the reach, and not because of the FOV.

WA is all about FOV, so the impact is definitely more noticeable. OTOH, telephoto is more about reach. So that eagle you take will appear larger on the frame, but he will not have more detail as if you take his picture with a 300mm lens.
04-01-2008, 02:38 PM   #13
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okay

now we need a chart of focal length vs reach

then combine the two

*GLEE*
04-01-2008, 03:33 PM   #14
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QuoteOriginally posted by moxfyre Quote
But in any case, you're applying the asymptotic formula, which is only valid in the case where the focal length is much greater than the sensor dimension, as I said above. In the case of short focal length / wide-angle, you need to use the exact formula:

FOV = 2 arctan (d/2f)

...........

EDIT: And the Scientific Python code to produce them:

[code]
f = array([14,19,24,35,55,90,105,150,200,220,320,430])
AOV_ff = (360/pi)*arctan(43.3/(2*f))
AOV_apsc = (360/pi)*arctan(28.8/(2*f))
etc.

Gooshin, you can do what you want, but me personally, I give up when somebody starts telling me that I screwed up because I was stupid enough to apply the asymptotic formula when I should have used 2 arctan (d/2f) whatever. ;-)

Will
(who wonders why he wandered into this thread)
04-01-2008, 03:52 PM   #15
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QuoteOriginally posted by aegisphan Quote
It's actually more an illusion of "better" for telephoto. A 200mm will have the FOV of a 300mm, but the reach and perspective stay the same. If i buy the 300mm, it's more because i need the reach, and not because of the FOV.
Perspective is not a function of focal length, only of camera-to-subject distance.

What is "reach" and how is it different from FOV???

QuoteOriginally posted by aegisphan Quote
WA is all about FOV, so the impact is definitely more noticeable. OTOH, telephoto is more about reach. So that eagle you take will appear larger on the frame, but he will not have more detail as if you take his picture with a 300mm lens.
The eagle certainly *will* have more detail if the lens-sensor combination can resolve it.
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