Originally posted by Gooshin 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.

Quote: 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")