Timeline for How do I convert lens focal length (mm) to x-times optical zoom?
Current License: CC BY-SA 3.0
15 events
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| Feb 15, 2016 at 5:16 | comment | added | Brandon Dube | @Pete that is not true. The bend to this plot is due to the perspective mapping function containing a factor of tangent(FoV). If you extended this down much past 10mm you would see it start bending the other way. What is lost is that for very wide angle lenses, they use a different mapping function out of necessity, and you would need to plot both to see how most lenses behave. | |
| Feb 17, 2014 at 1:01 | history | edited | mattdm | CC BY-SA 3.0 |
three years later, I don't think we care that there was an edit slightly after the original post, so no need to mar the flow of the answer with that in bold :)
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| Jul 2, 2013 at 5:56 | comment | added | Pete | Update the graph to have a logarithmical x-axis, and you would see a straight line :) | |
| Jul 5, 2011 at 21:57 | comment | added | Nick Bedford | @mattdm I guess you might say the derivative of the field of view function is linear :P (I think) | |
| Jul 5, 2011 at 0:12 | comment | added | mattdm | Linear field of view, as opposed to angular field of view. Both are "FoV". en.wikipedia.org/wiki/Field_of_view#Conversions | |
| Jul 5, 2011 at 0:08 | comment | added | ysap | @mattdm - I do understand what you mean. I am not sure what is the exact term for that dimension (which you called "dimensional FoV?), but you are correct in that it is proportional to the focal length. I just think the use of "FoV" is inappropriate here, as it has a different definition. | |
| Jul 4, 2011 at 23:54 | comment | added | mattdm | @ysap — It's simple. The zoom range is equivalent to the change in FoV. 2× zoom is the same as cropping out half (linearly) of the image. 10× zoom is the same as cropping out the middle tenth. (100th, by area.) | |
| Jul 4, 2011 at 23:50 | comment | added | mattdm | Yeah okay that's clearly not linear when you plot it that way. :) However, my point is that a "3x" zoom will be the same change in dimensional FOV, no matter where you start. 18mm to 54mm (3×) means horizontal FOV at 10m goes from 20m to 6.67m (⅓), and 70mm to 210mm (3×, again) at 10m goes from 5.14m to 1.71m — again, ⅓. | |
| Jul 4, 2011 at 22:27 | comment | added | Nick Bedford | Updated with a graph showing the field of view. | |
| Jul 4, 2011 at 22:26 | history | edited | Nick Bedford | CC BY-SA 3.0 |
added 375 characters in body
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| Jul 4, 2011 at 16:28 | comment | added | ysap | Nick Bedford, @mattdm - I'd stress that the actoal FoV change is indeed nonlinear. For relatively long focal lengths, the angles are small and the change is approximately linear. However, as you get to the wider side, the angles become large and the mapping from focal length to angle of view is nonlinear. That said, I never saw a definition of zoom range w.r.t change in FoV. | |
| Jul 3, 2011 at 23:28 | comment | added | Nick Bedford | slaps forehead Why didn't I even think of that... | |
| Jul 3, 2011 at 23:07 | comment | added | mattdm | Actually, I think it is linear, isn't it? In the first case, it'll be a 2/17=11.8% change, and in the second, it's 2/200=1%. That's because zooming is mathematically like cropping, so each doubling of focal length is halving dimensional field of view in a very straightforward way. | |
| Jul 3, 2011 at 23:03 | comment | added | dialex | Just focal length, I'm only considering the magnification of the image. | |
| Jul 3, 2011 at 22:57 | history | answered | Nick Bedford | CC BY-SA 3.0 |