Re: Zoom and magnify relation

A long time ago I wrote:
However, the sizes of objects in the image *is* accurately predicted by
the focal length ratio, all the way to the widest wide angle, as long as
you're still talking about rectilinear lenses (not fisheyes).

"David Ruether" <druether@xxxxxxxxxxxx> writes:
How can this be? If you shoot a very large grid of small squares from a
constant distance (assuming constant sensor size and distance - and with
the subject grid parallel with the sensor), and keep halving the lens focal
lengths, the angles of view will progressively not follow the FL reduction
ratio (as I showed earlier), resulting, I would think, in less than the
number of squares visible in any direction in the image than a straight
following of the ratio would predict. In other words, the size of subjects
as rendered in the image is also not proportional to the FL ratio when it
comes to short FL lenses (they are larger...). Am I missing something?;-)

Ah, I just finished a MUCH more detailed coverage of this, which
is going up now on my web page, listed in the "Articles" page as,
"On Lens Angles Of View, Magnification, And Perspective. The
direct URL is --
www.donferrario.com/ruether/lens-angle-of-view-and-perspective.htm

Sorry I didn't comment sooner - I never saw this reply. But you are
wrong when you say "resulting ... in less than the number of squares
visible ... than a straight following of ratio would predict".

Say you go from 36 to 18 mm lens focal length. The FOV goes from 62.86
to 101.32 degrees, less than a factor of 2 increase. But, as long as
you are shooting a flat wall with a camera aimed perpendicular to that
wall, you will still get twice as many squares visible. The true field
width, on the plane containing the grid, *is* doubled.

If you don't believe me, draw a scale diagram and measure. Or do the
math using similar triangles. You've decreased the lens-image distance
by a factor of two, while keeping the image width the same, so the
tangent of half the FOV has *exactly doubled*, even though the angle
itself has not doubled. On the subject side, the triangle is similar
to the image-side triangle, so the subject-side tangent of half the FOV
is *also* doubled. But the lens-subject distance has not changed, so
the amount of the subject visible has exactly doubled.

Or the handwaving argument: you haven't doubled the FOV angle, but the
additional squares you can see are being increasingly foreshortened by
the very wide angle they are off-axis, so you get more of them in each
degree of extra visual angle. The two effects cancel, and you get
exactly twice as many squares in not twice as many degrees.

By the way, your argument would be correct if the squares were drawn on
a sphere centered on the lens, since the squares would always appear a
certain number of degrees wide everywhere in the field. But we're
assuming a flat subject, not a spherical one.

As it happens, I write camera software for video games, so I can create
any wideangle lens I want, no matter how extreme, as long as it is a
distortion-free rectilinear lens. When I want, say, "50% more field of
view", I do *not* multiply the camera FOV by 1.5. I divide the
effective lens focal length by 1.5 instead. (This is actually
implemented by multiplying the tangent of half of the FOV angle by
1.5). This gives the desired effect: making all objects 2/3 the size
they were, and showing 1.5 times more width of any plane perpendicular
to the line of sight - even though it does not double the FOV angle.
I just recognize that FOV is nonlinearly related to what I really want
to control, which is magnification.

Dave
.

Relevant Pages

  • Re: Zoom and magnify relation
    ... the focal length ratio, all the way to the widest wide angle, as long as ... number of squares visible in any direction in the image than a straight ... "On Lens Angles Of View, Magnification, And Perspective. ... The FOV goes from 62.86 ...
    (rec.photo.digital)
  • re:Technical knowledge, its language.
    ... And how do you detect the ratio of the lengths? ... Ask your Purdue civil engineers what precision they could ... determine the angle. ...
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  • Re: Light gathering cone?
    ... Just a note on the angle you mention here. ... But suppose the CPC is made of solid glass (yes, ... ....the concentration ratio is one over the sine of half the acceptance ...
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  • Re: Zoom and magnify relation
    ... angle of view and image magnification does not follow those ratios ... the focal length ratio, all the way to the widest wide angle, as long as ... David Ruether ...
    (rec.photo.digital)
  • Re: Zoom and magnify relation
    ... the focal length ratio, all the way to the widest wide angle, as long as ... "On Lens Angles Of View, Magnification, And Perspective. ... The FOV goes from 62.86 ...
    (rec.photo.digital)