International Association of Panoramic Photographers [Newsletter], Volume [5], July 1988 Page: 3
8 p. : ill.View a full description of this periodical.
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ta ,
Beer Cans Prove It!
140° is Widely
Exaggerated
Technique Useful for Measuring
Any Horizontal Angle of View
By John Stamets
With two long wires and a case of beer
cans, I measured the horizontal angle of the
Widelux. It's not 140°, as many ads would
suggest, but only 126.5° ±1°, at least on
my camera (F7 353606). Another F7
Widelux, which had a noticeable shadowing
on one side, measured only 125°.
To be fair, literature from the camera's
manufacturer, Panon Camera Shoko in
Tokyo, states the camera's visual angle as
"140° by diagonal measurement." But those
who market the camera tend to drop the
diagonal part, leading most users to assume
incorrectly that 140° is the horizontal
panoramic sweep. At any rate, I was not
satisfied with saying "140° diagonally," so
I came up with the following simple
technique which I believe can measure the
horizontal view angle of any camera within
one degree.
Of course, for a normal fixed-lens camera,
the ‘angle of view can be accurately
estimated from the focal length of the lens
and the length of the image on the film (At
infinity, angle of view = 2a where tan(a) =
L/2f; L = image length; f = focal length.)
Even so, theory can be tested by empirical
fact using this "beer can" technique.
All you need is simple geometry, a large
flat space and about $20 worth of hardware,
including two cables about 10 meters long
(30 to 35 ft) and a somewhat longer tape
measure. And of course the soda or beer
cans, spray-painted white. If beer, these
are best emptied with your assistants a day
or two before the actual measurement is
made. This technique may not work if
emptied immediately beforehand.
In a nutshell, the technique is this: The
camera's position (tripod) defines the center
of a circle of about 10 m in radius. Around
the circumference, you place an array of
cans at accurately measured angular
intervals. In the extreme case, you could
set up 360 cans at 1° intervals (every
17.45 cm at 10 m). Then, with camera
level, simply snap a photo from the center
of the circle and count how many cans you
can see in the resulting picture.
Obviously, it's a lot of trouble to mark off
every degree on the circle when you already
have some idea of how wide the camera is.
Fortunately, it's easy to accurately mark off
smaller measurement arrays using a radius
cable (or two) and a tape measure. For
instance, using just two equal-length
cables, you can accurately mark off 60.0°
intervals, as shown in the diagram. For
smaller intervals, a useful formula is for
chord length between two points on a
circle. For 0 = 10° or less, use:
x = R sin(0) where x is the chord length
and R is the radius. For 1°, x = 0.01745 R.
A typical can is 6.75 cm wide, spanning
0.38° at 10 m.
Near the edges of the expected angle of
view, place the cans at 1° intervals, about
10 or 15 per side. For the technique to
work, the edges of the resulting image must
intersect these "1° arrays" on both sides.
For the Widelux measurement shown here
(made with the help of friends Skip Kerr
and Rich Lewis), we figured that the
horizontal angle of view was less than
140°, but probably more than 120°.
B
B
Two equal-length cables attached at A and B can be used to mark off equilateral triangles,
seen as 60° intervals from camera position at A. Cans at C and D are exactly 120° apart.
Therefore, we used the two radius cables
(each marked at exactly 31'6") to place
two cans at exactly 120° apart. Actually
the points were marked with spikes, and
the cans placed immediately behind the
spikes. Starting at these "120° cans," we
added 10 more cans/spikes at 1° intervals
on each side using the radius cable
attached at the camera position and a
piece of cardboard cut to the appropriate
chord length (6.6"). The final
measurement array spanned 140° and
consisted of 23 cans, including the
central can. To make the picture more
interesting, we added 14 more cans at
irregular intervals around the circle.
However, these additional cans were not
needed for making the measurement.
Back at the center of the circle, the
camera was leveled at the tripod's lowest
position and carefully aimed at the
central can, so that hopefully both "120°
cans" would appear in the final photo.
They did, and then it was a simple
manner of counting the other "1° cans"
visible at the photo's edges to arrive at
the angle of view.
In the photo above, five 1° cans are
visible on the left edge and three on the
right. Since the innermost of these cans
on either side define 120°, the horizontal
angle of view is 126°. Inspection of a
greater enlargement, as well as repeated
measurements, suggests that the actual
view is closer to 126.5°.
For more detailed methods, send a SASE
to: John Stamets, 403 14th Ave. E.,
Seattle, WA 98112.
3
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International Association of Panoramic Photographers. International Association of Panoramic Photographers [Newsletter], Volume [5], July 1988, periodical, July 1988; United States. (https://digital.library.unt.edu/ark:/67531/metadc2273831/m1/3/: accessed May 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .