Lens focal length for f 35 mm cameras are different for the Nikon D50 camera
by a ratio of about 1 : 1.5. The diagonal of a traditional camera is 43.3 mm (36 x 24 mm),
the sensor of the D50 is 23.7 x 15.6 mm and hence the diagonal 28.4 mm. There are 3008 x
2000 pixels with a pixel size of 7.8 µm x 7.8 µm (11 µm diagonal). |
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The diagonal for conventional cameras, 43.27 mm is assumed, 28.37 mm for the D50.
Formulae
- α = FoV — Field of View or viewing angle in °,
- d = diameter (width, height or diagonal) of receptor (e.g. CCD chip) in
mm (36 mm for example below),
- f = focal length of lens system in mm (55 mm for example below).
α = 2 • arctan (d / (2 • f ));
e.g.: 2 • arctan(36 / (2 • 55)) = 2 • arctan(0.327) = 2 • 18.1
= 36.2°. d = 2 • f • tan (α / 2);
e.g.: 2 • 55 • tan(36.2 / 2) = 2 • 55 • tan(18.1)
= 2 • 55 • 0.327 = 35.97 mm. f = d / (2 • tan(α / 2));
e.g.: f = 36 / (2 • tan(36.2 / 2)) = 36 / (2 • 0.326) =
36 / 0.654 = 55.04 mm.
Source: Die CCD Astrokamera für den Amateur (p.51) by Hans-Ruedi
Wernli; Birkhäuser 1995; ISBN 3-7643-5218-3.
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Focal Length to View Angle Converter for Fisheye lenses |
Lens focal length for the for the Nikon D50 camera is assumed for the
calculation. The diagonal of the sensor is 23.7 x 15.6 mm and hence the
diagonal 28.4 mm. There are 3008 x 2000 pixels with a pixel size of 7.8 µm x 7.8
µm (11 µm diagonal). |
|
Formulae
- α = FoV — Field of View or viewing angle in °,
- d = diameter (width, height or diagonal) of receptor (e.g. CCD chip) in
mm (28.4 mm for example below),
- f = focal length of lens system in mm (10 mm for example below).
α = 4 • arcsin (d / (4 • f ));
e.g.: 4 • arcsin(28.4 / (4 • 10)) = 4 • arcsin(0.71) = 4 • 45.2
= 180.9°. d = 4 • f • sin (α / 4);
e.g.: 4 • 10 • sin(180.9 / 4) = 4 • 10 • sin(45.2)
= 4 • 10 • 0.71 = 28.4 mm. f = d / (4 • sin(α / 4));
e.g.: f = 28.4 / (4 • sin(180.9 / 4)) = 28.4 / (4 • 0.71) =
28.4 / 2.84 = 10 mm.
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| © 2006 - 2010 by Hans-Rudolf Wernli. |