How do I calculate focal length for a required horizontal field of view on a 1/3-inch sensor?
Asked 12/4/2019
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I want to use a lens specified for another sensor format (such as 1/2-inch or similar) on a 1/3-inch sensor. I need a specific horizontal field of view: at a working distance of a cm, I want the scene width to be b cm.
What formula should I use to calculate the focal length I need on a 1/3-inch sensor? Also, does the lens’s original intended sensor format change the calculation?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
6y ago
2 Answers
1
https://en.wikipedia.org/wiki/Image_sensor_format#Table_of_sensor_formats_and_sizes offers a chart to determine approximate sensor size from the "1/x inch" descriptions. It may not be precisely exact, since a few sensors might all use the same description. Should be ballpark, close enough.
Crop Factor is (43.266 / that diagonal) The 43.266 mm is the 35 mm film diagonal, used for standard reference.
My site has some crop factor calculators at https://www.scantips.com/lights/cropfactor.html#crop that will do all of this.
For example, a 1/2.3" sensor is about 5.65x crop factor. A smaller 1/3" sensor is about 7.2x crop factor. These crop factors are relative to 35 mm film, as is standard.
Then if you have these two sensors to consider, in that case, the relative Crop Factor of the smaller sensor (larger crop factor) is 7.2/5.65 = 1.27x (relative to this larger sensor instead of 35 mm film). This is also the inverse ratio of the Equivalent focal length (to give the same field of view). This larger sensor needs a 1.27x longer focal length than the smaller one). Or vice versa.
Originally by user38978. Source · Licensed CC BY-SA 4.0
user38978
6y ago
0
Generated from our catalog & community — verify before relying on it.
For a rectilinear lens, use similar triangles:
f / w = a / b
So the focal length is:
f = (w × a) / b
where:
- f = focal length
- w = sensor width
- a = working distance to subject
- b = horizontal scene width you want at that distance
The key point is that you must use the actual width of your 1/3-inch sensor, not the nominal “1/3-inch” label directly. Those 1/x-inch sensor designations are just format names and do not equal the real sensor dimensions.
The lens being designed for a larger format sensor does not change the focal-length calculation for field of view on your 1/3-inch sensor. It just means the lens projects an image circle large enough for that larger sensor; on the smaller sensor you’ll capture a narrower portion of the image.
If you prefer angle of view first, horizontal AoV is:
AoV = 2 × atan(w / (2f))
Then relate that to your required scene width at distance a. In practice, look up the actual sensor dimensions for your specific 1/3-inch sensor model before calculating.
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