Why is my measured ground coverage smaller than the calculated field of view?

Asked 4/15/2015

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I’m using a Panasonic GH4 (Micro Four Thirds) with a 12mm lens, pointed straight down from about 120m altitude. Based on an 84° diagonal field of view, I calculated that the frame should cover about 216m across the diagonal:

2 × tan(84° / 2) × 120m = 216m

But in practice I’m seeing only about 180m. Does this mean my math is wrong, or could the real shooting setup be narrowing the field of view? What factors can make the measured coverage smaller than the nominal lens/camera angle of view?

Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0

Photography Stack Exchange contributor

11y ago

2 Answers

6

Here are some possible sources of error:

  1. Manufacturer stated focal lengths are often rounded favorably or sometimes plain exaggerated (e.g. a 200mm might well be only 190mm).

  2. Focal lengths are also stated at infinity focus, lenses change focal length when focusing (though it is more common for a lens to get wider as you focus closer not narrower).

  3. Sensor sizes are not always specified accurately (if this is how the AOV was calculated), even within the same format from the same manufacturer there will be variations of around 0.1mm that effect your angle of view.

  4. RAW editors crop your images, as most demosaicing algorithms use neighbourhood operations (where the value of a pixel depends on surrounding pixels) in the edges of the image there are no neighbouring pixels so these areas are cropped out of the final image. Usually the amount lost is only around 4 pixels from each edge.

  5. Lens distortion corrections applied by the camera JPEG engine or during RAW conversion change the effective focal length and/or result in the image needing to be cropped.

  6. Measurement errors in your 120m or 216m figures.

Some or all of these adding up are enough to explain the discrepancy. If lens corrections are being applied that will be the biggest factor and could probably explain the result on it's own. The next most likely/largest source of error will be in the 12mm focal length figure.

Here's a worked example. If the lens focal length is really 12.4mm and the sensor is 0.1mm smaller than spec then your diagonal angle of view will be 79.61°. If you're really at 117m and if lens corrections + demosaicing are causing you to lose 3% off each edge then you would expect to see 183m, which with less than 2% error could be measured as 180m.

Originally by user1375. Source · Licensed CC BY-SA 4.0

user1375

11y ago

0

AI Answer

Generated from our catalog & community — verify before relying on it.

Your math is basically fine if 84° is the true diagonal angle of view at the sensor. The mismatch is more likely due to real-world factors.

Common reasons the captured area is smaller than the simple calculation suggests:

  • Lens focal lengths are nominal and may be rounded; a “12mm” lens may not be exactly 12mm.
  • Stated angle of view usually assumes infinity focus; effective focal length can change with focus distance.
  • Actual sensor dimensions vary slightly, which changes angle of view.
  • Some RAW processing crops the image edges slightly.
  • Lens distortion and any in-camera or software distortion correction can reduce the usable field at the edges.
  • Your 84° figure may be diagonal, while your measurement method may not match the same frame dimension.

So the result does not necessarily mean your altitude is wrong. To verify, compare the actual image dimensions from the final file, make sure you’re measuring the same direction (diagonal vs width/height), and check whether any cropping or distortion correction is being applied.

UniqueBot

AI

11y ago

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