How can I estimate pixels per degree from a phone image using EXIF focal length and digital zoom?
Asked 5/25/2020
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I have a 4096×2304 image from a phone and want to estimate how many pixels correspond to one degree of field of view, or equivalently how many degrees span 400 pixels across the image. The EXIF reports a focal length of 3.5 mm and a Digital Zoom Ratio of 1.4.
My initial approach was to use the sensor diagonal and focal length with trigonometry, but I’m unsure whether the digital zoom means I should treat the effective focal length as 3.5 × 1.4 mm. I’m also confused about the quoted sensor format (for example, “1/3.1 inch”), since I’ve read that this does not equal the real sensor size.
What is the correct way to estimate pixels per degree from this metadata, and how should digital zoom and the phone sensor size be handled?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
6y ago
2 Answers
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I assume this is a still frame from a video, because 16:9 is a common video ratio. In order to maintain constant frame size, "digital zooming" needs to be reinterpolated. Thus, yes, you need to account for the "zoom ratio" by factoring in 1.4 times the focal length.
However, your calculations are off, because a "1/3.1-inch" sensor is not actually 1/3.1" in dimension. This is understandably very confusing, but it is merely a nomenclature referring to old circular 1" video tubes, which had a useful diagonal of about 16 mm, far from the actual 25.4 mm in an actual inch. See also, Why is a 1" sensor actually 13.2 × 8.8mm?
It took a little bit of Google searching, but I found the Sony Experia XA (Sony F3115) has a Sony EXMOR IMX258 sensor. Wikipedia's EXMOR article says the sensor is a 1/3.06" format, with a diagonal of 5.867 mm, and a pixel pitch of 1.12 µm. At 3.5 mm (the lens focal length), a 1.12 µm pixel subtends atan(0.00112 / (3.5 * 1.4)) = 0.0131°. Or if you prefer, 1/0.0131 = 76.4°/pixel at the center of the image. This distinction is important because near the edges, a 1.12 µm distance subtends a smaller angle — this is the nature of the tangent function.
A 400-pixel region subtends an arc of 2 * atan((0.00112 * 400 / 2) / (3.5 * 1.4)) = 5.23°
Normally, a very useful reference is Wikipedia's table of sensor format and sizes. Unfortunately, it doesn't list a 1/3.06" sensor. It does list a 1/3.09" Sony EXMOR IMX351 sensor, which is fairly close though.
Originally by user11924. Source · Licensed CC BY-SA 4.0
user11924
6y ago
0
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Yes—if the EXIF Digital Zoom Ratio is 1.4, you should treat the image as having a 1.4× narrower field of view than the native 3.5 mm lens, so using an effective focal length of about 3.5×1.4 mm is a reasonable estimate.
The bigger issue is sensor size: a “1/3.1-inch” sensor format is only a legacy naming convention, not the real physical diagonal. So calculations based on 8.19 mm diagonal will be inaccurate unless you know the actual sensor dimensions.
Once you have the true sensor width (best for horizontal calculations) or diagonal, compute the field of view with:
FOV = 2 × atan(sensor dimension / (2 × effective focal length))
Then:
pixels per degree = image pixels across that dimension / FOV in degrees
For a 4096-pixel-wide image, 400 pixels span:
400 / (pixels per degree)
If the image is a digitally zoomed still or a video frame, the zoomed image is usually cropped and resampled, so using the 1.4× factor is the right way to account for it approximately.
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