Calculating the True Field-of-View: e.g., it's 74.5° on Mavic Air video, not the advertised 85° !

[RonW]

According to this site (droningon.co), the M1P uses the Sony IMX377 CMOS sensor. DJI implements Sony's recommended 4000x3000 image transfer from it, as the specs from the DJI site for the M1P declare that as the image size. According to the Sony data sheet for the IMX377 sensor, it is 7.81mm on the diagonal. DJI specs the camera with a 78.8° field-of-view (again on the diagonal, I assume). So we can use the FoV formula to obtain the actual M1P lens focal length:
78.8 = 2 * arctan(7.81/2f)
39.4 = arctan (3.905/f)
tan(39.4) = 3.905/f
f = 3.905/tan(39.4)
f = 3.905/0.82141 = 4.754

So the M1P camera's true focal length is close to 4.75mm.

Now, the full image size is 4000x3000, so the full diagonal is (Pythagoras again) 5000 pixels. Recall that the sensor diagonal measures 7.81mm, so ... 5000px/7.81mm means about 640 pixels/mm. As with the MA , only part of the sensor gets used for 4K video. Using the numbers at hand, we find the effective sensor for video is 6mm x 3.374mm [(3840/640)mm x (2160/640)mm]. Our friend Pythagoras thus says the effective diagonal when shooting 4k video is 6.8836mm.

Finally, now that we know the true focal length and effective diagonal for video, we can calculate the effective FoV for video:
FoV = 2 * arctan(6.8836/(2(4.754)))
FoV = 2 * arctan(0.723976) = 71.8

And "Bob's your uncle": When shooting video, the M1P delivers a 71.8° field-of-view. Or, rather we should say, with intentional vagueness, "Something close to 72°." There's plenty of room for error in all this.

@Prismatic, many thanks for your reply - excellent tutoring again! I fully understand the maths involved, and now have it 'locked in'.
I can now see how it all fits together; have often noted that some of my videos were cut off, the view not concurring with what I'd seen in VLM. Thank you again for enlightening the masses in this regard. I shall now reset the FOV in VLM to reflect the True field of view.
Respect and regards, happy flying.
Ron

 

[wywh]

Thanks, that might get my Virtual Litchi Missions even more precise.

Attached are the calculations for P3P video FOV which seems to be about 84.4° (or 84.4-86.4° depending whichever sensor size you choose).

As far as I know, DJI Phantom 3 Professional DJI FC300X has:

Camera sensor Sony EXMOR 1/2.3” (diagonal ~7.81mm, 6.16 x 4.62mm)

Effective pixels: 4072 × 3046 = 12.40 M (total pixels: 4168 × 3062 = 12.76 M, active pixels: 4024 × 3036 = 12.22 M)

Lens FOV 94°, focal length 3.61mm (or 20mm @ 35mm format equivalent) f/2.8

ISO Range 100-3200 (video) 100-1600 (photo)

Electronic Shutter Speed 8s - 1/8000s

Image Max. Size 4000 × 3000

Video Recording Modes:
UHD: 4096 × 2160p 24/25, 3840 × 2160p24/25/30
FHD: 1920 × 1080p 24/25/30/48/50/60
HD: 1280 × 720p 24/25/30/48/50/60
Max. Bitrate Of Video Storage 60 Mbps