Accuracy of camera FOV and other specs

[tigerwillow1]

In comparing specs of cameras with different sensor sizes it felt to me like the specs were inconsistent. After a lot of number crunching I'm convinced they are. General conclusions listed first. They're based on only 2 specific camera models so it's premature to apply them widely. Corrections to math and logic errors welcome.

1. The sensor size (1/2.8", 1/1.8", etc.) is approximate and there's a good chance you don't know what it means, other than "bigger is better".
2. The lens focal length spec (3.6mm, 6mm, etc.) can be very inaccurate. Is Dahua fudging (i.e. "normalizing") it to a standard sensor size?
3. The camera FOV spec is fairly accurate.
4. Because of item #2, if you calculate the FOV, the answer could be way off. An online calculator will give garbage out based on the garbage in. Use the Dahua FOV specs.

Details....
What does sensor size mean? My answer is from logical conclusion, not from reading it anywhere. It's the sum of the horizontal and vertical dimensions of the sensor. The 1/2.8" etc. specs. are approximate. Kind of like the "55 inch class" specs used with televisions these days. To get the actual sensor size, you have to find the spec sheet for the sensor which gives the actual diagonal size, then apply the aspect ratio and pixel shape to get the horizontal and vertical dimensions. Fortunately the pixel shape is commonly square and can be ignored in the calculation. The IMX290 sensor in the 2mp starlight cameras is 6.46 mm diagonal from its spec sheet. Applying the 16:9 aspect ratio gives rectangular dimensions of 5.63x3.17mm. Adding these gives 8.80mm. 1/2.8" is 9.07mm, kinda close. The IMX347 sensor in the 4mp starlights is 9.04mm from the spec sheet. Applying 16:9 aspect gives rectangular dimensions of 7.88x4.43mm. Adding these together gives 12.31mm. 1/1.8" is 14.11mm, so unless I made a math error they're cheating a bit on this one. 1/2" instead would be pretty close.

I looked specifically at the horizontal angle of view for 2 cameras, with 3.6 and 6mm lenses, the 2mp HFW4231E-SE and 4mp T5442TM-AS. I'm able to make actual measurements for only the 6mm lenses because that's all I have.
The angle of view is calculated from the sensor width and focal length. I'm comparing the calculated angle, vs. camera spec angle, vs. actual tape measured results with the 6mm lenses.

HFW4231E-SE 3.6mm
Calculated 76 degrees, camera spec 87 degrees

HFW4231E-SE 6mm
Calculated 50.3 degrees, camera spec 52 degrees, actual measurement 51.56 degrees

T5442TM-AS 3.6mm
Calculated 95.2 degrees, camera spec 89 degrees

T5442TM-AS 6mm
Calculated 66.6 degrees, camera spec 56 degrees, actual measurement 54.2 degrees

Same conclusion, for at least the 2 models I was able to measure.: The camera's FOV spec. is pretty close and the lens focal length spec must be incorrect.
Since doing this the hard way I found an online calculator that gives the same answers: Camera Field of View Calculator (FoV)

It looks intimidating until you realize all you have to do is enter the focal length, any old number for the field distance, and the native sensor size. Then hit "recompute" and the answers pop out.

 

[pa4friends]

Hello tigerwillow1,

thank you for your tests.

I went in number crunching too with camera specs and I'm bit frustrated with the results and manufacturer's replies.
My experience was with Hikvision. I wanted verify the fields of view of the following four models:
DS-2DE4A425IW-DE
DS-2DE4A225IW-DE
DS-2DE4A404IW-DE
DS-2DE4A204IW-DE
In my opinion two of them are consistent. The other two are totally wrong.
To not bias your verify, if you have time for it, I don't tell more.
I found inconsistent many other models, even of other brands.

About your calculations, I think they are generally corrects,
just some decimals difference with respect to mine, that I list in same order:
75.4
49.8
94.5
66.0
I did them with my spreadsheet and I found consistent with this simple online calculator:

Camera Field of View Calculator | Advanced FoV Calculator

Wondering how to calculate the field of view of a camera? This web-based camera FoV Calculator provides the field of view from a sensor and camera lens.

commonlands.com

About the way you calculate the sensor size in inch fraction, what I knew is
(corrections are welcome) that the size is the diagonal of the sensor multiplied by 1.5 and not she sum of the horizontal and vertical dimension.
Actually the difference is not much and I agree with you it's a too approximated way to specify a sensor size. I guess manufacturers take advantage of the confusion.

I hope someone could give some light about all this. Thank you.

 

[tigerwillow1]

Since making the first post I've also learned that the stated size of a camera sensor is 150% of its diagonal measurement with very liberal rounding off. Taken from Video camera tube - Wikipedia:

Although the video camera tube is now technologically obsolete, the size of solid-state image sensors is still expressed as the equivalent size of a camera tube. For this purpose a new term was coined and it is known as the optical format. The optical format is approximately the true diagonal of the sensor multiplied by 3/2. The result is expressed in inches and is usually (though not always) rounded to a convenient fraction - hence the approximation. For instance, a 6.4 mm × 4.8 mm(0.25 in × 0.19 in) sensor has a diagonal of 8.0 mm (0.31 in) and therefore an optical format of 8.0*3/2=12 mm (0.47 in), which is rounded to the convenient imperial fraction of 1⁄2 inch (1.3 cm).
-and-
....the optical format size bears no relationship to any physical parameter of the sensor .....

So while the stated sizes in camera specs are not quite as arbitrary as I thought in the first post, they're still pretty misleading, and should not be expressed as inches. On at least some sensor spec sheets, Sony will say "1/2.8 class", which gets changed to "1/2.8"" on the camera spec sheet.

 

[john-ipvm]

This discrepancy is definitely a long term issue. For context, what we (IPVM) do in our Calculator is to enter manually all manufacturer's AoV information rather than estimate using the focal length. We have not heard significant problems using that approach.

 

[pa4friends]

Thank you tigerwillow1 for the exhaustive explanation about sensor sizes.
Thank you john-ipvm to let me know that useful calculator with huge camera database.

About camera Hikvision - DS-2CD2386G2-IU, an 8 Mpixel with resolucion 3840 x 2160, aspect ration 16/9 about = 1.778.
The version with focal length of 2.8 mm, says to have an horizontal AoV of 102°. This means that a given distance, for instance 10 m, the horizontal FoV is about 24.7 m.
It says to have a vertical AoV of 55°. So, at same distance of 10 m, a vertical FoV of about 10.4 m.
Here arises the first mismatch. What aspect ratio am I watching at? Answer should be 24.7/10.4 = about 2.372 far away from 1.778 (16/9).
The camera says to have a diagonal AoV of 120°. So, at same distance of 10 m, a diagonal FoV of about 34.6 m.
Here arise the second mismatch: the three FoVs don't respect the Pythagorean theorem, and for a lot, not just decimals.
I did the same verification for the other two versions of focal length of 4 and 6 mm, with no better luck.
This camera is in the database of IPVM Calculator where it is stated to have a 110.7° horizontal FoV for the 2.8 focal length version, instead of the 102° of its datasheet.
Sadly this doesn't give any better luck to my verification. I guess the mistake is in something else.

About camera Hikvision DS-2DE4A225IW-DE, that it's also in the IPVM Calculator database, I did the same verification with success.
The only wrong thing is that in the database it is stated to have three versions when it has just one. The first one is correct.
I noticed that the other two are actually the vertical and diagonal specifications, not useful in 2D map.

As I said in the previous message, I found these angle problems with other brands too.
For me it's important to know in advance a good estimation of what is possible to see in vertical too.
Do you think it's just a transcription mistakes on datasheets or could there be something else?
Months ago I wrote directly to Hikvision for other cameras too. They made me reply by the Italian commercial side saying "for anything, refer to the datasheet". Unacceptable.
Who could help to solve this?

Thank you.
Merry Christmas

 

[john-ipvm]

"Do you think it's just a transcription mistakes on datasheets or could there be something else?"

No, it's not a typo. Manufacturers actual AoV specification routinely vary, by design, from the listed imager size / focal length.

About camera Hikvision DS-2DE4A225IW-DE, that it's also in the IPVM Calculator database, I did the same verification with success.

The only wrong thing is that in the database it is stated to have three versions when it has just one.

Yes, this is our mistake and has been fixed. Thanks.

 

[Max Henkart]

Hi pa4friends, john-ipvm,

The root cause of this AoV / FoV discrepancy is lens distortion.

The FoV of a camera is a result of four items: focal length, distortion, pixel pitch, and pixel count. Most people forget about the distortion input, resulting in a large FoV / AoV calculation error for wide angle IP cameras.

This is why "Here arise the second mismatch: the three FoVs don't respect the Pythagorean theorem, and for a lot, not just decimals."
"Do you think it's just a transcription mistakes on datasheets or could there be something else?"
No, it's not a typo. Manufacturers actual AoV specification routinely vary, by design, from the listed imager size / focal length. "

When the lens has any distortion, the Pythagorean theorem calculation is inaccurate. This is why I built in optical distortion to one FoV calculators listed above. You can play around with the distortion slider options to see just how substantial this error can be.

Lens distortion is present in most wide-angle cameras with diagonal FoV >100°. Even some cameras with standard FoV have slight distortion. The FoV calculation (with distortion) is more complicated than Pythagorean theorem. I recommend empirical measurement if you have any doubt about the manufacturer's listed values.

Also, I suggest using the exact pixel count and pixel pitch, instead of the sensor size type and aspect ratio. Nominal cmos sensor size types are completely at the sensor manufacturer's discretion.

John's approach to use the manufacturer's listed values will be the most accurate, unless you are building a camera from the ground up.