90 Degree Lenses

VidThreeNorth

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[I am going to be posting about some 90 degree lenses that I have used shortly, so I am posting this information "here" to reference it later. I hope that some of you might find it interesting beyond what I will be writing about.]

[Following link added 2022-01-28]

The above mentioned topic is at "Modified Git2 Action Camera"
"Modified Git2 Action Camera"

What is a "90 degree lens"? For photographic purposes, it is a lens which is capable of recording an image with a "90 degree field of view". That is a superficially simple concept. But there are some pitfalls when applying the idea in concept.

I am writing this briefly and will be taking shortcuts that would upset a math teacher, but I do not have much time for this. Maybe someday I will re-write parts to be more complete. Don't expect me to do so, but it is possible.

What is a "90 degree field of view"? The first issue is what does this mean? Looked at in photographic terms, it means that the image can include points that are 90 degrees from each other when the angle is measured relative to the point of view. Because we use rectangular compositions, that means that diagonally opposed corners might be used to define the maximum angle of view. That is not the only way, but it is the way that is generally used. Also, it does not require the lens to be rectilinear. But generally, that is what most photographers would prefer. Also, mostly, we assume lenses are not anamorphic unless they are specifically described as such. So, for now, I will presume that we are describing a perfectly corrected rectilinear, non-anamorphic lens.

What is the maximum distance on a camera's image? If we are looking at a 35mm film camera, then the sides are 24 mm x 36 mm. The diagonal is the square root of "24 mm squared" + "36mm squared", which is the root of "576 + 1296", which is the root of 1872, which is about 43.27 mm. Apparently, most full frame digital cameras (except for Canon) use sensor with diagonals ranging from 43.1 mm - 43.3 mm ("Image sensor format - Wikipedia"). I will use 43.2 mm for this discussion.

So what focal length would give an undistorted 90 degree diagonal field of view on this 43.2 mm image? Well, we have a short cut. Starting from the fact that the angle between the light paths from the lens to the extreme corners of the film plane or sensor is going to be 90 degrees, then angles of the light path to the film plane at the corners will be 45 degrees. This is even more convenient because at the lens axis, the angle at the film plane will be 90 degrees, and the angle from the lens axis to the light path at the extreme corners will be 45 degrees. If you draw all this on paper, then it is obvious that the focal length is 1/2 (the diagonal of the image), or 1/2 * (43.2 mm) or 21.6 mm.
 
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VidThreeNorth

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90 Degree APS-C Lens

One could calculate this out for APS-C sensors, but the usual "equivalences" apply:

For APS-C (except for Canon), 21.6 / 1.5 = 14.4 mm
 
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VidThreeNorth

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90 Degree M4/3 Lens

One could calculate this out for M4/3 sensors, but again, the usual "equivalences" apply:

For Micro 4/3, 21.6 / 2 = 10.8 mm
 
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VidThreeNorth

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90 degree lens for 1/2.3" Sensor (GoPro, etc.)

For a GoPro type action camera, or any camera using a 1/2.3" sensor, the diagonal is 7.66 mm, so a 90 degree lens is ~ 3.83 mm
 

RAZKY

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90 degree lens for 1/2.3" Sensor (GoPro, etc.)

For a GoPro type action camera, or any camera using a 1/2.3" sensor, the diagonal is 7.66 mm, so a 90 degree lens is ~ 3.83 mm
You have quite a conversation going on with yourself here.
 
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mrca

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So what's the point? How about an image example?
 

480sparky

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What's so special about a 90° FOV?
 

Timppa

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I do not know if this info is any useful to me, but truly enjoyed the read. Thanks!
 

480sparky

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90. 180. What's next? 270?
 

zulu42

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360? Let's do a 180, then a 90, and get back on topic.
 

480sparky

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Such as..... what's so special about a 90° FOV?
 

mrca

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360? Let's do a 180, then a 90, and get back on topic.
What the heck IS the topic? He hasn't responded about the point of the computations and what is so special about a 90 degree lens. I don't understand but am always interested to learn.
 

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