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What are the lenses with a FOV 90-100 degrees (approximately) for 23mm diagonal sensor ? Is there any norm name for this kind of sensor or any named mount, to which is associated image-circle and sensor-lense distance ?

More specifically, the sensor is:

diagonal 23.1mm (type 1.4)
8432x5680 Mpixels = 47.9 Mpixels

I'm looking for rather compact lenses, if possible telecentric, with good resolution (8.5k in this case), but not too sharp (rather creamy/soft, like Arri signature).

EDIT: To a mount is associated an image circle and a given distance lense-sensor, hence the mount is not so much about the mechanical part but important lense features. Hence, a "mount system" is coupled in several ways to a sensor.

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    "Best" is often a matter of opinion. It depends what your actual use-case is. You're starting from an odd set of requirements. Normally people start with a known camera, with a known mount & sensor size [sensors are not measured on the diagonal, but yours sounds like what would be called 1.5"] What precisely are you trying to achieve?
    – Tetsujin
    Nov 8, 2021 at 8:12
  • Please take the time to take the Tour and read the Help pages, especially What topics can I ask about here? and What types of questions should I avoid asking?
    – Tetsujin
    Nov 8, 2021 at 8:15
  • The mount is completely independent of the sensor. You can't expect anyone to know for which kind of mount you need a lens just by describing the sensor.
    – jarnbjo
    Nov 8, 2021 at 16:22
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    You mention telecentric which is commonly used in machine vision. These are expensive lenses (in the USD 1k-10k range) and fixed focus. Do you really want telecentric? C-mount is common for telecentric lenses.
    – qrk
    Nov 8, 2021 at 18:24
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    @Soleil Check out Edmund Scientific as they have a large line of telecentric lenses in a few mounts. These are designed for industrial use (machine vision) in metrology. Telecentric lenses are not classified by angular field of view which is why this question is confusing.
    – qrk
    Nov 8, 2021 at 18:49

1 Answer 1

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Assuming this sensor has an aspect ratio of 3:2 (same as full frame 35mm sensor). If true, diagonal measure is 23mm, then the sensor height is 12.8mm and the sensor length is 19.2mm

Armed with these dimensions, I use conventional lens math to calculate what focal lengths will deliver an angle of view of 90° and 100°.

It’s the focal length combined with the sensor dimensions that dictate the resulting angles of view. It is industry standard to give the diagonal angle of view. This is because the diagonal measure of a rectangle is the longer of the three values which are height, length, and diagonal.

Since the diagonal is the longest of the three, the diagonal angle of view is the widest thus the one most often given. This might not make much sense but consider this industry standard is based on advertising puffing. Same for TV sets, their size is advertised based on their diagonal measurement.

That being said:

Mount a 11.5 mm lens and the angles of view will be – 58.2° vertical – 79.7° horizontal -- 90° diagonal

Mount a 9.7mm lens and the angles of view will be – 66.8° vertical – 89.4° horizontal -- 100° diagonal

It’s the focal length makes this happen, not the mount. Exception if the mount has an optical element that modifies the focal length of the mounted lens.

Formula: 35mm frame 24mm by 36mm with 50mm lens

Find diagonal = sq. root 24^2 + 36^2 = 43.27mm

Sove for angle of view ATAN(43.27/2/50)*2

ATAN(0.4327) = 23.4 * 2 = 46.8°

ATAN is ArcTan a trig function

This formula derives the angle of view when the camera is working at infinity.

d = format dimension such as the diagonal f = focal length

Angle of view = ATAN (d/2/f)2

An APS-C frame size is 16mm by 24mm diagonal = 28.8mm

Find angle of view if 30mm lens is mounted

ATAN(28.8/2/30)2

Angle of view = ATAN(0.48)2

Angle of view = 25.64 X 2 = 51.28°

Perhaps someone can post this formula better. I can't remember the text book of origin, been using it for more than 30 years.

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  • Well, see my edit. I'm invoking mount not as a mechanical feature but as a system with given image circle and lensse-sensor distance.
    – Soleil
    Nov 8, 2021 at 18:20
  • Can you update your answer with formulas which yield angles ?
    – Soleil
    Nov 8, 2021 at 19:38
  • Can you provide full formulas and their origin, instead of using numbers (no need for Pythagore) ? The simplicity of your formulas (with numbers) involve several approximations that you did not mentioned, and this feels suspect. You might want to use a latex notation and rendering (quicklatex.com) since there is no mathjax here.
    – Soleil
    Nov 9, 2021 at 2:40
  • Inside the camera a ray trace reveals a triangle The height is the focal length. The base is a one of the format dimensions. We know the dimensions of two sides of this triangle. We bisect to create a right triangle. The TAN of ½ the apex angle is opposite side divided by adjacent side. The ARTAN of this division is the angle in degrees. Twice this angle is apex of the image cone. The object cone (angle) is the same as the image angle. Nov 9, 2021 at 5:49
  • I believe you need somewhere the distance between the lens and the sensor, therefore it still seems suspect. This distance is also associated to the mount, because lenses are built to have the focus range [minimum distance-infinity] adapted to this distance (except few multimount lenses).
    – Soleil
    Nov 9, 2021 at 17:43

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