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Aperture angle

Angle that the lens can see in the direction of a given sensor measure.

The angles in horizontal, diagonal and vertical directions differ.
Please distinguish between the max. possible aperture angle and the actual aperture angle.
Actual aperture angles are influenced by the length of used extension rings,and even focus distances (because they are mostly achieved by simulating extension rings) max possible aperture angles aren’t
Changing the sensor size changes the actual aperture angle, max possible aperture angles aren’t
Datasheets of lenses usually show aperture angles for a given sensor size! Changing the sensor size changes the angles!
For lenses without distortion a lens that has the diagonal of the sensor as focal length has 53.1 degrees
A (no distortion) 6mm lens on a 1/3″ sensor,a 8mm lens on a 1/2″ sensor and a 16mm lens on a 1″ sensor have the same diagonal aperture angle of 53.1 degrees

aperture value

Number which characterizes the luminous sensitivity of a lens. Another term for aperture value is F-number.

Aperture Values

The smaller the number, the more light a lens can collect, the brighter the image, the smaller the depth of field.

The larger the number, the darker the image, but in generally the greater depth of field. At the same time, we generally lose resolution, see Rayleigh Criterion.

The f-number is the ratio of the focal length divided by the apparent size of the aperture (= entrance pupil diameter).

An f = 50mm lens with an F-number of F2.0  has to have least one front lens of \frac{50mm}{2.0} = 25mm diameter.
A lens with a focal length of f = 75, diameter 30mm and an F-number of F1.0  can’t exist!

The inverse of the square of the f-number is a measure for the image brightness of a lens.

The image through a F4.0 lens only has a quarter of the brightness of an F2.0 lens, since \frac{1}{4 * 4} four times smaller than \frac{1}{2 * 2}.
The image through a F5.6 lens has about twice the brightness of an image through an F8 lens, since \frac{1}{5.6 * 5.6} = \frac{1}{31.36} and \frac{1}{8 * 8} = \frac{1}{64}

back focal length

= BFL)
distance on the optical axis between last active optical surface and the sensor when the object is at infinity.

The value is only valid in paraxial optics, ie for objects close to the optical axis.
Further off the optical axis, the focal distance of distant objects is affected by the spherical aberration.
(back focal distance = Back Focal Length = BFL)

Note:
Not to be confused with the effective focal length EFL!

best form lens

Best Form Lenses are specifically designed optical components that aim to minimize spherical aberration while still utilizing spherical surfaces for their construction, rather than aspherical shapes. Here are the key points:

Spherical Surfaces: They maintain spherical geometry, which simplifies manufacturing while still providing effective optical performance.
Performance: These lenses are optimized for collimating and focusing light beams, making them ideal for various applications where precision is crucial.
Aberration Reduction: The design focuses on reducing optical distortions, particularly spherical aberrations, to enhance image quality.
For further details and calculations related to Best Form Lenses:

C-Mount

Standardized interface for the mounting of lenses, described in ISO 10935 (1996-12) Optics and optical instruments – Microscopes – Interface Type C

Standard interface for mounting of lenses.
The diameter of the thread is 1 “(one inch) and there are 32 threads to 1” in length.
The distance between the mechanical stop of the lens and the sensor in air is 17,526 mm

This is about 5mm more than for CS-mount lenses. C-mount lenses can be used with a 5mm extension ring (“C- to CS-mount adapter”) with CS-mount cameras.
CS-mount lenses however can not be used with C-mount cameras.

C-mount lenses are usually used for factory automation lenses.