# Abbe’s Invariant

In paraxial optics each single refracting surface satisfies the Abbe’s Invariant Q in the paraxial Area, that relates the front focal distance s of an axial object point with the back focal distance s’ of it’s conjugated point behind the surface

# 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.

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 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 four times smaller than .
The image through a F5.6 lens has about twice the brightness of an image through an F8 lens, since and

# 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!

# Bayer Pattern

The difference between the usual color and monochrome – ( ” black and white ” – ) cameras is an additional layer of small color filters , mostly arranged in the so-called ” Bayer pattern ” (patented by Bryce E. Bayer, 1976, employee of Eastman Kodak ) .

# Binary Image

A picture taken with a monochrome camera usually has 256 levels of gray.
If the image just has two gray levels, it’s called “binary” image.
An old style fax usually shows a binary image

# 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.

# Camera Obscura

The principle of the camera obscura (= pinhole camera) is like this:

The disadvantage is clearly, that the image on the image plane is very dark. The needed exposure times to take an image can well be minutes!

Idea: Lets use a larger hole :

Now, however, the image not only gets brighter (as intended) but also gets blurry, because the light not only passes through the center of the hole. So not only the correct position of the image is exposed to the light, but also the direct neighbours.

As a result, the image of an object point is not just a point, but instead a little disk, the so called “Circle of Confusion” (CoC).

For long distant Objects the diameter of the CoC equal the diameter of the hole!