Measuring method (named after Ernst Abbe) used to determine the focal length and the position of the principal planes of a lens singlet or a lens system (=objective) on the optical axis.
How to determine the focal length:
The position of the lens is fixed and the camera (or the screen ) is moved depending on the object position, that you get a focused image (in the image center). Different object positions result in different camera- or screen distances
How to determine the focal length of an objective (= (= lens system)):
The Position of a lens (and the lens singlets in it) are fixed and an arbitrary Point O on the optical axis is marked as reference point, for example the center of the lens or the center of the first lens element).
Now we measure the distance x from the reference point to the object, the distance x’ to the image and the image size B.
You get a list of Magnifications
and equations from refererence Point to object
and reference point to image:
Where h und h’ are the distances from object side resp. image side principal planw to the reference point.
(also known as v-number)
a measure of the materials dispersion (=variation of refractive index with wavelength),
with high values of V indicating low dispersion (low chromatic aberration).
The value Vd is given by
which defines the Abbe number with respect to the yellow Fraunhofer-Line d (or D3) helium line at 587.5618 nm wavelength.
It can also be defined using the green mercury E-line at 546.073 nm:
where F’ and C’ are the blue and red cadmium lines at 480.0 nm and 643.8 nm, respectively.
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