see lens equation
The Gauss beam describes the shape of the incoming light at pixel level
4 points on the main optical axis of lenses:
- first and second focal point F1,F2
- first and second principal point P1,P2
Knowledge about the position of these 4 points is enough to calculate the position of an image point from the position of an object point.
That holds for single lens elements, but also for complex lens systems.
is another term for paraxial optics.
Carl Friedrich Gauss (1755-1855) laid in 1840 the foundations for this subject. In his work “Dioptrische Untersuchungen” Gauss showed, that the behaviour of any lens system can be determinedform the knowledge of it’s six cardinal points (also called Gauss-Points), namely two focal points, two nodal points (of unit angular magnification) and two principal points (of unit linear magnification) .
Included in the paper were recipes for experimentally determining the positions of these points and iterative methods for calculating them in terms of the surface curvatures, separations and refractive indices of the lens system.
He explicitely mentioned two equations where ray height r and ray angle of an input and output ray are linked, as used in the the ABCD-Matrix.
But Matrix notation wasn’t known at that time. So instead he used an algorithm he learnt from Leonard Euler. It was a shorthand form of continuous fraction, now known as Gaussian Brackets.
It’s only allowed to use ABCD Matrices in the paraxial range, with
The angles and are measured in radians!
For a table of ray transfer matrixes for simple optical components see ABCD matrix