Paraxial Optics & Jones Matrices
CARDINAL Points & Planes
3 pairs cardinal points are defined on axis of a thick lens
(imaging properties can be deduced)
1st & 2nd
Set of focal points & focal planes
Principal points & Principal planes
Rays determining the focal points change direction at their intersection with principle plane.
Nodal Points & Nodal Planes
Permit correction to the rays that aim center of lens. Any ray that aims 1st nodal point emerge from 2nd nodal point are undeviated but slightly displaced.
All distance directed to left are (-ve) and right are (+ve)
Thick lens optical system
Thickness cannot be ignore.
Assume light refracted in 2 different surfaces.
It gives better results.
Helps define image's properties of an optical system.
paraxial region= region around system's axis of symmetry
Used to construct image of arbitrary point in space for object in paraxial region.
Prinicipal plane is an hypothetical plane that assumed refraction take place.
Principal point is the intersections of the principal plane with optical axis.
Nodal point- when light is incident at 1 of them, refracted beam come from other nodal point.
Define a location w/ unit angular magnification and lens optical center where nodal ray intersects with optical axis.
Matrix Method
Follow 2 parameter for each ray
Ray defined by its height & direction. Express y7 & α7 in terms of y1 & α1 and multiplied by transfer matrix of system.
Mathematical Representation of Polarizers
[0 0]
[0 1]
linear polarizer, transmission axis vertical
[0 0]
[0 1]
times 1/2
(linear polarizer, transmission axis at 45°)
[sin2θ sinθ cosθ] [sinθ cosθ sin2 θ] linear polarizer with TA at angle θ
Linear Polarizer
Phase Retarders
General [e^iɛx 0]
[0 e^iɛy]
Rotator
θ → θ + β