By A.; Burch, James M. Gerrard
This transparent, available consultant calls for little past wisdom and considers simply issues: paraxial imaging and polarization. For people with no earlier acquaintance with matrix algebra, bankruptcy One introduces uncomplicated rules of oblong matrix arrays and provides the principles for including them and for forming matrix items. next chapters take care of paraxial imaging homes of a situated optical approach, optical resonators and laser beam propagation, matrices in polarization optics and propagation of sunshine via crystals. Six necessary appendices care for such issues as aperture houses of founded lens structures, matrix illustration of centering and squaring blunders and derivation of Mueller and Jones matrices. This available consultant to tools should be nice counsel to scholars and employees not just in optics, yet in such parts as laser engineering, optoelectronics, mechanical engineering and extra.
desk of Contents
1. creation to Matrix Calculations
2. Matrix tools in Paraxial Optics
three. Optical Resonators and Laser Beam Propagation
four. Matrices in Polarization Optics
five. Propagation of sunshine via Crystals
Bibliography and end
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Extra info for Introduction to Matrix Methods in Optics
We now substitute U = 2/P in the expression for K, find K. m~n where lens. and and If we = 2/P + 2/P = 4/P = 4f f = 1 l/Pagain represents the focal length of the II. 8 EXPERIMENTAL DETERMINATION OF THE MATRIX ELEMENTS OF AN OPTICAL SYSTEM We shall assume initially that the system with which we are dealing is a positive lens system located in air. The first step is to choose two conveniently accessible planes near the first and last surfaces of the system: we shall regard these as our input reference plane RPI and our output reference plane RP2.
RP Z RP1 I I I 1 I I I ~=+8cm 1 I 1 I 0'03ml 01 I I I-_Q~2_4_~ II If = + 12·5 0 0·06 m --~---~---- 1 I P.. 14 49 Solution We shall work in metres and dioptres. The powers of the lenses are + 100/8 = + 12'5 dioptres for the positive lens and - 100/12 = - 8'33 dioptres for the negative. If the image is located at a distance X metres to the right of the negative lens, the matrix chain from image back to object is 0'06] [ 1 1 -12' 5 (image to (negative (lens negative lens) separation) lens) (positive (positive lens) lens to object) 0' 24] -2 Therefore, 0'25 [ -10' 42 = [0'25-1O'42X -10'42 0'12] -1 0'12-X] -1 For the object-image relationship to hold, we must have B = 0'12 - X = 0, so X = 0'12 metres.
T 1 Having seen that translation matrices produce the same product in whatever order they are taken, let us consider the optical corollary to this situation. If we are looking perpendicularly through a whole series of plane-parallel plates, then moving the plates or even interchanging them may affect the amount of light that is reflected, but the geometry of the transmitted images will remain exactly the same. (When we say that a plane-parallel glass plate of refractive index n and thickness t has a reduced thickness (tin) we are using quite appropriate language.