GeomOpt_Part23

# GeomOpt_Part23 - Department of Electrical and Computer...

This preview shows pages 1–11. Sign up to view the full content.

Department of Electrical and Computer Engineering ECSE 527 Optical Engineering Ray Matrices 9. Ray Matrices References: Hecht 6.2 Andrew Kirk 2010 Geometric Optics II 124

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Learning outcomes After taking this class you should be able to: • Explain the basis of ray matrices • Calculate matrices for compound reflecting and refracting stems systems • Select when to use matrices and when to use the y nu approach ©AGK 2010 Geometric optics II. 125
Contents • Introduction to ray matrix formulation •M a t r i c e s for refractive elements a t r i c e s for reflective elements i bt ti d fl t i • Comparison between ray matrices and y nu formulation ©AGK 2010 Geometric optics II. 126

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Refraction equation nn y u’ u l’ (+ve) l(+ve) •A s nu n n u n ' ' ' •T h e r e f o r e  R n n y nu u n y R y ' ' ' • Obtain:   C n n y nu u n ' ' ' ©AGK 2010 Geometric optics II. 127 (Curvature C =1/ R )
Matrix form for refraction •R e f r a c t i o n at surface modifies ray u’ slope: u y’ = y V 1 nn   C n n y nu u n ' ' ' e w r i t e ray transfer equations as C y y ' matrix operations: Be aware that there are ©AGK 2010 Geometric optics II. 128 other conventions for the location of the refractive index.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Matrix form for refraction •R e f r a c t i o n at surface u’ u y’ = y V 1 nn '   C n n y nu u n ' ' ' ewrite ray transfer equations as matrix operations: C y y • Rewrite ray transfer equations as matrix operations: Output Matrix Input e aware that there are C n n D ) ' ( y nu D y u n 1 0 1 ' ' ' Be aware that there are other conventions for the location of the refractive dex ©AGK 2010 Geometric optics II. 129 index.
Ray slope and height Input: Ray slope Ray height y u Output: Refraction matrix: Matrix operation: ©AGK 2010 Geometric optics II. 130

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Ray slope and height y nu r Input: Ray slope Ray height y u ' ' ' ' y u n r Output: 1 D R Refraction matrix: 1 0 r R r ' Matrix operation: ©AGK 2010 Geometric optics II. 131
Transfer equation Transfer the ray to the next surface n’ 1 12 y 1 u’ 1 y 2 t 1 ' f ti 1 1 2 tu y y • Transfer equation: ese values of y nd u’ n be passed to the refraction ©AGK 2010 Geometric optics II. 132 • These values of y 2 and u 1 can be passed to the refraction equation for surface 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Transfer Matrix ay propagation through lens: d 21
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/28/2010 for the course ECSE ECSE 527 taught by Professor Kirk during the Winter '10 term at McGill.

### Page1 / 32

GeomOpt_Part23 - Department of Electrical and Computer...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online