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Matrix methods in paraxial optics

Matrix methods in paraxial optics. Wednesday September 25, 2002. Matrices in paraxial Optics. Translation (in homogeneous medium). .  0. y. y o. L. Matrix methods in paraxial optics. Refraction at a spherical interface. . y. ’. . φ. ’. n. n’.

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Matrix methods in paraxial optics

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  1. Matrix methods in paraxial optics Wednesday September 25, 2002

  2. Matrices in paraxial Optics Translation (in homogeneous medium)  0 y yo L

  3. Matrix methods in paraxial optics Refraction at a spherical interface  y ’  φ ’ n n’

  4. Matrix methods in paraxial optics Refraction at a spherical interface  y ’  φ ’ n n’

  5. Matrix methods in paraxial optics Lens matrix n nL n’ For the complete system Note order – matrices do not, in general, commute.

  6. Matrix methods in paraxial optics

  7. Matrix properties

  8. Matrices: General Properties For system in air, n=n’=1

  9. System matrix

  10. System matrix: Special Cases (a) D = 0  f = Cyo (independent of o) f yo Input plane is the first focal plane

  11. yf o System matrix: Special Cases (b) A = 0  yf = Bo (independent of yo) Output plane is the second focal plane

  12. yf System matrix: Special Cases (c) B = 0  yf = Ayo yo Input and output plane are conjugate – A = magnification

  13. o f System matrix: Special Cases (d) C = 0  f = Do (independent of yo) Telescopic system – parallel rays in : parallel rays out

  14. Examples: Thin lens Recall that for a thick lens For a thin lens, d=0 

  15. Examples: Thin lens Recall that for a thick lens For a thin lens, d=0  In air, n=n’=1

  16. Imaging with thin lens in air ’ o yo y’ Input plane Output plane s s’

  17. Imaging with thin lens in air For thin lens: A=1B=0D=1 C=-1/f y’ = A’yo + B’o

  18. Imaging with thin lens in air For thin lens: A=1B=0D=1 C=-1/f y’ = A’yo + B’o For imaging, y’ must be independent of o  B’ = 0 B’ = As + B + Css’ + Ds’ = 0 s + 0 + (-1/f)ss’ + s’ = 0

  19. Examples: Thick Lens H’ ’ yo y’ f’ n nf n’ x’ h’ h’ = - ( f’ - x’ )

  20. Cardinal points of a thick lens

  21. Cardinal points of a thick lens

  22. Cardinal points of a thick lens Recall that for a thick lens As we have found before h can be recovered in a similar manner, along with other cardinal points

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