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Ray tracing and ABCD matrix

Ray tracing and ABCD matrix. Optics, Eugene Hecht, Chpt. 6. f = y ’. y. z. Basics of ray tracing. Consider 2D projection Ray uniquely defined by position and angle Make components of vector Paraxial approximation -- express angle as slope = y ’. Example: Propagate distance L.

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Ray tracing and ABCD matrix

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  1. Ray tracing and ABCD matrix Optics, Eugene Hecht, Chpt. 6

  2. f= y ’ y z Basics of ray tracing • Consider 2D projection • Ray uniquely defined by position and angle • Make components of vector • Paraxial approximation -- express angle as slope = y ’

  3. Example: Propagate distance L • Angle (slope) unchanged • Position depends on initial position and slope (y1, y1’) (y0, y0’)

  4. (y0, y0’) (y1, y1’) Example: Go through lens • Position unchanged • Angle (slope) change depends on position & focal length

  5. ABCD matrix • Generalize • Can cascade to make single matrix for system • Example: go through lens and propagate distance L = f (y1, y1’) (y0, y0’) (y2, y2’)

  6. (y1, y1’) (y3, y3’) (y0, y0’) (y2, y2’) f f Example: Fourier transform • Propagate distance f, go through lens, propagate f • Position and angle swap • note scale factors f and -1/f

  7. Example -- 4 f imaging • Cascade previous example (y1, y1’) (y3, y3’) (y0, y0’) (y4, y4’) (y2, y2’) (y5, y5’) f f f f (y6, y6’)

  8. Example -- dielectric interface • Snell’s law -- angle changes, position fixed n1 n2

  9. Other examples • Easy to generate ABCD matrices GRIN lens

  10. Optical resonator • Condition for stable cavity • Return to initial state after integer N round trips

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