1 / 10

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.

thanh
Download Presentation

Ray tracing and ABCD matrix

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related