Optics 430/530, week XII

1. Optics 430/530, week XII Geometric optics Application of ABCD formalism This class notes freely use material from http://optics.byu.edu/BYUOpticsBook_2015.pdf P. Piot, PHYS430-530, NIU FA2018

2. ABCD formalism • Consider a ray that stays close to the optical beamline axis . • Consider the ray divergence angle so that • Take the example of a drift space with length • Given a ray with position angle coordinate at what is the final position-angle coordinate at ? • Which can be written in the matrix form P. Piot, PHYS430-530, NIU FA2018

3. ABCD matrix for reflection on curved mirror • On the surface we have • So that the transformation writes =-1/f P. Piot, PHYS430-530, NIU FA2018

4. ABCD matrix at a curved interface • On the surface we have • So that the transformation writes P. Piot, PHYS430-530, NIU FA2018

5. ABCD matrix of a thin lens • Using the results from the previous slides: • So that the transformation writes P. Piot, PHYS430-530, NIU FA2018

6. ABCD matrix for a glass slide • Consider a piece of glass with parallel faces and thickness d • The transfer matrix is P. Piot, PHYS430-530, NIU FA2018

7. Imaging • Optical beamlines are often use to image an object • Consider the case of a spherical mirror • That is P. Piot, PHYS430-530, NIU FA2018

8. Imaging (II) • The condition for image formation is which givesor • Generalizing to a system shown on the side figure we can write the condition for imaging to be • The system magnification is P. Piot, PHYS430-530, NIU FA2018

9. ABCD formalism applied to a single lens • Let’s use ABCD formalism to recover basic feature of rays with special input/output conditions P. Piot, PHYS430-530, NIU FA2018

10. Principal planes of an optical system • The principal planes are input (first) and output (second) plane between which a complex optical system is located • The planes are defined such that the overall matrix between the two plane adopt a form similar to a (thin lens) P. Piot, PHYS430-530, NIU FA2018

11. ABCD matrix formalism application • The ABCD matrix formalism is useful to understand the overall properties of a system and imaging condition • Ultimately it can also be used to track the transverse beam size of a wave (e.g. a laser beam) as it propagate through an optical system • To do so consider • Then if the intensity distribution is. We can defined the second order moments as =1 = We assume ==0 P. Piot, PHYS430-530, NIU FA2018

12. Practical use of ABCD formalism • Ray tracing: many programsmodel a light as a bunch of rays • Trace each ray to compute the final image • This approach is often use as a first step to design, e.g., an optical transport system P. Piot, PHYS430-530, NIU FA2018

13. Covariance matrix (I) • Computing gives • Similar equations are obtained for and • In optics it is customary to define the covariance matrix as with contains all the 2nd-order moment (~size) of the beam P. Piot, PHYS430-530, NIU FA2018

14. Covariance matrix (II) • A convenient property is that the ABCD formalism can be used to propagate the covariance at any point using where P. Piot, PHYS430-530, NIU FA2018