1 2014-01-21 Minyi Zhong [email protected] Moritz Eßlinger [email protected] Herbert Gross [email protected] Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str. 15 07745 Jena Examples Practiced in Lectures Advanced Optical Design Contents 1 Introduction (none) ................................................................................................................................ 2 2 Optimization I ......................................................................................................................................... 2 2.1 System layout with ideal lenses ..................................................................................................... 2 2.2 Delano Diagram ............................................................................................................................. 3 2.3 Insertion of Finite Lens Thickness ................................................................................................. 6 3 Optimization II ........................................................................................................................................ 9 3.1 Influence of initial system .............................................................................................................. 9 3.2 Influence of criteria selection ....................................................................................................... 11 4 Optimization III ..................................................................................................................................... 13 4.1 Achromate ................................................................................................................................... 13 4.2 Mirror constrained beam shaping ................................................................................................ 17 5 Structural modifications ....................................................................................................................... 21 5.1 Adding a lens ............................................................................................................................... 21 5.2 Removing a lens .......................................................................................................................... 23 6 Aberrations and Performance (none) .................................................................................................. 27 7 Aspheres and Freeforms ..................................................................................................................... 27 7.1 Forbes Aspheres ......................................................................................................................... 27 7.2 Aspherical cylindrical lens ........................................................................................................... 29 7.3 Aspherical Singlet ........................................................................................................................ 32 8 Field flattening ..................................................................................................................................... 34 8.1 Field lens flattener ....................................................................................................................... 34 8.2 Pair of thick meniscus lenses ...................................................................................................... 40 9 Chromatic correction ........................................................................................................................... 43 9.1 Apochromate ............................................................................................................................... 43 9.2 Correction with Burried Surface ................................................................................................... 47 10 Special Topics ................................................................................................................................. 52 10.1 Skew spherical aberration ........................................................................................................... 52 2 10.2 Endoscope system ...................................................................................................................... 54 11 Higher order aberration ................................................................................................................... 58 11.1 High-NA Collimator ...................................................................................................................... 58 11.2 Induced aberrations ..................................................................................................................... 63 12 Advanced optimization strategies .................................................................................................... 64 12.1 Optimization of Insensitivity ......................................................................................................... 64 12.2 Global Optimization ..................................................................................................................... 69 13 Mirror systems ................................................................................................................................. 74 13.1 Astigmatism of oblique curved Mirrors ........................................................................................ 74 13.2 Cassegrain telescope .................................................................................................................. 79 1.1 Hybrid DOE .................................................................................................................................. 82 1.2 Correction with diffractive lens ..................................................................................................... 88 1.3 Tolerance sensitivity .................................................................................................................... 91 1.4 Tolerancing a splitted achromate ................................................................................................ 94 1 Introduction (none) 2 Optimization I 2.1 System layout with ideal lenses A collimated laser beam with wavelength 1.064 m and diameter D = 2 mm should be expanded by a Kepler-type afocal telescope made of ideal lenses with a first focallength f1 = 50 mm and a factor of 5. The enlarged collimated beam is then focussed down by a cylindrical lens with focal length f = 100 mm to get a line focus. a) Setup the system described above by ideal lenses b) Show the line focus graphically Solution: a) 3 The ideal lens can also bemodelled as an ABCD-system. b) Spot diagram, more points, scale fixed, bad resolution A footprint is an alternative option. It has to be noted, that the footprint only gives the line pattern, if the diameter of the final image plane is fixed to the corresponding finite vaue, e.g. 10 mm. Due to the perfect system property, otherwise the diameter in the image plane are near to zero. 2.2 Delano Diagram Load the Zemax sample data sequential / afocal / afocal riflescope. a) Show the Delano diagram of the system. How many intermediate images and pupil planes are found ? Where are the corresponding locations ? What is the special property of the exit pupil ? b) Draw a layout and determine the position with the largest diamater of the ray fan. Show, that this can also be seen in the Delano diagram. c) The strongest kinks in the diagram ocuur at the surfaces 4 and 16. What is the corresponding interpretation in the layout, if only the chief ray is concidered. Why is the kink at surface 12 not seen by the chief ray path ? Solution: a) 4 There are two intermediate image planes, one is exactly at surface No 6, the other between the surfaces 12 and 13. These are the intersection points of the line with the horizinthal axis. Furthermore, there are two pupils, one at surface 8, the other in the final plane. The Delano plane at the final pupil position is parallel to the horizionthal axis, this means, the beam is collimated (constant marginal ray height) and the image lies in infinity. b) According to the layout, the largest diameter occurs at surface 16. This point in the Delano diagram has the largest distance form the origin, which is also an indication for the bundle diameter. Surfaces 7 – 12 in enlarged representation: c) The chief ray shows the largest deviations at the surfaces 4 and 16. 5 The strong bending at surface 12 is mainly affecting the marginal ray and has only minar impact on the chief ray. This can be seen in the enlarged layout. 6 2.3 Insertion of Finite Lens Thickness Introduce a single perfect lens with focal length f = 60 mm at a wavelength of 546.07 nm. The object has a distance of 50 mm to the front stop, the lens follows in a distance 40 mm. The object has a diameter of 2y = 10 mm, the entrance pupil diameter is also 10 mm. a) Establish the system and determine the optimal image plane distance. Determine the ideal intersection point and the ray angle of the chief and the marginal ray in the image plane. b) Now substitute the ideal lens by a real lens with thickness t = 25 mm made of BK7. Determine the values for the radii and the object and image distance to match exact these values again by paraxial raytrace. Prove that the first principal plane is exactly at the position of the formerly ideal lens. What is the enlargement of the overall system