2013-06-03Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax for PhD -Part 55.1 Transverse aberration curveEstablish a system with an ideal lens of focal length f 100.mm,a wavelength of 600 nm and acollimated input bundle of diameter 10 mm.a)Define the slider option with the image distance as a variable.Open the transverse aberration chartwith a fixed scale of 100 um.What happens with the aberration curve,if the slider is movedb)Now introduce a thin glass plate in front of the perfect lens and define one side as a Zemikesurface with coma as type (c8)of one wavelength.What is now the result for the moving sliderExplain the result,if c7 is taken instead of c8.c)If now spherical aberration is introduced by the plate in selecting c9,what is seen for the defocusOpen also a spot diagram with fixed scale.Determine the best image plane for an overall small spotdiameterSolution:Setup of the initial system:a)The slider option is used in the following setting:1/92Slider 1100.72SurfaceThicknessStart:99Stop:101As a result,the transverse aberration curve is tilted corresponding to the interpretation of thetransverse aberrations in the case of defocussing.b)The system looks as follows:For a defocussing by the slider,99SurfaceStart:99a strong parabolic shape due to the coma in the meridional plane is seen,which is tilted by thedefocus.If c7 is chosen the orintation of the coma is rotated and the parabola switches from the meridional tothe sagittal plane.c)For spherical aberration a cubic curve is superposed on the linear change.If the scale of theaberration curve is fixed to 300 um,the best image plane is estimated to be at 101.44 mm.For thisvalue,the residual zonal deviation has approximately the same size at the edge emor.35.2 Strehl ratio and geometrical vs Psf spot sizeA single lens made of K5 with focal length f 25 mm and thickness d 5 mm is illuminated by adiverging beam with numerical aperture NA 0.1.After the lens the light should be collimated.If thecollimated beam is refocussed without further aberrations,the point spread function is not diffractionlimited.a)Calculate the accurate Strehl ratio,the estimated Strehl ratio and the geometrical and diffractionencircled energy inside the ideal Airy diameter.b)If now the numerical aperture is reduced,the Marechal estimation becomes better.Calculate thelargest NA,for which the relative error is smaller then 2%.What amount for the geometrical anddiffraction encircled energy inside the Airy diameter is obtained herec)Show the Strehl ratio as a function of the numerical aperture as a universal plot.What is themaximum value for getting a diffraction limited correction with Ds>0.8Solution:a)System data and layout:If the cardinal points of the lens are calculated,the unknown first distance is obtained paraxially ast1=25-3.280=21.72mmIf the lens is reverted in its orientation and the distance is optimized over the complete pupil,theoptimal distance seems to be 21.88 mm.