2012-11-13Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaExercisesLecture Optical design with Zemax-Part 33Aberrations…3.1Performance of an achromate.......3.2Aplanatic lens.…3.3Transverse aberration curve.3.4Aspherical lens...........3Aberrations3.1 Performance of an achromateLoad a classical achromate out of a vendor catalog with focal length f=100 mm.a)What is the numerical aperture of the system in the image side Is the system diffraction limitedb)Determine the longitudinal aberrations for the colors eFC'.What is the largest spherical aberrationin the green What is the height of the corresponding ray in the pupil What is the largest differenceof the axial color aberrationc)Calculate the Seidel surface contributions of the system in the desired orientation and for thereversed lens.d)Determine the range of finite field angles,for which the original achromate is diffraction limited,if546 nm and a reduced aperture diameter of 15 mm is considered.3.2 Aplanatic lensConsider a collimated incoming beam with wavelength 500 nm and diameter 10 mm.This bundleshould be focussed by a perfect lens of focal length f=50 mm.a)Place an aplanatic-concentric lens shortly behind the ideal lens with the material SF57.What is theresulting numerical aperture in the image space Show at least two different methods to find the bestimage position.b)Show that the spherical aberration of this setup is exactly zero for all orders.c)Aplanatic means,that the linear coma vanishes and the imaging is free of coma for a small butfinite field size.Show this property by using a small field of 2 for the current system.What is thelargest present aberration3.3Transverse aberration curve1/2Establish 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 Zernikesurface 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 spotdiameter3.4 Aspherical lensLoad the catalof lens A20-18HPX form Asphericon.a)What is the residual correction in wave aberrations and in spot sizeb)Show,that the asphere is sensitive for finite field sizes by introducing a field with angle 0.1.Whatis the dominating type of aberrationc)What is the highest order of the chosen Taylor expansion Calculate the performance on axis,ifthe three highest expansion coefficients are set to zero.Is the system still diffraction limited