2013-05-08Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax for PhD-Part 11.1Stair-mirror-setup11.2Symmetrical 4f-system11.3System layout with ideal lenses1.1Conic surface 21.1 Stair-mirror-setupSetup a system with a stair mimrro pair,which decenters an incoming collimated ray bundel with 10mm diameter by 40 mm in the -y direction.The wavelength of the beam is 632.8 nm.After thispair of mirrors a decentered main objectiv lens with focal length f =200 mm made of BK7 is located25 mm below the optical axis and focusses the beam.a)setup the systemb)generate layout drawings in 2D and in 3Dc)calculate the beam cross section on the second mirror,what is the size of the patternd)determine the optimal final sensor plane location.Calculate the spot of the focussed beam.Discussthe shape of this pattern.e)now extend the separation between the two mirros to 200mm.The system now should be modifiedto have an intermediate focal point in the midpoint between the mirrors.Calculate the radii of themirrors to recollimate the beam before the refractive lens.Determine again the best image plane.Ifthe spot diagram is considered,what is the reason for the drastic change1.2 Symmetrical 4f-systemSetup a telecentric 4f-imaging system with two identical plano-convex lenses made of BK7 withthickness d 10 mm and approximate focal lengths f=100 mm.The wavelength of the system is546.07 nm and the numerical aperture in the object space is NA =0.2.The object has a diameter of10mm.a)Determine the layout and the spot diagram of the system,if the setup is perfectly symmetrical.b)Optimize the image location.Why is the spot size improvedc)If the starting aperture is decreased,the system becomes more and more diffraction limited.Whatis the value of the NA to get a diffraction limited system on axis Take in mind here,that thelowered spherical aberrations needs a re-focussing,which depends on the aperture.1/21.3 System layout with ideal lensesA collimated laser beam with wavelength 1.064 um and diameter D=2 mm should be expanded by aKepler-type afocal telescope made of ideal lenses with a first focallength f=50 mm and a factor of 5.The enlarged collimated beam is then focussed down by a cylindrical lens with focal length f 100mm to get a line focus.a)Setup the system described above by ideal lensesb)Show the line focus graphically1.4 Conic surfaceA system with an ellipsoidal mirror should be installed.For this task,the following steps should beperformed:a)A source with wavelength =1.064 um and numerical aperture NA =0.1 is imaged by a sphericalmirror in a 1:1 setup with a mirror radius of 20 mmb)The image distance is enlarged to 40 mm.The radius of the mirror and the conical constant isoptimized for this geometryc)The coordinate system is rotated by 60 directly after the object.For a proper layout,thesubaperture of the mirror which is used should be explicitly defined.Make a shaded model layout withthis setup.What is the bending angle of the central ray at the mirror Determine the shape and the approximatex/y-aspect ratio of the illuminated area on the mirror.