2013-05-22Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax for PhD -Part 44.2 Aspherical lensLoad the catalog lens A20-18HPX from 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 limitedSolution:The lens is established as follows:a)The Zernike coefficients are zero in the available accuracy.The plots of the residual transverseaberrations shows a maximum value of 103 um =1 pm.1/8b)For the desired field,the spot shows coma in the range of the diffraction limit.The Zernike expansion is domated by coma.FieldPeak to Valley(to chief0.9680965waves0.00376443 wavea aquared0.861901890,00000023Mave8Maximum fit error0.00000112 waves210.00496625:123-0,29390723:(p)*SIN (A)0.004933620.003530740,00000000-0,00005601+120.00000000120.00011117:130.0000000012p^216-0.00002371:170.00000000：0,00000000:c)If the 10th to the 14th order coefficients are set to zero the following data are obtained:35722214atdWith a Strehl niumber of 89%per definition the system is diffraction limited.4.4Anamorphotic Diode collimatorA semiconductor diode with wavelength 650 nm and the divergence aperture values 0.4 /0.1 in thefast ans slow axis respectively should be collimated in a circular beam with a diameter ofapproximarely 8 mm.The collimated beam is now focussed into a fiber with numerical aperture of NA=0.1.diodecircular beamNAy=0.4D=8 mmL4NAx=0.1L21=650nmcylindrical lensfocussing lensfiberNA=0.1L1L3asphericalcylindrical lenscollimatorFind a solution for this problem with only available catalog lenses.Is the setup diffraction limited Explain the shape of the residual spot pattern.What are the reasonsfor the residual aberrations in the system What can be done to further improved the resultDiscuss possible steps to get a shorter system.What are the consequences of a compact layoutSolutionIf the desired beam diameter after the collimation of the fast axis is 8 mm,the focal length of the firstlens isf=D/2/NA,=10mmSince the numerical aperture of the fast axis is high,it is recommended to use an asphericalcollimator lens,which is corrected for spherical aberration on axis.If such a lens is found in the lenscatalogs,it must be considered:1.the lens should be used without cover glas plate2.if a working wavelength near to the 650 nm is found,it is an advantage