Multiple solutions in simple optical designsDavid ShaferDavid Shafer Optical Designspherical aberration correctionUNITS:MMFOCAL LENGTH 100 NA 0.1DES:ShaferAchromatic doublet ofSK5 and F2 glass,withspherical aberrationcorrection.There are always twodifferent bendings of aspherical aberration correctionUNITS:MMlens,with fixed power,FOCAL LENGTH 100 NA 0.1DES:Shafer10.8that give the same人Same negative lens power,sameamount of 3rd-orderspherical aberrationspherical aberration.Alternate solutionStill achromaticDall-Kirkham telescopeUNITS:MFOCAL LENGTH 936.5 NA 0.1068DES:ShaferDall-Kirkham telescope,42.4with elliptical primary mirrorand spherical secondarymirror.There are two radiifor the secondary mirror withthe same amount of sphericalFocusaberration,opposite to that ofshiftsthe primary mirror.Here,forthis arbitrary case,these twovalues for the secondaryDall-Kirkham telescopeS:MMFOCAL LENGTH 628.8 NA =0.159DES:/Shafermirror radius are -204.6 and42.4249,both the same distancefrom the primary mirror.For an intermediate radiusvalue,between these two,thesecondary mirror sphericalaberration reaches amaximum.