2013-06-17Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax for PhD -Part 71.1 Fourier filtering and Imaging (ODZ 12)Set up a telecentric 4f-system with a magnification of m =4.The system should be arranged by twoappropriate achromates from conventional vendor catalogs with the focal lengths f=25 mm and f2=100 mm.The wavelength of the application is the e-line,the object size is 3 mm and the numericalaperture should be NA=0.1.a)Set up the system with telecentric behavior in the object and the image space.In particular adjustthe system and a rectangular stop with approporiate size in the intermediate focal plane.Theadjustment should be perfommed on axis only.b)Check the magnification of the realized lens.Calculate the performance of the system in the centerand the edge of the field size.Is the system diffraction limited What are the dominant aberrations inthe fieldc)Show,that the resolution of the system in the field is anisotropic due to the elongated shape of thespot by inspecting the MTF of the system.d)Calculate a diffraction based imaging of the complete object field.Take a rectangular grid as anobject.Can the anisotropic resolution be seenNow calculate a geometrical imaging model of the same grid.What is the difference betweenthe results of both modelse)To demonstrate the Fourier filtering in the pupil plane,removechange the rectangular pupil stop bya slit with dimensions Dx=5 mm,Dy=0.15 mm.What changes with the diffraction limited imageWhat is the consequence for the geometrical imagef)Calculate the Airy diameter of the system and constitute an object with size 10 times the Airydiameter.Put this small object in the center and at the edge of the field.Discuss the results andcompare them.Is the grid resolvedSolution:a)Corresponding achromates are found for example in the catalog of Melles&Griot as:First lens with f=25 mm:LAO -25.0-12.5Second lens with f =100 mm:LAO-25.0-12.5The first achromate must be reversed.The distances must be adjusted in a way to guarantee acollimated ray bundle between the lenses and to let the chief ray cross the optical axis in the backfocal plane of the first lens.The system stop has to be fixed at the intermediate focal point.Correspondingly the distance between the stop and the second lens must be arranged to gettelecentricity in the image space,the final image distance must be adjusted to get a sharp image.find t1,merit function angular radius1/52find t2,not telecentric,initial distance infinity,entrance pupil at lens with diameter D 3mmafter adding the second lens:adjusting the distance behind the stop:chief ray parallel to axis,merit function withREAB=05th step:focusing image plane on axis;merit function with spot criterionThe result is (for this choice of lenses):Lens Data EditorEdit Solves ViewHelpSurf:TypeRadiusSemi-DiameterInfinity0.00000001.00000001StandardInfinity22.02150001.000000041.5210000N-SF1012.41900004,5000000N-BAK6,2500000-15.796000029,25350006,2500000可SeandardInfinity97.46174912,49861426Standard65.786000014.0000000Standard-50.0570000N-SF1025.0000000=155.17000090.5770317VSeandardInfinity0,0000000IMASeandardInfinity4.0586688In the intermediate focal plane,a rectangular diaphragm with half widths 2.5 is placed.0b)The perfommance of the system can be estimated by a spot diagram as follows.From this diagram or the Prescription data -menu we get a magnification of m =-4.004.In the center,the system is nearly diffraction limited,for the field of y 1.5 mm,it is worse.3Spot Diagram2114.B39If the spoit diagram is considered,mainly coma,and defocus seems to be the reasons for thedecrease of the performance.The defocus can be astigmatism or field curvature.To decide about thisquestion,the Seidel diagram is considered.It is seen,that both aberration types are there but theastigmatism dominates by a factor of 2.飘c)The MTF shows a large separation of the tangential and sagittal contrast curves.This describes theanisotropic resolution of the coma/elliptical spot shape.4