2013-05-18Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax for PhD -Part 31.1Grin lens1.2Grating spectrometer 31.3Alvarez Lens 41.1 Grin lensEstablish a grin rod focussing Wood lens.A component of diameter D=8 mm,a length L =25 mmand a refractive index no =1.5 on axis has circular symmetric a radial gradient profile with quadraticcoefficient n2=-0.0046262.The lens should be illuminated by a centered collimated beam withwavelength =500 nm and diameter 4 mm.a)Determine the paraxial pitch length of the lens.It is defined by the length of the periodically sine-wave path of the marginal ray.b)Cut the lens exactly in the focal point and determine the spot diameter in this location.Compare thediameter with the diffraction limited Airy diameter.Why is the spot so large What is the smallest spotradius rms value and where is this optimal focus positionc)Compare the marginal ray path in the paraxial approximation with the real ray.What is the size ofthe numerical aperture in the focal pointd)Now give the lens a length of 60 mm.Introduce a finite field angle of 25,the front surface of thelens should be the stop location.Discuss the ray path in the lens drawing considering the diameterand the field ray bundle.Solution:The system is established according to the data with the surface 2 as a surface of the typeGRADIENT 1 and the parameters no =1.5 and nr2 =-0.0046262.According to the ray path in thelayout,a focal point is seen in a certain distance before the exit surface of the lens.eSems-Diameter14.0000003.51584959.5158495a)If the aperture is reduced to a small value of approximately 0.1 mm diameter and in the menueGENERAL the global coordinate reference is located at the front surface of the grin lens,it is seenthat the smallest caustic diameter is obtained in the distance z 20 mm after the entrance surface ofthe lens.If the spot diagram over defocus is calculated with the delta of 5000 um,the following figure isobtained,which also shows this result.Dateci-090Therefore the quarter pitch length is 20 mm,the pitch is 80 mm.b)If the thickness t2 is set to 20 mm,the spot looks as follows.The diameter is 12.9 um and is afactor of 10 larger than the Airy diameter.The reason for this is the spherical aberration of the finite出If the option rms spot size vs defocus is used it is seen,that the smallest focus is located 68 um insidethe rod and has a radisu of 4.03 um.23c)If the raytrace is calculated,we get the following tableX-cocrdinateY-coordinateZ-cogine1.00000000001.00000000000,97202657220,97202657222-cgordisateIt is seen,that the very small y-height in the paraxial calculation of 3.6 105 mm is enlarged to 0.0244mm for the real marginal ray.The numerical aperture in the focus point issin(u)=cos(a)=0.235d)If the corresponding data are established,we get the following figure:It is seen that the focal point for the field ray bundle lies to the left of the axis bundle.Thiscorresponds to a large field curvature.The diameter of the rod is not sufficient for the field rays,in reality,the outer coma rays are vignettedor reflected from the boundary.This is not noticed by Zemax1.2 Grating spectrometerA linear grating with a line density of 0.3 Lp/um is illuminated by a collimated beam with a spectralbroad wavelength between 400 nm and 700 nm.The grating is blazed and is used in the +1st order.The spectrum is observed in a sensor plane,which is obtained after a symmetrical bi-convex lens withfocal length f=100 mm,a thickness of10 mm and SF6 as material in a telecentric arrangement.a)Set the system in Zemaxb)What is the spreading of the spectrum in the sensor planeSolution:a)System data and layout