2012-09-115 Imaging and lllumination5.1Fourier filtering and ImagingSet 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 100mm.The wavelength of the application is the e-line,the object size is 3 mm and the numerical apertureshould be NA 0.1.a)Set up the system with telecentric behavior in the object and the image space.In particular adjust thesystem and a rectangular stop with approporiate size in the intermediate focal plane.The adjustmentshould be performed on axis only.b)Check the magnification of the realized lens.Calculate the performance of the system in the center andthe edge of the field size.Is the system diffraction limited What are the dominant aberrations in thefieldc)Show,that the resolution of the system in the field is anisotropic due to the elongated shape of the spotby inspecting the MTF of the system.d)Calculate a diffraction based imaging of the complete object field.Take a rectangular grid as an object.Can the anisotropic resolution be seenNow calculate a geometrical imaging model of the same grid.What is the difference between theresults of both modelse)To demonstrate the Fourier filtering in the pupil plane,removechange the rectangular pupil stop by a slitwith dimensions Dx=5 mm Dy 0.15 mm.What changes with the diffraction limited image What isthe consequence for the geometrical imagef)Calculate the Airy diameter of the system and constitute an object with size 10 times the Airy diameter.Put this small object in the center and at the edge of the field.Discuss the results and compare them.Is the grid resolved5.2Ring illumination with axiconEstablish an illumination system with a ring shaped profile with the help of an axicon.First load an achromatic lens with focal alength f=100 mm out of a vendor catalog und create a collimatedmonochromatic beam with diameter D=20 mm and the wavelength 632.8 nm of HeNe as a laser sourceThe axicon consists of a plane an a conic surface.The conic surface can be approximated by a classicalhyperbolic conic section with an extremme small radius of curvature.The conic constant must have a largenegative value.What happens,if the 'Quick focus'option is usedNow insert between the lens and the axicon a 'negative axicon',which diverges the light.What happens,ifnegative axicon is moved along the optical axis5.3Fiber coupling and radiationAn initial collimated laser beam of an Ar-Laser at =505 nm and diameter D=4 mm has to be coupled intoa fiber of diameter 4 um,length L =20 mm and numerical aperture of NA =0.1.As a second step,the lightshould be re-collimated.a)Extract an appropriate achromate out of a vendors catalog and check,if a good and efficient couplingcan be achieved.b)Estimate the coupling efficiency in the geometrical and the diffraction model.c)Establish a fiber component with length 20 mm length as a non-sequential component and calculate theradiation profile at the exit surface in the geometrical optical model.d)Now the emitted light should be collimated again by an achromate with focal length of f=50 mm.e)Discuss the homogeneity of the light behind this lens in the spatial domain.Are the rays perfectlycollimated