2012-11-28Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax-Part 44AberrationS.4.1Strehl ratio and geometrical vs Psf spot size.14.2Aberrations and Performance of an Diode Collimator.......34.3Anamorphotic Diode collimator.64Aberrations4.1 Strehl ratio and geometrical vs diffraction Psf spot sizeA single plano-convex lens made of K5 with focal length f 25 mm and thickness d 5 mm isilluminated by a diverging beam with numerical aperture NA =0.1 and wavelength 546.07 nm.After the lens the light should be collimated.If the collimated beam is refocussed without furtheraberrations,the point spread function is not diffraction limited.a)Calculate the accurate Strehl ratio,the estimated Strehl ratio and the geometrical and diffractionencircled energy inside the ideal Airy diameter.b)If now the numerical aperture is reduced,the Marechal estimation becomes better.Calculate thelargest NA,for which the relative error is smaller then 2%.What amount of the beam power forgeometrical and diffraction encircled energy is inside the Airy diameter obtained hereSolution:aSystem data and layout:1/112b)If the numerical aperture is changed,the following steps are performed:1.Reduce NA2.Determine the Airy diameter out of the spot diagram window3.Set the apertur in the image plane exactly to the Airy value4.Calculate the estimated Strehl ratio from the Zernike window5.Calculate the accurate Strehl ratio from the Huygens PSF window with appropriate sampling6.Calculate the geometrical encircled energy by the footprint diagram(with option:delete vignetted)7.Calculate the diffraction encircled energy by the text output of the EE window.Then the following table is obtained:NAStrehlStrehlrelative errorAiry radiusgeometricaldiffractionexactestimatedEE insideEE insideAiryAiry0.10.019000.0032990.03890.03940.080.058000.0041230.08890.08890.070.053000.0047120.14490.14430.060.1720.21580.2550.0054970.25140.34030.0550.3420.36620.06610.0059960.34140.46110.0510.4860.49580.01980.0064660.44670.55340.050.5200.52770.01460.0066000.47800.56500.0450.6760.67530.001040.0073280.68870.66070.040.7980.79400.005010.0082441.00.7281The relative error of the estimated Strehl ratio is smaller than 2%for NA 0.051.Here thegeometrical encircled energy is 45%,the diffraction calculated encircled energy 55%.0.0000000134.2 Aberrations and Performance of an Diode CollimatorLoad the lens GLC-6.5-8.0-830 DIODE LASER COLLIMATING LENS from the catalog of CVI MellesGriot.a)What is the numerical aperture of the lens in the image?Determine the Strehl ratio and comparethe estimated and the exact value.b)What are the two surfaces with the largest contribution to the spherical aberration The first lensgroups looks like an achromate.Corresponds the correction of this part of the system to anachromatec)Show,that all intersection points of the spot diagram are inside the Airy diameter.If the spot isanalysed it is seen,that there is a bright kemel with a surrounding halo.What is the relative powercontent of the inner kernel region What is the diameter of this inner partd)What is the image contrast of a grating object with 100 line pairs per millimeter of this systemDetermine the MTF of the lens for defocussing.What is the depth of focus intervall,where inside thecontrast is larger than 50%Explain the asymmetry of the curve.Solution:a)The system looks as follows.Lens Data EditorSurf:Type我adiusThicknessSemi-DiameterStandardInfinityInfinity1StandardInfinity5.00000004.0000000Standard GLC-6.5-8.0-..15.01794644.4410000N-BAK25.0000000U3Standard-6.94849771.28300005.0000000U-39.0091670.12800005.00000000510.50894843.6400000N-SF115.0000000可23.92516210.97900005.0000000U7Standard5.65610865.1320000N-5F11Infinity1.2124989MStandardInfinity5.509E-004The numerical aperture is NA=0.524 in the image space.