2013-06-13Prof.Herbert GrossFriedrich Schiller University JenaInstitute of Applied PhysicsAlbert-Einstein-Str 1507745 JenaSolution of ExercisesLecture Optical design with Zemax for PhD -Part 66.1 CPP expressed in Zernike polynomialsA cubic phase plate can be used to enhance the depth of focus.It is described by the simplepolynomialin normalized pupil coordinates and can be expressed by a superpostion of Zernike functions in theFringe convention asa)Establish a simple system with an imcoming collimated beam at the wavelength=546 nm,adiameter D =7 mm and a focussing perfect lens of focal length f=100 mm.A thin plane parallel plateof BK7 with thickness t=5 mm is used as a phase plate.To get this functionality,one side is shapedas a Zernike surface according to the representation above with a normalization radius of 3.5 mm.The constant a should be 0.0080.Visualize the surface contour of the cubic phase plate.b)Calculate the variation of the spot size over a defocus range of -20...+20 mm.Find the extendeddepth of focus,which should be defined as the interval,where the rms-spot is doubled in comparisonto the best image plane.c)Calculate the shape of the spot in the best image plane and at a distance of z=95 mm.What isobserved Calculate the MTF of the system in the surface representation for all azimuthal angles.What is the transfer behavior for different rotational settings of a bar patternd)Try to model the phase plate with another aspherical surface representation in Zemax.Solution:a)System with a Zemike Sag surface in Fringe convention with 11 terms,a normalization radius of3.5 mm and the corresponding values.The user defined semi aperture in the lens datza editor shouldhave teh same value as the normalization radius in the extra data editor.Sens-Dsaneter1/8The surface sag is illustrated here:Comment:According to the manual,it is also possible to select the Zernike phase surface type.In this case,thesubstrate surface,where the ray deviation takes place,remains unchanged (plane).In the currentcase of small deviations,thisis equivalent.The scaling in this case is on the one side morecomplicated (a factor of 2 n has to be taken into acount,the phase is scaled in radiant),on the otherside,a common prefactor M can be used to scale the complete surface by changing only one numbercorresponding to the number a in the above fommula).b)By using a universal plot with the spot diameter as criterion,we get the two plots4020.1The minimum spot size is 0.1774 mm.The double value is obtained for z 87 mm,therefore thedepth of focus is 26 mm.c)The spot diagram in the best image plane at z=100 mm and for z=110 mm look as followsThe spot is quite large and is of triangular shape.There is only s small change in size for thisdefocussing.The MTF looks like the following figure.It is seen,that the transfer behavior is quite good forstructures oriented along the x-and y-axis,but for rotated structures,the resolution is quite bad.d)The surface list offers an EXTENDED POLYNOMIAL surface,which in principle is a 2-dimensionalTaylor expansion in x and y.This representation can be used to describe the cubic phase plate byselecting a normalization radius of 5 mm and taking 9 terms.The coefficients XOY3 and X3Y0 arechosen with the same coefficient 0.008.The surface sag is identical to the model above.Par ()Par 1(unused)100,00000