Solutions: Lens Design I Part 2. Exercise 2-1: Apertures, stops and vignetting

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2016-04-25 Prof. Herbert Gross Mateusz Oleszko, Norman G.

1 Prof. Herbert Gross Mateusz Oleszko, Norman G. Worku Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str Jena Solutions: Lens Design I Part 2 Exercise 2-1: Apertures, stops and vignetting Load the achromate out of the lens catalog from the vendor Comar with a focal length f = 100mm called 100_DQ_25. Set the Entrance Pupil Diamter to EPD=20mm and insert the field points 0, 3 and 5. Vary the position of the stop. a) With the stop surface at the rear lens surface a. Generate the wavefront map without ray aiming b. Generate the wavefront map with ray aiming b) With the stop surface at the front focal plane Solution: a)a. a. Generate the wavefront map without vignetting b. Generate the wavefront map with vignetting

2 a)b.

3 b)a.

4 b)b. Open field and click set vignetting

Exercise 2-2: Paraxial system layout a) Suppose a divergent ray bundle with numerical aperture of NA = 0.2 at the wavelength = 500 nm.

Behind the focal point a third paraxial lens should collimated the beam again for a diameter of 36 mm. c) Now in a distance of 20 mm a foxussing oaraxial lens with focal lengt f = 100 is added.

What ist the magnification of the system? Solution: a) Wavelength and numerical aperture are inserted. Then we set the focal length by a pickup to have the same value as the first object distance.

5 Exercise 2-2: Paraxial system layout a) Suppose a divergent ray bundle with numerical aperture of NA = 0.2 at the wavelength = 500 nm. Establish a first paraxial lens with a focal length to get a collimated beam with diameter 24 mm. b) After a distance of 10 mm a second paraxial lens with focal length f2 = 30 mm fousses the ray. Behind the focal point a third paraxial lens should collimated the beam again for a diameter of 36 mm. c) Now in a distance of 20 mm a foxussing oaraxial lens with focal lengt f = 100 is added. Finally a negative lens with f = -70 mm is added in an appropriate distance to change the numericalaperture in the image space to Find the final image distance. What ist the magnification of the system? Solution: a) Wavelength and numerical aperture are inserted. Then we set the focal length by a pickup to have the same value as the first object distance. This guarantees a collimated output beam. In the merit function a PARY value of D/2 = 12 mm is required, the first distance is variable. Alternatively without using the optimization, the value can be calculated by hand with tan(u) = sin(u)/cos(u) = D/2/f = mm or approximated with the slider. b) The 3rd lens must have a focal length of 36/24 x 30 = 45 mm. The air distances are correspondingly.

6 c) A second optimization selects the distance of lens 4 to obtain the numerical aperture by PARB to be The image distance is obtained by QUICK FOCUS. Thelens data ar The magnification is 0.2 / 0.05 = 4.

Exercise 2-3: Grating spectrometer A linear grating with a line density of 0.

The grating is blazed and is used in the +1 st order.

mm, a thickness of10 mm and SF6 as material in a telecentric arrangement.

7 Exercise 2-3: Grating spectrometer A linear grating with a line density of 0.3 Lp/ m is illuminated by a collimated beam with a spectral broad wavelength between 400 nm and 700 nm. The grating is blazed and is used in the +1 st order. The spectrum is observed in a sensor plane, which is obtained after a symmetrical bi-convex lens with focal length f = 100 mm, a thickness of10 mm and SF6 as material in a telecentric arrangement. a) Set the system in Zemax b) What is the spreading of the spectrum in the sensor plane? Solution: a) System data and layout b) If a single raytrace is made for the extreme wavelengths 400 nm and 700 nm, one gets the ray heights in the sensor plane of mm and mm. Therefore the spectral spreading is y = mm.

8 Exercise 2-4: CPP expressed in Zernike polynomials A cubic phase plate can be used to enhance the depth of focus. It is described by the simple polynomial 3 3 W( x, y) x y in normalized pupil coordinates and can be expressed by a superpostion of Zernike functions in the Fringe convention as W( x, y) 2 Z2 2 Z3 Z7 Z8 Z10 Z11 4 a) Establish a simple system with an imcoming collimated beam at the wavelength = 546 nm, a diameter D = 7 mm and a focussing perfect lens of focal length f = 100 mm. A thin plane parallel plate of BK7 with thickness t = 5 mm is used as a phase plate. To get this functionality, one side is shaped as a Zernike surface according to the representation above with a normalization radius of 3.5 mm. The constant should be Visualize the surface contour of the cubic phase plate. b) Calculate the variation of the spot size over a defocus range of mm. Find the extended depth of focus, which should be defined as the interval, where the rms-spot is doubled in comparison to 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 is observed? 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 pattern? d) Try to model the phase plate with another aspherical surface representation in Zemax. Solution: a) System with a Zernike Sag surface in Fringe convention with 11 terms, a normalization radius of 3.5 mm and the corresponding values. The user defined semi aperture in the lens datza editor should have teh same value as the normalization radius in the extra data editor. The surface sag is illustrated here:

Comment: According to the manual, it is also possible to select the Zernike phase surface type. In this case, the substrate surface, where the ray deviation takes place, remains unchanged (plane).

The scaling in this case is on the one side more complicated (a factor of 2 has to be taken into acount, the phase is scaled in radiant), on the other side, a common prefactor M can be used to scale

9 Comment: According to the manual, it is also possible to select the Zernike phase surface type. In this case, the substrate surface, where the ray deviation takes place, remains unchanged (plane). In the current case of small deviations, thisis equivalent. The scaling in this case is on the one side more complicated (a factor of 2 has to be taken into acount, the phase is scaled in radiant), on the other side, a common prefactor M can be used to scale the complete surface by changing only one number corresponding to the number in the above formula). b) By using a universal plot with the spot diameter as criterion, we get the two plots The minimum spot size is mm. The double value is obtained for z = 87 mm, therefore the depth 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 follows

The spot is quite large and is of triangular shape. There is only s small change in size for this defocussing. The MTF looks like the following figure.

10 The spot is quite large and is of triangular shape. There is only s small change in size for this defocussing. The MTF looks like the following figure. It is seen, that the transfer behavior is quite good for structures 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-dimensional Taylor expansion in x and y. This representation can be used to describe the cubic phase plate by

11 selecting a normalization radius of 5 mm and taking 9 terms. The coefficients X0Y3 and X3Y0 are chosen with the same coefficient The surface sag is identical to the model above.

Lens Design I Seminar 1

Xiang Lu, Ralf Hambach Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str 15 07745 Jena Lens Design I Seminar 1 Warm-Up (20min) Setup a single, symmetric, biconvex lens