Tutorial Zemax Introduction 1

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1 Tutorial Zemax Introduction Introduction Exercise 1-1: Stair-mirror-setup Exercise 1-2: Symmetrical 4f-system Introduction 1.1 Exercise 1-1: Stair-mirror-setup Setup a system with a stair mirror pair, which decenters an incoming collimated ray bundle with 10 mm diameter by 40 mm in the -y direction. The wavelength of the beam is = nm. After this pair of mirrors a decentered main objective lens with focal length f = 200 mm made of BK7 is located 25 mm below the optical axis and focusses the beam. a) setup the system b) generate layout drawings in 2D and in 3D c) calculate the beam cross section on the second mirror, what is the size of the pattern? d) determine the optimal final sensor plane location. Calculate the spot of the focussed beam. Discuss the shape of this pattern. e) now extend the separation between the two mirros to 200mm. The system now should be modified to have an intermediate focal point in the midpoint between the mirrors. Calculate the radii of the mirrors to recollimate the beam before the refractive lens. Determine again the best image plane. If the spot diagram is considered, what is the reason for the drastic change? Solution: a) The best way to introduce the folding mirror is to used the option 'add folding mirror'. Here two explicite surfaces of the type coordinate break are introduced before and after the surface with a pickup of the angles. The idea ist to: 1. change the orientation by 45 to get the local coordinate system of the mirror befor the surface 2. mirror operation, the help function automatically introduces negative thicknesses behind the first mirror 3. perform the second 45 rotation to get the final 90 -axis orientation of the propagation axis after the mirror 4. fixe the next distance (negative after the first mirror) aftre that second coordinate break In princple, it is also possible to use the local coordinate changes of a surface. But this does not allow for general pickups, optimization etc. and is more cumbersome to change. Furthermore the input data are not seen in the lens data editor. To setup a lens with a pregiven focal length, there are several possibilities. An optimization of one of the surface radii with a focal length requirement in the merit function (EFFL, target value 200) is one general option. In addition, the first surface can be fixed and the second surface is obtained by the program with a solve, that forces the element power to be F=1/f = Unfortunatelly, this doen't work with the first surface. The system could be setup in the following scheme:

2 2 b) c) Footprint: the size of the beam in the local system is D x = 20 mm, D y = 28.3 mm

3 d) The final image location is determined by the quick focus option. The spot has a typical coma-shaped structure due to the off-axis usgae of the lens.

3 3 d) The final image location is determined by the quick focus option. The spot has a typical coma-shaped structure due to the off-axis usgae of the lens. e) The modified data are now with the radii -282 mm and +282 mm (due to the change of sign by the first mirror) respectively The layout and the spot diagram looks as follows:

4 Since the spherical mirrors induce a large astigmatism, the focussing only looks fine the the y-z-plane. The elliptical shape neat the circle of least confusion dominates over the coma. 4

5 1.2 Exercise 1-2: Symmetrical 4f-system Setup a telecentric 4f-imaging system with two identical plano-convex lenses made of BK7 with thickness d = 10 mm and approximate focal lengths f = 100 mm.

$c) If the starting aperture is decreased, the system becomes more and more diffraction limited. What is the value of the NA to get a diffraction limited system on axis?$

5 5 1.2 Exercise 1-2: Symmetrical 4f-system Setup a telecentric 4f-imaging system with two identical plano-convex lenses made of BK7 with thickness d = 10 mm and approximate focal lengths f = 100 mm. The wavelength of the system is = nm and the numerical aperture in the object space is NA = 0.2. The object has a diameter of 10 mm. a) Determine the layout and the spot diagram of the system, if the setup is perfectly symmetrical. b) Optimize the image location. Why is the spot size improved? c) If the starting aperture is decreased, the system becomes more and more diffraction limited. What is the value of the NA to get a diffraction limited system on axis? Take in mind here, that the lowered spherical aberrations needs a re-focussing, which depends on the aperture. Solution: a) The sysytem layout can be set up in the follwoing way with the corresponding inputs. The pickups force the system to be symmetrical. The distances between the object, the lenses, the stop and the image plane are all not exactly 100 mm, because the focal length is measured with respect to the principal planes, which are located inside the lenses. The exact determination of the distances befor the lens (87 mm) and from thew lens to the stop (96 mm) can be determined exactly by optimization, by solves or by try and error with single rays.

6 6 b) The best image location is approximately 1 mm nearer to the system with a considerably smaller size due to the spherical aberration of the system. c) If the numerical aperture is reduced to a value of NA = 0.05, the system approximately is diffraction limited, as can be seen on the spot diagram on axis and the corresponding Airy diameter.

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