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Lens Design I – Seminar 1 Exercise 1-1: Stair-Mirror-Setup (Homework)

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Lens Design I – Seminar 1 Exercise 1-1: Stair-Mirror-Setup (Homework) Y. Sekman, X. Lu, H. Gross Friedrich Schiller University Jena Institute of Applied Physics Albert-Einstein-Str 15 07745 Jena Lens Design I – Seminar 1 Exercise 1-1: Stair-mirror-setup (Homework) 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 λ = 632.8 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 focused beam. Discuss the shape of this pattern. Solutions: a) Add fold mirror -90,thickness -40, then fold mirror 90, thickness 40 Rotate in coordinate brake: clock-wise: positive counter-clockwise: negative Add lens, power solve=0.005, y decenter -25 b) c) d) Tangential focus in front of sagittal focus 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 λ = 546.07 nm and the numerical aperture in the object space is NA = 0.2. The object has a diameter of 10 mm. a) If the setup is perfectly symmetrical, determine the layout and the spot diagram of the system. b) Optimize the image location. Why is the spot size improved? c) If the starting aperture is decreased, the system becomes more and more close to diffraction limited. What is the value of the NA to get a diffraction limited system on axis? Take in mind here, that a re-focussing might be necessary due to the lowered spherical aberrations, which depends on the aperture. Solution: a) Find object distance, find stop position by ‘chief ray height’, compare with principle planes. a) b) NA=0.018 Exercise 1-3: Apertures, stops and vignetting Load the achromate f = 100mm AAP-125.0-25.4, Melles Griot. Set the entrance pupil diameter to be 20mm. Show the wavefront of the achromate for the field points 0°, 3° and 5° with the following configurations. a) The stop surface is at the rear surface of the achromate b) The stop surface is at the front focal plane of the achromate, without setting vignetting. Use the ‘Cardinal Point Data’ button in Analyze->Reports to find this stop position. c) Set vignetting in the ‘Field Data Editor’ and repeat b). d) Insert a 6mm obscuration at the rear surface and calculate the wavefront, compare the wavefronts with / without ‘set vignetting’. e) Clear all vignetting, then calculate the ray intersection coordinates (REAY) at the rear surface for the marginal rays and the chief ray of field 5° in the merit function editor. Interpret the result. Solutions: a) b) Wavefront is truncated by the lens, vignetting occurs. c) ‘set vignetting’: Recomputes the vignetting factors for each field based upon the current lens data. Vignetting factors (VDX, VDY, VCX, VCY) are coefficients which describe the apparent entrance pupil size and location for different field positions. These vignetting factors should be left at zero if there is no vignetting in the system. The factors are further described in “Conventions and Definitions” under “Vignetting factors”. The set vignetting algorithm estimates the vignetting decenter and compression factors so that the four marginal rays in the top, bottom, left, and right edges of the pupil pass within the apertures of each surface. Only the primary wavelength is used. Set vignetting evaluates the truncated pupil and approximate the truncated pupil with a shifted and compressed circle, then it calculates the vignetting factors, which defines the shift and compression of the original pupil in the x and y direction, With these factors a coordinate transformation can be performed to transform the original pupil coordinates to the truncated pupil. VCX VCY: compression factor VDC VDY: shift factor Vignetting factors are coefficients which describe the apparent entrance pupil size and location for different field positions. OpticStudio uses five vignetting factors: VDX, VDY, VCX, VCN, and TAN. These factors represent decenter x, decenter y, compression x, compression y, and tangential angle, respectively. The default values of all five factors are zero, which indicates no vignetting. d) Clear vignetting Set vignetting For on axis field, the compression factor is 1, compressed to 0; not applicable for the ring shaped apodization, no concave structure can be approximated. e) Clear vignetting: Set vignetting: The exercises will be discussed on Thursday, 19.04.2018, at 10.15 am in the Computer Pool of the ACP. Please solve task 1-1 on your own and save your intermediate results. .
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