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 for imaging a point object. The lens is made of the glass N-BK7, has a radius of curvature of R = 32.3 mm, and a thickness of t = 5 mm. The numerical aperture in object space has a value of NA = 0.05 and the corresponding object has a distance of s = 100 mm. The initial wavelength is set to λ = 632.8 nm. a) Calculate the effective focal length of the lens analytically using the thin lens formula and estimate the image location s. b) Determine the image location numerically such that the spot RMS becomes minimal. c) Modify the object distance to achieve a collimated beam (Use: Quick Adjust). d) Modify the surface curvature to refocus the beam to the original image position. Inspect the spot diagram (Use: Quick Adjust). Solution: a) For a thin lens in air, we have: 1 f = (n 1) ( 1 1 ) 0.5 2 R 1 R 2 R = 1 32.3mm 1 s 1 s = 1 f, 1 s = 1 f + 1 s = 1 32.3mm + 1 100mm = 1 47.71mm b) s =44.124mm, RMS(dy) = 38um (10x Airy diameter) c) s=29.613mm, RMS(du) = 0.914 mrad (4x Airy diameter) d) Quick Adjust Spot size on Radius of Surface 2 RMS(dy) = 5.73um (0.5x Airy) If we use a simple Spot minimization for the merit function RMS(dy) = 5.013um (0.5x Airy) Comments: Number format: 23,3 (if Regional Settings of operating system are set to German) 23.3 (if Regional Settings are set to English) Save file: Ctrl + S Spot Diagram: Ctrl + Shift + S Layout Diagram: Ctrl + (Shift) + L undo (F3), redo (Shift + F3) System Explorer / Aperture / Afocal Image Space for collimated beam in image space Quick Adjust (Thickness or Radius only, more complicated: Merit Function Editor) o first select element that should be varied in LDE, then click Quick Adjust o Adjust has to be pressed several times (single iteration of optimizer)!
Exercise 1-1: Symmetrical 4f-System (30min) 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 = 546.07 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 symmetric. 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 radius of curvature is approximately 50 mm. A more exact value can be obtained by setting a solve with component power F = 1/f = 0.01 mm -1 at the second lens surface. To find the first distance, the easiest solution without optimization is to reverse the lens, start with collimated light of 21 mm diameter and find the optimal distance behind the lens with quick focus. This value is inserted in the system, where the best orientation is to have the plane surface towards the object. It has to be noticed, that due to the finite residual aberrations of the single lens, a perfect collimation cannot be obtained for all rays in the aperture cone. The distance between the lens and the stop plane can be found by forcing the system to be telecentric (System Explorer / Aperture) and to force the chief ray height at the STOP to be 0.
The best image location is approximately 5 mm nearer to the system with a considerably smaler size due to the spherical aberration of the system. 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. Comments: first sketch layout, marginal and chief ray, telecentric system (entrance pupil at infinity) How to start? With which specification we should start? o First, determine radius of plano-convex lens (reverse system, or use solve). o Second, get distances right. Problem: principal planes are not known start with object distance to get collimated intermediate rays (Use Quick Adjust). Then determine distance to STOP (Chief ray height 0). o Third, make second lens symmetric (copy and reverse system) in perfectly symmetric system: o all odd aberrations vanish: coma, lateral color, distortion (but ray path is not exactly symmetric about STOP so that small contributions remain), o all even aberrations are doubled: spherical, astigmatism, field curvature, axial color refocusing improves spot size in presence of spherical aberration and field curv reducing the NA reduces aberrations and we obtain diffraction limited system Hint: use shortcuts (or set preferences of often used shortcuts, like quick adjust) undo (F3), redo (Shift + F3) Quick Focus (Ctrl + Shift + Q)
Exercise 1-2: Stair-Mirror Setup (30min) Setup a system with a stair mirror pair, which decenters an incoming collimated ray bundle with 20 mm diameter by 40 mm in the -y direction. The wavelength of the beam is = 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 focuses 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. What is the spot RMS of the focused beam. Discuss the shape of this pattern. e) Now, extend the separation between the two mirrors to 200mm. The system should be then modified to have an intermediate focal point in the midpoint between the mirrors. Calculate the radii of the mirrors to re-collimate the beam in front of the refractive lens. Determine again the best image plane. If the spot diagram is considered, what is the reason for the drastic change? Solution: Note: the decenter should be set up with a separate coordinate break. Here, the decenter is performed before the rotation, i.e. in the direction of 45 degree (1/ 2 decenter in global y) Footprint: the size of the beam in the local system is D x = 20 mm, D y = 28.3 mm
The final image location is determined by the quick focus option. The spot has a typical comashaped structure due to the off-axis usage of the lens. 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 (adjust radius to have intermediate focus at right position in YZ plot by hand, alternative: Quick Adjust at intermediate plane) Since the spherical mirrors induce a large astigmatism, the focussing only looks fine the the y- z-plane. The elliptical shape near the circle of least confusion dominates over the coma.
Comments: add fold mirrors (button in LDE), angle positive ccw thickness after odd number of mirrors: negative (propagation in z direction) reason: how to specify reflection in raytracer (ToDo) How to create lens of given EFFL (in new Zemax file): o set up biconvex lens: R 1 = R 2 f, o then scale the lens to exact EFFL (button in LDE), o then adjust distance to spot using quick focus (Ctrl + Shift + Q) o insert lens in original Zemax file: File / Insert Lens add coordinate break (changing optical axis), pay attention with the order of rotation / decenter show macroscopic astigmatism in 3D layout (ring with >20 rays), two foci use Quick Adjust with intermediate plane to find ideal radius of curvature for intermediate focus.
Exercise 1-3: Apertures, Stops, and Vignetting (20min) Load the achromate AAP-125.0-25.4 from the lens catalogue (CVI Melles Griot, f = 125mm). Set the diameter of the entrance pupil to 20mm and the wavelength to 546.1nm. Display the wavefront of the achromate for the field points 0, 3 and 5 with different stops and apertures: a) with the stop surface at the rear lens plane, b) with the stop surface at the front focal plane (for finding the position of the focal plane, use Analysis / Rays and Spots / Cardinal Points), c) with adjusted entrance pupils using System Data / Fields / Settings / Set Vignetting. d) Insert a circular central obscuration of 6mm radius at the rear surface of the achromate and recalculate the wavefront with and without using vignetting factors. Expansion: Compare the wavefronts with / without ray aiming - Remove the obscuration -Add at front face a circular surface aperture radius 9 - built up a default sequential merit function RMS wavefront, 6rings, 6arms Calculate the ray intersection coordinates (REAY) for the marginal rays of field 5 and the paraxial ray What happens with the marginal rays? Solution: a) b) without c) with ray aiming via set vig d) without d) With the obscuration set the VCX = VCY = 0 for th axis
Zu d) to show the effect use the operand reay at surface 3 Semi-Diameter (12.7) Circular aperture with radius 9 at surface 4 Merit function after clear vignetting: Merit function after set vignetting:
The surface aperture becomes visible by set semi-diameter to automatic, u here means fix The asterix indicates a aperture If no set vig command is done, the merit function may be wrong. Use menu modify, remove all apertures Comments: wavefront plots show the optical path length of a ray from a given field point to a reference sphere (centered upon the ideal image point, crossing the exit pupil on axis) which is mapped to the entrance pupil intersection point of the ray front focal plane as stop location image sided telecentric system! if vignetting occurs, the pupil is truncated (typically an intersection of decentered circles) vignetting factors describe the offset and half axes of an ellipse which approximates the real vignetted pupil
Exercise 1-3 (alt): 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
a)b.
b)a.
b)b. Open field and click set vignetting