Verallgemeinerte Optische Abbildungssysteme ("VopSys")
Final Report Abstract
Design and strategies of optimization are investigated for optical systems with freeform elements in the project VopSys. Step 1: After creating a ZEMAX compatible raytracing tool, optical systems with spherical lenses and mirrors are optimized w.r.t. several usual objectives, mainly the square of the RMS error, by using standard least square algorithms. The gradients of the objective in dependence of the geometric and optical parameters are calculated approximately by symmetric differences (SD) or by automatic differentiation (AD) (usage of ADOL-C). However, the fixed point iteration caused by Newton method for determining the cutting point of the ray with surface of an optical element is only executed by elementary realization of the finite iteration. Therefore, the result is not more exact than the use of (SD) but considerably shorter in the CPU-time. The integration of the 2nd tape for fixed point iterations into the (AD) was not managed. Replacing the asphere by some radial NURBS does not, as expected, improve the results received with the asphere. Step 2: Using the "Geometric Modelling Library"(GML) in C++ freeform elements can be approximated by non-radial NURBS with high degree of freedom’s. It is not convenient to approximate already the asphere of the ZEMAX start configuration by a NURBS. Because of the high degree of freedom’s one gets a lot of local minima which are much worse than the result fund by the optimization of the system with the asphere. The approximation of the optimal asphere by a NURBS yields a better starting configuration for further improvements. The best approximations w.r.t. local behavior and sufficiently large smoothness one gets with a NURBS of degree 4, chordal selection of the knots and a grid of at least 13 x 13 knots. It is only successful with GML whenever the root term of the formula for the asphere is not too close to zero since the GML only works with Cartesian coordinates. Higher degrees of the NURBS have not essential impact to the quality of approximation but overlapping of patches of the NURBS becomes larger what increases the local regions. That is counterproductive and deteriorates the local properties of the NURBS. Lower degrees destroy the continuous differentiability of the curvature of the NURBS in coordinates of the control points. Least square methods are now obsolete since the NURBS has in comparison to the image points too much free parameters. Nocedal‘s Limited Memory Quasi-Newton-method does not yield under use of (SD) suitable improvements: R-sublinear convergence, a lot of CPU time for each iteration because of the (SD), (SD) - not exact enough for further improvements, considerable oscillations. Step 3: The following decomposition algorithm yields some small improvements (1 decimal place) w.r.t. the NURBS starting configuration already in case of the use of (SD). S1: Do a raytracing with all rays -> result: baric centers / adjustment of baric centers. S2: Stop whenever the RMS-error is small enough. S3: Determine for each object point the ray where the image point has the largest distance to its baric center. This ray and a small selection of rays around it create with their sum of distance squares w.r.t. its fixed baric center according to S1 the new RMS-square objective, summed up over all object points (partial objective). S4: Minimize the partial objective with the fixed baric centers then go to S1. The minimization of the RMS-Square of systems with NURBS with the help of raytracing is under standard optimization methods from our point of view only then successfully and fast performable whenever the 2nd tape for fixed point iterations of (AD) is embedded in the algorithm. It is therefore necessary to possess own source files for the computation and change of NURBS approximations. Such sources are not available in GML. Further these source files must be compatible with the ADOLC software. The determination of the cut of a ray with the NURBS is critical and needs professional numeric considerations since the NURBS is not defined outside its parametrization.
Publications
- "Optical performance of coherent and incoherent imaging systems in the presence of ghost images", Appl. Opt. 51, 7134-7143 (2012)
R. H. Abd El-Maksoud, M. Hillenbrand, S. Sinzinger, J. Sasian
(See online at https://doi.org/10.1364/AO.51.007134) - "Optical system for trapping particles in air", Applied Optics, Vol. 53, Issue 4, pp. 777-784 (2014)
R. Kampmann, A. K. Chall, R. Kleindienst, S. Sinzinger
(See online at https://doi.org/10.1364/AO.53.000777) - "Wavefront-coding technique for inexpensive and robust retinal imaging", Optics Letters, Vol. 39 Issue 13, pp.3986-3988 (2014)
J. Arines, R. O. Hernandez, S. Sinzinger, A. Grewe, E. Acosta
(See online at https://doi.org/10.1364/OL.39.003986) - "Subaperture stitching for measurement of freeform wavefront," Appl. Opt. 54, 10022-10028 (2015)
K. K. Pant, D. R. Burada, M. Bichra, M. P. Singh, A. Ghosh, G. S. Khan, S. Sinzinger, and C. Shakher
(See online at https://doi.org/10.1364/AO.54.010022) - “Ultrathin Alvarez lens system actuated by artificial muscles”, Appl. Opt. 55, 2718-2723 (2016)
S. Petsch, A. Grewe, L. Köbele, S. Sinzinger, H. Zappe
(See online at https://doi.org/10.1364/AO.55.002718)
