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Aehle M, Alme J, Gábor Barnaföldi G, Blühdorn J, Bodova T, Borshchov V, van den Brink A, Eikeland V, Feofilov G, Garth C, Gauger NR, Grøttvik O, Helstrup H, Igolkin S, Keidel R, Kobdaj C, Kortus T, Kusch L, Leonhardt V, Mehendale S, Ningappa Mulawade R, Harald Odland O, O'Neill G, Papp G, Peitzmann T, Pettersen HES, Piersimoni P, Pochampalli R, Protsenko M, Rauch M, Ur Rehman A, Richter M, Röhrich D, Sagebaum M, Santana J, Schilling A, Seco J, Songmoolnak A, Sudár Á, Tambave G, Tymchuk I, Ullaland K, Varga-Kofarago M, Volz L, Wagner B, Wendzel S, Wiebel A, Xiao R, Yang S, Zillien S. Exploration of differentiability in a proton computed tomography simulation framework. Phys Med Biol 2023; 68:244002. [PMID: 37949060 DOI: 10.1088/1361-6560/ad0bdd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 11/10/2023] [Indexed: 11/12/2023]
Abstract
Objective.Gradient-based optimization using algorithmic derivatives can be a useful technique to improve engineering designs with respect to a computer-implemented objective function. Likewise, uncertainty quantification through computer simulations can be carried out by means of derivatives of the computer simulation. However, the effectiveness of these techniques depends on how 'well-linearizable' the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications.Approach.This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques.Main results.The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. However, the observed high density and magnitude of jumps was likely to preclude most meaningful uses of the derivatives. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path, and could be reduced in magnitude by a 'fuzzy voxels' approach. The investigated jumps in the MC function arose from local changes in the control flow that affected the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem.Significance.Besides the technical challenges of merely applying AD to existing software projects, the MC and MBIR codes must be adapted to compute smoother functions. For the MBIR code, we presented one possible approach for this while for the MC code, this will be subject to further research. For the tracking subprocedure, further research on surrogate models is necessary.
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Affiliation(s)
- Max Aehle
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Johan Alme
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Johannes Blühdorn
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Tea Bodova
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | | | - Viljar Eikeland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Christoph Garth
- Scientific Visualization Lab, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Nicolas R Gauger
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Ola Grøttvik
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Håvard Helstrup
- Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, NO-5020 Bergen, Norway
| | | | - Ralf Keidel
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Chinorat Kobdaj
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Tobias Kortus
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Lisa Kusch
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Viktor Leonhardt
- Scientific Visualization Lab, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Shruti Mehendale
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Raju Ningappa Mulawade
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Odd Harald Odland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- Department of Oncology and Medical Physics, Haukeland University Hospital, NO-5021 Bergen, Norway
| | - George O'Neill
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Gábor Papp
- Institute for Physics, Eötvös Loránd University, 1/A Pázmány P. Sétány, H-1117 Budapest, Hungary
| | - Thomas Peitzmann
- Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands
| | | | - Pierluigi Piersimoni
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- FSN Department, ENEA, Frascati Research Center, I-00044, Frascati, Italy
| | - Rohit Pochampalli
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Maksym Protsenko
- Research and Production Enterprise 'LTU' (RPE LTU), Kharkiv, Ukraine
| | - Max Rauch
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Attiq Ur Rehman
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Dieter Röhrich
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Max Sagebaum
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Joshua Santana
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Alexander Schilling
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Joao Seco
- Department of Biomedical Physics in Radiation Oncology, DKFZGerman Cancer Research Center, Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Arnon Songmoolnak
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Ákos Sudár
- Wigner Research Centre for Physics, Budapest, Hungary
| | - Ganesh Tambave
- Center for Medical and Radiation Physics (CMRP), National Institute of Science Education and Research (NISER), Bhubaneswar, India
| | - Ihor Tymchuk
- Research and Production Enterprise 'LTU' (RPE LTU), Kharkiv, Ukraine
| | - Kjetil Ullaland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Lennart Volz
- Biophysics, GSI Helmholtz Center for Heavy Ion Research GmbH, Darmstadt, Germany
- Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom
| | - Boris Wagner
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Steffen Wendzel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Alexander Wiebel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - RenZheng Xiao
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- College of Mechanical & Power Engineering, China Three Gorges University, Yichang, People's Republic of China
| | - Shiming Yang
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Sebastian Zillien
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
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Kortus T, Keidel R, Gauger NR. Towards Neural Charged Particle Tracking in Digital Tracking Calorimeters With Reinforcement Learning. IEEE Trans Pattern Anal Mach Intell 2023; 45:15820-15833. [PMID: 37581965 DOI: 10.1109/tpami.2023.3305027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/17/2023]
Abstract
We propose a novel technique for reconstructing charged particles in digital tracking calorimeters using reinforcement learning aiming to benefit from the rapid progress and success of neural network architectures without the dependency on simulated or manually-labeled data. Here we optimize by trial-and-error a behavior policy acting as an approximation to the full combinatorial optimization problem, maximizing the physical plausibility of sampled trajectories. In modern processing pipelines used in high energy physics and related applications, tracking plays an essential role allowing to identify and follow charged particle trajectories traversing particle detectors. Due to the high multiplicity of charged particles and their physical interactions, randomly deflecting the particles, the reconstruction is a challenging undertaking, requiring fast, accurate and robust algorithms. Our approach works on graph-structured data, capturing track hypotheses through edge connections between particles in the detector layers. We demonstrate in a comprehensive study on simulated data for a particle detector used for proton computed tomography, the high potential as well as the competitiveness of our approach compared to a heuristic search algorithm and a model trained on ground truth. Finally, we point out limitations of our approach, guiding towards a robust foundation for further development of reinforcement learning based tracking.
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Schilling A, Aehle M, Alme J, Barnaföldi GG, Bodova T, Borshchov V, van den Brink A, Eikeland V, Feofilov G, Garth C, Gauger NR, Grøttvik O, Helstrup H, Igolkin S, Keidel R, Kobdaj C, Kortus T, Leonhardt V, Mehendale S, Ningappa Mulawade R, Harald Odland O, O'Neill G, Papp G, Peitzmann T, Pettersen HES, Piersimoni P, Protsenko M, Rauch M, Ur Rehman A, Richter M, Röhrich D, Santana J, Seco J, Songmoolnak A, Sudár Á, Tambave G, Tymchuk I, Ullaland K, Varga-Kofarago M, Volz L, Wagner B, Wendzel S, Wiebel A, Xiao R, Yang S, Zillien S. Uncertainty-aware spot rejection rate as quality metric for proton therapy using a digital tracking calorimeter. Phys Med Biol 2023; 68:194001. [PMID: 37652034 DOI: 10.1088/1361-6560/acf5c2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 08/31/2023] [Indexed: 09/02/2023]
Abstract
Objective.Proton therapy is highly sensitive to range uncertainties due to the nature of the dose deposition of charged particles. To ensure treatment quality, range verification methods can be used to verify that the individual spots in a pencil beam scanning treatment fraction match the treatment plan. This study introduces a novel metric for proton therapy quality control based on uncertainties in range verification of individual spots.Approach.We employ uncertainty-aware deep neural networks to predict the Bragg peak depth in an anthropomorphic phantom based on secondary charged particle detection in a silicon pixel telescope designed for proton computed tomography. The subsequently predicted Bragg peak positions, along with their uncertainties, are compared to the treatment plan, rejecting spots which are predicted to be outside the 95% confidence interval. The such-produced spot rejection rate presents a metric for the quality of the treatment fraction.Main results.The introduced spot rejection rate metric is shown to be well-defined for range predictors with well-calibrated uncertainties. Using this method, treatment errors in the form of lateral shifts can be detected down to 1 mm after around 1400 treated spots with spot intensities of 1 × 107protons. The range verification model used in this metric predicts the Bragg peak depth to a mean absolute error of 1.107 ± 0.015 mm.Significance.Uncertainty-aware machine learning has potential applications in proton therapy quality control. This work presents the foundation for future developments in this area.
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Affiliation(s)
- Alexander Schilling
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Max Aehle
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Johan Alme
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Tea Bodova
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | | | - Viljar Eikeland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Christoph Garth
- Scientific Visualization Lab, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Nicolas R Gauger
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Ola Grøttvik
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Håvard Helstrup
- Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, NO-5020 Bergen, Norway
| | | | - Ralf Keidel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
- Chair for Scientific Computing, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Chinorat Kobdaj
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Tobias Kortus
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
| | - Viktor Leonhardt
- Scientific Visualization Lab, University of Kaiserslautern-Landau, D-67663 Kaiserslautern, Germany
| | - Shruti Mehendale
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Raju Ningappa Mulawade
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
| | - Odd Harald Odland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- Department of Oncology and Medical Physics, Haukeland University Hospital, NO-5021 Bergen, Norway
| | - George O'Neill
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Gábor Papp
- Institute for Physics, Eötvös Loránd University, 1/A Pázmány P. Sétány, H-1117 Budapest, Hungary
| | - Thomas Peitzmann
- Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands
| | | | - Pierluigi Piersimoni
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- UniCamillus-Saint Camillus International University of Health Sciences, Rome, Italy
| | - Maksym Protsenko
- Research and Production Enterprise 'LTU' (RPELTU), Kharkiv, Ukraine
| | - Max Rauch
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Attiq Ur Rehman
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Matthias Richter
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Dieter Röhrich
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Joshua Santana
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
| | - Joao Seco
- Department of Biomedical Physics in Radiation Oncology, DKFZ-German Cancer Research Center, Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Arnon Songmoolnak
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Ákos Sudár
- Wigner Research Centre for Physics, Budapest, Hungary
- Budapest University of Technology and Economics, Budapest, Hungary
| | - Ganesh Tambave
- Center for Medical and Radiation Physics (CMRP), National Institute of Science Education and Research (NISER), Bhubaneswar, India
| | - Ihor Tymchuk
- Research and Production Enterprise 'LTU' (RPELTU), Kharkiv, Ukraine
| | - Kjetil Ullaland
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | | | - Lennart Volz
- Biophysics, GSI Helmholtz Center for Heavy Ion Research GmbH, Darmstadt, Germany
- Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom
| | - Boris Wagner
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Steffen Wendzel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
| | - Alexander Wiebel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
| | - RenZheng Xiao
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
- College of Mechanical & Power Engineering, China Three Gorges University, Yichang, People's Republic of China
| | - Shiming Yang
- Department of Physics and Technology, University of Bergen, NO-5007 Bergen, Norway
| | - Sebastian Zillien
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, D-67549 Worms, Germany
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Pettersen HES, Aehle M, Alme J, Barnaföldi GG, Borshchov V, van den Brink A, Chaar M, Eikeland V, Feofilov G, Garth C, Gauger NR, Genov G, Grøttvik O, Helstrup H, Igolkin S, Keidel R, Kobdaj C, Kortus T, Leonhardt V, Mehendale S, Mulawade RN, Odland OH, Papp G, Peitzmann T, Piersimoni P, Protsenko M, Rehman AU, Richter M, Santana J, Schilling A, Seco J, Songmoolnak A, Sølie JR, Tambave G, Tymchuk I, Ullaland K, Varga-Kofarago M, Volz L, Wagner B, Wendzel S, Wiebel A, Xiao R, Yang S, Yokoyama H, Zillien S, Röhrich D. Investigating particle track topology for range telescopes in particle radiography using convolutional neural networks. Acta Oncol 2021; 60:1413-1418. [PMID: 34259117 DOI: 10.1080/0284186x.2021.1949037] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
BACKGROUND Proton computed tomography (pCT) and radiography (pRad) are proposed modalities for improved treatment plan accuracy and in situ treatment validation in proton therapy. The pCT system of the Bergen pCT collaboration is able to handle very high particle intensities by means of track reconstruction. However, incorrectly reconstructed and secondary tracks degrade the image quality. We have investigated whether a convolutional neural network (CNN)-based filter is able to improve the image quality. MATERIAL AND METHODS The CNN was trained by simulation and reconstruction of tens of millions of proton and helium tracks. The CNN filter was then compared to simple energy loss threshold methods using the Area Under the Receiver Operating Characteristics curve (AUROC), and by comparing the image quality and Water Equivalent Path Length (WEPL) error of proton and helium radiographs filtered with the same methods. RESULTS The CNN method led to a considerable improvement of the AUROC, from 74.3% to 97.5% with protons and from 94.2% to 99.5% with helium. The CNN filtering reduced the WEPL error in the helium radiograph from 1.03 mm to 0.93 mm while no improvement was seen in the CNN filtered pRads. CONCLUSION The CNN improved the filtering of proton and helium tracks. Only in the helium radiograph did this lead to improved image quality.
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Affiliation(s)
| | - Max Aehle
- Chair for Scientific Computing, Technische Universität Kaiserslautern, Kaiserslautern, Germany
| | - Johan Alme
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | | | | | | | - Mamdouh Chaar
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Viljar Eikeland
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Grigory Feofilov
- Department of High Energy and Elementary Particles Physics, St. Petersburg University, St. Petersburg, Russia
| | - Christoph Garth
- Scientific Visualization Lab, Technische Universität Kaiserslautern, Kaiserslautern, Germany
| | - Nicolas R. Gauger
- Chair for Scientific Computing, Technische Universität Kaiserslautern, Kaiserslautern, Germany
| | - Georgi Genov
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Ola Grøttvik
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Håvard Helstrup
- Department of Computer Science, Electrical Engineering and Mathematical Sciences, Western Norway University of Applied Sciences, Bergen, Norway
| | - Sergey Igolkin
- Department of High Energy and Elementary Particles Physics, St. Petersburg University, St. Petersburg, Russia
| | - Ralf Keidel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Chinorat Kobdaj
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Tobias Kortus
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Viktor Leonhardt
- Scientific Visualization Lab, Technische Universität Kaiserslautern, Kaiserslautern, Germany
| | - Shruti Mehendale
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Raju Ningappa Mulawade
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Odd Harald Odland
- Department of Oncology and Medical Physics, Haukeland University Hospital, Bergen, Norway
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Gábor Papp
- Institute for Physics, Eötvös Loránd University, Budapest, Hungary
| | - Thomas Peitzmann
- Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands
| | | | - Maksym Protsenko
- Research and Production Enterprise “LTU” (RPE LTU), Kharkiv, Ukraine
| | - Attiq Ur Rehman
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | | | - Joshua Santana
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Alexander Schilling
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Joao Seco
- Department of Biomedical Physics in Radiation Oncology, DKFZ-German Cancer Research Center, Heidelberg, Germany
- Department of Physics and Astronomy, Heidelberg University, Heidelberg, Germany
| | - Arnon Songmoolnak
- Department of Physics and Technology, University of Bergen, Bergen, Norway
- Institute of Science, Suranaree University of Technology, Nakhon Ratchasima, Thailand
| | - Jarle Rambo Sølie
- Department of Diagnostic Physics, Division of Radiology and Nuclear Medicine, Oslo University Hospital, Oslo, Norway
| | - Ganesh Tambave
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Ihor Tymchuk
- Research and Production Enterprise “LTU” (RPE LTU), Kharkiv, Ukraine
| | - Kjetil Ullaland
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | | | - Lennart Volz
- Department of Biophysics, GSI Helmholtz Center for Heavy Ion Research GmbH, Darmstadt, Germany
- Department of Medical Physics and Biomedical Engineering, University College London, London, UK
| | - Boris Wagner
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Steffen Wendzel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Alexander Wiebel
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - RenZheng Xiao
- Department of Physics and Technology, University of Bergen, Bergen, Norway
- College of Mechanical & Power Engineering, China Three Gorges University, Yichang, People’s Republic of China
| | - Shiming Yang
- Department of Physics and Technology, University of Bergen, Bergen, Norway
| | - Hiroki Yokoyama
- Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht, Netherlands
| | - Sebastian Zillien
- Center for Technology and Transfer (ZTT), University of Applied Sciences Worms, Worms, Germany
| | - Dieter Röhrich
- Department of Physics and Technology, University of Bergen, Bergen, Norway
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Niederberger ACR, Fattal DA, Gauger NR, Fan S, Beausoleil RG. Sensitivity analysis and optimization of sub-wavelength optical gratings using adjoints. Opt Express 2014; 22:12971-12981. [PMID: 24921494 DOI: 10.1364/oe.22.012971] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Numerical optimization of photonic devices is often limited by a large design space the finite-differences gradient method requires as many electric field computations as there are design parameters. Adjoint-based optimization can deliver the same gradients with only two electric field computations. Here, we derive the relevant adjoint formalism and illustrate its application for a waveguide slab, and for the design of optical sub-wavelength gratings.
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