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Licensed Unlicensed Requires Authentication Published by De Gruyter March 9, 2019

Simulation and analysis of optical imaging systems including real freeform components

Johannes Stock, Matthias Beier, Johannes Hartung, Sebastian Merx and Herbert Gross


In recent years, the precision of the manufacturing process for optical surfaces has improved tremendously. As a result, freefrom surfaces have become more attractive options for imaging applications with increased accuracy requirements. However, with regards the integration into an optical system, performance is often limited due to surface imperfections, such as mid-spatial frequency errors and alignment errors. This demonstrates the need for a more holistic description of systems, including multiple freeform components, which enable performance predictions based on the system as a whole. In this work, a solution for such a simulation is presented and verified by a comparison with the experimental data. This procedure not only predicts system performance but also supports tolerancing and easier alignment.


The authors would like to thank the Federal Ministry of Education and Research (BMBF) for funding this work, as part of the project Wk+fo+ (Funder Id: 10.13039/501100002347, 03WKCX1C). Parts of the research were supported by the German Aerospace Center (DLR) within the project VISTEL (Funder Id: 10.13039/501100002946, 50EE1224). Johannes Stock would like to thank the Carl-Zeiss-Stiftung for supporting the research and Joshua Goncalves for several comments on the manuscript.


[1] F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang and C. Evans, CIRP Ann. 62, 823–846 (2013).10.1016/j.cirp.2013.05.003Search in Google Scholar

[2] B. Chen and A. M. Herkommer, Appl. Opt. 56, 901–906 (2017).10.1364/AO.56.000901Search in Google Scholar PubMed

[3] C. Liu and H. Gross, Appl. Opt. 57, 5758–5768 (2018).10.1364/AO.57.005758Search in Google Scholar PubMed

[4] J. Hartung, M. Beier and S. Risse, in ‘SPIE Optical Systems Design’, 10 (2018).Search in Google Scholar

[5] G. Yu, H. Li and D. Walker, J. Eur. Opt. Soc. RP 6, 11044 (2011).10.2971/jeos.2011.11044Search in Google Scholar

[6] G. W. Forbes, in ‘SPIE Optical Measurement Systems for Industrial Inspection’, 95251B (2015).10.1117/12.2191135Search in Google Scholar

[7] M. Maksimovic, in ‘SPIE Optical Systems Design’, 14 (2015).Search in Google Scholar

[8] M. Pohl and R. Börret, J. Eur. Opt. Soc. RP 11, 16010 (2016).Search in Google Scholar

[9] O. Faehnle, M. Doetz, and O. Dambon, Adv. Opt. Technol. 6, 349–358 (2017).Search in Google Scholar

[10] R. J. Noll, Opt. Eng. 18, 137–142 (1979).Search in Google Scholar

[11] W. B. Wetherell, in ‘SPIE Image Quality’, 77–93 (1981).10.1117/12.932854Search in Google Scholar

[12] J. M. Tamkin, T. D. Milster and W. J. Dallas, Appl. Opt. 49, 4825–4835 (2010).10.1364/AO.49.004825Search in Google Scholar PubMed

[13] J. M. Tamkin, W. J. Dallas and T. D. Milster, Appl. Opt. 49, 4814–4824 (2010).10.1364/AO.49.004814Search in Google Scholar PubMed

[14] J. Stock, A. Broemel, J. Hartung, D. Ochse and H. Gross, Appl. Opt. 56, 391–396 (2017).10.1364/AO.56.000391Search in Google Scholar PubMed

[15] M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, et al., Appl. Opt. 54, 3530–3542 (2015).10.1364/AO.54.003530Search in Google Scholar

[16] G. W. Forbes, Opt. Exp. 20, 2483–2499 (2012).10.1364/OE.20.002483Search in Google Scholar PubMed

[17] A. Broemel, U. Lippmann and H. Gross, Adv. Opt. Technol. 6, 327–336 (2017).Search in Google Scholar

[18] G. E. Fasshauer, Meshfree Approximation Methods with MATLAB. World Scientific, (2007).10.1142/6437Search in Google Scholar

[19] T. Pertermann, J. Hartung, M. Beier, M. Trost, S. Schröder, et al., Appl. Opt. 57, 8692–8698 (2018).10.1364/AO.57.008692Search in Google Scholar PubMed

[20] R. N. Youngworth and B. D. Stone, Appl. Opt. 39, 2198 (2000).10.1364/AO.39.002198Search in Google Scholar

[21] Zemax, OpticStudio 18.7 User Manual. Zemax LLC, (2018).Search in Google Scholar

[22] J. M. Tamkin and T. D. Milster, Appl. Opt. 49, 6522–6536 (2010).10.1364/AO.49.006522Search in Google Scholar PubMed

Received: 2018-12-04
Accepted: 2019-02-08
Published Online: 2019-03-09
Published in Print: 2019-04-24

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