Subpixel localization of optical vortices using artificial neural networks

Journal title

Metrology and Measurement Systems




Popiołek-Masajada, Agnieszka : Wrocław University of Science and Technology, Faculty of Fundamental Problems of Technology, Department of Optics and Photonics, Poland ; Frączek, Ewa : Wrocław University of Science and Technology, Department of Telecommunication and Teleinformatics, Poland ; Burnecka, Emilia : Wrocław University of Science and Technology, Faculty of Fundamental Problems of Technology, Department of Optics and Photonics, Poland



optical vortex ; spiral phase map ; pseudo phase ; deep learning ; neural network

Divisions of PAS

Nauki Techniczne




Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation


[1] Gbur, G. (2016). Singular Optics. CRC Press.
[2] Vasnetsov, M. & Staliunas, K. (1999). Optical vortices. Nova Science.
[3] Andrews, D. (2008). Structured light and its applications, Academic Press.
[4] Wang, W., Ishii, N., Hanson, S., Miyamoto, Y., & Takeda, M. (2005). Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: Statistical properties of the analytic signal of a white-light speckle pattern applied to the microdisplacement measurement. Applied Optics, 44(23), 4916–4921.
[5] Wang,W., Yokozeki, T., Ishijima, R., & Takeda, M. (2006). Optical vortex metrology based on the core structures of phase singularities in Laguerre- Gauss transform of a speckle pattern. Optics Express, 14(22), 10195–10206.
[6] Popiołek-Masajada, A., Borwinska, M., & Frączek, W. (2006). Testing a new method for small-angle rotation measurements with the optical vortex interferometer. Measurement Science and Technology, 17(4), 653–658.
[7] Frączek E., & Mroczka, J. (2009). An accuracy analysis of small angle measurement using the optical vortex interferometer. Metrology and Measurement System, 15(1), 3–8.
[8] Eastwood, S. A., Bishop, A. I., Petersen, T. C., Paganin, D. M., & Morgan, M. J. (2012). Phase measurement using an optical vortex lattice produced with a three-beam interferometer. Optics Express, 20(13), 13947–13957.
[9] Bouchal, P., Štrbková, L., Dostál, Z., & Bouchal, Z. (2017). Vortex topographic microscopy for full-field reference-free imaging and testing. Optics Express, 25(18), 21428–21443.
[10] Schovanek, P., Bouchal, P., & Bouchal, Z. (2020). Optical topography of rough surfaces using vortex localization of fluorescent markers. Optics Letters, 45(16), 4468–4471. OL.392072
[11] Rockstuhl, C., Märki, I., Scharf, T., Salt, M., Herzig, H. P., & Dändliker, R. (2006). High Resolution Interference Microscopy: A Tool for Probing Optical Waves in the Far-Field on a Nanometric Length Scale, Current Nanoscience, 2(4), 337–350.
[12] Symeonidis, M., Nakagawa,W., Kim, D. C., Hermerschmidt, A., & Scharf, T. (2019). High-resolution interference microscopy of binary phase diffractive optical elements. OSA Continuum, 2(9), 2496– 2510.
[13] Spektor, B., Normatov, A., & Shamir, J. (2008). Singular beam microscopy. Applied Optics, 47(4), A78–A87.
[14] Masajada, J., Leniec, M., Drobczynski, S., Thienpont, H., & Kress, B. (2009). Micro-step localization using double charge optical vortex interferometer. Optics Express, 17(18), 16144–1615.
[15] Serrano-Trujillo, A., & Anderson, M. E. (2018). Surface profilometry using vortex beams generated with a spatial light modulator. Optics Communications, 427, 557–562. j.optcom.2018.07.003
[16] Doster, T., &Watnik, A. T. (2017). Machine learning approach to OAM beam demultiplexing via convolutional neural networks. Applied Optics, 56(12), 3386–3396.
[17] Zhao, Q., Hao, S., Wang, Y., Wang, L., Wan, X., & Xu, C. (2018). Mode detection of misaligned orbital angular momentum beams based on convolutional neural network. Applied Optics, 57(35), 10152–10158.
[18] Knutson, M., Lohani, S., Danac, O., Huver, S. D., & Glasser, R.T. (2016). Deep learning as a tool to distinguish between high orbital angular momentum optical modes. Proceedings SPIE, 9970, 997013.
[19] Frączek, E., Popiołek-Masajada, A., & Szczepaniak, S. (2020). Characterization of the Vortex Beam by Fermat’s Spiral. Photonics, 7(4), 102.
[20] Płocinniczak, Ł., Popiołek-Masajada, A., Masajada, J., & Szatkowski, M. (2016). Analytical model of the optical vortex microscope. Applied Optics, 55(12), B20–B27.
[21] Popiołek-Masajada, A., Masajada, J., & Szatkowski, M. (2018). Internal scanning method as unique imaging method of optical vortex scanning microscope. Optics and Laser in Engineering, 105, 201– 208.
[22] Popiołek-Masajada, A., Masajada, J., & Kurzynowski, P. (2017). Analytical model of the optical vortex scanning microscope with the simple phase object. Photonics, 4(2), 38. 10.3390/photonics4020038
[23] Takeda, T. M., Ina, H., Kobayashi, S. (1982). Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. Journal of the Optical Society of America, 72(1), 156–60.
[24] Larkin, K. G., Bone, D. J., & Oldfield, M. A. (2001). Natural demodulation of two-dimensional fringe patterns. I.General background of the spiral phase quadrature transform. Journal of the Optical Society of America A, 18(8), 1862–1870.
[25] Frączek, E., & Idzkowski, W. (2020). Artificial intelligent methods for the location of vortex points. In Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz R., & Zurada, J. M. (Eds.). Artificial Intelligence and Soft Computing (pp. 71–77). Springer.






DOI: 10.24425/mms.2021.137131