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An algorithm of unordered wavefront propagation in terahertz phase retrieval with dense multiplane data acquisition
E.G. Tsiplakova 1, A. Chopard 2,3, N.S. Balbekin 1, O.A. Smolyanskaya 1, J.-B. Perraud 4, J.-P. Guillet 2, P. Mounaix 2, N.V. Petrov 1

1 ITMO University, 197101, Saint Petersburg, Russian Federation, Kronverksky Pr. 49;
2 IMS Laboratory, University of Bordeaux, UMR CNRS 5218,
33405, Talence, France, 351 Cours de la Libération Bâtiment A31;
3 Lytid SAS, 92120, Montrouge, France, rue la Fontaine 8;
4 Optikan SAS 33000, Bordeaux, France, rue Permentade 64

 PDF, 2546 kB

DOI: 10.18287/2412-6179-CO-1253

Pages: 901-912.

Full text of article: Russian language.

Abstract:
Iterative phase retrieval algorithms from multiple diffraction patterns in the terahertz (THz) frequency range are a promising tool of computational imaging capable of providing high spatial resolution of reconstructed phase images. One of the commonly used algorithms is SBMIR, which employs multiple intensity distributions of the diffraction object wavefield as input data. Compared with single-frame methods, the multi-plane approach allows for a faster convergence, but requires time-consuming data acquisition from a receiver positioned at a variety of distances from the object. Previously, we proposed a method for THz data acquisition in a single scan mode, which allows one to quickly obtain an exhaustive set of diffraction distributions. In this paper we evaluate an up-to-date phase retrieval algorithm based on the SBMIR/R-SBMIR method (which utilizes stochastic wavefront propagation) on the experimental data captured by a single-scan technique. Unlike a number of conventional phase retrieval algorithms, which may require a series of numerical experiments for determining optimal intensity distributions from a large dataset, disordered propagation of the estimation wavefront guarantees the high-contrast and high-resolution image reconstruction  without pre-setting the parameters. It is shown that the package use of the single-scan technique with the subsequent data processing using the R-SBMIR algorithm has application potential for automation of the multi-plane phase retrieval in the THz range.

Keywords:
phase retrieval, terahertz radiation, iterative algorithm, stochastic optimization, phase imaging, quantum cascade laser.

Citation:
Tsiplakova EG, Chopard A, Balbekin NS, Smolyanskaya OA, Perraud GB, Guillet JP, Mounaix P, Petrov NV. An algorithm of unordered wavefront propagation in terahertz phase retrieval with dense multiplane data acquisition. Computer Optics 2023; 47(6): 901-912. DOI: 10.18287/2412-6179-CO-1253.

Acknowledgements:
This work was supported by the Russian Foundation for Basic Research and Centre National de la Recherche Scientifique under grant No. 21-52-15035/21.

References:
  1. Mittleman DM. Twenty years of terahertz imaging. Opt Express 2018; 26(8): 9417-9431. DOI: 10.1364/OE.26.009417.
  2. Amenabar I, Lopez F, Mendikute A. In introductory review to THz non-destructive testing of composite mater. J Infrared Millim Terahertz Waves 2013; 34(2): 152-169. DOI: 10.1007/s10762-012-9949-z.
  3. Zeitler JA, Gladden LF. In-vitro tomography and non-destructive imaging at depth of pharmaceutical solid dosage forms. Eur J Pharm Biopharm 2009; 71(1): 2-22. DOI: 10.1016/j.ejpb.2008.08.012.
  4. Son JH, ed. Terahertz biomedical science and technology. Boca Raton: CRC Press; 2014. ISBN: 978-1-4665-7045-0.
  5. Wan M, Healy JJ, Sheridan JT. Terahertz phase imaging and biomedical applications. Opt Laser Technol 2020; 122: 105859. DOI:10.1016/j.optlastec.2019.105859.
  6. Mohr T, et al. Two-dimensional tomographic terahertz imaging by homodyne self-mixing. Opt Express 2015; 23(21): 27221-27229. DOI: 10.1364/OE.23.027221.
  7. Petrov NV, et al. Application of terahertz pulse time-domain holography for phase imaging. IEEE Trans Terahertz Sci Technol 2016; 6(3): 464-472. DOI: 10.1109/TTHZ.2016.2530938.
  8. Karpowicz N, et al. Comparison between pulsed terahertz time-domain imaging and continuous wave terahertz imaging. Semicond Sci Technol 2005; 20(7): S293. DOI: 10.1088/0268-1242/20/7/021.
  9. Johnson JL, Dorney TD, Mittleman DM. Interferometric imaging with terahertz pulses. IEEE J Sel Top Quantum Electron 2001; 7(4): 592-599. DOI: 10.1109/2944.974230.
  10. Li Z, et al. Terahertz synthetic aperture in-line holography with intensity correction and sparsity autofocusing reconstruction. Photonics Res 2019; 7(12): 1391-1399. DOI: 10.1364/prj.7.001391.
  11. Mahon RJ, Murphy JA, Lanigan W. Digital holography at millimetre wavelengths. Opt Commun 2006; 260(2): 469-473.
  12. Ding SH, et al. Continuous-wave terahertz digital holography by use of a pyroelectric array camera. Opt Lett 2011; 36(11): 1993-1995.
  13. Zolliker P, Hack E. THz holography in reflection using a high resolution microbolometer array. Opt Express 2015; 23(9): 10957-10967.
  14. Locatelli M, et al. Real-time terahertz digital holography with a quantum cascade laser. Sci Rep 2015; 5(1): 13566.
  15. Zhang Y, et al. Lensless Fourier-transform terahertz digital holography for real-time full-field phase imaging. Photonics Res 2022; 10(2): 323-331. DOI: 10.1364/PRJ.435769.
  16. Choporova Y, Knyazev B, Pavelyev V. Holography with high-power CW coherent terahertz source: optical components, imaging, and applications. Light: Advanced Manufacturing 2022; 3(3): 525-541. DOI: 10.37188/lam.2022.031.
  17. Richter H, et al. Terahertz wavefront measurement with a Hartmann sensor. Appl Phys Lett 2012; 101(3): 031103. DOI: 10.1063/1.4737164.
  18. Agour M, et al. Terahertz referenceless wavefront sensing by means of computational shear-interferometry. Opt Express 2022; 30(5): 7068-7081. DOI: 10.1364/oe.450708.
  19. Valzania L, et al. Terahertz ptychography. Opt Lett 2018; 43(3): 543-546.
  20. Rong L, et al. Continuous-wave terahertz reflective ptychography by oblique illumination. Opt Lett 2020; 45(16): 4412-4415. DOI: 10.1364/OL.400506.
  21. Petrov NV, et al. The features of optimization of a phase retrieval technique in THz frequency range. Speckle 2012: V Int Conf on Speckle Metrology 2012; 8413: 387-391. DOI: 10.1117/12.978688.
  22. Junkin G. Planar near-field phase retrieval using GPUs for accurate THz far-field prediction. IEEE Trans Antennas Propag 2012; 61(4): 1763-1776. DOI: 10.1109/TAP.2012.2220324.
  23. Gao X, Li C, Fang GY. The realization of terahertz image reconstruction with high resolution based on the amplitude of the echoed wave by using the phase retrieval algorithm. Chinese Phys Lett 2013; 30(6): 068401. DOI: 10.1088/0256-307X/30/6/068401.
  24. Ren Y, et al. Development of terahertz two-dimensional phase gratings for multiple beam generation based on a high-accuracy phase retrieval algorithm. Opt Express 2021; 29(12): 17951-17961. DOI: 10.1364/OE.425838.
  25. Rong L, et al. Transport of intensity equation-based terahertz lensless full-field phase imaging. Opt Lett 2021; 46(23): 5846-5849. DOI: 10.1364/ol.442625.
  26. Petrov NV, et al. Terahertz multiple-plane phase retrieval. Digital Holography and Three-Dimensional Imaging 2020: HF4G.8. DOI: 10.1364/DH.2020.HF4G.8.
  27. Jin X, et al. Iterative denoising phase retrieval method for twin-image elimination in continuous-wave terahertz in-line digital holography. Opt Lasers Eng 2022; 152: 106986.
  28. Gerchberg RW. A practical algorithm for the determination of phase from image and diffraction pictures. Optik 1972; 35(2): 237-246.
  29. Kotlyar VV, Khonina SN, Soifer VA. Iterative calculation of diffractive optical elements focusing into a three-dimensional domain and onto the surface of the body of rotation. J Mod Opt 1996; 43(7): 1509-1524. DOI: 10.1080/09500349608232822.
  30. Pavelyev VS, Soifer VA, Duparre M, Kowarschik R, Ludge B, Kley B. Iterative calculation, manufacture and investigation of DOE forming unimodal complex distribution. Opt Lasers Eng 1998; 29(4-5): 269-279. DOI: 10.1016/S0143-8166(97)00115-2.
  31. Miao J, Charalambous P, Kirz J, Sayre D. Extending the methodology of Х-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 1999; 400: 342-344.
  32. Zuo J, Vartanyants I, Gao M, et al. Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 2003; 300: 1419.
  33. Fienup C, Dainty J. Phase retrieval and image reconstruction for astronomy. Ch 7. In Book: Stark H, ed. Image Recovery: Theory and Application. Academic Press; 1987: 231-275.
  34. Fienup JR, et al. Hubble Space Telescope characterized by using phase-retrieval algorithms. Appl Opt 1993; 32(10): 1747-1767.
  35. Shevkunov I, et al. Super-resolution microscopy for biological specimens: lensless phase retrieval in noisy conditions. Biomed Opt Express 2018; 9(11): 5511-5523.
  36. Shechtman Y, et al. Phase retrieval with application to optical imaging: a contemporary overview. IEEE Signal Process Mag 2015; 32(3): 87-109.
  37. Boikov IV, Zelina YaV. Approximate methods of solving amplitude-phase problem for continuous signals [In Russian]. Measurement Techniques 2021; 5: 37-46. DOI: 10.32446/0368-1025it.2021-5-37-46.
  38. Rong L, Pan F, Xiao W, Li Y, Wang F. Twin image elimination from two in-line holograms via phase retrieval. Chinese Opt Lett 2012; 10(6): 060902.
  39. Nalegaev SS, Petrov NV, Bespalov VG. Special features of iteration methods for phase problem in optics [In Russian]. Nauchno-Tekhnicheskii Vestnik Informatsionnykh Tekhnologii, Mekhaniki i Optiki 2012; 6(82): 30-35.
  40. Pedrini G, Osten W, Zhang Y. Wave-front reconstruction from a sequence of interferograms recorded at different planes. Opt Lett 2005; 30(8): 833-835. DOI: 10.1364/ol.30.000833.
  41. Allen LJ, Oxley MP. Phase retrieval from series of images obtained by defocus variation. Opt Commun 2001; 199(1-4): 65-75. DOI: 10.1016/S0030-4018(01)01556-5.
  42. Petrov NV, Bespalov VG, Volkov MV. Wavefront reconstruction with a reference-free digital CCD-registration of multispectral speckle-patterns [In Russian]. Nanosyst Phys Chem Math 2011; 2(1): 82-90.
  43. Bao P, et al. Phase retrieval using multiple illumination wavelengths. Opt Lett 2008; 33(4): 309-311. DOI: 10.1364/OL.33.000309.
  44. Petrov NV, Bespalov VG, Gorodetsky AA. Phase retrieval method for multiple wavelength speckle patterns. Proc SPIE 2010; 7387: 73871T. DOI: 10.1117/12.871433.
  45. Chen N, Yeom J, Lee B. Optimized phase retrieval algorithm with multiple illuminations. In Book: Osten W, ed. Fringe 2013: 7th international workshop on advanced optical imaging and metrology. – Berlin, Heidelberg: Springer; 2014: 337-340. DOI: 10.1007/978-3-642-36359-7_60.
  46. Katkovnik V, et al. Computational wavelength resolution for in-line lensless holography: phase-coded diffraction patterns and wavefront group-sparsity. Proc SPIE 2017; 10335: 1033509. DOI: 10.1117/12.2269327.
  47. Shevkunov I, et al. Super-resolution microscopy for biological specimens: lensless phase retrieval in noisy conditions. Biomed Opt Express 2018; 9(11): 5511-5523. DOI: 10.1364/BOE.9.005511.
  48. Katkovnik V, et al. Computational super-resolution phase retrieval from multiple phase-coded diffraction patterns: simulation study and experiments. Optica 2017; 4(7): 786-794. DOI: 10.1364/OPTICA.4.000786.
  49. Ivanov VY, Sivokon VP, Vorontsov MA. Phase retrieval from a set of intensity measurements: theory and experiment. J Opt Soc Am A 1992; 9(9): 1515-1524. DOI: 10.1364/JOSAA.9.001515.
  50. Lu CH, et al. Phase retrieval using nonlinear diversity. Appl Opt 2013; 52(10): D92-D96. DOI: 10.1364/AO.52.000D92.
  51. Lu JT, Lu CH, Fleischer JW. Enhanced phase retrieval using nonlinear dynamics. Opt Express 2016; 24(22): 25091-25102.
  52. Chopard A, et al. Single-scan multiplane phase retrieval with a radiation of terahertz quantum cascade laser. Appl Phys B 2022; 128(3): 63. DOI: 10.1007/s00340-022-07787-x.
  53. Xing C, Qi F, Guo S. Improved terahertz phase imaging with single-beam multiple-plane reconstruction. 46th Int Conf on Infrared, Millimeter and Terahertz Waves (IRMMW-THz) 2021: 1-2.
  54. Xu C, et al. Enhancing multi-distance phase retrieval via unequal interval measurements. Photonics 2021; 8(2): 48. DOI: 10.3390/PHOTONICS8020048.
  55. Valušis G, et al. Roadmap of terahertz imaging 2021. Sensors 2021; 21(12): 4092. DOI: 10.3390/s21124092.
  56. Liang G, Liu T, Wang QJ. Recent developments of terahertz quantum cascade lasers. IEEE J Sel Top Quantum Electron 2016; 23(4): 1-18. DOI: 10.1109/JSTQE.2016.2625982.
  57. Wang X, et al. High-power terahertz quantum cascade lasers with~ 0.23 W in continuous wave mode. AIP Advances 2016; 6(7): 075210. DOI: 10.1063/1.4959195.
  58. Hack E, Zolliker P. Terahertz holography for imaging amplitude and phase objects. Opt Express 2014; 22(13): 16079-16086. DOI: 10.1364/OE.22.016079.
  59. Huang H, et al. Continuous-wave terahertz multi-plane in-line digital holography. Opt Lasers Eng 2017; 94: 76-81. DOI: 10.1016/J.OPTLASENG.2017.03.005.
  60. Locatelli M, et al. Real-time terahertz digital holography with a quantum cascade laser. Sci Rep 2015; 5(1): 13566. DOI: 10.1038/srep13566.
  61. Deng Q, et al. High-resolution terahertz inline digital holography based on quantum cascade laser. Opt Eng 2017; 56(11): 113102. DOI: 10.1117/1.OE.56.11.113102.
  62. Petrov NV, et al. Terahertz diffractive reflection phase imaging. 2020 45th Int Conf on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) 2020: 1-1. DOI: 10.1109/IRMMW-THz46771.2020.9370854.
  63. Petrov NV, et al. Terahertz phase retrieval imaging in reflection. Opt Lett 2020; 45(15): 4168-4171. DOI: 10.1364/OL.397935.
  64. Mandel L, Wolf E. Optical coherence and quantum optics. Cambridge university press; 1995.
  65. Fienup JR. Invariant error metrics for image reconstruction. Appl Opt 1997; 36(32): 8352-8357. DOI: 10.1364/AO.36.008352.
  66. Huang Z, Kuang C, Xu L, Cao L. Multiplane digital holography based on extrapolation iterations. Opt Commun 2021; 481: 126526.
  67. Latychevskaia T, Fink HW. Resolution enhancement in digital holography by self-extrapolation of holograms. Opt Express 2013; 21(6): 7726-7733.
  68. Balbekin NS, Kulya MS, Belashov AV, Gorodetsky A, Petrov NV. Increasing the resolution of the reconstructed image in terahertz pulse time-domain holography. Sci Rep 2019; 9(1): 180.

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