doi: 10.17586/2226-1494-2015-15-1-14-21


I. A. Shevkunov, N. V. Petrov

Read the full article  ';
Article in Russian

For citation: Shevkunov I.A., Petrov N.V. Comparison of holographic and iterative methods for amplitude object reconstruction. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol. 15, no. 1, pp. 14–21 (in Russian)


Experimental comparison of four methods for the wavefront reconstruction is presented. We considered two iterative and two holographic methods with different mathematical models and algorithms for recovery. The first two of these methods do not use a reference wave recording scheme that reduces requirements for stability of the installation. A major role in phase information reconstruction by such methods is played by a set of spatial intensity distributions, which are recorded as the recording matrix is being moved along the optical axis. The obtained data are used consistently for wavefront reconstruction using an iterative procedure. In the course of this procedure numerical distribution of the wavefront between the planes is performed. Thus, phase information of the wavefront is stored in every plane and calculated amplitude distributions are replaced for the measured ones in these planes. In the first of the compared methods, a two-dimensional Fresnel transform and iterative calculation in the object plane are used as a mathematical model. In the second approach, an angular spectrum method is used for numerical wavefront propagation, and the iterative calculation is carried out only between closely located planes of data registration. Two digital holography methods, based on the usage of the reference wave in the recording scheme and differing from each other by numerical reconstruction algorithm of digital holograms, are compared with the first two methods. The comparison proved that the iterative method based on 2D Fresnel transform gives results comparable with the result of common holographic method with the Fourier-filtering. It is shown that holographic method for reconstructing of the object complex amplitude in the process of the object amplitude reduction is the best among considered ones.

Keywords: phase retrieval problem, wavefront reconstruction, digital holography

Acknowledgements. The authors express their gratitude to the Ministry of Education and Science of the Russian Federation for support, project #2014/190 for government projects in the area of scientific activities within the basic part of the government task.


1. Gerchberg R.W., Saxton W.O. A practical algorithm for the determination of phase from image and diffraction plane pictures // Optics. 1972. V. 35. P. 237–246.
2. Petrov N.V., Volkov M.V., Bespalov V.G. Iterative phase retrieval based on the use of additional intensities measurements // Frontiers in Optics. San Jose,USA, 2011.
3. Almoro P., Pedrini G., Osten W. Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field // Applied Optics. 2006. V. 45. N 34. P. 8596–8605.
4. Almoro P., Maalo A.M.S., Hanson S.G. Fast-convergent algorithm for speckle-based phase retrieval and a design for dynamic wavefront sensing // Applied Optics. 2009. V. 48. N 8. P. 1485–1493. doi: 10.1364/AO.48.001485
5. Petrov N.V., Volkov M.V., Gorodetsky A.A., Bespalov V.G. Image reconstruction using measurements in volume speckle fields formed by different wavelengths // Progress in Biomedical Optics and Imaging - Proceedings of SPIE. 2011.V. 7907. Art. 790718. doi: 10.1117/12.876151
 6. Bao P., Zhang F., Pedrini G., Osten W. Phase retrieval using multilple illumination wavelengths // Optics Letters. 2008. V. 33. N 4. P. 309–311. doi: 10.1364/OL.33.000309
7. Bao P., Situ G., Pedrini G., Osten W. Lensless phase microscopy using phase retrieval with multiple illumination wavelengths // Applied Optics. 2012. V. 51. N 22. P. 5486–5494. doi: 10.1364/AO.51.005486
8. Налегаев С.С., Петров Н.В., Беспалов В.Г. Итерационные методы решения фазовой проблемы в оптике и их особенности // Научно-технический вестник информационных технологий, механики и оптики. 2012. № 6 (82). С. 30–35.
9. Kim W. Comparison among iterative algorithms for phase retrieval // Proc. Int. Conf. on Signal Processing and Multimedia Applications (SIGMAP 2010). Athens, Greece, 2010. P. 112–117.
10. Osherovich E., Zibulevsky M., Yavneh I. Algorithms for phase retrieval with a (rough) phase estimate available: a comparison. Technical Report CS-2010-22. 2010.
11.Johansson M., Fhager A., Lui H.-S., Persson M. Comparison between two phase retrieval methods for electromagnetic source modeling // Progress inElectromagnetics Research B. 2011. N 30. P. 239–253.
12. Kim D., Magnusson R., Jin M., Lee J., Chegal W. Complex object wave direct extraction method in off-axis digital holography // Optics Express. 2013. V. 21. N 3. P. 3658–3668. doi: 10.1364/OE.21.003658
13. Falaggis K. Reduction of the stagnation effect by combined iterative and deterministic single beam phase retrieval techniques // Proceedings of SPIE - The International Society for Optical Engineering. 2014. V. 9203. P. 92030U. doi: 10.1117/12.2061995
14. Martinez-Carranza J., Falaggis K., Jozwik M., Kozacki T. Comparison of phase retrieval techniques based on the transport of intensity equation using equally and unequally spaced plane separation criteria // Proceedings of SPIE - The International Society for Optical Engineering. 2014. V. 9204. P. 92040G. doi: 10.1117/12.2061976
15. Pedrini G., Osten W., Zhang Y. Wave-front reconstruction from a sequence of interferograms recorded at different planes // Optics Letters. 2005. V. 30. N 8. P. 833–835. doi: 10.1364/OL.30.000833
16. Liebling M., Blu T., Unser M. Complex-wave retrieval from a single off-axis hologram // Journal of the Optical Society of America A: Optics and Image Science, and Vision. 2004. V. 21. N 3. P. 367–377.
17. Takeda M., Ina H., Kobayashi S. Fourier-transform method of fringe-pattern analysis for computerbasedtopography and interferometry // Journal of the Optical Society of America A: Optics and Image Science, and Vision. 1982. V. 72. N 1. P. 156.
18. Petrov N.V., Galiaskarov A.N., Nikolaeva T.Yu., Bespalov V.G. The features of optimization of a phase retrieval technique in THz frequency range // Proceedings of SPIE - The International Society for Optical Engineering. 2012. V. 8413. Art. 84131T. doi: 10.1117/12.97868
19. Fienup J.R., Kowalczyk A.M. Phase retrieval for a complex-valued object by using a low-resolution image // Journal of the Optical Society of America A: Optics and Image Science, and Vision. 1990. V. 7. N 3. P. 450– 458. doi: 10.1364/JOSAA.7.000450
20.Демин В.В., Каменев Д.В. Критерии качества изображений в цифровой голографии частиц // Оптический журнал. 2012. Т. 79. № 4. С. 17–21.
21. Shevkunov I.A., Petrov N.V. Experimental comparison of phase retrieval methods which use intensity distribution at different planes // Journal of Physics: Conference Series. 2014. V. 536. Art. 012028. doi: 10.1088/1742-6596/536/1/012028
22. Zhang Y., Zhang X. Reconstruction of a complex object from two in-line holograms // Optics Express. 2003. V. 11. N 6. P. 572–578.
23. Dudley A., Milione G., Alfano R.R., Forbes A. All-digital wavefront sensing for structured light beams // Optics Express. 2014. V. 22. N 11. P. 14031–14040. doi: 10.1364/OE.22.014031

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2022 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.