Using the Transport of Intensity and the Transport of Phase Equation for Phase Retrieval
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917733935874048 |
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| author | Kirisits, Clemens Raik, Kemal Scherzer, Otmar Strohmenger, Christina Yan, Jikai |
| author_facet | Kirisits, Clemens Raik, Kemal Scherzer, Otmar Strohmenger, Christina Yan, Jikai |
| contents | We investigate the transport of intensity equation (TIE) and the transport of phase equation (TPE) for solving the phase retrieval problem. Both the TIE and the TPE are derived from the paraxial Helmholtz equation and relate phase information to the intensity. The TIE is usually favored since the TPE is nonlinear. The main contribution of this paper is a discussion of preferential use of either one of the two equations or potential benefits of a hybrid use. Moreover, we discuss the solution of the TPE with the method of characteristics and with viscosity methods. Both the TIE and the viscosity method are numerically implemented with finite element methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_14143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Using the Transport of Intensity and the Transport of Phase Equation for Phase Retrieval Kirisits, Clemens Raik, Kemal Scherzer, Otmar Strohmenger, Christina Yan, Jikai Numerical Analysis 65Z05 We investigate the transport of intensity equation (TIE) and the transport of phase equation (TPE) for solving the phase retrieval problem. Both the TIE and the TPE are derived from the paraxial Helmholtz equation and relate phase information to the intensity. The TIE is usually favored since the TPE is nonlinear. The main contribution of this paper is a discussion of preferential use of either one of the two equations or potential benefits of a hybrid use. Moreover, we discuss the solution of the TPE with the method of characteristics and with viscosity methods. Both the TIE and the viscosity method are numerically implemented with finite element methods. |
| title | Using the Transport of Intensity and the Transport of Phase Equation for Phase Retrieval |
| topic | Numerical Analysis 65Z05 |
| url | https://arxiv.org/abs/2406.14143 |