A two-point phase recovering from holographic data on a single plane
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914058062528512 |
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| author | Novikov, Roman Sivkin, Vladimir |
| author_facet | Novikov, Roman Sivkin, Vladimir |
| contents | We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb{R}^d,$ $d\geq 2$. In this region, we consider a hyperplane $X$ with sufficiently large distance $s$ from the origin in ${\mathbb R}^d.$ We give two-point local formulas for approximate recovering the radiation solution restricted to the plane $X$ from the intensity of the total solution at $X$, that is, from holographic data. The recovering is given in terms of the far-field pattern of the radiation solution with a decaying error term as $s \to +\infty.$ A numerical implementation is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A two-point phase recovering from holographic data on a single plane Novikov, Roman Sivkin, Vladimir Analysis of PDEs Spectral Theory We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb{R}^d,$ $d\geq 2$. In this region, we consider a hyperplane $X$ with sufficiently large distance $s$ from the origin in ${\mathbb R}^d.$ We give two-point local formulas for approximate recovering the radiation solution restricted to the plane $X$ from the intensity of the total solution at $X$, that is, from holographic data. The recovering is given in terms of the far-field pattern of the radiation solution with a decaying error term as $s \to +\infty.$ A numerical implementation is also presented. |
| title | A two-point phase recovering from holographic data on a single plane |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2509.22048 |