Accurate semiclassical analysis of light propagation on tilted hyperplanes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918051942760448 |
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| author | Gioia, Patrick Ngoc, San Vu |
| author_facet | Gioia, Patrick Ngoc, San Vu |
| contents | In the scalar light model given by Helmholtz' equation in R^{1+d} , we consider the transformation of an initial scene (a hologram) in {0}xR^d by an arbitrary affine transformation (which can be viewed as a propagation into a tilted hyperplane). In the high frequency regime, we use microlocal and semiclassical analysis to describe the propagator as a semiclassical Fourier integral operator, thus generalising the well-known Angular Spectrum formula from optics. We then prove new precise Egorov theorems, including subprincipal terms, which indicate how to take into account the propagation along rays of geometric optics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13485 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accurate semiclassical analysis of light propagation on tilted hyperplanes Gioia, Patrick Ngoc, San Vu Signal Processing Mathematical Physics Analysis of PDEs Symplectic Geometry In the scalar light model given by Helmholtz' equation in R^{1+d} , we consider the transformation of an initial scene (a hologram) in {0}xR^d by an arbitrary affine transformation (which can be viewed as a propagation into a tilted hyperplane). In the high frequency regime, we use microlocal and semiclassical analysis to describe the propagator as a semiclassical Fourier integral operator, thus generalising the well-known Angular Spectrum formula from optics. We then prove new precise Egorov theorems, including subprincipal terms, which indicate how to take into account the propagation along rays of geometric optics. |
| title | Accurate semiclassical analysis of light propagation on tilted hyperplanes |
| topic | Signal Processing Mathematical Physics Analysis of PDEs Symplectic Geometry |
| url | https://arxiv.org/abs/2504.13485 |