Skip to Main content Skip to Navigation
Journal articles

Uniqueness results in an extension of Pauli's phase retrieval problem

Abstract : In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if $u$ and $v$ are such that fractional Fourier transforms of order $\alpha$ have same modulus $|F_\alpha u|=|F_\alpha v|$ for some set $\tau$ of $\alpha$'s, then $v$ is equal to $u$ up to a constant phase factor. The set $\tau$ depends on some extra assumptions either on $u$ or on both $u$ and $v$. Cases considered here are $u$, $v$ of compact support, pulse trains, Hermite functions or linear combinations of translates and dilates of Gaussians. In this last case, the set $\tau$ may even be reduced to a single point ({\it i.e.} one fractional Fourier transform may suffice for uniqueness in the problem).
Complete list of metadatas

Cited literature [42 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00518472
Contributor : Philippe Jaming <>
Submitted on : Friday, September 17, 2010 - 1:44:00 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Saturday, December 18, 2010 - 3:06:25 AM

Files

multiple00228.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Philippe Jaming. Uniqueness results in an extension of Pauli's phase retrieval problem. Applied and Computational Harmonic Analysis, Elsevier, 2014, 37, pp.413-441. ⟨10.1016/j.acha.2014.01.003⟩. ⟨hal-00518472⟩

Share

Metrics

Record views

617

Files downloads

475