Uniqueness results in an extension of Pauli's phase retrieval problem
JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Institut de Mathématiques de Bordeaux [IMB]
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
Language
en
Article de revue
This item was published in
Applied and Computational Harmonic Analysis. 2014, vol. 37, p. 413-441
Elsevier
English 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 ...Read more >
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).Read less <
English Keywords
Phase retrieval
Pauli problem
Fractional Fourier transform
entire function of finite order
ANR Project
Analyse Harmonique et Problèmes Inverses - ANR-07-BLAN-0247
Origin
Hal imported