Uniqueness results for the phase retrieval problem of fractional Fourier transforms of variable order

Understand

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 $v$.