Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
THU: Thursday Contributed Sessions
THU 10: Foundational / Mathematical Aspects – Methods and Approximations
THU 10.8: Vortrag
Donnerstag, 11. September 2025, 16:00–16:15, ZHG103
Improved Gerchberg-Saxton Approach to the One-Dimensional Pauli Phase Retrieval Problem — Felipe de Andrade Ferreira da Silva, Karen Fernanda Pagnoni, and •Alexys Bruno-Alfonso — Department of Mathematics, School of Sciences, UNESP - São Paulo State University, Bauru, 17033-360, Brazil
The iterative Gerchberg-Saxton algorithm retrieves the phases of a Fourier pair from the corresponding intensities. It can deal with the one-dimensional phase-retrieval Pauli problem: the calculation of the state representations ψ(x) and φ(k) from the probability densities ρ(x)=|ψ(x)|2 and µ(k)=|φ(k)|2. We improve the algorithm in several ways. First, we find compatibility tests between two given densities ρ(x) and µ(k). Second, we enhance the algorithm stability by adding two stages after each Fourier transformation: (i) we replace the exact absolute value of the transform by its weighted harmonic mean with the approximate one, (ii) we multiply the transform by a factor that reproduces the expected values and variances of x and k as given by ρ(x) and µ(k).
Keywords: quantum mechanics; Pauli problem; phase retrieval; Gerchberg-Saxton algorithm; Fourier transform