Iterative virtual Moiré reconstruction: simultaneous recovery for topological charge and phase from a single-frame aberrated interferogram

Traditional vortex beam parameter determination methods are all designed for aberration-free vortex beams. In the case of aberrations and turbulence, they tend to struggle in mutual restraint between phase recovery and topological charge (TC) detection. Most recent methods depend on complex interferometric setups and precise phase singularity localization. An iterative virtual Moiré reconstruction (IVMR) technique is proposed based on the blind conformal mapping, achieving simultaneous demodulation of TC and phase from a single-frame aberrated interferogram, not needing precise phase singularity positioning. Experimental validation reveals an unprecedented dual-parameter characterization capability, demonstrating robustness across general aberration (root mean square ≤3 λ ) with an accuracy of 0.1 and Kolmogorov-type turbulence (atmospheric turbulence strength D / r 0 =12.5) with an accuracy of 0.15 for both integer and fractional topological charges. The simultaneous phase recovery accuracy achieves 3% and 10% root mean square error under general aberrations and turbulence, respectively. This approach demonstrates remarkably robust performance coupled with system simplicity, enabling efficient and accurate parameter quantification of vortex beams in real-world applications.