Quantitative uncertainty determination of phase retrieval in RABBITT

Abstract

Reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) is one of the most widely used approaches to measure the time delays in photoionization. The time delay, which corresponds to a phase difference of two oscillating signals, is usually retrieved by cosine fitting or fast Fourier transform (FFT). We propose two estimators for the phase uncertainty of cosine fitting from the signal per se of an individual experiment: (i) σ ( φ fit ) ≈ B A 2 N , where B / A is the mean-value-to-amplitude ratio, and N is the total count number, and (ii) σ ( φ fit ) ≈ 1 − R 2 R 2 n bins , where n bins is the total number of bins in the time domain, and R 2 is the coefficient of determination. The former estimator is applicable for the statistical fluctuation, while the latter includes the effects from various uncertainty sources, which is mathematically proven and numerically validated. This leads to an efficient and reliable approach to determining quantitative uncertainties in RABBITT experiments and evaluating the observed discrepancy among individual measurements, as demonstrated on the basis of experimental data.