Quantitative uncertainty analysis of extracting attosecond delays from spectrally overlapping RABBIT experiments
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Date
2025-07-14
Publication Type
Journal Article
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yes
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Abstract
A two-dimensional spectrogram with oscillations along the temporal dimension and partially overlapping peaks along the spectral dimension is the typical outcome of interferometric measurements, e.g. the reconstruction of attosecond beating by interference of two-photon transitions experiment of complex systems. It is necessary to retrieve the oscillation phases of the individual components in order to extract the attosecond photoionisation time delays. One can use either the global-fit method (simulating the oscillations of each component and adding them together) or the complex-fit method (first Fourier transforming along the temporal dimension and then fitting the Fourier coefficients at the relevant frequency in the spectral dimension). Here, we prove that the two methods are mathematically equivalent in the frame of least-squares fitting, and we derive the formula for the variance of the extracted phases based on the Poisson distribution. The fitting and the uncertainty formula are not limited to specific peak shapes. For the special case of two Gaussian peaks, there is a relatively simple expression for the phase uncertainty. The method can be further extended to fitting with peaks that have known phase structures or peaks with relative phase constraints. The uncertainty formula (with multiple peaks and a background) is verified by numerical simulations, and the results show that phase retrieval is possible as long as the peaks do not fully overlap (having exactly the same shape, position and phase structure), although the uncertainty rises with the degree of overlap. We also find that the correctness of fitting relies on properly assigning all the peaks in the energy domain, which is particularly important for extracting the phase from a relatively weak peak overlapped with other peaks.
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published
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Volume
58 (13)
Pages / Article No.
135601
Publisher
IOP Publishing
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Subject
attosecond interferometry; RABBIT; photoionisation delays; uncertainty analysis; phase retrieval
Organisational unit
03888 - Wörner, Hans Jakob / Wörner, Hans Jakob
Notes
Funding
- Time-resolved measurements of intermolecular Coulombic decay ()