Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optics Letters

Binning method for artifact-free time-tag based correlation function calculations

Oscar Urquidi, Johanna Brazard, Takuji Adachi

Published Jul 19, 2024• 1 citation
Publisher

Abstract

Correlation functions are nowadays routinely computed using time-tagged photon information instead of a hardware autocorrelator. The algorithm developed by Laurence et al. [ Opt. Lett. 31 , 829 ( 2006 ) 10.1364/OL.31.000829 ] is a powerful example. Despite its ease of implementation and fast computation process, it presents a prevalent noisy feature at the short time-lag range when computed on commonly used logarithmically spaced bins. We identified that arbitral logarithmic spacing produces the mismatch between the edges of generated bins and acquisition frequency, resulting in an aliasing artifact at the short time-lag range of the correlation function. We introduce a binning method that considers the acquisition frequency during the bin generation. It effectively eliminates the artifact and improves the accuracy of the autocorrelation. Applying the binning method herein can be particularly crucial when one extracts photophysical processes from fluorescence correlation spectroscopy or the diffusion coefficient of nanoparticles from dynamic light scattering at the time range below 10 −5 s lag time.

DOI
10.1364/ol.532069

Related papers

A fast, flexible algorithm for calculating correlations in Fluorescence Correlation Spectroscopy

Ted A. Laurence, Samantha Fore, Thomas R. Huser

A new algorithm is introduced for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The correlation is first rewritten as a counting operation on photon pairs. For each photon, the contribution to the correlation function for each subsequent photon is calculated for arbitrary bin spacings of the correlation time lag. By retaining the bin positions in the photon sequence after each photon, the correlation can be performed efficiently. Example correlations for simulations of FCS experiments are shown, with comparable execution speed to the commonly used multiple-tau correlation technique. Also, wide bin spacings are possible that allow for real-time software calculation of correlations even for high count rates ({approx}350 kHz). The flexibility and broad applicability of the algorithm is demonstrated using results from single molecule photon antibunching experiments.

Optics Letters•Oct 13, 2005•1 citation

Fast, flexible algorithm for calculating photon correlations

Ted A. Laurence, Samantha Fore, Thomas R. Huser

We introduce a new algorithm for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The algorithm is based on rewriting the correlation as a counting operation on photon pairs and can be used with arbitrary bin widths and spacing. The flexibility of the algorithm is demonstrated by use of FCS simulations and single-molecule photon antibunching experiments. Execution speed is comparable to the commonly used multiple-tau correlation technique. Wide bin spacings are possible that allow for real-time software calculation of correlations, even for high count rates.

Optics Letters•Mar 15, 2006•70 citations

High-precision nonlocal temporal correlation identification of entangled photon pairs for quantum clock synchronization

Runai Quan, Ruifang Dong, Xiao Xiang +3 more

High-precision nonlocal temporal correlation identification in entangled photon pairs is critical to measure the time offset between remote independent time scales for many quantum information applications. The first nonlocal correlation identification was reported in 2009, which extracts the time offset via the algorithm of iterative fast Fourier transformations and their inverse. The best identification resolution is restricted by the peak identification threshold of the algorithm, and thus the time offset calculation precision is limited. In this paper, an improvement for the identification is presented both in resolution and precision via a modified algorithm of direct cross correlation extraction. A flexible resolution down to 1 ps is realized, which is only dependent on the least significant bit resolution of the time-tagging device. The attainable precision is shown to be mainly determined by the inherent timing jitter of single photon detectors, the acquired pair rate, and acquisition time, and a sub-picosecond precision (0.72 ps) has been achieved at an acquisition time of 4.5 s. This high-precision nonlocal measurement realization provides a solid foundation for the field applications of entanglement-based quantum clock synchronization, ranging, and communications.

arXiv:1907.08925•Review of Scientific Instruments•Dec 1, 2020•26 citations

Noise on photon correlation data. I. Autocorrelation functions

Klaus Schätzel

An adequate analysis of photon correlation data requires knowledge about the statistical accuracy of the measured data. For the model of gamma-distributed intensities, that is including the effect of a finite intercept, the full covariance matrix is calculated for all the channels of the photon autocorrelation functions. A thorough discussion of multiple sample time correlation illuminates the importance of temporal averaging effects at large lag times. A practical estimation scheme is given for the noise in photon correlation data from a multiple sample time measurement.

Quantum Optics Journal of the European Optical Society Part B•Aug 1, 1990•118 citations

Spectral correlations of dynamical resonance fluorescence

Santiago Bermúdez Feijoo, Eduardo Zubizarreta Casalengua, Kai Müller +1 more

Frequency-filtered photon correlations have been proven to be extremely useful in grasping how the detection process alters photon statistics. Harnessing the spectral correlations also permits refinement of the emission and unraveling of previously hidden strong correlations in a plethora of quantum-optical systems under continuous-wave excitation. In this work, we investigate such correlations for time-dependent excitation and develop a methodology to compute efficiently time-integrated correlations, which are at the heart of the photon-counting theory, and subsequently apply it to analyze the photon emission of pulsed systems. By combining this formalism with the —which facilitates frequency-resolved correlations—we demonstrate how spectral filtering enhances single-photon purity and suppresses multiphoton noise in time-bin-encoded quantum states. Specifically, filtering the central spectral peak of a dynamically driven two-level system boosts temporal coherence and improves the fidelity of time-bin entanglement preparation, even under conditions favoring multiphoton emission. These results establish spectral filtering as a critical tool for tailoring photon statistics in pulsed quantum light sources.

arXiv:2504.05242•Physical Review Research•Jul 29, 2025•4 citations

Intensity-Correlation Spectroscopy

Vittorio Degiorgio, J. B. Lastovka

In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.

Physical Review A•Nov 1, 1971•103 citations
Correlation functions are nowadays routinely computed using time-tagged photon information instead of a hardware autocorrelator. The algorithm developed by Laurence et al. [ Opt. Lett. 31 , 829 ( 2006 ) 10.1364/OL.31.000829 ] is a powerful example. Despite its ease of implementation and fast computation process, it presents a prevalent noisy feature at the short time-lag range when computed on commonly used logarithmically spaced bins. We identified that arbitral logarithmic spacing produces the mismatch between the edges of generated bins and acquisition frequency, resulting in an aliasing artifact at the short time-lag range of the correlation function. We introduce a binning method that considers the acquisition frequency during the bin generation. It effectively eliminates the artifact and improves the accuracy of the autocorrelation. Applying the binning method herein can be particularly crucial when one extracts photophysical processes from fluorescence correlation spectroscopy or the diffusion coefficient of nanoparticles from dynamic light scattering at the time range below 10 −5 s lag time.
A new algorithm is introduced for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The correlation is first rewritten as a counting operation on photon pairs. For each photon, the contribution to the correlation function for each subsequent photon is calculated for arbitrary bin spacings of the correlation time lag. By retaining the bin positions in the photon sequence after each photon, the correlation can be performed efficiently. Example correlations for simulations of FCS experiments are shown, with comparable execution speed to the commonly used multiple-tau correlation technique. Also, wide bin spacings are possible that allow for real-time software calculation of correlations even for high count rates ({approx}350 kHz). The flexibility and broad applicability of the algorithm is demonstrated using results from single molecule photon antibunching experiments.
We introduce a new algorithm for computing correlations of photon arrival time data acquired in single-molecule fluorescence spectroscopy and fluorescence correlation spectroscopy (FCS). The algorithm is based on rewriting the correlation as a counting operation on photon pairs and can be used with arbitrary bin widths and spacing. The flexibility of the algorithm is demonstrated by use of FCS simulations and single-molecule photon antibunching experiments. Execution speed is comparable to the commonly used multiple-tau correlation technique. Wide bin spacings are possible that allow for real-time software calculation of correlations, even for high count rates.
High-precision nonlocal temporal correlation identification in entangled photon pairs is critical to measure the time offset between remote independent time scales for many quantum information applications. The first nonlocal correlation identification was reported in 2009, which extracts the time offset via the algorithm of iterative fast Fourier transformations and their inverse. The best identification resolution is restricted by the peak identification threshold of the algorithm, and thus the time offset calculation precision is limited. In this paper, an improvement for the identification is presented both in resolution and precision via a modified algorithm of direct cross correlation extraction. A flexible resolution down to 1 ps is realized, which is only dependent on the least significant bit resolution of the time-tagging device. The attainable precision is shown to be mainly determined by the inherent timing jitter of single photon detectors, the acquired pair rate, and acquisition time, and a sub-picosecond precision (0.72 ps) has been achieved at an acquisition time of 4.5 s. This high-precision nonlocal measurement realization provides a solid foundation for the field applications of entanglement-based quantum clock synchronization, ranging, and communications.
An adequate analysis of photon correlation data requires knowledge about the statistical accuracy of the measured data. For the model of gamma-distributed intensities, that is including the effect of a finite intercept, the full covariance matrix is calculated for all the channels of the photon autocorrelation functions. A thorough discussion of multiple sample time correlation illuminates the importance of temporal averaging effects at large lag times. A practical estimation scheme is given for the noise in photon correlation data from a multiple sample time measurement.
Frequency-filtered photon correlations have been proven to be extremely useful in grasping how the detection process alters photon statistics. Harnessing the spectral correlations also permits refinement of the emission and unraveling of previously hidden strong correlations in a plethora of quantum-optical systems under continuous-wave excitation. In this work, we investigate such correlations for time-dependent excitation and develop a methodology to compute efficiently time-integrated correlations, which are at the heart of the photon-counting theory, and subsequently apply it to analyze the photon emission of pulsed systems. By combining this formalism with the —which facilitates frequency-resolved correlations—we demonstrate how spectral filtering enhances single-photon purity and suppresses multiphoton noise in time-bin-encoded quantum states. Specifically, filtering the central spectral peak of a dynamically driven two-level system boosts temporal coherence and improves the fidelity of time-bin entanglement preparation, even under conditions favoring multiphoton emission. These results establish spectral filtering as a critical tool for tailoring photon statistics in pulsed quantum light sources.
In recent years the utilization of "optical mixing" spectroscopic techniques in laser light scattering experiments has proved to be a successful method for the investigation of the dynamical properties of physical systems. By illuminating a photosensitive detector with the scattered light and measuring the spectrum or autocorrelation function of the resulting photocurrent, one can, in general, obtain the ensemble-average time dependence of specific collective excitations within the scattering medium. We present here a detailed quantitative analysis of the statistical errors inherent in such measurements due to the stochastic nature of both the scattering and photoemission processes. We determine the statistical errors on the optical-intensity correlation function as measured by two photocounting digital correlator models and on the intensity spectrum as measured by a "self-beat" optical mixing spectrometer. From these errors and a generalized least-mean-squares fitting procedure we calculate the uncertainty on the measured correlation time (linewidth) for the case of a Gaussian optical field with an exponential intensity correlation function (a Lorentzian spectrum). Scaling relationships are given which permit our numerical results to be applied to an arbitrary set of experimental parameters.