[Paper Review] Fluorescence-detected Fourier transform electronic spectroscopy by phase-tagged photon counting

Amr Tamimi, Tiemo Landes+3 more|arXiv (Cornell University)|Jun 21, 2020

Spectroscopy and Quantum Chemical Studies24 references27 citations

TL;DR

This paper introduces phase-tagged photon counting (PTPC), a novel method for low-signal fluorescence-detected Fourier transform spectroscopy that assigns interferometer phase to individual photon events. PTPC outperforms conventional lock-in detection by a factor of ~2 or more in signal-to-noise ratio under ultralow-flux conditions, with measurement uncertainty dominated by statistical sampling noise rather than instrumental instabilities, enabling high-precision spectroscopy of weakly fluorescent molecular systems including single molecules.

ABSTRACT

Fluorescence-detected Fourier transform (FT) spectroscopy is a technique in which the relative paths of an optical interferometer are controlled to excite a material sample, and the ensuing fluorescence is detected as a function of the interferometer path delay and relative phase. A common approach to enhance the signal-to-noise ratio in these experiments is to apply a continuous phase sweep to the relative optical path, and to detect the resulting modulated fluorescence using a phase-sensitive lock-in amplifier. In many important situations, the fluorescence signal is too weak to be measured using a lock-in amplifier, so that photon counting techniques are preferred. Here we introduce an approach to low-signal fluorescence-detected FT spectroscopy, in which individual photon counts are assigned to a modulated interferometer phase ('phase-tagged photon counting,' or PTPC), and the resulting data are processed to construct optical spectra. We studied the fluorescence signals of a molecular sample excited resonantly by a pulsed coherent laser over a range of photon flux and visibility levels. We compare the performance of PTPC to standard lock-in detection methods and establish the range of signal parameters over which meaningful measurements can be carried out. We find that PTPC generally outperforms the lock-in detection method, with the dominant source of measurement uncertainty being associated with the statistics of the finite number of samples of the photon detection rate.

Motivation & Objective

• To develop a method for fluorescence-detected Fourier transform spectroscopy under ultralow-flux conditions where photon counting is necessary.
• To overcome the limitations of lock-in amplifiers in low-signal regimes by using individual photon detection with phase tagging.
• To establish the regime of signal parameters—flux and visibility—where meaningful spectroscopic measurements can be made with minimal statistical uncertainty.
• To compare PTPC performance directly with standard lock-in detection using a model molecular system with tunable flux and visibility.
• To validate the method through experimental measurements and numerical simulations of statistical error in photon detection rate sampling.

Proposed method

• A Mach-Zehnder interferometer with acousto-optic modulators applies a continuous phase sweep at 5 kHz to the excitation beam.
• Individual fluorescence photons are detected using a photomultiplier tube or avalanche photodiode, and their arrival times are recorded with high-precision timing electronics.
• A field-programmable gate array (FPGA) assigns each detected photon to a specific interferometer phase based on the real-time phase of the reference beam.
• The phase-tagged photon data stream is processed to reconstruct quadrature signals (X and Y components) and the absolute signal magnitude (Z), enabling Fourier transform analysis.
• Signal-to-noise ratio (SNR) and rate-normalized standard error (SE) are calculated from the phase-resolved photon counts to evaluate performance.
• Numerical simulations model statistical uncertainty from finite sampling of the phase-dependent photon rate, validating theoretical predictions.

Experimental results

Research questions

• RQ1 Can phase-tagged photon counting (PTPC) achieve higher signal-to-noise ratios than conventional lock-in detection in ultralow-flux fluorescence-detected FT spectroscopy?
• RQ2 What is the dominant source of measurement uncertainty in PTPC under low-photon-flux conditions?
• RQ3 How do signal flux and visibility affect the performance of PTPC relative to lock-in detection?
• RQ4 To what extent does statistical sampling noise limit the precision of PTPC measurements compared to instrumental noise?
• RQ5 What minimum number of detected photons are required to achieve a target SNR of 10 in PTPC experiments?

Key findings

• PTPC outperforms lock-in detection by a factor of approximately 2 or more in signal-to-noise ratio across a wide range of flux and visibility levels.
• For a visibility of 𝑣 ≈ 1.0, approximately 200 detected photons within a 1-second integration window are required to achieve an SNR ≈ 10 for the X-quadrature signal.
• For a visibility of 𝑣 ≈ 0.5, approximately 2,000 detected photons are needed to achieve the same SNR of 10, indicating a strong dependence on visibility.
• The measured SNRs for both X and Y quadrature signals agree closely with theoretical predictions based on Poisson statistics, confirming that statistical sampling noise is the dominant uncertainty source.
• Instrumental noise such as mechanical vibrations or detector shot noise is negligible in PTPC, as evidenced by the excellent agreement between experiment and theory.
• The method enables post-acquisition isolation of higher harmonic signal components (e.g., two-photon absorption) from the phase-tagged photon stream, supporting nonlinear spectroscopy applications.