Noise biases exciton transport measurements in nanocrystal solids: CNR-calibrated correction restores accuracy

CNR-calibrated correction restores accuracy

Joseph J. Thiebes, Marc Meléndez, Enrique Arévalo Rodríguez, Ferry Prins

Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid
Departamento de Física de la Materia Condensada, Facultad de Ciencias, Universidad Autónoma de Madrid

Presented at the Gordon Research Seminar and Gordon Research Conference on Colloidal Nanocrystals
Les Diablerets, Switzerland, July 4–10, 2026.

A0 landscape conference poster. Header: title and authors. A purple banner reads 'for: fragile samples, earliest/latest times, weak absorbers/emitters — averaging won't save you.' Panels below cover: highlights; a schematic of frames growing wider, dimmer, and noisier over time; the truncated width-estimator distribution ('a width can't go negative, so noise only inflates it') with a biased MSD; a panel showing inverse-variance weighting failing to remove the bias; the fft-cnr spectral CNR estimate with its AIC knee; the subdiffusive exponent biased toward the ballistic ceiling and recovered by the correction; and the correction applied to real stroboSCAT data on a MoSSe alloy.
Download the poster (PDF).

The problem: a width can’t go negative

Transport microscopy extracts diffusion parameters from the frame-by-frame broadening of an excited-state population: fit a profile width σ² at each time delay, build the mean-squared displacement, read off the diffusion coefficient D or the transport exponent α. The width fit has a wall at zero. When contrast falls, the estimator’s distribution piles up against that wall and skews high — low-CNR fits can only err upward. The result is an inflated D (by up to an order of magnitude) and an apparent α pushed toward the ballistic limit.

This is a bias, not mere imprecision: averaging fitted values across repeated measurements does not remove it, and neither does inverse-variance weighting of the MSD. Since signal decays over the measurement, every frame is wider, dimmer, and noisier than the last, so the bias grows with time delay and distorts the functional form of the MSD rather than offsetting it. This regime is not exotic: it covers fragile samples, the earliest and latest time points of any decay, and weak absorbers or emitters.

Report the CNR, whatever regime you work in

The bias scales with contrast: negligible at high CNR, severe at low CNR. So the CNR is the number to report. If your measurements sit well above the noise, fft-cnr puts a figure on it for the methods section; if they sit closer to the edge than you assumed, the same call tells you before the artifact reaches your conclusions. In both cases you have reported a quantity a reader can use to judge the measurement, alongside the integration time and excitation power you already report. It costs one function call.

fft-cnr is an open-source Python package that measures the CNR of a 1-D profile from a single acquisition, with no repeat frames and no separate background region. Low-frequency signal power stands above a flat high-frequency noise floor in the power spectrum; an Akaike-information-criterion knee locates the boundary; the package returns the CNR with a 95% confidence interval. Beyond that number it detects when noise is signal-dependent — the shot-noise regime, where the naive CNR overstates the true peak SNR — and reports a corrected value; it flags frames where a low-frequency baseline or an opposite-sign feature makes the amplitude read ambiguous; and it returns the fitted profile parameters when you want center, width, and shape alongside the contrast. Installation is pip install fft-cnr; the CNR of a profile is fft_cnr(profile).cnr.

The bias correction builds on that measurement. A calibration keyed on the per-frame CNR subtracts the width bias from each frame, independent of the D or α being measured; its only data input is the CNR. It is validated across Gaussian, Voigt, and generalized-Gaussian profile shapes.

Results

On a realistic test bed built from an exciton-hopping map of a disordered perovskite nanocrystal solid (nominal α = 0.883; 250 × 250 spatial bins, 20 frames, 7 ns exciton lifetime, 64,000 independent noise realizations), the naive exponent climbs as CNR falls and saturates at the ballistic ceiling of α = 2: noise alone converts subdiffusion into apparent ballistic transport. The CNR-calibrated correction recovers the nominal exponent down to the low-contrast regime. Applied to real stroboSCAT data on a MoSSe alloy, the corrected width separates cleanly from the naive fit on every binned point: binning removes the frame-to-frame scatter, but the systematic bias survives averaging, so the correction shows on each point.

Links

Acknowledgments

This work was carried out in the group of Prof. Ferry Prins at IFIMAC, Universidad Autónoma de Madrid, funded by the European Commission through the ERC EnVision project (GA 101125962).