Fast, accurate, and predictive method for atom detection in site-resolved images of microtrap arrays

TL;DR

This work tackles real-time detection of individual atoms in site-resolved microtrap images, where inter-site distances can be comparable to the PSF radius. It presents a generalized Wiener-filter framework yielding an Optimal Linear Estimator (OLE) with $\mathbf{H}_{\text{opt}} = \big(\mathbf{M}^T \Sigma_n^{-1} \mathbf{M} + \Sigma_x^{-1}\big)^{-1} \mathbf{M}^T \Sigma_n^{-1}$, enabling fast, linear reconstruction of site brightnesses under Poisson-Gaussian noise. The study shows dramatic improvements over Wiener deconvolution in the unresolved regime, while maintaining scalability ( runtime ~ linear in the number of sites and under 100 ms for $100 \times 100$ arrays) and robustness to calibration errors; it also defines a rigorous SNR metric that predicts detection performance and guides experimental design. A learning protocol for priors from data yields a posteriori OLE that further enhances accuracy, and the authors provide open-source code and tutorials to facilitate adoption and future scaling to larger arrays.

Abstract

We introduce a new method, rooted in estimation theory, to detect individual atoms in site-resolved images of microtrap arrays, such as optical lattices or optical tweezers arrays. Using labelled test images, we demonstrate drastic improvement of the detection accuracy compared to the popular method based on Wiener deconvolution when the inter-site distance is comparable to the radius of the point spread function. The runtime of our method scales approximately linearly with the number of sites, and remains well below 100 ms for an array of 100 x 100 sites on a desktop computer. It is therefore fully compatible with a real-time usage. Finally, we propose a rigorous definition for the signal-to-noise ratio of the problem, and show that it can be used as a predictor for the detection error rate. Our work opens the prospect for future experiments with increased array sizes, or reduced inter-site distances.

Figures (6)

• Figure 1: Example of test image. The model parameters used to generate the image are given in \ref{['tab:params']}. The inset shows a zoom into the white square, with the white dots indicating the site positions. The signal-to-noise ratio of this image is about 15, see \ref{['sec:SNR']}. Our reconstruction method detects the atoms with an error rate of 0.2 +- 0.1, compared to 1.2 +- 0.2 with a standard deconvolution estimator, see \ref{['sec:deconvolution']}. The uncertainties represent the standard deviation over 1000.0 images.
• Figure 2: Optimizing the hyperparameter of the a priori OLE. The optimal value $\gamma_\text{opt}$ is found by minimizing the kurtosis of $\hat{\mathbold{x}}(\gamma)$, which simultaneously minimizes the DER. Each point is the average over 500.0 test images. The error bars represent the standard deviation. The same set of images is used for all values of $\gamma$. The top panel compares the distributions of $\hat{\mathbold{x}}(\gamma)$ for a singe test image, and $\gamma = \gamma_\text{opt} / 20$, $\gamma_\text{opt}$, and $\gamma_\text{opt} \! \times \! 20$. The three plots are drawn using the same scale for each axis.
• Figure 3: OLEs for the test image in \ref{['fig:image']}. The top and bottom panels show the distribution of estimated brightnesses for the a priori and a posteriori OLEs, respectively. In both panels, the subplots on the right show the underlying occupancy probability and brightness variance, and the gray histogram in the background represents the true brightness distribution. In the top panel, the dashed lines are the two modes of the most likely Gaussian mixture distribution, with weights, means and variances $(1 - \phi), \mu_0, \sigma_0^2$ (empty sites), and $\phi, \mu_1, \sigma_1^2$ (filled sites), see \ref{['eq:gaussian_mixture']}.
• Figure 4: Detection error rate and signal-to-noise ratio. Top panel: The colored lines are the DER level curves at 0.1 as a function of $\mu$ and $a$, with the other parameters as in \ref{['tab:params']}. Each point is averaged over 100.0 test images. The gray lines are the SNR level curves at 10;15;20;25;30, see \ref{['sec:SNR']}. Lower panel: Cuts through the upper panel along the lines $\mu = 1000.0$ (A), and $a = 1.5 \, r_\textsc{psf}$ (B). The SNR is shown in gray.
• Figure 5: Runtime. The runtime is the averaged over 5.0 test images generated with the parameters of \ref{['tab:params']}, except for the varying number of sites.