Mikado strategy for the detection of atoms in images of microtrap arrays

TL;DR

The paper addresses detecting atoms in high-resolution images of microtrap arrays where PSF overlap complicates occupancy inference. It introduces the mikado strategy, a model-free, iterative approach that alternates estimation and detection to progressively simplify the problem without relying on an explicit posterior occupancy model. The method builds on a generalized Wiener filter that relates the image to site brightness through the linear model $y = M x + k + n$, using covariances Sigma_x and Sigma_n that encode occupancy statistics and measurement noise. Benchmarking shows improved detection accuracy in strong overlap regimes, while well-resolved cases are comparable across methods; the approach remains computationally practical for large arrays and is illustrated with an Erbium lattice imaging use case.

Abstract

Building on top of our recent work [arXiv:2502.08511], we introduce a new strategy to solve the problem of detecting atoms in high-resolution images of microtrap arrays. By alternating estimation and detection steps, we get rid of the need for an explicit model to compute the posterior occupancy probability of each site given its a priori optimal estimate. As direct benefits, we show an improved detection accuracy compared to our previous work when the sites are not optically well resolved, and we expect a greater robustness against real experimental conditions.

Figures (4)

• Figure 1: Working principle of the mikado strategy. The method is applied to a simulated image corresponding to a square array of 50 x 50 sites with a uniform occupancy probability $p = 0.6$. Each step consists of three phases: the prior update, the estimation, and the classification. Using two thresholds $t_<$ and $t_>$ indicated by the dashed vertical lines, the sites are classified as empty (abbreviated "e", gray bins), filled ("f", yellow bins), or with unknown occupancy ("u", blue bins). Empty sites are not included in the estimation since they do not contribute to the signal. The parameters used to generate the image are as described in \ref{['sec:benchmarking']}, with $\mu = 500$ and $a = 1.25\,r_\text{PSF}$. With these parameters, the detection error rate of the mikado strategy is 0.1 +- 0.1, where the uncertainty is the standard deviation over 100.0 similar images. As a comparison, the detection error rate of the method based on the Wiener deconvolution is 2.6 +- 0.4, that of the a priori optimal estimator is 2.0 +- 0.3, and that of the a posteriori optimal estimator is 0.5 +- 0.2.
• Figure 2: Detection error rate (DER) and signal-to-noise ratio (SNR) as a function of the brightness mean and ratio of the inter-site distance to the PSF half width at half maximum. Top panel: The thick colored lines are the loci of the points where the DER of each estimator is equal to $10^{-3}$. The thin gray lines are the SNR level curves at 10;15;20;25;30, see Cheneau2025. Lower panels: Variations of the DER with $a$ for $\mu = 10^3$ (left), and with $\mu$ for $a = 1.5 \, r_\text{PSF}$ (right). The thick colored lines represent the DER, and the thin gray lines represent the SNR. The DER is averaged over 100 images. The LU decomposition is parameterized with a threshold of $10^{-3}$ and a fill-in of $10^3$. The mikado estimator proceeds in 10 steps.
• Figure 3: Runtime comparison. The runtime is the averaged over 10 test images and 10 repetitions for each image. We adapt the number of nonzero entries to keep in the LU matrices to the ratio $a/r_\text{PSF}$ by checking the convergence of the CG algorithm. The conjugate gradient algorithm stops when the relative difference between the left and right-hand side of \ref{['eq:linear_system']} is less than $10^{-2}$. The LU decomposition is parameterized with a threshold of $10^{-2}$ and a fill-in of $10^2$. The mikado strategy proceeds in 5 steps.
• Figure 4: Influence of the number of steps (left) and of the final threshold position (right) on the detection error rate (DER) of the mikado strategy. Both measures are performed with $\mu = 500$, $\sigma = \mu / 10$, $r_\text{PSF} = \qty{2}{pixels}$, $a = 1.25\,r_\text{PSF}$, $k = 0$ and $r = 1$. The error bars represent the standard deviation over a set of 100.0 images.