Detection of small atom numbers through image processing

We demonstrate improved detection of small trapped atomic ensembles through advanced postprocessing and optimal analysis of absorption images. A fringe-removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation in well-localized ensembles and is applied to real experimental data to measure the population differences and intrinsic atom shot noise between spatially separated ensembles each comprising between $10$ and $2000$ atoms. The combined techniques improve our signal-to-noise ratio by a factor of $3$, to a minimum resolvable population difference of $17$ atoms, close to our ultimate detection limit.