  Measuring a weak gravitational lensing signal to the level required by the
next generation of space-based surveys demands exquisite reconstruction of the
point-spread function (PSF). However, unresolved binary stars can significantly
distort the PSF shape. In an effort to mitigate this bias, we aim at detecting
unresolved binaries in realistic Euclid stellar populations. We tested methods
in numerical experiments where (i) the PSF shape is known to Euclid
requirements across the field of view, and (ii) the PSF shape is unknown. We
drew simulated catalogues of PSF shapes for this proof-of-concept paper.
Following the Euclid survey plan, the objects were observed four times. We
propose three methods to detect unresolved binary stars. The detection is based
on the systematic and correlated biases between exposures of the same object.
One method is a simple correlation analysis, while the two others use
supervised machine-learning algorithms (random forest and artificial neural
network). In both experiments, we demonstrate the ability of our methods to
detect unresolved binary stars in simulated catalogues. The performance depends
on the level of prior knowledge of the PSF shape and the shape measurement
errors. Good detection performances are observed in both experiments. Full
complexity, in terms of the images and the survey design, is not included, but
key aspects of a more mature pipeline are discussed. Finding unresolved
binaries in objects used for PSF reconstruction increases the quality of the
PSF determination at arbitrary positions. We show, using different approaches,
that we are able to detect at least binary stars that are most damaging for the
PSF reconstruction process.
