  Optical imaging deep inside scattering media remains a fundamental problem in
bio-imaging. While wavefront shaping has been shown to allow focusing of
coherent light at depth, achieving it non-invasively remains a challenge.
Various feedback mechanisms, in particular acoustic or non-linear
fluorescence-based, have been put forward for this purpose. Non-invasive
focusing at depth on fluorescent objects with linear excitation is, however,
still unresolved. Here we report a simple method for focusing inside a
scattering medium in an epi-detection geometry with a linear signal: optimizing
the spatial variance of low contrast speckle patterns emitted by a set of
fluorescent sources. Experimentally, we demonstrate robust and efficient
focusing of scattered light on a single source, and show that this variance
optimization method is formally equivalent to previous optimization strategies
based on two-photon fluorescence. Our technique should generalize to a large
variety of incoherent contrast mechanisms and holds interesting prospects for
deep bio-imaging.
