  Non-invasive optical focusing inside scattering media is still a big
challenge because inhomogeneous media scatter both incoming photons for
focusing and outgoing photons for observation. Various approaches, utilizing
non-linear fluorescence or ultrasound, have been reported to address this
difficulty. However, implementation of these methods is complicated and highly
expensive, as ultrafast laser systems or photo-acoustic equipment must be
employed. Here, we demonstrate a wavefront shaping technique to achieve
non-invasive focusing (NiF) inside scattering media using only a linear
fluorescent signal. Contrast and mean of incoherent speckles, produced by the
linear fluorescence, are utilized as feedback signals to optimize the input
wavefront. While increasing speckle contrast makes the focus tighter, and
increasing the speckle mean enhances the intensity, fine-tuning the
contribution of these two factors in our two-step optimization is essential. An
optimal wavefront is found to achieve simultaneously both a micrometer focal
spot size (down to 20 um diameter) and high intensity (more than a 100-fold
enhancement) inside the scattering media. Our method promises a new route in
life science towards focusing, imaging or manipulating deep into biological
tissues with linear fluorescent agents.
