Overcoming the diffraction limit by exploiting unmeasured scattering media

Scattering is not necessarily an obstacle to imaging. It can help enhance imaging performance beyond the reach of a lens system. However, current scattering-enhanced imaging systems require prior knowledge of the transmission matrix. There are also some techniques that do not require such prior knowledge to see through strongly scattering media, but the results are still limited by the optics used. Here we propose overcoming the diffraction limit through a visually opaque diffuser. By controlling the distance between the diffuser and lens system, light with higher spatial frequencies is scattered into the entrance pupil. With the deformed wavefront corrected, we experimentally achieved imaging with 3.39 \times$3.39 \times$ enhancement of the Rayleigh limit. In addition, our method works well for objects that are 4 \times$4 \times$ larger than the memory effect range and can maintain super-resolution performance for a depth of field 6.6 \times$6.6 \times$ larger than a lens can achieve. Using our method, an obstructive scattering medium can enhance the throughput of the imaging system, even though the transmission matrix of the scattering medium has not been measured beforehand.