  Using conventional refraction-based optical lens, it is challenging to
achieve both high-resolution imaging and long-working-distance condition. To
increase the numerical aperture of a lens, the working distance should be
compensated, and vice versa. Here we propose and demonstrate a new concept in
optical microscopy that can achieve both high-resolution imaging and
long-working-distance conditions by utilising a scattering layer instead of
refractive optics. When light passes through a scattering layer, it creates a
unique interference pattern. To retrieve the complex amplitude image from the
interference pattern without introducing a reference beam, we utilised a
speckle-correlation scattering matrix method. This property enables holographic
microscopy without any lens or external reference beam. Importantly, the
proposed method allows high-resolution imaging with a long working distance
beyond what a conventional objective lens can achieve. As an experimental
verification, we imaged various microscopic samples and compared their
performance with off-axis digital holographic microscopy.

Optics