  High-resolution wide field-of-view (FOV) microscopic imaging plays an
essential role in various fields of biomedicine, engineering, and physical
sciences. As an alternative to conventional lens-based scanning techniques,
lensfree holography provides a new way to effectively bypass the intrinsical
trade-off between the spatial resolution and FOV of conventional microscopes.
Unfortunately, due to the limited sensor pixel-size, unpredictable disturbance
during image acquisition, and sub-optimum solution to the phase retrieval
problem, typical lensfree microscopes only produce compromised imaging quality
in terms of lateral resolution and signal-to-noise ratio (SNR). Here, we
propose an adaptive pixel-super-resolved lensfree imaging (APLI) method which
can solve, or at least partially alleviate these limitations. Our approach
addresses the pixel aliasing problem by Z-scanning only, without resorting to
subpixel shifting or beam-angle manipulation. Automatic positional error
correction algorithm and adaptive relaxation strategy are introduced to enhance
the robustness and SNR of reconstruction significantly. Based on APLI, we
perform full-FOV reconstruction of a USAF resolution target ($\sim$29.85
$m{m^2}$) and achieve half-pitch lateral resolution of 770 $nm$, surpassing
2.17 times of the theoretical Nyquist-Shannon sampling resolution limit imposed
by the sensor pixel-size (1.67 $\mu m$). Full-FOV imaging result of a typical
dicot root is also provided to demonstrate its promising potential applications
in biologic imaging.
