  Fourier ptychographic microscopy (FPM) is a recently developed computational
imaging technique for wide-field, high-resolution microscopy with a high
space-bandwidth product. It integrates the concepts of synthetic aperture and
phase retrieval to surpass the resolution limit imposed by the employed
objective lens. In the FPM framework, the position of each sub-spectrum needs
to be accurately known to ensure the success of the phase retrieval process.
Different from the conventional methods with mechanical adjustment or
data-driven optimization strategies, here we report a physics-based defocusing
strategy for correcting large-scale positional deviation of the LED
illumination in FPM. Based on a subpixel image registration process with a
defocused object, we can directly infer the illumination parameters including
the lateral offsets of the light source, the in-plane rotation angle of the LED
array, and the distance between the sample and the LED board. The feasibility
and effectiveness of our method are validated with both simulation study and
experiments. We show that the reported strategy can obtain high-quality
reconstruction of both the complex object and pupil even the LED array is
randomly placed under the sample with both unknown lateral offsets and
rotations. As such, it enables the development of robust FPM systems by
reducing the requirement on fine mechanical adjustment and data-driven
correction in the construction process.
