  We present geometric-phase microscopy allowing a multipurpose quantitative
phase imaging in which the ground-truth phase is restored by quantifying the
phase retardance. The method uses broadband spatially incoherent light that is
polarization sensitively controlled through the geometric (Pancharatnam-Berry)
phase. The assessed retardance possibly originates either in dynamic or
geometric phase and measurements are customized for quantitative mapping of
isotropic and birefringent samples or multi-functional geometric-phase
elements. The phase restoration is based on the self-interference of
polarization distinguished waves carrying sample information and providing pure
reference phase, while passing through an inherently stable common-path setup.
The experimental configuration allows an instantaneous (single-shot) phase
restoration with guaranteed subnanometer precision and excellent ground-truth
accuracy (well below 5 nm). The optical performance is demonstrated in advanced
yet routinely feasible noninvasive biophotonic imaging executed in the
automated manner and predestined for supervised machine learning. The
experiments demonstrate measurement of cell dry mass density, cell
classification based on the morphological parameters and visualization of
dynamic dry mass changes. The multipurpose use of the method was demonstrated
by restoring variations in the dynamic phase originating from the electrically
induced birefringence of liquid crystals and by mapping the geometric phase of
a space-variant polarization directed lens.
