  In this work, we present a highly efficient quantitative phase imaging (QPI)
approach using programmable annular LED illumination based on traditional
bright-field microscope. As a new type of coded illumination, the LED array
provides a flexible and compatible way to realize QPI. The proposed method
modulates the transfer function of system by changing the LED illumination
pattern, which achieves twice resolution of objective NA and gives noise-robust
response of transfer function. The phase of a sample could be recovered from
the intensity images with the inversion of transfer function. Moreover, the
weak object transfer function (WOTF) of axisymmetric oblique source is derived,
and the noise-free and noisy simulation results sufficiently validate the
applicability of discrete annular source. The quantitative phase measurements
of micro polystyrene bead and visible blazed transmission grating demonstrate
the accuracy of proposed method. Finally, the experimental investigations of
unstained human cancer cells using different types objective are presented, and
these results show the possibility of widespread adoption of QPI in the
morphology study of cellular processes and biomedical community.
