Three-dimensional phase contrast imaging by an annular illumination microscope

A method of observing 3-D phase structures through a microscope incorporating computer reconstruction is discussed. This microscope is equipped with an annular pupil in illumination optics, but no phase shifter is included in the imaging optics. The sample stage is longitudinally (z-axial) scanned to collect a focus image series. The 3-D phase transfer function is derived and computer-plotted based on Streibl's 3-D image transfer theory under the first-order Born approximation and the mutual intensity propagation theorem. Experimental results of 3-D phase reconstruction are shown with cultured tobacco cells by Helstrom's inverse filtering of the transfer function to a series of focused images.