Digital refocusing and extended depth of field reconstruction in Fourier ptychographic microscopy

Fourier ptychography microscopy (FPM) is a recently developed microscopic imaging method that allows the recovery of a high-resolution complex image by combining a sequence of bright and darkfield images acquired under inclined illumination. The capacity of FPM for high resolution imaging at low magnification makes it particularly attractive for applications in digital pathology which require imaging of large specimens such as tissue sections and blood films. To date most applications of FPM have been limited to imaging thin samples, simplifying both image reconstruction and analysis. In this work we show that, for samples of intermediate thickness (defined here as less than the depth of field of a raw captured image), numerical propagation of the reconstructed complex field allows effective digital refocusing of FPM images. The results are validated by comparison against images obtained with an equivalent high numerical aperture objective lens. We find that post reconstruction refocusing (PRR) yields images comparable in quality to adding a defocus term to the pupil function within the reconstruction algorithm, while reducing computing time by several orders of magnitude. We apply PRR to visualize FPM images of Giemsa-stained peripheral blood films and present a novel image processing pipeline to construct an effective extended depth of field image which optimally displays the 3D sample structure in a 2D image. We also show how digital refocusing allows effective correction of the chromatic focus shifts inherent to the low magnification objective lenses used in FPM setups, improving the overall quality of color FPM images.