  This article presents a method to perform diffraction tomography in a
standard microscope that includes an LED array for illumination. After
acquiring a sequence of intensity-only images of a thick sample, a
ptychography-based reconstruction algorithm solves for its unknown complex
index of refraction across three dimensions. The experimental microscope
demonstrates a spatial resolution of 0.39 $\mu$m and an axial resolution of 3.7
$\mu$m at the Nyquist-Shannon sampling limit (0.54 $\mu$m and 5.0 $\mu$m at the
Sparrow limit, respectively), across a total imaging volume of 2.2 mm $\times$
2.2 mm $\times$ 110 $\mu$m. Unlike competing methods, the 3D tomograms
presented in this article are continuous, quantitative, and formed without the
need for interferometry or any moving parts. Wide field-of-view reconstructions
of thick biological specimens demonstrate potential applications in pathology
and developmental biology.
