  Microtubules (MTs) are filamentous protein polymers roughly 25 nm in
diameter. Ubiquitous in eukaryotes, MTs are well known for their structural
role but also act as actuators, sensors, and, in association with other
proteins, checkpoint regulators. The thin diameter and transparency of
microtubules classifies them as sub-resolution phase objects, with concomitant
imaging challenges. Label-free methods for imaging microtubules are preferred
when long exposure times would lead to phototoxicity in fluorescence, or for
retaining more native structure and activity.
  This method approaches quantitative phase imaging of MTs as an inverse
problem based on the Transport of Intensity Equation. In a co-registered
comparison of MT signal-to-background-noise ratio, TIE Microscopy of MTs shows
an improvement of more than three times that of video-enhanced bright field
imaging.
  This method avoids the anisotropy caused by prisms used in differential
interference contrast and takes only two defocused images as input. Unlike
other label-free techniques for imaging microtubules, in TIE microscopy
background removal is a natural consequence of taking the difference of two
defocused images, so the need to frequently update a background image is
eliminated.
