  Quadriwave lateral shearing interferometry (QLSI) is a quantitative phase
imaging technique based on the use of a diffraction grating placed in front of
a camera. This grating creates a wire-mesh-like image, called an interferogram,
that is postprocessed to retrieve both the intensity and phase profiles of an
incoming light beam. Invented in the 90s, QLSI has been used in numerous
applications, e.g., laser beam characterization, lens metrology, topography
measurements, adaptive optics, or gas jet metrology. More recently, the
technique has been implemented on optical microscopes to characterize micro and
nano-objects for bioimaging and nanophotonics applications. However, not much
effort has been placed on disseminating this powerful technology so far, while
it is yet a particularly simple technique. In this article, we intend to
popularize this technique by describing all its facets in the framework of
optical microscopy, namely the working principle, its implementation on a
microscope and the theory of image formation, using simple pictures. Also, we
provide and comment an algorithm of interferogram processing, written in
Matlab. Then, following the new extension of the technique for microscopy and
nanophotonics applications, and the deviation from what the technique was
initially invented for, we propose to revisit the description of the technique,
in particular by discussing the terminology, insisting more on a grating-shadow
description rather than a quadriwave process, and proposing an alternative
appellation, namely "grating shadow phase microscopy" or "grating-assisted
phase imaging".
