  The study of astrophysical plasma lensing, such as in the case of extreme
scattering events, has typically been conducted using the geometric limit of
optics, neglecting wave effects. However, for the lensing of coherent sources
such as pulsars and fast radio bursts (FRBs), wave effects can play an
important role. Asymptotic methods, such as the so-called Eikonal limit, also
known as the stationary phase approximation, have been used to include
first-order wave effects; however, these methods fail at Stokes lines. Stokes
lines are generic features of a variety of lens models, and are regions in
parameter space where imaginary images begin to contribute to the overall
intensity modulation of lensed sources. Using the mathematical framework of
Picard-Lefschetz theory to compute diffraction integrals, we argue that these
imaginary images contain as much information as their geometric counterparts,
and may potentially be observable in data. Thus, weak-lensing events where
these imaginary images are present can be as useful for inferring lens
parameters as strong-lensing events in which multiple geometric images are
present.
