  The gravitational field of compact objects, such as primordial black holes,
can create multiple images of background sources. For transients such as fast
radio bursts (FRBs), these multiple images can be resolved in the time domain.
Under certain circumstances, these images not only have similar burst
morphologies but are also phase-coherent at the electric field level. With a
novel dechannelization algorithm and a matched filtering technique, we search
for repeated copies of the same electric field waveform in observations of FRBs
detected by the FRB backend of the Canadian Hydrogen Mapping Intensity
Experiment (CHIME). An interference fringe from a coherent gravitational
lensing signal will appear in the time-lag domain as a
statistically-significant peak in the time-lag autocorrelation function. We
calibrate our statistical significance using telescope data containing no FRB
signal. Our dataset consists of $\sim$100-ms long recordings of voltage data
from 172 FRB events, dechannelized to 1.25-ns time resolution. This coherent
search algorithm allows us to search for gravitational lensing signatures from
compact objects in the mass range of $10^{-4}-10^{4} ~\mathrm{M_{\odot}}$.
After ruling out an anomalous candidate due to diffractive scintillation, we
find no significant detections of gravitational lensing in the 172 FRB events
that have been analyzed. In a companion work [Leung, Kader+2022], we interpret
the constraints on dark matter from this search.
