  Over the past decade, the gravitational lensing of the Cosmic Microwave
Background (CMB) has become a powerful tool for probing the matter distribution
in the Universe. The standard technique used to reconstruct the CMB lensing
signal employs the quadratic estimator (QE) method, which has recently been
shown to be suboptimal for lensing measurements on very small scales in
temperature and polarization data. We implement a simple, more optimal method
for the small-scale regime, which involves taking the direct inverse of the
background gradient. We derive new techniques to make continuous maps of
lensing using this "Gradient-Inversion" (GI) method and validate our method
with simulated data, finding good agreement with predictions. For idealized
simulations of lensing cross- and autospectra that neglect foregrounds, we
demonstrate that our method performs significantly better than previous
quadratic estimator methods in temperature; at $L=5000-9000$, it reduces errors
on the lensing auto-power spectrum by a factor of $\sim 4$ for both idealized
CMB-S4 and Simons Observatory-like experiments and by a factor of $\sim 2.6$
for cross-correlations of CMB-S4-like lensing reconstruction and the true
lensing field. We caution that the level of the neglected small-scale
foreground power, while low in polarization, is very high in temperature;
though we briefly outline foreground mitigation methods, further work on this
topic is required. Nevertheless, our results show the future potential for
improved small-scale CMB lensing measurements, which could provide stronger
constraints on cosmological parameters and astrophysics at high redshifts.

Cosmology and Nongalactic Astrophysics