  Euclid and the Roman Space Telescope (Roman) will soon use grism spectroscopy
to detect millions of galaxies via H$\alpha$ and [O III] $\lambda 5007$
emission. To better constrain the expected galaxy counts from these
instruments, we use a vetted sample of 4,239 emission-line galaxies from the
3D-HST survey to measure the H$\alpha$ and [O III] $\lambda 5007$ luminosity
functions between $1.16<z<1.90$; this sample is $\sim 4$ times larger than
previous studies at this redshift. We find very good agreement with previous
measurements for H$\alpha$, but for [O III], we predict a higher number of
intermediate-luminosity galaxies than previous works. We find that for both
lines, the characteristic luminosity, $\mathcal{L}_*$, increases monotonically
with redshift, and use the H$\alpha$ luminosity function to calculate the
epoch's cosmic star formation rate density. We find that H$\alpha$-visible
galaxies account for $\sim 81\%$ of the epoch's total star formation rate, and
this value changes very little over the $1.16<z<1.56$ redshift range. Finally,
we derive the surface density of galaxies as a function of limiting flux and
find that previous predictions for galaxy counts for the Euclid Wide Survey are
unchanged, but there may be more [O III] galaxies in the Roman High Latitude
Survey than previously estimated.
