  The Merian survey is mapping $\sim$ 850 degrees$^2$ of the Hyper Suprime-Cam
Strategic Survey Program (HSC-SSP) wide layer with two medium-band filters on
the 4-meter Victor M. Blanco telescope at the Cerro Tololo Inter-American
Observatory, with the goal of carrying the first high signal-to-noise (S/N)
measurements of weak gravitational lensing around dwarf galaxies. This paper
presents the design of the Merian filter set: N708 ($\lambda_c = 7080
\unicode{x212B}$, $\Delta\lambda = 275\unicode{x212B}$) and N540 ($\lambda_c =
5400\unicode{x212B}$, $\Delta\lambda = 210\unicode{x212B}$). The central
wavelengths and filter widths of N708 and N540 were designed to detect the $\rm
H\alpha$ and $\rm [OIII]$ emission lines of galaxies in the mass range $8<\rm
\log M_*/M_\odot<9$ by comparing Merian fluxes with HSC broad-band fluxes. Our
filter design takes into account the weak lensing S/N and photometric redshift
performance. Our simulations predict that Merian will yield a sample of $\sim$
85,000 star-forming dwarf galaxies with a photometric redshift accuracy of
$\sigma_{\Delta z/(1+z)}\sim 0.01$ and an outlier fraction of $\eta=2.8\%$ over
the redshift range $0.058<z<0.10$. With 60 full nights on the Blanco/Dark
Energy Camera (DECam), the Merian survey is predicted to measure the average
weak lensing profile around dwarf galaxies with lensing $\rm S/N \sim 32$
within $r<0.5$ Mpc and lensing $\rm S/N \sim 90$ within $r<1.0$ Mpc. This
unprecedented sample of star-forming dwarf galaxies will allow for studies of
the interplay between dark matter and stellar feedback and their roles in the
evolution of dwarf galaxies.
