Diffuser-assisted Photometric Follow-up Observations of the Neptune-sized Planets K2-28b and K2-100b

We present precision transit observations of the Neptune-sized planets K2-28b and K2-100b, using the Engineered Diffuser on the ARCTIC imager on the ARC 3.5m Telescope at Apache Point Observatory. K2-28b is a $R_{p} = 2.56 R_\oplus$ mini-Neptune transiting a bright (J=11.7) metal-rich M4 dwarf, offering compelling prospects for future atmospheric characterization. K2-100b is a $R_{p} = 3.45 R_\oplus$ Neptune in the Praesepe Cluster and is one of few planets known in a cluster transiting a host star bright enough ($V=10.5$) for precision radial velocity observations. Using the precision photometric capabilities of the diffuser/ARCTIC system, allows us to achieve a precision of $105^{+87}_{-37}$ppm, and $38^{+21}_{-11}$ppm in 30 minute bins for K2-28b, and K2-100b, respectively. Our joint-fits to the K2 and ground-based light-curves give an order of magnitude improvement in the orbital ephemeris for both planets, yielding a timing precision of 2min in the JWST era. Although we show that the currently available broad-band measurements of K2-28b's radius are currently too imprecise to place useful constraints on K2-28b's atmosphere, we demonstrate that JWST/NIRISS will be able to discern between a cloudy/clear atmosphere in a modest number of transit observations. Our light-curve of K2-100b marks the first transit follow-up observation of this challenging-to-observe transit, where we obtain a transit depth of $819 \pm 50 \mathrm{ppm}$ in the SDSS $i^\prime$ band. We conclude that diffuser-assisted photometry can play an important role in the TESS era to perform timely and precise follow-up of the expected bounty of TESS planet candidates.