An atmospheric dispersion corrector design with milliarcsecond-level precision from 1 to 4 microns for high dispersion coronagraphy

Differential atmospheric refraction (DAR) limits the amount of light that can be coupled into a single mode fiber and provides additional complications for any fiber tracking system. We present an atmospheric dispersion corrector (ADC) design based off of two counter-rotating prisms to fit the needs of exoplanet spectroscopy for the Keck Planet Imager and Characterizer (KPIC) from 1.1 to 4.2 microns. Due to strong telluric effects, we find that the default Zemax prescription for DAR between 2 and 4.2 microns to be inaccurate up to 15 mas when comparing against DAR models computed from first principles. Using first-principle models, we developed our own custom ADC optimization solution and achieve less than 4 mas residual dispersion in any individual science band (J, K, L) down to 60 degree zenith angles, while the whole time maintaining less than 3 mas of residual dispersion in the tracking band (H) and less than 2 mas of residual dispersion between the tracking and science bands