Theoretical analysis of a Rayleigh-Raman polychromatic laser guide star

Wavefront tilt correction is extremely important in the adaptive optics systems of large astronomical telescopes, for tilt makes up most of the aberration induced by atmospheric turbulence. Tilt measurement methods typically used in adaptive optics systems today involve light from a natural guide star in the vicinity of the object of interest, or from the object itself. A typical laser guide star does not allow for tilt measurement due to the double-pass nature of the reference light; the deflection of the upward traveling reference light is unknown. Polychromatic laser guide stars allow for object-independent tilt measurement by utilizing the dispersion of the refractive index of air and differential tilt measurements at different wavelengths. Existing research has been focused on polychromatic sodium laser guide stars (PSLGS), while Rayleigh-Raman polychromatic laser guide stars (RRPLGS) have seemingly been overlooked. It is shown that RRPLGS have a number of advantages, including scalability of returned flux and flexibility in selection of short wavelengths, allowing for a combination of multiple tilt measurements. RRPLGS are applicable to all sizes of telescopes, keeping in mind that for large telescopes the cone effect is minimized by assuming a tomographic wavefront sensing system. A theoretical analysis of a specific RRPLGS system is presented to address the feasibility of RRPLGS, focusing on fundamental constraints.