High-precision amplitude-modulated continuous-wave lunar laser ranging

Abstract Lunar laser ranging (LLR) currently delivers millimeter-class tests of relativistic gravity and the lunar interior, but further gains are limited by photon-starved pulsed returns, reflector-array broadening, and atmosphere/station systematics. This paper develops the metrology and covariance layer for high-power amplitude-modulated continuous-wave (AM-CW) LLR. The optical link and kW-class CW architecture are taken from the companion high-power CW analysis; the present focus is the commanded RF phase history, multi-tone ambiguity resolution, range and range-rate estimators, receiver requirements, Doppler derotation, and a full block-structured observation-covariance framework. For a 1 GHz precision tone, c / ( 4 π f m ) = 2.38567 × 10 − 2 m rad − 1 . We use the conservative design convention σ ϕ = 1 / SNR AM , which includes a factor- 2 margin relative to the leading ideal Poisson phase bound; under this convention, 0.10 mm photon-statistical range uncertainty requires SNR AM ≃ 240 . For effective detected modulation depth a = 0.5 – 0.7 and negligible post-filter background, at T = 100 s the corresponding conservative photon terms are 0.08 – 0.14 mm for a generic high-power link, 30 –