High-Precision Amplitude-Modulated Continuous-Wave Lunar Laser Ranging

Lunar laser ranging (LLR) currently delivers mm-class tests of relativistic gravity and the lunar interior, but further gains are limited by photon-starved pulsed systems, array-induced pulse broadening, and atmospheric variability. Pushing into the sub-0.1 mm regime is required to probe ultra-slow tidal dissipation, long-period librations, and potential microhertz gravitational waves. We develop a complete amplitude-modulated continuous-wave (AM–CW) framework for high-power LLR, including measurement models, estimators, a unified covariance description, and an observatory concept of operations. In the AM–CW architecture, LLR is treated as RF phase metrology on a bright CW optical carrier: two-way range is obtained from the mean phase (after multi-tone ambiguity removal) and one-way line-of-sight range–rate from the phase slope. The joint estimators are characterized by a covariance matrix C(T ) decomposed into photon, atmospheric, instrumental, oscillator, and nonlinearity contributions, which we map into quantitative subsystem requirements. The model includes a closed-form range–rate bias from modulation-frequency slew across the∼ 2.56 s round trip and synthetic-wavelength constraints on multi-tone nonlinearity. For a 1 kW transmitter at 1064 nm on a 1 m telescope ranging to 10 cm corner-cube retroreflectors (CCRs), a 1 GHz precision tone places the photon-statistical floor for two-way range at a few×10 µm on T∼ 10^2 s windows. With realistic allocations to atmospheric and instrumental residuals, the resulting single-station two-way precision is∼ 0.08 mm, with range–rate sensitivities in the 0.1–1 µm s^-1 band. Differential LLR between reflectors separated on the Moon by baselines ∼10^3 km is capable of delivering 20–50 µm and few×(0.1–1) µm s^-1 differential range and range–rate. These targets are translated directly into hardware and CONOPS requirements for next-generation high-power AM–CW LLR stations.