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. This paper develops the metrology and covariance layer for high-power amplitude-modulated continuous-wave (AM-CW) LLR. The optical link budget and kW-class CW architecture are taken from the companion high-power CW LLR analysis; here the focus is on RF-envelope phase observables, multi-tone ambiguity removal, range and range-rate estimators, detector requirements, Doppler derotation, and observation-level covariances. For a GHz-class precision tone, $c/(4\pi f_m)$ =2.38567 cm/rad, so 0.10 mm photon-limited range precision requires SNR ~ 240. With detected photon rates appropriate to a 1 kW, 1064 nm transmitter on a 1-2 m class telescope ranging to 10 cm corner-cube retroreflectors, the T ~ 100 s photon-statistical range floor is 0.08-0.14 mm in a generic high-power case, 30-60 um in a dedicated AM-CW case, and <30 um in a photon-rich case. With representative residual atmosphere and instrument allocations, a dedicated station can plausibly reach 0.08 mm absolute range precision under favorable conditions. Range-rate precision below 1 um/s requires several-hundred-second windows, or shorter windows only in photon-rich operation. Differential LLR between nearby lunar reflectors suppresses common-mode station and atmospheric terms, but it cannot suppress independent photon noise. Robust design bands are ~45-90 um for the dedicated AM-CW case and ~35-60 um in photon-rich excellent-seeing operation. The resulting requirements on link SNR, Doppler derotation, detector mode, instrument PSD/Allan stability, oscillator slew, multi-tone nonlinearity, and differential CONOPS are presented.