Normal point generation and first photon bias correction in APOLLO Lunar Laser Ranging

The APOLLO Lunar Laser Ranging (LLR) system studies gravity by tracing out the orbit of the moon to 1̃ mm, over many years. LLR in general provides extensive tests of many aspects of gravity, including deviations from General Relativity (GR), and time rate-of-change of the gravitational constant, G. APOLLO's precision is approximately 10x better than previous LLR measurements, enabling about an order of magnitude improvement in tests of gravity over the coming years. APOLLO requires complex data reduction methods to extract the distance so precisely. There are currently three choices for determining the round-trip-time to the moon from the data: the correlation method, the Augmented Calculation method, and the PDF-fit method. The results here suggest the PDF- fit method as preferable, for minimum random uncertainty over the full operating range of conditions, and stable systematic error below 1̃ mm. As a second topic, the APOLLO system includes a systematic error called "First Photon Bias," which causes time measurements to be skewed early. An algorithm is presented and simulated, showing that it is inherently capable of achieving < 1 mm systematic error under normal operating conditions. However, the final algorithm requires a correction table calibrated from a more accurate model of shot-to-shot intensity fluctuations. Such a table could be the subject of future investigation