Distance corrections for single- and dual-color lasers by ray tracing

The physical arc length difference between the red and blue beam of a dual-color laser generates an error term in determining Delta-n as well as n (the refractive index) and D (the line length). Numerical ray trace examples and theoretical approximations show that the resulting relative error Delta-D/D increases as D-squared. Error reduction by a factor of nearly 10 is possible by using the pressure, temperature, and humidity of both endpoints to calculate n. The present study results from a desire to improve the precision of monitoring the local and regional position of the Lunar Laser Ranging Observatory atop Haleakala, Maui, Hawaii; the monitoring of the earth's crustal deformation and strain is a primary concern of the study.