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

Abstract

The appendix is available with entire article on microfiche. Order from the American Geophysical Union, 2000 Florida Avenue, N.W., Washington, D.C. 20009. Document J80‐007; $1.00. Payment must accompany order. The physical arc length difference between the red and blue beam of a dual‐color laser generates an error term in determining Δn (and thus n, the refractive index, and D, the line length). Numerical ray trace examples and theoretical approximations show the resulting relative error ΔD/D to increase as D2. The error reaches 1 part in 108 (107) at D of 12 (40) km, respectively, through an atmospheric structure of a line with Δh ≅ 2000 m. Error reduction by a factor of nearly 10 is possible by using the pressure, temperature, and humidity of both endpoints to calculate n or, to a lesser degree, by assuming a standard coefficient of refraction k. Two lines, approximately 30 km each, with Δh of 2000 and 3000 m, were sampled by helicopter on the island of Maui through an inversion layer. The two ray trace lengths were compared to standard reductions. Hypothetical shorter and longer lines through the same atmospheric structures and elevation difference Δh are also reduced by both methods. Length differences from the two methods appear at 10−7 level for lines longer than 60 km and depend on the sharpness of the temperature inversion. The dual zenith angle method of determining Δh would yield errors of the order of 60 cm for the real line.