Abstract: We gave the mathematical expression of analytical solution of Doppler spectra of laser backscattering from rotating Lambertian cones, and compared the analytical solution with the numerical solution. The results show that with the increase of the calculation accuracy of numerical solution, the difference between the numerical solution and the analytical solution becomes smaller,  the analytical solutions and the numerical solutions can be mutually validated.

Key words: laser Doppler velocimeter, mathematical method in physics, laser ladar, backscattering