The practical inversion of optical data for a micrometeorological temperature profile requires a nonlinear inversion of a system of polynomial equations. A method of nonlinear least squares can produce a physically acceptable solution of this nonlinear inversion problem. Because this method, which is demonstrated with the inversion of simulated optical data, does not produce an unique solution, the images of targets are calculated and used to examine the solution. A solution of the nonlinear inversion problem is physically acceptable when these calculated images agree with an independent set of simulated images to within expected errors of measurement. The nonlinear inversion of optical data contaminated with errors is shown not to be a difficult problem, because the numerical method of inversion is designed to find efficiently the coefficients used to represent the temperature profile. The geometric properties of the equations used in the method of inversion are compared for a linear and nonlinear inversion of optical data.