Coherent Doppler lidar signal spectrum with wind turbulence. 
The average signal spectrum (periodogram) for coherent Doppler lidar is calculated for a turbulent wind field.  Simple approximations are compared with the exact calculation.  The effects of random errors in the zero velocity reference, the effects of averaging spectral estimates by use of multiple lidar pulses, and the effects of the range dependence of the lidar signal power over the range gate are included.  For high spatial resolution measurements the lidar signal power is concentrated around one spectral estimate (spectral bin), and correct interpretation of the contribution from turbulence is difficult because of the effects of spectral leakage.  For range gates that are larger than the lidar pulse volume, the signal power is contained in many spectral bins and the effects of turbulence can be determined accurately for constant signal power over the range gate and for the far-field range dependence of the signal power.