We established a model for an airborne wind lidar. Numerical optimization algorithms should be used to solve this nonlinear model. We designed a Levenberg–Marquardt (L–M) algorithm and tested it with the modeled data. The retrieved velocity and the true velocity agree very well, and the adjusted R2 is 0.99947. We have carried out an airborne coherent wind lidar experiment in January 2015, and we used the model and the L–M algorithm to process the wind lidar experiment data, and compared the retrieved results with the radiosonde wind profile. The consistency is very good, especially at an altitude above 1.8 km. We may speculate that when the atmosphere flows are not so dramatic, the lidar and the radiosonde measurements are strictly synchronous, it is possible to retrieve horizontal wind speeds and directions consistently with the radiosonde using our wind lidar model and the L–M algorithm.
We propose a method for generating axial multifocal spots (AMS) with a high numerical aperture (NA) objective. The AMS is generated by using phase-only modulation at the back aperture of the objective. Without using any iteration algorithm, the modulated phase distribution is directly calculated by an additional phase analytical formula with different focal distances. By dividing the back aperture of the objective into multi sectorial zones and applying the corresponding additional phase with different focal distances, the AMS can be created. Numerical simulation shows that the numbers of the axial focus depends solely on the different phase distribution calculated by different focal distances. By engineering the phase pattern with different focal distances, axial multifocal spots with different spacing can be realized. Furthermore, combined with vortex phase, the AMS with specific shape spots also can be created. In addition, the AMS focused by incident beams of circular polarization, radial polarization and angular polarization are also studied. This kind of AMS may be found applications in optical imaging, especially in three-dimensional (3D) biological imaging, and also be attractive in mult-plane optical trapping.
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