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Through analytical derivation and numerical analysis, the propagation properties of the chirped Airy(CAi) beams in the gradient-index medium are investigated. The intensity and the phase distributions, the propagation trajectory and the Poynting vector of the CAi beams are demonstrated to investigate the propagation properties. Owing to the special and symmetrical refractive index profile of the gradient-index medium, the CAi beams propagate periodically. The effects of the distribution factor and the chirped parameter on the propagation of the CAi beams are analyzed. As the increasing of the distribution factor, the intensity distribution of the CAi beams is more scattering. However, with the chirped parameter increasing, the focusing property of the CAi beams strengthens. The variation of the chirped parameter can change the position of the peak intensity maximum, but it cannot alter the period of the peak intensity. The variations of the initial phase and the energy of the beams in the transverse plane expedite accordingly.

Determination of overlap function is a key step in the calibration of a high-spectral-resolution lidar (HSRL). In this work, an iterative-based general determination (IGD) method for overlap function in HSRL is proposed. Error analysis with Monte-Carlo (MC) simulation is performed and illustrates the algorithm shows high accuracy and has high stability with an accurate lidar ratio assumption. A comparison experiment shows the overlap function from the proposed algorithm agrees well with that from a dual-field-of-view (dual-FOV) HSRL system. Since no modified optical system in HSRL is needed, this method shows great potential in real-time recording of overlap function in the HSRL system.