In the atmospheric transmission, due to the effect of atmospheric turbulence, the Coherent Synthetic Vortex (CSV) beam will undergo wavefront distortion and lead to intensity profile aberration and Orbital Angular Momentum (OAM) mode expansion, making the CSV beam quality unable to meet the practical application requirements. In order to mitigate the wavefront phase distortion brought by turbulence, the phase correction technology based on adaptive optics is particularly important. The SPGD algorithm is widely used in adaptive optical systems without wavefront sensing because of its fast convergence speed and high convergence accuracy. However, the performance of the Stochastic Parallel Gradient Descent (SPGD) algorithm depends on the accuracy of metric function.Given the uniqueness of the CSV beam, it is necessary to develop a new metric function by evaluating the light field features of the CSV beam. By theoretical analysis, it is known that the intensity of the CSV beam is distributed periodically in the angular direction. Since the periodic variation feature is independent of transmission distance and array structure parameters, the angular fringe contrast, which evaluates energy concentration in the bright fringe and prevents energy accumulation in the dark fringe, is an appropriate metric function.Whenthe angular fringe contrast is used as the metric function, the chosen bright and dark fringe angle width α will affect the SPGD algorithm performance. To establish the selection criteria of angular fringe contrastmetric function, the SPGD correction experiment is performed when the value of α is changed in steps of 1.41°, which shows that a smaller value of α can result in higher convergence accuracy and the faster convergence speed for the SPGD algorithm. On the basis of this, the wavefront distortion of CSV beam is corrected by SPGD algorithm with the angular fringe contrast as the metric function. In order to verify the validity of the angular fringe contrast as metric function, comparative experiment is carried out to verify the effectiveness with different metric function: OAM mode energy ratio, intensity correlation coefficient and angular fringe contrast. The experimental results show that the SPGD algorithm with the angular fringe contrast has higher convergence accuracy and faster convergence speed, compared with the intensity correlation coefficient and OAM mode energy ratio. In the result of single-loop structure CSV beam SPGD wavefront correction usingthe angular fringe contrast, the angular fringe contrast is improved from 0.575 to 0.877, and the mode energy ratio is improved from 0.167 to 0.229. Compared with OAM mode energy ratio and intensity correlation coefficient, the convergence speed of SPGD algorithm is improved by 12.7 times and 3.4 times, respectively.What's more, a dual-ring fiber array is developed to achieve higher output power and improved SPGD correction accuracy. In addition, to ensure a high proportion of the expected OAM mode in CCV beam, the waist radius of the sub-beam in inner and outer rings needs to be proportional to the inner and outer ring array radius. We used the above light source structure and performed SPGD correction, the simulation experiment results show that the SPGD algorithm with the angular fringe contrast as the metric function can also effectively improve the beam quality of CSV beam with complex dual-ring array structure.In summary, the metric function's angular fringe contrast' proposed in this paper can satisfy the needs of quality evaluation of CSV beam and its practical long-range transmission applications.