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AO (adaptive optics) systems have been extensively used to improve the beam quality in high-energy lasers; however, few studies have focused on how much the beam quality could be improved. A novel evaluation criteria and factor is presented in this paper. The factor, defined as power in ring (PIR), is expressed by distinguishing the low- and high-spatial frequency components in the far-field laser intensity distribution. Beams with different PIR values are generated in our model, and then they are compensated by AO systems. Calculation result shows that the PIR factor could evaluate a laser beam’s improvement potential by an AO system quantitatively.

Modal cross coupling between basis functions in modal wavefront reconstruction is discussed. Eigenfunctions of Laplacian are proposed in modal approach for wavefront reconstruction. As the gradients of the eigenfunctions are orthogonal to each other, the modal cross coupling can be avoided theoretically. Wavefront reconstructions by use of Zernike polynomials and eigenfunctions of Laplacian with different sampling densities are compared. The results show that modal cross coupling between eigenfunctions of Laplacian is much smaller than that between Zernike polynomials.

A direct method for compensation of low order aberrations with large PV value was presented in this paper. In which, the relationship between the optical layout parameters and the output aberration coefficients were derived by ray matrix method. Then, the adjustment parameters calculated by the equations were used to change the optical layout parameters to compensate the low order aberrations with defocus and astigmatism. The effectiveness of this method was verified by simulations based on the optical models built in a optical design software. It shows that the low order aberrations can be accurately compensated to a level below 0.5λ by the direct method.

Based on the computational fluid dynamics (CFD) software, an emluator for the optics and fluency coupling effects is established by means of the user defined function (UDF). Thermal blooming effects in a special tube with axial pipe flow are modeled. The simulated results indicate that the velocity distribution of the pipe flow is very asymmetric. However, the fluid density distribution is almost not changed without laser beam heating. As laser beam couples with the fluency, the fluid density distribution varies greatly. The heterogeneous fluid density distribution induces the optical path distinction of the double pearl eye form. This phenomenon is also observed in the previous experiments.

Thermal blooming anisoplanatic effect of the circular-symmetric flattened beam is analysed by the method of Gaussian beam expansion. Wave-front distortion of the thermal blooming anisoplanatic effect is expanded by the Zernike polynomials, and the Zernike coefficient and fitting error are obtained. The corrected error of the thermal blooming calculated by the numerical method is consistent with the outcome of the theoretical formula. The numerical simulation results also indicate that the angular anisoplanatic error varies proportionally to the square of the anisoplanatic angle, and the focus anisoplanatic error is in inverse proportion to the 1.71th power of the beacon height, if the caliber size is invariable.

Modal cross coupling usually exists in wavefront estimation through Zernike polynomials. In order to cope with the problem, the eigenfunctions of Laplacian with Neumann boundary condition are proposed instead of Zernike polynomials to reconstruct phase from wavefront gradient or curvature sensing. It is proved theoretically that these modals can avoid modal cross coupling in both wavefront gradient sensing and curvature sensing. In wavefront gradient sensing, the coefficients of eigenfunctions of Laplacian can be obtained from the integral of the scalar product between the gradient of Laplacian's eigenfunctions and wavefront gradient signal. In wavefront curvature sensing, the coefficients of eigenfunctions of Laplacian can be calculated from the integral of the product of Laplacian's eigenfunctions and wavefront curvature signal. This approach is applicable on arbitrary apertures as long as eigenfunctions of Laplacian on apertures of arbitrary shape can be obtained.

The optimum phase defocus grating for wavefront curvature sensing is proposed. It features an equidistantly quantized, binary-phase-step defocus grating with a phase-step height of pi. The diffractive efficiency of the phase defocus grating is theoretically computed. The optical transfer function is obtained. The optimum phase defocus grating is fabricated. The high diffractive efficiencies of the +/-1 diffraction orders are verified experimentally, the average values of which are 38.08% and 40.36%, respectively.