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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.

We investigate the performance and capability of a holographic modal wavefront sensor (HMWS) that is based on a multiplexed phase computer-generated hologram (MPCGH). The theoretical treatments of the HMWS are presented with scalar diffraction approximations and Fourier analysis. Several MPCGHs have been designed with different linear carrier frequencies, by using of the multiplexed coding scheme we have proposed, and by coding some common Zernike modes. The numerical simulation is carried out to investigate the performance of the HMWS to detect particular aberration mode(s), by considering the effect of different carrier frequency selections and the capability of coding a large number of modes. The results exhibit the expected characteristics of a corresponding symmetric spot pair, and indicate that the wavefront distorted by a particular Zernike mode(s) can be retrieved immediately through solving the amplitude of each mode coded in MPCGHs through the response curves of the HMWS.

We propose an approach for implementing a modal wavefront sensor using a binary phase-only multiplexed computer-generated hologram (BPMCGH). To simplify the coding and fabricating processes, a model based on tilt plane reference waves and an effective coding scheme for BPMCGH have been developed. The necessary number of subholograms to be recorded or coded is significantly reduced, from two or even more to just one per aberration mode, accordingly. The numerical and experimental demonstration results are presented and discussed and show that this approach is convenient for producing a BPMCGH and efficient for sensing the aberration modes.

In this paper we determine the optimum propagation distance between measurement planes and the plane of the lens in a wavefront curvature sensor with the diffraction optics approach. From the diffraction viewpoint, the measured wavefront aberration can be decomposed into Fourier harmonics at various frequencies. The curvature signal produced by a single harmonic is analyzed with the wave propagation transfer function approach, which is the frequency analysis of wavefront curvature sensing. The intensity of the curvature signal is a sine function of the product of the propagation distance and the squared frequency. To maximize the curvature signal, the optimum propagation distance is proposed as one quarter of the Talbot length at the critical frequency (average power point at which the power spectrum density is the average power spectrum density). Following the determination of the propagation distance, the intensity of the curvature signal varies sinusoidally with the squared frequencies, vanishing at some higher frequency bands just like a comb filter. To cover these insensitive bands, wavefront curvature sensing with dual propagation distances or with multi-propagation distances is proposed.