Example of the nonlinear simulation on Zernike 55. The projection of Z₅₅ in the Fourier plane gives the Z_m,n/W_m,n coefficients. The Airy-type stress function φ_s,m,n is evaluated by the W_m,n coupling (see Eq. (D.17)). The nonlinear part of the Eq. (29) (G(φ_s,σ)) is calculated and the I_z,m,n is directly obtained. A deconvolution by the Gaussian laser beam distribution (E_gxy) and the final projection on the DM plane gives . All images are given in linear brightness except for φ_s,m,n where the intensity is power of 0.1.