Simulated and computed power patterns. The upper row corresponds to a simulated beam, using up to order n = 5 for the Zernike circle polynomials, with a centered illumination with c_dB = −14.5 dB taper strength, q = 1.4, and (x₀, y₀) = (0,0). The tilt parameters were also set to zero (K₁₁ = K₁₋₁ = 0). The simulated axial offset is d_z = 2.2λ. The left and right columns show the defocused pattern and the center column is the in-focus beam. The Zernike circle polynomial coefficients, K_nℓ, were generated randomly with a normal distribution. Gaussian noise was added until a S/N of 750 in the in-focus beam (top middle panel) was achieved.