Accuracy comparisons (a)–(f) at six positions on the unit circle: (x, y) ≈ (−0.5000000, −0.8660254), (−0.7071068, −0.7071068), (−0.5000000, 0.8660254), (0.5000000, 0.8660254). (0.5000000, −0.8660254), and (−0.8660254, −0.5000000). Each comparison includes three curves: the one above for 5050 Zernike components of orders 0 to 99, calculated using the direct transformation method, as the comparison reference; the middle one for the absolute difference of the component-wise recursive method to the reference; and the curve below for the block-wise recursive method. All difference curves are shown with the same value scale: ≤4 × 10⁻¹³.