Fig. 1. Cartesian coordinate system representation of aspheric surface

Fig. 2. Cross sections of reference quadric surfaces with different values of K_t

Fig. 3. Curves of aspheric surface additive polynomials based on even power series polynomials

Fig. 4. Positive and negative sign alternating curves of aspheric surface coefficient of additional polynomial based on even power series polynomial

Fig. 5. Diagram of deviation between aspheric surface and datum quadric

Fig. 6. Cartesian and polar coordinates of any point P in unit circle plane

Fig. 7. Curves of radial function VZ,2m4r of Zernike polynomials

Fig. 8. Schematic of Q_con aspheric surface and reference quadric surface

Fig. 9. Curves of Q_con aspheric surface with additional polynomial orthogonal basis

Fig. 10. Schematic of Q_bfs aspheric surface and best-fitting sphere

Fig. 11. Orthogonal basis curves of Q_bfs aspheric surface with additional polynomial

Fig. 12. Slope function curves Q_bfs aspheric surface with additional polynomial orthogonal basis

Fig. 13. First-order partial derivative curves of different additional polynomial pairs with respect to h. (a) Even power series polynomial; (b) Zernike polynomial; (c) Q_con polynomial; (d) Q_bfs polynomial

Fig. 14. Lens structure drawing and spot diagram. (a) Lens structure of aspheric surface based on even power series polynomials; (b) spot diagram of aspheric surfaces based on even power series polynomials; (c) lens structure of aspheric surface based on Zernike polynomials; (d) spot diagram of aspheric surface based on Zernike polynomials

Fig. 15. Lens structure and spot diagram of Q_con aspheric surface based on Q-type polynomials. (a) Initial lens structure； (b) initial spot diagram； (c) lens structure to control deviation of RMS sag; (d) point diagram to control deviation of RMS sag

Fig. 16. Lens structure and spot diagram of Q_bfs aspheric surface based on Q-type polynomials. (a) Initial lens structure; (b) initial spot diagram; (c) lens structure to control deviation of RMS sag; (d) point diagram to control deviation of RMS sag

Fig. 17. Third piece of plastic aspheric surface contrast. (a) Aspheric surface based on even power series polynomials; (b) aspheric surface based on Zernike polynomials; (c) Q_con aspheric surface based on Q-type polynomials; (d) Q_con aspheric surface based on Q-type polynomial for controlling RMS sag deviation; (e) Q_bfs aspheric surface based on Q-type polynomials; (f) Q_bfs aspheric surface based on Q-type polynomial to controlling RMS slope of aspheric surface