Fig. 1. Schematic diagram of double helix phase encoding imaging system. (a) No defocus; (b) negative defocus; (c) positive defocus

Fig. 2. Annular double helix phase encoded aperture and corresponding PSF

Fig. 3. Schematic diagram of DH-PSF encoded imaging process

Fig. 4. Joint optimization algorithm framework for DH-PSF encoded imaging system

Fig. 5. Influence of the number of rings on imaging characteristics. (a) Corresponding relationship between the rotation angle and defocus of DH-PSF for different numbers of rings with γ=0.7; (b) relationship between maximum defocus for maintaining effective DH-PSF and number of rings under different γ

Fig. 6. Influence of γ on imaging characteristics. (a) Relationship between the relative distance of the two main lobes of double helix phase mask with different numbers of rings and γ under focus; (b) DH-PSF of five-ring double helix phase mask with different γ under different defocus

Fig. 7. Relationship between DH-PSF rotation angle and depth

Fig. 8. Variation of γ with epochs during end-to-end joint optimization process

Fig. 9. PSF of double helix phase masks with different aperture sizes at different depths

Fig. 10. Depth estimation and recovery images with extended depth for double helix phase masks with different numbers of rings on FlyingThings3D dataset. (a) Scene 1; (b) scene 2

Fig. 11. Test results of double helix phase masks with different ring numbers on NYU Depth V2 dataset. (a) Scene 1; (b) scene 2

Fig. 12. Relationship between rotational angle of DH-PSF and depth in different ranges. (a) 0.71-9.99 m; (b) 0.71-2.20 m; (c) 10.71-19.99 m

Fig. 13. Influence of different ranges on depth estimation performance. (a) 0.71-9.99 m; (b) 0.71-2.20 m; (c) 10.71-19.99 m

Fig. 14. Influence of overexposure on depth estimation performance. (a) Clean image; (b) depth ground truth; (c) predicted depth map

Fig. 15. Phase mask and imaging system diagram. (a) Yongnuo YN50 mm F1.8 standard prime lens; (b) processed ring-type double helix phase mask; (c) double helix encoded imaging system

Fig. 16. Comparison of simulated DH-PSF and actually acquired DH-PSF. (a) DH-PSF simulated at different depths; (b) actually captured DH-PSF at different depths

Fig. 17. Performance of the double helix encoded imaging system in real scenes. (a) Scene 1; (b) scene 2; (c) scene 3

Fig. 18. Difference between estimated values measured by the system and true values at different depths

Fig. 19. Visual results of depth estimation and image reconstruction under different noise levels

Fig. 20. System depth resolution test images. (a) Encoded image obtained from two flat objects taken at 1 cm interval; (b) depth map corresponding to Fig. 20(a); (c) column average value within the dashed box in Fig. 20(b)