High-order-helix point spread functions for monocular three-dimensional imaging with superior aberration robustness.

An approach for designing purely refractive optical elements that generate engineered, multi-order-helix point spread functions (PSFs) with large peak separation for passive, optical depth measurement is presented. The influence of aberrations on the PSF's rotation angle, which limits the depth retrieval accuracy, is studied numerically and analytically. It appears that only Zernike modes with an azimuthal index that is an integer multiple of the number of PSF peaks introduce PSF rotation, and hence depth estimation errors. This implies that high-order-helix designs have superior robustness with respect to aberrations. This is experimentally demonstrated by imaging an extended scene in the presence of severe system aberrations using novel, cost-efficient phase elements based on UV-replication on the wafer-scale.