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

René Berlich,Sjoerd Stallinga

doi:10.1364/oe.26.004873

Abstract

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.

Highlights

The depth dependence of the Point Spread Function (PSF) of an imaging system can be customized by engineering the pupil phase with a Computer Generated Hologram (CGH)
The steps provide a significant advancement in the manufacturing of phase elements for monocular depth estimation compared to previous elements [9, 15]
The main challenge relies in minimizing surfaces distortions during the replication process, which would directly compromise the performance of the CGH with respect to the introduced wave front error

Summary

Introduction

The depth dependence of the Point Spread Function (PSF) of an imaging system can be customized by engineering the pupil phase with a Computer Generated Hologram (CGH) This approach has been widely studied with the goal to extend the depth of focus of conventional imaging systems [1,2,3]. If the relationship between the rotation angle α and the distance of an object point z is known, a measurement of α enables retrieving the axial location of an object point in addition to its lateral location This method has mainly been applied for three-dimensional particle localization and tracking [7,8,9,10,11,12,13]. Further studies have demonstrated that the entire depth map of an extended, three-dimensional scene can be obtained for a broadband illumination [14, 15]

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Conclusion