Phase retrieval (PR) and Shack-Hartmann Sensor (SHS) are the two preferred methods of image-based wavefront sensing widely used in various optical testbeds, adaptive optical systems, and ground- and space-based telescopes. They are used to recover the phase information of an optical system from defocused point source images (PR) and focused point source or extended scene images (SHS). For example, the Terrestrial Planet Finder Coronagraph’s (TPF-C’s) High-Contrast Imaging Testbed (HCIT) uses a PR camera (PRC) to estimate, and subsequently correct, the phase error at the exit pupil of this optical system. Several other test-beds at JPL were, and will be, equipped with both a PRC and a Shack-Hartmann camera (SHC).

PR provides high resolution, high (sub-nm) accuracy, and absolute wavefront estimation, so it is used for the calibration and the fine-alignment of an optical system. It is also used to control the wavefront error (WFE) of a system below sub-nm level. However, PR requires iterative Fourier transformations over large matrices, requiring significant processing time compared with an SHS. Also, it has small bandwidth and small dynamic range, so it cannot be used in the initial alignment phase of an optical system that has many waves of wavefront error. In addition to that, it is necessary to move the PRC to obtain defocused images, and in the case of sharing a science camera with the PR process, this causes an interruption in the normal operation of the optical system.

On the other hand, an SHS measures wavefront slopes and has advantages in sensing WFE in low spatial frequencies with high bandwidth and high dynamic range. Therefore, it is extremely useful during the initial alignment phase of an optical system, especially large optical systems whose initial wavefront errors can range from a fraction of a wave to many waves, and those that are held in a mechanically and thermally unstable environment. It can also be used during normal operation of an optical system to sense and maintain its WFE below some pre-determined level. One disadvantage of the SHS is that it can only measure WFE relative to a reference state, not the absolute one as PR does, due to a non-common path error it introduces relative to the PRC sub-system.

Therefore, it is extremely useful, and sometimes necessary, to obtain a PRC-WFE estimate from the images captured by an SHC in order to have a fast turnaround time of wavefront sensing and control (WFS&C), to save operation cost, and to achieve high dynamic range. This new algorithm is used for such purposes. It first generates a calibration WFE map by measuring one WFE map with both the PRC and the SHC. Then it utilizes that calibration map as well as the existing optical sensitivity matrices measured with the PRC and the SHC to estimate the PRC WFE from a newly measured SHC image.

This work was done by Erkin Sidick and Fai H. Mok of Caltech for NASA’s Jet Propulsion Laboratory.

The software used in this innovation is available for commercial licensing. Please contact Dan Broderick at This email address is being protected from spambots. You need JavaScript enabled to view it.. Refer to NPO-47785.

This Brief includes a Technical Support Package (TSP).
Algorithm for Estimating PRC Wavefront Errors from Shack-Hartmann Camera Images

(reference NPO47785) is currently available for download from the TSP library.

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This article first appeared in the February, 2015 issue of NASA Tech Briefs Magazine.

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