Tech Briefs

Broadband Phase Retrieval for Image-Based Wavefront Sensing

Broadband light can be approximated as monochromatic in phase-retrieval computations.

A focus-diverse phase-retrieval algorithm has been shown to perform adequately for the purpose of image-based wavefront sensing when (1) broadband light (typically spanning the visible spectrum) is used in forming the images by use of an optical system under test and (2) the assumption of monochromaticity is applied to the broadband image data. Heretofore, it had been assumed that in order to obtain adequate performance, it is necessary to use narrow-band or monochromatic light.

Some background information, including definitions of terms and a brief description of pertinent aspects of image-based phase retrieval, is prerequisite to a meaningful summary of the present development. “Phase retrieval” is a general term used in optics to denote estimation of optical imperfections or “aberrations” of an optical system under test. The term “image-based wavefront sensing” refers to a general class of algorithms that recover optical phase information, and phase-retrieval algorithms constitute a subset of this class.

These Point-Spread-Function Images were obtained as the response of a test optical system (a deformable mirror) at the two noted wavelengths. The overall trefoil shape, representative of loworder aberrations, does not differ much between the two wavelengths. The “bumpy” higher-spatialfrequency image components of the two images differ noticeably, but these components represent higher-order aberrations that, typically, are smaller than the lower-order aberrations.
In phase retrieval, one utilizes the measured response of the optical system under test to produce a phase estimate. The optical response of the system is defined as the image of a point-source object, which could be a star or a laboratory point source. The phase-retrieval problem is characterized as “imagebased” in the sense that a charge-coupled- device camera, preferably of scientific imaging quality, is used to collect image data where the optical system would normally form an image. In a variant of phase retrieval, denoted phasediverse phase retrieval [which can include focus-diverse phase retrieval (in which various defocus planes are used)], an additional known aberration (or an equivalent diversity function) is superimposed as an aid in estimating unknown aberrations by use of an image-based wavefront-sensing algorithm.

Image-based phase-retrieval differs from such other wavefront-sensing methods, such as interferometry, shearing interferometry, curvature wavefront sensing, and Shack-Hartmann sensing, all of which entail disadvantages in comparison with image-based methods. The main disadvantages of these non-imagebased methods are complexity of test equipment and the need for a wavefront reference. This concludes the background information.

The present development began with a theoretical observation that the loworder aberration content of the pointspread- function of an optical system is not strongly affected by wavelength over the visible spectrum (see figure). As a result, variations in wavelength do not significantly affect what a phase-retrieval algorithm “sees” as input. This lack of variability of effective input is what makes it possible to assume monochromaticity when processing image data acquired while using broadband light.

The validity of the assumption of monochromaticity was demonstrated by comparing wavefront-sensing performances for broadband and monochromatic light in a known aberration test case. The significance of this development is that phase-retrieval algorithms can produce accurate phase estimates when test light is passed through filters having pass bands broader than were previously thought to be useable. Because more light is transmitted by broadband than by narrow-band filters, image-detector integration times can be significantly reduced and, therefore, time needed to perform wavefront sensing can be reduced. In some applications, filters can be eliminated entirely, thereby minimizing the complexity and cost of equipment for testing optical systems.

This work was done by Bruce H. Dean of Goddard Space Flight Center. For more information, download the Technical Support Package (free white paper) at under the Physical Sciences category.

This Brief includes a Technical Support Package (TSP).

Broadband Phase Retrieval for Image-Based Wavefront Sensing (reference GSC-14899-1) is currently available for download from the TSP library.

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