Image-plane multidither sensing has been found to be suitable for adaptive wavefront correction in a large telescope in which the main optic is a precise reflector divided into lightweight, controllably actuated segments. In image-plane multidither sensing, the telescope is aimed at a star or other distant point source and image data are recorded as each segment in turn is dithered slightly about a nominal position and orientation. The image data are processed into actuator-control signals for adjusting the nominal segment positions and orientations to obtain the desired wavefront correction.

For this method to be effective, the telescope system must be quasi-static in the sense that any mechanical and optical disturbances in the system must be characterized by times appreciably longer than the time needed to complete the corrective cycle of dithers and measurements, processing of measurement data, and controlled actuation. The position and orientation errors of each segment, and the corresponding translational and rotational displacements needed to effect correction, are called "piston" (simple translation along the line of sight) and "tilt" (angular displacements about two axes perpendicular to the line of sight). The tilt-correction procedure is based on geometric optics and can be performed at any time. However, the piston-correction procedure is based partly on phase coherence; therefore, in practice, the tilt correction must be made first to provide the coherence needed for the piston correction.

In the tilt-correction procedure, a segment is dithered in tilt and initial and final images are recorded. Although the image plane can be cluttered with subimages from multiple segments, the subimages of all other segments can be suppressed and the displacement of the segment in question tracked by subtracting the initial image from the final image and finding the centroid of the difference image. Subtraction and centroiding are common operations in image processing, and circuit boards that perform these operations are commercially available.

The angular displacement of the dither should be at least twice the diffractive size (wavelength ÷ aperture width) of a segment to enable clear differentiation of the initial and final images. Once the centroid has been located, the segment of interest is tilted to move the subimage cast by that segment to the desired location, which is ordinarily the center of the image plane. This procedure is repeated for each segment in turn, until all have been thus corrected in tilt.

In comparison with tilt corrections, piston corrections are more difficult. The piston measurement for each segment is a measurement of the response of the speckle pattern to a small dither of that segment. There are several alternative piston-correction procedures, each based on a different combination of (1) a quantitative measure of the speckle pattern and (2) determining the signs and magnitudes of piston displacements needed to correct the speckle pattern according to the quantitative measure.

To the extent to which the piston-correction procedures are based on phase coherence, they are subject to the integer-multiple-of-2π - radians phase ambiguity at a given wavelength. Measurements can be performed at multiple wavelengths to resolve this ambiguity; alternatively, one could use broadband light from a stellar source, although this can entail complications at large displacements. The use of less-accurate electronic or mechanical edge sensors might be a more-practical solution.

This work was done by Glenn W. Zeiders of The Sirius Group for Marshall Space Flight Center. For further information, contact the Sirius Group at This email address is being protected from spambots. You need JavaScript enabled to view it..

Inquiries concerning rights for the commercial use of this invention should be addressed to

the Patent Counsel
Marshall Space Flight Center; (256) 544-0021.

Refer to MFS-31352.

NASA Tech Briefs Magazine

This article first appeared in the May, 2000 issue of NASA Tech Briefs Magazine.

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