A broadband phase-contrast wave-front sensor has been proposed as a real-time wave-front sensor in an adaptive-optics system. The proposed sensor would offer an alternative to the Shack-Hartmann wave-front sensors now used in high order adaptive-optics systems of some astronomical telescopes. Broadband sensing gives higher sensitivity than does narrow- band sensing, and it appears that for a given bandwidth, the sensitivity of the proposed phase-contrast sensor could exceed that of a Shack-Hartmann sensor. Relative to a Shack-Hartmann sensor, the proposed sensor may be optically and mechanically simpler.

As described below, an important element of the principle of operation of a phase-contrast wave-front sensor is the imposition of a 90° phase shift between diffracted and undiffracted parts of the same light beam. In the proposed sensor, this phase shift would be obtained by utilizing the intrinsic 90° phase shift between the transmitted and reflected beams in an ideal (thin, symmetric) beam splitter. This phase shift can be characterized as achromatic or broadband because it is 90° at every wavelength over a broad wavelength range.

Figure 1. Phase-Contrast Imaging would use 90° phase shifting to generate phase feedback for adaptive optics.

The phase-contrast approach was originally devised by Frits Zernike for microscopy as a means of obtaining intensity images from such phase objects as transparent biological samples. samples. Figure 1 schematically illustrates an adaptation of the phase-contrast approach to real-time wave-front sensing for adaptive optics. The incident light from a guide star can be described in terms of a pupil field function Aexp(if), where A is an aperture function that expresses the effect of the shape and size of the telescope pupil and f is the difference between the actual instantaneous phase and the nominal (e.g., planewave) phase of the wave front at a given position within the pupil. If the pupil were simply re-imaged, the phase signal would not normally be observable. To make the phase signal observable, one reasons as follows:

Assuming a small-signal approximation (f << 1), the phase part of the pupil field function could be approximated as 1 + if. Hence, the phase-difference (diffracted) component would be 90° out of phase with the larger undiffracted component. To a first approximation, the undiffracted rays would be localized within the central ˜?/D portion of the telescope focal plane (where ? is wavelength and D is the diameter of the primary mirror or lens of the telescope), while the diffracted rays that contribute to the phase component would impinge on the telescope focal plane at off-axis positions. If a ±90°-phase-shift filter (e.g., a dielectric disk of suitable thickness) having approximately the diffraction-limited size ?/D were placed at the focal point, then the undiffracted component would be shifted by ±90° and would thereby be brought into phase (or phase opposition) with the diffracted component. As a result, the phase component would become observable as a small variation in intensity across the pupil, superposed on the bright, uniform illumination of the undiffracted component. In the small-signal approximation, the total intensity in the re-imaged pupil would be proportional to 1±2f, the sign of 2f depending on whether the focal-spot filter advances or retards the phase.

Figure 2. A Broad-Band Phase-Contrast Wave-Front Sensor, shown here schematically, can be realized by using the intrinsic properties of a beam splitter to give an achromatic 90°-phase-shifting element.

Figure 2 schematically illustrates an optical assembly, according to the proposal, for implementing the 90°-phase-shift filter needed in a phase-contrast sensor like that of Figure 1. An incident beam from a telescope would strike a 50:50 beam splitter. The reflected and transmitted beams would be recombined by an arrangement of mirrors, schematically represented by flats M1 in Figure 2; one component is directed through a diffraction- limited pinhole in two-sided mirror M2. The pinhole would pass the central ˜?/D portions of the beams, while the M2 surfaces surrounding the pinhole would reflect the off-axis portions. The total beam going to the output port on each side of M2 would comprise the desired combination of central rays and 90°-shifted off-axis rays. The output beams could be directed into telescope-pupil-re-imaging optics equipped with a chargecoupled- device (CCD) or similar quantum detector, as in Figure 1. Optionally, the phase-contrast images contained in both beams could be combined optically or electronically to increase the signal-to-noise ratio.

This work was done by Eric Bloemhof and J. Kent Wallace of Caltech for NASA’s Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/ tsp under the Physical Sciences category. In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:

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Refer to NPO-41401, volume and number of this NASA Tech Briefs issue, and the page number.

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This article first appeared in the October, 2005 issue of NASA Tech Briefs Magazine.

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