Abstract

A new wave-front sensor for adaptive optics that gives signals for the curvature and the two gradient components of the wave front simultaneously is proposed. The sensor uses quad cells placed at the foci of an array of astigmatic lenslets, giving three intensity-normalized differential signals. The parameters of a single subdetector are optimized to maximize the curvature signal. The performance of such a sensor designed for a membrane curvature mirror is analyzed. The good match between sensor and mirror is exhibited by an almost diagonal response matrix between the mirror actuator controls and the curvature signals.

© 2000 Optical Society of America

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References

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    [CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

Foci produced on a quad cell by a single lenslet of the astigmatic lenslet array with (a) unaberrated, (b) negative-curvature, and (c) positive-curvature input waves. (d) Quad-cell element labeling convention.

Fig. 2
Fig. 2

Curvature-signal sensitivity to defocus, sc/b5, for different values of astigmatic parameter a and quad-cell element size Δx.

Fig. 3
Fig. 3

Responses of the curvature signal to input phase aberrations corresponding to the first 37 Zernike polynomials. Note that most responses are close to zero.

Fig. 4
Fig. 4

Small-signal responses of (solid curve) the curvature signal to pure defocus, sc/c5, and (dashed curve) the x-tilt signal to pure Zernike x-tilt, sx/c3, for different values of astigmatic parameter a.

Fig. 5
Fig. 5

Geometry of the membrane mirror and the hybrid curvature-sensor lenslets.

Fig. 6
Fig. 6

System response matrix for the membrane mirror and matched hybrid curvature sensor. Left-hand third, curvature signal; right-hand two thirds, vertical and horizontal gradient signals.

Fig. 7
Fig. 7

Modal sensitivities of the membrane mirror–hybrid sensor system.

Fig. 8
Fig. 8

Modal sensitivities of the membrane mirror–hybrid sensor system using 19 inner lenslets only.

Equations (6)

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sc=s1-s2+s3-s4s1+s2+s3+s4,
sx=s1+s2-s3-s4s1+s2+s3+s4,  sy=s1-s2-s3+s4s1+s2+s3+s4.
ϕ=ar2cos2θ-θ0,
ϕr,θ=b5Z5r,θ,
r1Zir,θ2dθrdr=1.
ϕr,θ=biZir,θ,

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