Abstract

We discuss a technique that permits branch points in the phase function to be localized in real-time adaptive-optics systems and that is unambiguous and robust in the presence of noise.

© 1999 Optical Society of America

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References

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1997

1996

1995

1992

1980

Aksenov, V.

Banakh, V.

Fried, D. L.

Herrmann, J.

Kibblewhite, E. J.

Le Bigot, E. O.

W. J. Wild, E. J. Kibblewhite, E. O. Le Bigot, and F. Shi, Proc. SPIE 3381, 57 (1998).
[CrossRef]

E. O. Le Bigot, W. J. Wild, and E. J. Kibblewhite, Opt. Lett. 23, 10 (1998).
[CrossRef]

Lee, D. J.

Roggemann, M. C.

Shi, F.

W. J. Wild, E. J. Kibblewhite, E. O. Le Bigot, and F. Shi, Proc. SPIE 3381, 57 (1998).
[CrossRef]

Szeto, R. K.-H.

Tikhomirova, O.

Vaughn, J. J.

Vuilleumier, R.

Wild, W. J.

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Figures (2)

Fig. 1
Fig. 1

(a) Vector field of a 19×19 subaperture array of noiseless slopes, showing the presence of four branch points. (b) Contour plot of hi5, where all elements of h are raised to the fifth power to emphasize the peaks.

Fig. 2
Fig. 2

(a) Same vector field as in Fig.  1(a) with random noise added. (b) Analogous contour plot to Fig.  1(b). The peaks for the four branch points have been preserved with no ambiguities present.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ϕ=ϕcf+ϕhid,
s=Aφ+n
A=AxAy.
ϕ=A+s,A+ Limδ0ATA+δIp-1AT,
A,·-AT,2ATA,×W.
Aφhid=Wh.
×h=|ijkAxAyAz00h|,A=[AxAyAz],h0,0,h.
W=[Ay-Ax].
h=W+s=A+Rπ/2s,

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