Abstract

In this Letter, we introduce a wavefront slope sensor based on a diffractive element. The diffractive element wavefront sensor (DEWS) produces four double overlapping copies of the incoming wavefront acting like a combination of shearing and pyramidal sensors. The DEWS allows a simple and fast slope estimate. The wavefront sampling can be as high as the number of pixel assigned to cover a wavefront copy, and it can be modified with only binning the CCD pixels. The theory for designing the sensor, its application to extract local slope information, and a simple noise analysis are presented. An application example for atmosphere aberrated wavefronts is demonstrated.

© 2012 Optical Society of America

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References

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2012

2005

J. E. Oti, V. F. Canales, and M. P. Cagigal, MNRAS 360, 1448 (2005).
[CrossRef]

2000

1996

R. Ragazzoni, J. Mod. Opt. 43, 289 (1996).
[CrossRef]

1995

1990

N. Rodier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Booth, M. J.

Cagigal, M. P.

P. J. Valle and M. P. Cagigal, Opt. Lett. 37, 1121 (2012).
[CrossRef]

J. E. Oti, V. F. Canales, and M. P. Cagigal, MNRAS 360, 1448 (2005).
[CrossRef]

Canales, V. F.

J. E. Oti, V. F. Canales, and M. P. Cagigal, MNRAS 360, 1448 (2005).
[CrossRef]

Neil, M. A. A.

Oti, J. E.

J. E. Oti, V. F. Canales, and M. P. Cagigal, MNRAS 360, 1448 (2005).
[CrossRef]

Primot, J.

Ragazzoni, R.

R. Ragazzoni, J. Mod. Opt. 43, 289 (1996).
[CrossRef]

Rodier, N.

N. Rodier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Sogno, L.

Valle, P. J.

Wilson, T.

J. Mod. Opt.

R. Ragazzoni, J. Mod. Opt. 43, 289 (1996).
[CrossRef]

J. Opt. Soc. Am. A

MNRAS

J. E. Oti, V. F. Canales, and M. P. Cagigal, MNRAS 360, 1448 (2005).
[CrossRef]

Opt. Eng.

N. Rodier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Opt. Lett.

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Figures (4)

Fig. 1.
Fig. 1.

Set up consisting of a diffractive element (DE) placed at the common focal plane of lenses L1 and L2.

Fig. 2.
Fig. 2.

Typical diffractive mask transmittance function.

Fig. 3.
Fig. 3.

Simulated image where four pupil copies used for estimating the x and y wavefront derivatives simultaneously appear.

Fig. 4.
Fig. 4.

(a) Incoming wavefront with D/r0=5. (b) Wavefront x derivative estimated applying Eq. (12). (c) Actual wavefront x derivative. (d) Difference between actual and estimated.

Equations (16)

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M1x=exp(iαrcosθ)+exp(iαrcosθ)=2cos(αrcosθ),
M2x=iexp(iαrcosθ)iexp(iαrcosθ)=2sin(αrcosθ).
Mx=(M1x+M2x)/2=cos(αrcosθ)sin(αrcosθ).
My=cos(αrsinθ)sin(αrsinθ).
M=(Mx+My)/2.
EF(x,y)=E(x,y)*{[δ(xα)+iδ(xα)]+[δ(x+α)iδ(x+α)]+[δ(yα)+iδ(yα)][δ(y+α)iδ(y+α)]},
EF(x,y)=E(x,y)*{[δ(xα)+iδ(xα)]+[δ(x+α)iδ(x+α)]+[δ(yα)+iδ(yα)][δ(y+α)iδ(y+α)]+δ(0)}.
Ix+=A2|exp[iϕ(xα,y)]+iexp[iϕ(xα,y)]|2=A2{2+2sin[ϕ(xα,y)ϕ(xα,y)]}.
Ix=A2|exp[iϕ(x+α,y)]iexp[iϕ(x+α,y)]|2=A2{2+2sin[ϕ(x+α,y)ϕ(x+α,y)]}.
Δx+ϕ=ϕ(xα,y)ϕ(xα,y)Δxϕ=ϕ(x+α,y)ϕ(x+α,y),
sin(Δxϕ)=Ix++Ix2A22Δxϕ.
ϕx=Δxϕ/Δx=(Ix++Ix4A21)/(αα).
σrn2=NP[2A2(αα)]2σr2,
SNRrn=ϕNP2A2(αα)σr,
σpn2=[2A2(αα)]2σI2,
SNRpn=ϕ2(αα)nP,

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