Abstract

High resolution wavefront sensors are devices with a great practical interest since they are becoming a key part in an increasing number of applications like extreme Adaptive Optics. We describe the optical differentiation wavefront sensor, consisting of an amplitude mask placed at the intermediate focal plane of a 4-f setup. This sensor offers the advantages of high resolution and adjustable dynamic range. Furthermore, it can work with polychromatic light sources. In this paper we show that, even in adverse low-light-level conditions, its SNR compares quite well to that corresponding to the Hartmann-Shack sensor.

© 2003 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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Appl. Opt. (1)

R. Irwan and R. G.Lane, �??Analysis of optimal centroid estimation applied to Shack-Hartmann sensing,�?? Appl. Opt. 32, 6737-6743 (1999).
[CrossRef]

Astron. Astrophys. Suppl. Ser. (1)

V. F. Canales and M. P. Cagigal, �??Gain estimate for exoplanet detection with adaptive optics,�?? Astron. Astrophys. Suppl. Ser. 145, 445-449 (2000)
[CrossRef]

J. Mod. Opt. (1)

R. Ragazzoni, �??Pupil plane wavefront sensing with an oscillating prism,�?? J. Mod. Opt. 43, 289-293 (1996).
[CrossRef]

J. Opt. Soc. Am (1)

R. Cubalchini, �??Modal wave-front estimation from phase derivative measurements,�?? J. Opt. Soc. Am 69, 972-977 (1979)
[CrossRef]

J. Opt. Soc. Am A (3)

M. A. Neil, M. J. Booth, T. Wilson, �??New modal wave-front sensor: a theoretical analysis,�?? J. Opt. Soc. Am A 17, 1098-1107 (2000)
[CrossRef]

J. Primot, G. Rousset, and J. C. Fontanella, �??Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,�?? J. Opt. Soc. Am A 7, 1598-1608 (1990)
[CrossRef]

B. M. Welsh and C. S. Gardner, �??Performance analysis of adaptive optics systems using laser guide stars and slope sensors,�?? J. Opt. Soc. Am A 12, 1913-1923 (1989)
[CrossRef]

Opt. Eng. (2)

N. Roddier, �??Atmospheric wavefront simulation using Zernike polynomials,�?? Opt. Eng. 29, 1174-1180 (1990)
[CrossRef]

O. von der Lühe, �??Wavefront error measurement technique using extended, incoherent light sources,�?? Opt. Eng. 27, 1078-1087 (1988).

Opt. Lett. (2)

Proc. SPIE (1)

J. C. Bortz and B. J. Thompson, �??Phase retrieval by optical phase differentiation,�?? Proceedings of the SPIE 351, 71-79 (1983)
[CrossRef]

Other (3)

K. Iizuka, Engineering optics (Springer-Verlag, Berlin, 1987)

J. M. Geary, Introduction to wavefront sensors (SPIE Press, Washington, 1995).
[CrossRef]

G. Vdovin, �??Micromachined membrane deformable mirrors�?? in Adaptive Optics Engineering Handbook, R. Tyson, ed. (Marcel Dekker Inc, New York, 1998)

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Figures (4)

Fig. 1.
Fig. 1.

Set-up of the OD sensor. OF is the amplitude mask for optical differentiation. L1 and L2 are achromatic lenses of equal focal length.

Fig. 2.
Fig. 2.

Ratio of SNR of both sensors as a function of the number of photons in each sensing area of the OD sensor for different sensing area number: N s=27 (solid curve), 30 (dashed curve) and 35 (dotted curve).

Fig. 3.
Fig. 3.

Residual phase variance obtained using the H-S (dashed-dot curve) and the OD sensor (solid curve) with 80 sampling areas. The behaviour of OD with a higher resolution is also shown (dotted curve: 112 sampling areas, long-dashed curve: 177 sampling areas). The values of the masks parameters are a=0.5 and b=0.0013 D/2.

Fig. 4.
Fig. 4.

(a) Atmospherically distorted wavefront. (b) Distorted wavefront slope estimation on the x direction. (c) Compensated wavefront

Equations (20)

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M x = 2 π b r r x + a = 2 π b u x + a
M y = 2 π b r r y + a = 2 π b u y + a
I x ( x , y ) = FT 1 [ FT ( E ( x , y ) ) · M x ] 2 = j b E ( x , y ) x + a E ( x , y ) 2
I y ( x , y ) = FT 1 [ FT ( E ( x , y ) ) · M y ] 2 = j b E ( x , y ) y + a E ( x , y ) 2
α x = ϕ ( x , y ) x = I x A a b = I x A a b r λ f
α y = ϕ ( x , y ) y = I y A a b = I y A a b r λ f
σ α 2 = i , j ( 1 2 Ab I i , j ) 2 σ r 2 = N p ( 1 2 Ab I i , j ) 2 σ r 2
SNR OD = 2 α Ab I i , j N p σ r = α n OD 2 b N p σ r
SNR OD = 2 α n OD σ r ( 1 a ) D lens 2 π 1.22 N A
σ α 2 = σ I 2 [ 2 Ab I ] 2
SNR OD = α 2 Ab = α n OD 2 b
SNR OD = α n OD ( 1 a ) D lens π 1.22 N A
SNR OD = α 2 Ab = α n OD 0.0087 D lens
α x = 2 π λ f 1 x c
SNR H S = α 3 n H S N t d π σ r N w 2
SNR H S = α n H S d 0.86 π
SNR OD SNR H S = 2 b 0.86 π n OD d n H S = 0.0087 D lens 0.86 π d 2
D R OD = 1 b
D R H S = 2 π d λ f 1
σ rec 2 = Pupil [ ϕ ( r ) ϕ rec ( r ) ] 2 d r i = 1 N [ a i a i rec ] 2

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