Abstract

The pyramid wavefront sensor is known for its high sensitivity and dynamic range that can be tuned by mechanically altering its modulation amplitude. Here, a novel modulating digital scheme employing a reflecting phase only spatial light modulator is demonstrated. The use of the modulator allows an easy reconfigurable pyramid with digital control of the apex angle and modulation geometry without the need of any mechanically moving parts. Aberrations introduced by a 140-actuator deformable mirror were simultaneously sensed with the help of a commercial Hartmann-Shack wavefront sensor. The wavefronts reconstructed using the digital pyramid wavefront sensor matched very closely with those sensed by the Hartmann-Shack. It is noted that a tunable modulation is necessary to operate the wavefront sensor in the linear regime and to accurately sense aberrations. Through simulations, it is shown that the wavefront sensor can be extended to astronomical applications as well. This novel digital pyramid wavefront sensor has the potential to become an attractive option in both open and closed loop adaptive optics systems.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (2)

2010 (1)

M. B. Roopashree, V. Akondi, and B. R. Prasad, “Multilayered temporally evolving phase screens based on statistical interpolation” Proc. SPIE7736, 77363Z (2010).
[CrossRef]

2009 (2)

2007 (1)

2006 (2)

2005 (2)

C. Verinaud, M. Le Louarn, V. Korkiakoski, and M. Carbillet, “Adaptive optics for high-contrast imaging: pyramid sensor versus spatially filtered ShackHartmann sensor,” Mon. Not. R. Astron. Soc.: Letters357: L26–L30 (2005).
[CrossRef]

J. Costa, “Modulation effect of the atmosphere in a pyramid wave-front sensor,” Appl. Opt.44, 60–66 (2005).
[CrossRef] [PubMed]

2004 (1)

C. Vèrinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun.233, 27–38 (2004).
[CrossRef]

2003 (1)

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

2002 (2)

R. Ragazzoni, E. Diolaiti, and E. Vernet, “A pyramid wavefront sensor with no dynamic modulation,” Opt. Commun.208, 51–60 (2002).
[CrossRef]

I. Iglesias, R. Ragazzoni, Y. Julien, and P. Artal, “Extended source pyramid wave-front sensor for the human eye,” Opt. Express10, 419–428 (2002).
[CrossRef] [PubMed]

2001 (1)

S. Esposito and Armando Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys.369, 9–12 (2001).
[CrossRef]

1996 (1)

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Optic.43, 289–293 (1996).
[CrossRef]

1994 (1)

1980 (1)

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am.61, 656 (1971).

Akondi, V.

M. B. Roopashree, V. Akondi, and B. R. Prasad, “Multilayered temporally evolving phase screens based on statistical interpolation” Proc. SPIE7736, 77363Z (2010).
[CrossRef]

V. Akondi, M. B. Roopashree, and B. R. Prasad, “Advanced methods for improving the efficiency of a Shack Hartmann wavefront sensor,” in Topics in Adaptive Optics, B. Tyson, ed. (InTech, 2012), pp. 167–196.

Artal, P.

Bille, J.

Bradley, C.

Burvall, A.

Carbillet, M.

C. Verinaud, M. Le Louarn, V. Korkiakoski, and M. Carbillet, “Adaptive optics for high-contrast imaging: pyramid sensor versus spatially filtered ShackHartmann sensor,” Mon. Not. R. Astron. Soc.: Letters357: L26–L30 (2005).
[CrossRef]

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Castillo, S.

Chamot, S.

Conan, R.

Costa, J.

J. Costa, “Modulation effect of the atmosphere in a pyramid wave-front sensor,” Appl. Opt.44, 60–66 (2005).
[CrossRef] [PubMed]

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Dainty, C.

Daly, E.

de Araujo, R.

Diolaiti, E.

R. Ragazzoni, E. Diolaiti, and E. Vernet, “A pyramid wavefront sensor with no dynamic modulation,” Opt. Commun.208, 51–60 (2002).
[CrossRef]

Esposito, S.

S. Chamot, C. Dainty, and S. Esposito, “Adaptive optics for ophthalmic applications using a pyramid wavefront sensor,” Opt. Express14, 518–526 (2006).
[CrossRef] [PubMed]

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

S. Esposito and Armando Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys.369, 9–12 (2001).
[CrossRef]

Farinato, J.

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Feldt, M.

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Ghedina, A.

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Goelz, S.

Gomes, A.

Grimm, B.

Iglesias, I.

Jolissaint, L.

Julien, Y.

Korkiakoski, V.

V. Korkiakoski, C. Vèrinaud, M. Le Louarn, and R. Conan, “Comparison between a model-based and a conventional pyramid sensor reconstructor,” Appl. Opt.46, 6176–6184 (2007).
[CrossRef] [PubMed]

C. Verinaud, M. Le Louarn, V. Korkiakoski, and M. Carbillet, “Adaptive optics for high-contrast imaging: pyramid sensor versus spatially filtered ShackHartmann sensor,” Mon. Not. R. Astron. Soc.: Letters357: L26–L30 (2005).
[CrossRef]

Le Louarn, M.

V. Korkiakoski, C. Vèrinaud, M. Le Louarn, and R. Conan, “Comparison between a model-based and a conventional pyramid sensor reconstructor,” Appl. Opt.46, 6176–6184 (2007).
[CrossRef] [PubMed]

C. Verinaud, M. Le Louarn, V. Korkiakoski, and M. Carbillet, “Adaptive optics for high-contrast imaging: pyramid sensor versus spatially filtered ShackHartmann sensor,” Mon. Not. R. Astron. Soc.: Letters357: L26–L30 (2005).
[CrossRef]

LeDue, J.

Liang, J.

Liu, Z.

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am.61, 656 (1971).

Prasad, B. R.

M. B. Roopashree, V. Akondi, and B. R. Prasad, “Multilayered temporally evolving phase screens based on statistical interpolation” Proc. SPIE7736, 77363Z (2010).
[CrossRef]

V. Akondi, M. B. Roopashree, and B. R. Prasad, “Advanced methods for improving the efficiency of a Shack Hartmann wavefront sensor,” in Topics in Adaptive Optics, B. Tyson, ed. (InTech, 2012), pp. 167–196.

Puga, E.

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Ragazzoni, R.

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

R. Ragazzoni, E. Diolaiti, and E. Vernet, “A pyramid wavefront sensor with no dynamic modulation,” Opt. Commun.208, 51–60 (2002).
[CrossRef]

I. Iglesias, R. Ragazzoni, Y. Julien, and P. Artal, “Extended source pyramid wave-front sensor for the human eye,” Opt. Express10, 419–428 (2002).
[CrossRef] [PubMed]

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Optic.43, 289–293 (1996).
[CrossRef]

Rao, C.

Rativa, D.

Riccardi, Armando

S. Esposito and Armando Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys.369, 9–12 (2001).
[CrossRef]

Roopashree, M. B.

M. B. Roopashree, V. Akondi, and B. R. Prasad, “Multilayered temporally evolving phase screens based on statistical interpolation” Proc. SPIE7736, 77363Z (2010).
[CrossRef]

V. Akondi, M. B. Roopashree, and B. R. Prasad, “Advanced methods for improving the efficiency of a Shack Hartmann wavefront sensor,” in Topics in Adaptive Optics, B. Tyson, ed. (InTech, 2012), pp. 167–196.

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am.61, 656 (1971).

Southwell, W.

Verinaud, C.

C. Verinaud, M. Le Louarn, V. Korkiakoski, and M. Carbillet, “Adaptive optics for high-contrast imaging: pyramid sensor versus spatially filtered ShackHartmann sensor,” Mon. Not. R. Astron. Soc.: Letters357: L26–L30 (2005).
[CrossRef]

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Vèrinaud, C.

Vernet, E.

R. Ragazzoni, E. Diolaiti, and E. Vernet, “A pyramid wavefront sensor with no dynamic modulation,” Opt. Commun.208, 51–60 (2002).
[CrossRef]

Vohnsen, B.

Vran, J.

Wang, J.

Wang, S.

Xian, H.

Zhang, J.

Appl. Opt. (2)

Astron. Astrophys. (1)

S. Esposito and Armando Riccardi, “Pyramid wavefront sensor behavior in partial correction adaptive optic systems,” Astron. Astrophys.369, 9–12 (2001).
[CrossRef]

J. Mod. Optic. (1)

R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Optic.43, 289–293 (1996).
[CrossRef]

J. Opt. Soc. Am. (2)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am.61, 656 (1971).

W. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am.70, 998–1006 (1980).
[CrossRef]

J. Opt. Soc. Am. A (1)

Mon. Not. R. Astron. Soc.: Letters (1)

C. Verinaud, M. Le Louarn, V. Korkiakoski, and M. Carbillet, “Adaptive optics for high-contrast imaging: pyramid sensor versus spatially filtered ShackHartmann sensor,” Mon. Not. R. Astron. Soc.: Letters357: L26–L30 (2005).
[CrossRef]

Opt. Commun. (2)

C. Vèrinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun.233, 27–38 (2004).
[CrossRef]

R. Ragazzoni, E. Diolaiti, and E. Vernet, “A pyramid wavefront sensor with no dynamic modulation,” Opt. Commun.208, 51–60 (2002).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Proc. SPIE (2)

M. B. Roopashree, V. Akondi, and B. R. Prasad, “Multilayered temporally evolving phase screens based on statistical interpolation” Proc. SPIE7736, 77363Z (2010).
[CrossRef]

J. Costa, R. Ragazzoni, A. Ghedina, M. Carbillet, C. Verinaud, M. Feldt, S. Esposito, E. Puga, and J. Farinato, “Is there need of any modulation in the pyramid wavefront sensor?” Proc. SPIE4839, 288–298 (2003).
[CrossRef]

Other (1)

V. Akondi, M. B. Roopashree, and B. R. Prasad, “Advanced methods for improving the efficiency of a Shack Hartmann wavefront sensor,” in Topics in Adaptive Optics, B. Tyson, ed. (InTech, 2012), pp. 167–196.

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Figures (11)

Fig. 1
Fig. 1

Schematic of the reflective digital pyramid wavefront sensor

Fig. 2
Fig. 2

Experimental setup to demonstrate a digital pyramid wavefront sensor: all lenses are achromatic doublets and the focal length of the lenses is shown in mm units.

Fig. 3
Fig. 3

(a) Simulated aberrations (in μm units): (top to bottom) No aberrations, defocus ( Z 0 2), astigmatism ( Z 2 2), coma ( Z 1 3), secondary astigmatism ( Z 2 4) and a combination of defocus and astigmatism aberrations ( Z 0 2 + Z 2 2) and corresponding (b) simulated pupil plane images, (c) simulated x-slope matrix, (d) simulated y-slope matrix and (e) reconstructed wavefronts (in μm units). RMS wavefront reconstruction error for sensing these reconstructed aberrations (top to bottom): 0.01, 17.06, 22.12, 15.10, 20.93 and 30.43 nm. The generated aberrations have a peak-to-valley of 0.50 μm. The modulation amplitude is 0.80 mm. The reconstructed peak-to-valley values are shown above the plots. The slope values are in × 10−3.

Fig. 4
Fig. 4

A portion of the phase map addressed on the SLM to simulate the pyramid phase. The five grayscale steps used in this map are 255, 191, 128, 64 and 0; starting from the center, moving outward.

Fig. 5
Fig. 5

A comparison of the wavefronts reconstructed using the novel digital pyramid wavefront sensor (modulation radius = 0.4 mm) with that measured by the HS.

Fig. 6
Fig. 6

Simulations: Influence of the modulation amplitude on the RMS wavefront error while sensing primary defocus aberration of different peak-to-valley (PV).

Fig. 7
Fig. 7

Simulation: RMS wavefront error in a closed loop adaptive optics with a pyramid wavefront sensor.

Fig. 8
Fig. 8

(a) Experimentally observed RMS wavefront error and (b) theoretically predicted RMS wavefront error for the introduced aberrations: primary astigmatism, primary defocus and a combination of these aberrations. The corresponding HS measured peak-to-valley values of the introduced aberrations are shown in the legend.

Fig. 9
Fig. 9

Simulation: Testing the effect of offset of the pyramid apex with respect to the aberrated point spread function. One pixel equals an offset of 20 μm.

Fig. 10
Fig. 10

Test of linearity of the digital pyramid wavefront sensor with defocus aberration. (a) Experimental results (b) Theoretical prediction for different modulation radii.

Fig. 11
Fig. 11

Simulations: closed-loop high resolution wavefront correction of an atmospheric phase screen using the digital pyramid wavefront sensor. (a) Simulated atmospheric turbulence phase screen; (b) pupil plane image corresponding to (a); (c) X and (d) Y slopes (in × 10−3) corresponding to (a); (e) reconstructed wavefront corresponding to (a). (f) Residual wavefront after four closed loop operations; (g) pupil plane image corresponding to (f); (h) X and (i) Y slopes (in × 10−3) corresponding to (f); (i) reconstructed wavefront after five closed loop operations.

Equations (9)

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T ( X , Y ) = n = 0 1 m = 0 1 H ( ( 1 ) n X , ( 1 ) m Y ) e i β [ ( 1 ) n X + ( 1 ) m Y c ]
I pyr ( x , y ) = | F T ( F T ( P ( x , y ) . e i ϕ ( x , y ) ) . T ( x , y ) ) | 2
S x ( x , y ) = ξ f sin [ π 2 I 1 ( x , y ) I 2 ( x , y ) I 3 ( x , y ) + I 4 ( x , y ) I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y ) + I 4 ( x , y ) ]
S y ( x , y ) = ξ f sin [ π 2 I 1 ( x , y ) + I 2 ( x , y ) I 3 ( x , y ) I 4 ( x , y ) I 1 ( x , y ) + I 2 ( x , y ) + I 3 ( x , y ) + I 4 ( x , y ) ]
S x i + 1 , j + S x i , j 2 = ϕ ^ i + 1 , j ϕ ^ i , j h ,
S y i , j + 1 + S y i , j 2 = ϕ ^ i , j + 1 ϕ ^ i , j h ,
ϕ ^ = U Λ 1 V T A T D S .
ϕ ( x , y ) = α Z m n ( x , y ) .
RMS = i j | ϕ i j ϕ ^ i j | 2 N × M

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