Abstract

We present the experimental performance of a 91-actuator deformable mirror made of a magnetic liquid (ferrofluid) using a new technique that linearizes the response of the mirror by superposing a uniform magnetic field to the one produced by the actuators. We demonstrate linear driving of the mirror using influence functions, measured with a Fizeau interferometer, by producing the first 36 Zernikes polynomials. Based on our measurements, we predict achievable mean PV wavefront amplitudes of up to 30 µm having RMS residuals of λ/10 at 632.8 nm. Linear combination of Zernikes and over-time repeatability are also demonstrated.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Liang, D. R. Williams, and D. T. Miller, “Supernormal Vision and High-Resolution Retinal Imaging Through Adaptive Optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
    [CrossRef]
  2. R. El-Agmy, H. Bulte, A. H. Greenaway, and D. Reid, “Adaptive beam profile control using a simulated annealing algorithm,” Opt. Express 13(16), 6085–6091 (2005).
    [CrossRef] [PubMed]
  3. M. Ogasawara, and M. Sato, “The applications of a liquid crystal aberration compensator for the optical disc systems,” in Adaptive Optics for Industry and Medicine, Ed. J C Dainty, Imperial College Press, London, 369–375 (2008).
  4. P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
    [CrossRef]
  5. E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
    [CrossRef]
  6. G. Vdovin, “Closed-loop adaptive optical system with a liquid mirror,” Opt. Lett. 34(4), 524–526 (2009).
    [CrossRef] [PubMed]
  7. D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
    [CrossRef] [PubMed]
  8. D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
    [CrossRef]
  9. A. Iqbal and F. B. Amara, “Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems,” Int. J. Optomechatronics 1(2), 180–208 (2007).
    [CrossRef]
  10. A. Iqbal and F. B. Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” International Journal of Optomechatronics 2(2), 126–143 (2008).
    [CrossRef]
  11. J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48(1), 1–6 (2009).
    [CrossRef]
  12. R. S. Caprari, “Optimal current loop systems for producing uniform magnetic fields,” Meas. Sci. Technol. 6(5), 593–597 (1995).
    [CrossRef]
  13. K. E. Moore and G. N. Lawrence, “Zonal model of an adaptive mirror,” Appl. Opt. 29(31), 4622–4628 (1990).
    [CrossRef] [PubMed]
  14. J. Alda and G. D. Boreman, “Zernike-based matrix model of deformable mirrors: optimization of aperture size,” Appl. Opt. 32, 2431–2438 (1993).
    [CrossRef] [PubMed]
  15. M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
    [CrossRef]
  16. L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in OSA Trends in Optics and Photonics35, 232–244 (2000).
  17. S. Thibault, 2006 Feb. 14 “Method and System for Characterizing Aspheric Surfaces of Optical Elements.” United States Patent US 6,999,182.

2009

2008

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

A. Iqbal and F. B. Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” International Journal of Optomechatronics 2(2), 126–143 (2008).
[CrossRef]

2007

A. Iqbal and F. B. Amara, “Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems,” Int. J. Optomechatronics 1(2), 180–208 (2007).
[CrossRef]

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

2005

2004

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

1999

M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
[CrossRef]

1997

1995

R. S. Caprari, “Optimal current loop systems for producing uniform magnetic fields,” Meas. Sci. Technol. 6(5), 593–597 (1995).
[CrossRef]

1993

1990

Alda, J.

Amara, F. B.

A. Iqbal and F. B. Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” International Journal of Optomechatronics 2(2), 126–143 (2008).
[CrossRef]

A. Iqbal and F. B. Amara, “Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems,” Int. J. Optomechatronics 1(2), 180–208 (2007).
[CrossRef]

Bergamasco, R.

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Bergamesco, R.

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

Boreman, G. D.

Borra, E. F.

J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48(1), 1–6 (2009).
[CrossRef]

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

Brousseau, D.

J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48(1), 1–6 (2009).
[CrossRef]

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

Bulte, H.

Caprari, R. S.

R. S. Caprari, “Optimal current loop systems for producing uniform magnetic fields,” Meas. Sci. Technol. 6(5), 593–597 (1995).
[CrossRef]

Da Silva, L.

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Dallaire, M.

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Dery, J.-P.

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

Déry, J.-P.

El-Agmy, R.

Faucher, L.

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

Gingras, J.

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Greenaway, A. H.

Iqbal, A.

A. Iqbal and F. B. Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” International Journal of Optomechatronics 2(2), 126–143 (2008).
[CrossRef]

A. Iqbal and F. B. Amara, “Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems,” Int. J. Optomechatronics 1(2), 180–208 (2007).
[CrossRef]

Laird, P.

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

Lawrence, G. N.

Liang, J.

M-Hernandez, D.

M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
[CrossRef]

M-Hernandez, M.

M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
[CrossRef]

Miller, D. T.

Moore, K. E.

Naderian, A.

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

Paez, G.

M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
[CrossRef]

Parent, J.

J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48(1), 1–6 (2009).
[CrossRef]

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

Reid, D.

Ritcey, A.

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

Ritcey, A. M.

J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48(1), 1–6 (2009).
[CrossRef]

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Seddiki, O.

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

Servin, M.

M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
[CrossRef]

Thibault, S.

J. Parent, E. F. Borra, D. Brousseau, A. M. Ritcey, J.-P. Déry, and S. Thibault, “Dynamic response of ferrofluidic deformable mirrors,” Appl. Opt. 48(1), 1–6 (2009).
[CrossRef]

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

D. Brousseau, E. F. Borra, and S. Thibault, “Wavefront correction with a 37-actuator ferrofluid deformable mirror,” Opt. Express 15(26), 18190–18199 (2007).
[CrossRef] [PubMed]

Truong, L.

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

Vassallo, J.

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

Vdovin, G.

Williams, D. R.

Yockell-Lelievre, H.

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

E. F. Borra, A. M. Ritcey, R. Bergamasco, P. Laird, J. Gingras, M. Dallaire, L. Da Silva, and H. Yockell-Lelievre, “Nanoengineered Astronomical Optics,” Astron. Astrophys. 419(2), 777–782 (2004).
[CrossRef]

Int. J. Optomechatronics

A. Iqbal and F. B. Amara, “Modeling of a Magnetic-Fluid Deformable Mirror for Retinal Imaging Adaptive Optics Systems,” Int. J. Optomechatronics 1(2), 180–208 (2007).
[CrossRef]

International Journal of Optomechatronics

A. Iqbal and F. B. Amara, “Modeling and experimental evaluation of a circular magnetic-fluid deformable mirror,” International Journal of Optomechatronics 2(2), 126–143 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

R. S. Caprari, “Optimal current loop systems for producing uniform magnetic fields,” Meas. Sci. Technol. 6(5), 593–597 (1995).
[CrossRef]

Opt. Commun.

M. M-Hernandez, M. Servin, D. M-Hernandez, and G. Paez, “Wavefront fitting using Gaussian functions,” Opt. Commun. 163, 259–269 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

D. Brousseau, E. F. Borra, S. Thibault, A. M. Ritcey, J. Parent, O. Seddiki, J.-P. Dery, L. Faucher, J. Vassallo, and A. Naderian, “Wavefront correction with a ferrofluid deformable mirror: experimental results and recent developments,” Proc. SPIE 7015, 70153J (2008).
[CrossRef]

P. Laird, E. F. Borra, R. Bergamesco, J. Gingras, L. Truong, and A. Ritcey, “Deformable mirrors based on magnetic liquids,” Proc. SPIE 5490, 1493–1501 (2004).
[CrossRef]

Other

M. Ogasawara, and M. Sato, “The applications of a liquid crystal aberration compensator for the optical disc systems,” in Adaptive Optics for Industry and Medicine, Ed. J C Dainty, Imperial College Press, London, 369–375 (2008).

L. Thibos, R. A. Applegate, J. T. Schweigerling, and R. Webb, “Standards for reporting the optical aberrations of eyes,” in OSA Trends in Optics and Photonics35, 232–244 (2000).

S. Thibault, 2006 Feb. 14 “Method and System for Characterizing Aspheric Surfaces of Optical Elements.” United States Patent US 6,999,182.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Schematic of a Maxwell coil. The number of ampere-turns of the lower and upper coils must be exactly in the ratio 49/64 relative to the middle coil. Adjusting the number of turns following this proportion, instead of adjusting the current for each coil, represents the best choice as it allows assembling the three coils in a series circuit.

Fig. 2
Fig. 2

Pictures of the 91-actuator FDM (left) and Maxwell coil (right). The Maxwell coil is shown prior to winding. The three winding areas of Fig. 1 can clearly be seen.

Fig. 3
Fig. 3

Schematic of the FDM assembly. The total height is 120 mm and the inside diameter of the container is 80 mm. A 1-mm thick layer of EFH1 ferrofluid is used.

Fig. 4
Fig. 4

Diameter of the pupil (shaded area) relative to the full diameter of the mirror used in for the ZYGO measurements. Pupil size is 23 mm and full diameter of the actuator array is 33 mm. The outer ring of actuators is kept active when using the FDM.

Fig. 5
Fig. 5

Typical x and y profiles of the influence function of a single actuator when supplied with a current of 20 mA. The wavefront profiles were obtained using the HASO wavefront sensor.

Fig. 6
Fig. 6

Linear addition of influence functions. Data shown in blue are for actuator #1 (at pupil center) and actuator #2 (nearest left neighbor) when both are actuated separately in opposite directions. The red dashed line shows the response of the FDM when both actuators are driven simultaneously. The black dashed curve shows the arithmetic addition of the individual responses. The wavefront profiles were obtained using the HASO wavefront sensor.

Fig. 7
Fig. 7

(a) Amplitude response of the FDM central actuator as a function of current when the Maxwell coil is supplied with a constant current of 0.5 A. (b) Amplitude response of the FDM central actuator when the current in the Maxwell coil is varied from 0.2 to 1.0 A. A current of 20 mA in the central actuator was used for (b). Linear fits of the data are shown in red. The wavefront amplitudes were obtained using the HASO wavefront sensor.

Fig. 8
Fig. 8

Zernike polynomials from Z20 to Z40 produced by the FDM and measured with a ZYGO interferometer. Grid units are in millimeters and wavefront amplitude is measured in µm.

Fig. 10
Fig. 10

Amplitude of Z20 as a function of a current scaling factor relative to the currents that were found to produce a Z20 wavefront having a PV amplitude of 4 µm. A linear fit of the data is shown in red.

Fig. 9
Fig. 9

(a) Residual wavefront RMS error for the first 36 Zernike polynomials (excluding piston, tip and tilt) obtained with the FDM. Targeted PV wavefront amplitude of the Zernikes was 4 µm. (b) Computed maximum achievable Zernike amplitudes for a targeted residual wavefront RMS error of λ/10 (at 632.8 nm) using the data from (a).

Fig. 11
Fig. 11

A 20 µm PV astigmatism produced by the 91-actuator FDM (left). The residual wavefront (right) has a RMS error of 0.044 µm. Grid units are in millimeters and amplitude is measured in µm. Wavefronts measured using an Imagine Optics HASO HR44 wavefront sensor.

Fig. 12
Fig. 12

Wavefronts obtained by combination of Zernikes polynomials. The targeted wavefront can be seen at left while the FDM experimental wavefront is at center. The residual wavefront is shown at right. Residual wavefront RMS error is 0.01 µm. Grid units are in millimeters and amplitude is measured in µm.

Tables (1)

Tables Icon

Table 1 Repeatability measurements of the 91-actuator FDM

Equations (7)

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

h = k B 2 = k ( b + B 0 ) 2 = k ( b 2 + 2 b B 0 + B 0 2 ) ,
B 0 = 15 16 μ 0 N I R ,
w m = H a ,
a = ( H t H ) 1 H t w ,
σ 2 = ε t ε ,
ε = w w m .
σ R M S = ε t ε N .

Metrics