Abstract

We present the mechanical and actuator design of an adaptive secondary mirror that matches the optical requirements of the active and adaptive corrections. Conceived for the particular implementation for the 6.5-m conversion of the multiple-mirror telescope, with small variations of the input parameters this study is suitable for applications for telescopes of the same class. We found that a three-layer structure, i.e., a thin deformable shell, a thick reference plate, and a third plate that acts as actuator support and heat sink, is able to provide the required mechanical stability and actuator density. We also found that a simple electromagnetic actuator can be used. This actuator, when optimized, will dissipate a typical power of a few tenths of watts.

© 1998 Optical Society of America

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References

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  1. P. Salinari, C. Del Vecchio, V. Biliotti, “A study of an adaptive secondary mirror,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1993), pp. 247–253.
  2. C. Del Vecchio, W. Gallieni, P. Salinari, P. M. Gray, “Preliminary mechanical design of an adaptive secondary unit for the MMT-conversion telescope,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 243–249.
  3. R. Biasi, D. Gallieni, P. Mantegazza, “Simulation of adaptive secondary mirror dynamic response,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 221–227.
  4. V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.
  5. D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.
  6. H. M. Martin, D. S. Anderson, “Steps toward optical fabrication of an adaptive secondary mirror,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 401–406.
  7. J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.
  8. M. C. Roggemann, B. M. Welsh, D. Montera, T. A. Rhoadarmer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Appl. Opt. 34, 4037–4051 (1995).
    [Crossref] [PubMed]

1995 (1)

Aiello, R.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

Anderson, D. S.

H. M. Martin, D. S. Anderson, “Steps toward optical fabrication of an adaptive secondary mirror,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 401–406.

Angel, R.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Barret, T.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Biasi, R.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

R. Biasi, D. Gallieni, P. Mantegazza, “Simulation of adaptive secondary mirror dynamic response,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 221–227.

Biliotti, V.

P. Salinari, C. Del Vecchio, V. Biliotti, “A study of an adaptive secondary mirror,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1993), pp. 247–253.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

Bruns, D.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Brusa, G.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Del Vecchio, C.

C. Del Vecchio, W. Gallieni, P. Salinari, P. M. Gray, “Preliminary mechanical design of an adaptive secondary unit for the MMT-conversion telescope,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 243–249.

P. Salinari, C. Del Vecchio, V. Biliotti, “A study of an adaptive secondary mirror,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1993), pp. 247–253.

Gallieni, D.

R. Biasi, D. Gallieni, P. Mantegazza, “Simulation of adaptive secondary mirror dynamic response,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 221–227.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Gallieni, W.

C. Del Vecchio, W. Gallieni, P. Salinari, P. M. Gray, “Preliminary mechanical design of an adaptive secondary unit for the MMT-conversion telescope,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 243–249.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.

Gray, P. M.

C. Del Vecchio, W. Gallieni, P. Salinari, P. M. Gray, “Preliminary mechanical design of an adaptive secondary unit for the MMT-conversion telescope,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 243–249.

Mantegazza, P.

R. Biasi, D. Gallieni, P. Mantegazza, “Simulation of adaptive secondary mirror dynamic response,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 221–227.

Martin, H.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Martin, H. M.

H. M. Martin, D. S. Anderson, “Steps toward optical fabrication of an adaptive secondary mirror,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 401–406.

Montera, D.

Rhoadarmer, T. A.

Roggemann, M. C.

Salinari, P.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

P. Salinari, C. Del Vecchio, V. Biliotti, “A study of an adaptive secondary mirror,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1993), pp. 247–253.

C. Del Vecchio, W. Gallieni, P. Salinari, P. M. Gray, “Preliminary mechanical design of an adaptive secondary unit for the MMT-conversion telescope,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 243–249.

Sandler, D.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

Spairani, R.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

Welsh, B. M.

Appl. Opt. (1)

Other (7)

P. Salinari, C. Del Vecchio, V. Biliotti, “A study of an adaptive secondary mirror,” in Active and Adaptive Optics, F. Merkle, ed., Vol. 48 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1993), pp. 247–253.

C. Del Vecchio, W. Gallieni, P. Salinari, P. M. Gray, “Preliminary mechanical design of an adaptive secondary unit for the MMT-conversion telescope,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 243–249.

R. Biasi, D. Gallieni, P. Mantegazza, “Simulation of adaptive secondary mirror dynamic response,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 221–227.

V. Biliotti, R. Biasi, G. Brusa, D. Gallieni, R. Spairani, R. Aiello, “High accuracy capacitive displacement transducer for position local control loops at the adaptive secondary,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 213–219.

D. Bruns, T. Barret, D. Sandler, H. Martin, G. Brusa, R. Angel, R. Biasi, D. Gallieni, P. Salinari, “Force-actuated adaptive secondary mirror prototype,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 251–256.

H. M. Martin, D. S. Anderson, “Steps toward optical fabrication of an adaptive secondary mirror,” in Adaptive Optics, M. Cullum, ed., Vol. 54 of ESO Conference Proceedings Series (European Southern Observatory, Garching, Germany, 1995), pp. 401–406.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985), Chap. 8.

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Figures (12)

Fig. 1
Fig. 1

Overall view of the adaptive secondary unit.

Fig. 2
Fig. 2

Bottom view of the reference plate. The hole axes correspond to the actuator locations.

Fig. 3
Fig. 3

FEA model of the reference plate of the adaptive mirror unit. The element edges are not shown. The typical mesh around an actuator hole is shown in detail at the lower left-hand corner of the figure.

Fig. 4
Fig. 4

rms values of the uncorrected wave front, the tip–tilt (tt) removed wave front, and the residual wave front, plotted against the wave-front number (wf#).

Fig. 5
Fig. 5

Structure function of the reference-plate deformations divided by atmospheric structure functions (scaled from the primary mirror) for various zenith angles. The structure function is expressed in terms of the reflected wave front from the secondary mirror. The atmospheric structure function is calculated for r 0 = 0.9 m at λ = 2.2 μm.

Fig. 6
Fig. 6

Structure functions S w [l(i, i*)] and S u (i, i*) of node 3603 of the thin mirror as a function of its distance from all the other nodes. wf, wave front.

Fig. 7
Fig. 7

Structure function S r (i, i*) of node 3603 of the thin mirror as a function of its distance from all the other nodes.

Fig. 8
Fig. 8

Wave front 84 (in meters) tip-tilt removed (left) and associated deformations uz (in meters) (right) of the thin mirror.

Fig. 9
Fig. 9

Residual wave-front deformation (in meters) for wave front 84.

Fig. 10
Fig. 10

Optimization of the coil cross section for a 0.25-in.-diameter magnet with an aspect ratio of 1. The regions of the field (top left) not available to the coil are not shown. The values of the efficiency are for a 30 MGOe grade permanent magnet.

Fig. 11
Fig. 11

Actuator forces on the thin mirror. The rms, the mean, and the maximum values of the absolute values are plotted as functions of the wave-front number.

Fig. 12
Fig. 12

Efficiencies and average dissipated powers versus magnet mass and for various aspect ratios. The values are for a 30 MGOe grade permanent magnet.

Tables (3)

Tables Icon

Table 1 Reference-Plate Peak-to-Valley (ptv) and rms Deflections at Various Zenith Angles

Tables Icon

Table 2 Average Achieved Strehl Ratios for Several Wavelengths

Tables Icon

Table 3 Effects of Tilt or Decenter on the Force Moment Applied on the Magneta

Equations (8)

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D d i = j = 1 N i   δ j 2 N i ,
D a x = 6.88   λ 2 π 2 x r 0 5 / 3 ,
PSD k = 0.033 C n 2 k - 11 / 3 ,
S w l i ,   i * = k = 1 M w i , k - w i * , k 2 M ,
F = coil J r B r d V ,
P = coil   ρ | J | 2 r d V ,
= 2 μ 0 E m ρ 1 / 2 ,
F w = 2   sin θ 1 + sin θ 2 1 / 2 ρ air Av g 2 ,

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