Abstract

The measured characteristics of two different deformable mirror designs are presented. Each mirror is uncooled and has 37 piezoelectric actuators. The mirrors have comparable frequency response usable to over 20 kHz, but possess quite different actuator influence functions. One exhibits an exp(−αr1.5) characteristic and the other has an exp(−γr2.5) characteristic. The latter mirror is used in an 18-channel multidither adaptive optical system to perform both phase dither and phase correction functions. The measured characteristics of this system’s performance include a 2 ms convergence time and effective turbulence compensation. Evidence is presented of “2” servo ambiguities, a behavior which reduces an adaptive system’s overall phase compensation performance. The performance of the deformable mirror adaptive system is compared to an equivalent segmented (piston) mirror system.

© 1977 Optical Society of America

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References

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  1. T. R. O’Meara, “The multidither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977) (this issue).
    [Crossref]
  2. W. B. Bridges, P. T. Brunner, S. P. Lazzara, T. A. Nussmeier, T. R. O’Meara, J. A. Sanguinet, and W. P. Brown, “Coherent optical adaptive techniques,” Appl. Opt. 13, 291–300 (1974).
    [Crossref] [PubMed]
  3. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier, and M. E. Pedinoff, “Coherent optical adaptive techniques: Design and performance of an 18-element visible multidither COAT system,” Appl. Opt. 15, 611–621 (1976).
    [Crossref] [PubMed]
  4. J. E. Pearson, “Atmospheric turbulence compensation using coherent optical adaptive techniques,” Appl. Opt. 15, 622–631 (1976).
    [Crossref] [PubMed]
  5. T. R. O’Meara, “Theory of multidither adaptive optical systems operating with zonal control of deformable mirrors,” J. Opt. Soc. Am. 67, 318–325 (1977) (preceding paper).
    [Crossref]
  6. R. A. Muller and A. J. Buffington, “Real-time phase correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [Crossref]
  7. J. Hardy, J. Feinleib, and J. C. Wyant, “Real-time phase correction of optical imaging systems,” Proceedings of OSA Topical Meeting on Optical Propagation Through Turbulence, paper ThB1, Boulder, Colo., July 1974.
  8. W. P. Brown, (unpublished).
  9. Ratio of peak focal-plane irradiance to the peak diffraction-limited irradiance.
  10. This requirement is not an absolute necessity; but it greatly simplifies the servo design.
  11. Each dither frequency is used in two control channels; one uses sinωt and one uses cosωt.
  12. J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
    [Crossref]

1977 (2)

1976 (2)

1974 (3)

Bridges, W. B.

Brown, W. P.

Brunner, P. T.

Buffington, A. J.

Cone, P. F.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[Crossref]

Feinleib, J.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[Crossref]

J. Hardy, J. Feinleib, and J. C. Wyant, “Real-time phase correction of optical imaging systems,” Proceedings of OSA Topical Meeting on Optical Propagation Through Turbulence, paper ThB1, Boulder, Colo., July 1974.

Hansen, S.

Hardy, J.

J. Hardy, J. Feinleib, and J. C. Wyant, “Real-time phase correction of optical imaging systems,” Proceedings of OSA Topical Meeting on Optical Propagation Through Turbulence, paper ThB1, Boulder, Colo., July 1974.

Lazzara, S. P.

Lipson, S. G.

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[Crossref]

Muller, R. A.

Nussmeier, T. A.

O’Meara, T. R.

Pearson, J. E.

Pedinoff, M. E.

Sanguinet, J. A.

Wyant, J. C.

J. Hardy, J. Feinleib, and J. C. Wyant, “Real-time phase correction of optical imaging systems,” Proceedings of OSA Topical Meeting on Optical Propagation Through Turbulence, paper ThB1, Boulder, Colo., July 1974.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J. Feinleib, S. G. Lipson, and P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[Crossref]

J. Opt. Soc. Am. (3)

Other (5)

J. Hardy, J. Feinleib, and J. C. Wyant, “Real-time phase correction of optical imaging systems,” Proceedings of OSA Topical Meeting on Optical Propagation Through Turbulence, paper ThB1, Boulder, Colo., July 1974.

W. P. Brown, (unpublished).

Ratio of peak focal-plane irradiance to the peak diffraction-limited irradiance.

This requirement is not an absolute necessity; but it greatly simplifies the servo design.

Each dither frequency is used in two control channels; one uses sinωt and one uses cosωt.

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Figures (14)

FIG. 1
FIG. 1

Comparison of the phase-correction ability of three types of mirror systems. Piston-plus-tilt correction requires 3 actuators per mirror element whereas piston-only and deformable correction have 1 actuator per element. The curves are computed using a one-dimensional computer simulation. As a result, 7 piston-plus-tilt correction elements correspond approximately to the same number of actuators (degrees of freedom) as 12 piston-only or 12 deformable-mirror elements.

FIG. 2
FIG. 2

All-beryllium, 37-actuator deformable mirror. Each preloaded-spring actuator cell has a PZT stack driver. (a) Overall mirror schematic. (b) Faceplate view showing 3-ring, circularly symmetric arrangement of actuators. (c) Photograph of unpolished mirror.

FIG. 3
FIG. 3

Influence function profiles of beryllium mirror. (a) Center actuator. (b) First ring actuator. (c) Second ring actuator. (d) Third (outermost) ring actuator. An empirical curve fit to the central actuator profile is shown as a dotted line in (a); the curve is exp(−3.62r1.5), where r is the radial distance from the profile peak (actuator center) in inches. The interactuator center-center spacing is 0.55 in.

FIG. 4
FIG. 4

Amplitude and phase response of beryllium mirror measured on the central actuator. The drive voltage to the actuator is 42.4 V rms, producing 0.079 μm of peak faceplate motion.

FIG. 5
FIG. 5

(a) Photograph of Pyrex backplate, molybdenum faceplate mirror. (b) Actuator geometry. The actuators are arranged in a symmetrical, hexagonal, 3-ring pattern rather than the circular geometry of Fig. 2(b).

FIG. 6
FIG. 6

Influence function profile of the central actuator in the mirror shown in Fig. 5. The dotted line is an empirical fit with the functional dependence of exp(−9.05 r2.5), with r the radial distance from the actuator center in inches. The interactuator center-center spacing is 0.72 in.

FIG. 7
FIG. 7

Frequency-response characteristics of the central actuator in the mirror shown in Fig. 5. The first major resonance occurs at 22 kHz.

FIG. 8
FIG. 8

Servo coupling Csn from Eqs. (7) and (8) and peak-to-peak mirror ripple plotted as a function of mirror mechanical coupling CM [Eq. (9)]. Three different influence functions are considered, each described by a different value of n in Eq. (6).

FIG. 9
FIG. 9

Schematic diagram of optical arrangement for experimental COAT studies: L, 0.488 μm argon laser; L1, expanding lens; SF, spatial filter; L2, recollimating and reducing lens; DM, deformable mirror; M, mask; L3, recollimating lens; AM, annular receiver mirror; PMT, photomultiplier tube; S, COAT servo electronics.

FIG. 10
FIG. 10

Typical convergence sequence for the 18-channel multidither deformable-mirror COAT system. The final converged beam is achieved 2 ms after the COAT servo loop is closed.

FIG. 11
FIG. 11

Turbulence compensation performance of COAT system across a 120 m outdoor range in strong turbulence ( C N 2 4 × 10 - 13 m - 2 / 3). (a) Uncorrected beam profile. (b) COAT-corrected beam profile. (c) Peak irradiance fluctuations, 50 ms per major division. The vertical scale in (a) and (b) is 3 db per 2 major divisions.

FIG. 12
FIG. 12

Servo error signals occurring in a single COAT control channel under conditions of high turbulence. The rapid transitions indicated by the arrows are attributed to the channel recovering from a 2 lockup state.

FIG. 13
FIG. 13

Beam profiles illustrating the presence or absence of 2 servo ambiguities under strong turbulence conditions. (a) Near-ideal convergence. (b) Degraded convergence due to 2 errors produced by atmospheric turbulence; a distinct two-lobe pattern is seen.

FIG. 14
FIG. 14

Comparison of beam profiles obtained with a segmented-aperture COAT system, (a) and (b), to those produced by a deformable-mirror system, (c) and (d). No turbulence is present. (a), (c): Ideal convergence on a fixed boresight glint. (b), (d): Target glint, with detector behind it, is moved slowly across the beam. There are four scans, two from right to left, two from left to right in each figure. The random behavior in (d) is caused by 2 states occurring in and dropping out of the servo.

Equations (10)

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N a = ( 0.051 k 2 C N 2 Z D T 5 / 3 ln ( 1 / SR ) ) 6 / 5 ,
B W 0.65 V ( k 2 C N 2 Z ) 3 / 5 ,
( Δ ϕ ) max = 0.57 k ( C N 2 Z D T 5 / 3 ) 1 / 2 ,
f max = [ 10 + 1.6 ( N a - 1 ) ] f s .
C S 2 = exp [ - 1 2 ( S / r 0 ) 2 ] ,
I N ( r ) = exp [ - ( r / r 0 ) n ] ,
C s n = n 2 2 / n - 1 π Γ ( 2 / n ) I n ,
I n = mirror exp { - [ x 2 + y 2 ] n / 2 - [ ( x - β ) 2 + y 2 ] n / 2 } d x d y .
C M = exp [ - ( S / r 0 ) n ] .
β = S / r 0 = ( - ln C M ) 1 / n .