Journal of the European Optical Society - Rapid publications, Vol 7 (2012)

Active Optics: deformable mirrors with a minimum number of actuators

M. Laslandes, E. Hugot, M. Ferrari


We present two concepts of deformable mirror to compensate for first order optical aberrations. Deformation systems are designed using both elasticity theory and Finite Element Analysis in order to minimize the number of actuators. Starting from instrument specifications, we explain the methodology to design dedicated deformable mirrors. The work presented here leads to correcting devices optimized for specific functions. The Variable Off-Axis paraboLA concept is a 3-actuators, 3-modes system able to generate independently Focus, Astigmatism and Coma. The Correcting Optimized Mirror with a Single Actuator is a 1-actuator system able to generate a given combination of optical aberrations.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2012.12036]

Full Text: PDF

Citation Details

Cite this article


P. Murdin (ed.), Active Optics (Institute of Physics Publishing, Bristol, 2000).

R. N. Wilson, F. Franza, and L. Noethe, "Active optics. I. A system for optimizing the optical quality and reducing the costs of large telescopes.," J. Mod. Opt. 34, 485-509 (1987).

E.-D. Knohl, "VLT primary support system," Proc. SPIE 2199, 271-283 (1994).

M. Ferrari, "Development of a variable curvature mirror for the delay lines of the VLT interferometer," Astronomy and Astrophysics 128, 221-227 (1998).

B. Schmidt, "A coma-free telescope," Mitt. Hamburg Sternv. 7, 15 (1932).

G. Lemaitre, "New procedure for making Schmidt corrector plates," Appl. Optics 11, 1630-1636 (1972).

J. E. Nelson, G. Gabor, L. K. Hunt, J. Lubliner, and T. S. Mast, "Stressed mirror polishing. 2: Fabrication of an off-axis section of a paraboloid," Appl. Optics 19, 2341-2352 (1980).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University Press, Oxford, 1998).

R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).

L. E. Cohan, and D. W. Miller, "Integrated modeling for design of lightweight, active mirrors," Opt. Eng. 50, 063003-063003-13 (2011).

D. C. Redding, S. A. Basinger, A. E. Lowman, A. Kissil, P. Y. Bely, R. Burg, R. G. Lyon,, "Wavefront sensing and control for a Next-Generation Space Telescope," Proc. SPIE 3356, 758-772 (1998).

M. Laslandes, M. Ferrari, E. Hugot, and G. Lemaitre, "In-flight aberrations corrections for large space telescopes using active optics," Proc. SPIE 7739, 77393A-77393A-12 (2010).

M. Laslandes, N. Rousselet, M. Ferrari, E. Hugot, J. Floriot, S. Vivès, G. Lemaitre,, "Stress polishing of E-ELT segment at LAM: full-scale demonstrator status," Proc. SPIE 8169, 816903-816903-10 (2011).

S. P. Timoshenko, and S. Woinowsky-Krieger, Theory of Plates and Shells (McGRAW-Hill International Editions, New York, 1959).

G. R. Lemaître, Astronomical Optics and Elasticity Theory - Active Optics Methods (Springer, Berlin, Heidelberg, 2009).

J. C. Dainty, A. V. Koryabin, and A. V. Kudryashov, "Low-Order Adaptive Deformable Mirror," Appl. Optics 37, 4663-4668 (1998).

R. H. Freeman, and J. E. Pearson, "Deformable mirrors for all seasons and reasons," Appl. Optics 21, 580-588 (1982).

M. Laslandes, E. Hugot, M. Ferrari, and A. Liotard, "Mirror with mechanical device to generate optical aberrations" French Patent FR1102805 (2011).

M. Laslandes, E. Hugot, and M. Ferrari, "Correcting device with a deformable mirror for the compensation of at least one aberration with a known evolution" French Patent FR1153390 (2011).

I. Smith, and D. Griffiths, Programming the Finite Element Method (Fourth Edition, Wiley, Hoboken, 2004).

J. Bonnans, J. Gilbert, C. Lemarechal, and C. Sagastizabal, Numerical optimization: theoretical and practical aspects (Springer, Berlin, Heidelberg, 2009).

J. Lubliner, and J. E. Nelson, "Stressed mirror polishing. 1: A technique for producing nonaxisymmetric mirrors," Appl. Optics 19, 2332-2340 (1980).

E. Hugot, G. R. Lemaître, and M. Ferrari, "Active optics: single actuator principle and angular thickness distribution for astigmatism compensation by elasticity," Appl. Optics 47, 1401-1409 (2008).

E. Hugot, M. Ferrari, K. E. Hadi, P. Vola, J. L. Gimenez, G. R. Lemaitre, P. Rabou,, "Active Optics: stress polishing of toric mirrors for the VLT SPHERE adaptive optics system," Appl. Optics 48, 2932-2941 (2009).

M. Laslandes, C. Hourtoule, E. Hugot, M. Ferrari, C. Lopez, C. Devilliers, A. Liotard, and F. Chazallet, "Space active optics: performance of a deformable mirror for in-situ wave-front correction in space telescopes," Proc. SPIE 8442 (2012).

K. Patterson, S. Pellegrino, and J. Breckinridge, "Shape correction of thin mirrors in a recongurable modular space telescope," Proc. SPIE 7731, 773121-773121-12 (2010).

D. Wick, B. Bagwell, T. Martinez, D. Payne, S. Restaino, and R. Romeo, "Lightweight, Active Optics for Space and Near Space," in Proceedings to The Advanced Maui Optical and Space Surveillance Technologies Conference, 13 (The Maui Economic Development Board, Maui, 2006).