Abstract
The elastic deformation modes corresponding to the first-order modes of the optical matrix characterizing the wavefront shape are the curvature (Cv 1) and tilt (Tilt 1). These are the two fundamental modes involved in Gaussian optics. Because a tilt is easily obtained by a global rotation of a rigid substrate, this chapter only reduces to mirrors generating a Cv 1 mode. Such variable curvature mirrors (VCM) are also sometimes called zoom mirrors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.M. Beckers, Field of view considerations for telescope arrays, SPIE Proc., 628, 255 (1986)
J.M. Beckers et al., The VLTI implementation plan, ESO/VLT Report No. 59b (1989)
J.M. Beckers, Interferometric imaging with the VLTI, J. Optics (Paris), 22, 73 (1991)
R.N. Bracewell, in The Fourier Transform and Its Applications, McGraw-Hill ed., New York (1965)
J.W. Brault, Fourier transform spectroscopy, in High Resolution in Astronomy, 15th Advanced Course, SAAS-FEE, 1–62 (1985)
R. Hanbury Brown, Measurement of stellar diameters, Ann. Rev. Astron. Astrophys., 6, 13–38 (1968)
P. Casal, C. Fayard, B. Authier, Calculations of the elastic deformations of revolution membranes, Appl. Opt., 20(11), 1983–1989 (1981)
A.A. Christy, Y. Ozaki, V.G. Gregoriou, in Modern Fourier Transform Infrared Spectroscopy, Elsevier ed., ISBN 0444 500 448, (2001)
P. Connes, Astronomical Fourier spectroscopy, Ann. Rev. Astron. Astrophys., 8, 209–230 (1970)
P. Connes, G. Michel, Astronomical Fourier spectrometers, Appl. Opt., 14, 9, 2067–2084 (1975)
S.P. Davis, M.C. Clark, J.W. Brault, in Fourier Transform Spectroscopy, Academic Press, San Diego ISBN 0120 425 106 (2001)
F. Derie, VLTI delay lines: Design, development and performance requirements, in Interferometry in Optical Astronomy, SPIE Proc., 4006, 25–30 (2000)
T. Dohi and T. Suzuki, Appl. Opt., 10, 1137 (1971)
K. Dohlen, Design of a FTS for environmental surveillance, Doctoral dissertation, University of London (1994)
K. Dohlen, Interferometric spectrometer for liquid mirror survey telescopes, in Optical Telescopes of Today and Tomorrow, SPIE/ESO Proc., 2871,1359–1364 (1997)
J.A. Ewing, The Strength of Materials, Cambridge Univ. Press, 2nd ed., (1906). See also S.P. Timoshenko, Résistance des Matériaux, Dunod edt., Paris, 365–366 (1968)
M. Ferrari, G.R. Lemaitre, Analysis of large deflection zoom mirrors for the ESO VLTI, Astron. Astrophys. 274, 12–18 (1993)
M. Ferrari, Optique active et grandes déformations élastiques, Doctoral dissertation, University Aix-Marseille I (1994)
M. Ferrari, F. Derie, B. Delabre, J.-M. Mariotti, VLTI’s VCMs – Pupil transfer inside the delay line cat’s eye, ESO Report No VLT-TRE-ESO-15220-1509 (1997)
M. Ferrari, Development of variable curvature mirrors for the delay lines of the VLTI, Astron. Astrophys. Suppl. Ser., 128, 221–227 (1998)
M. Ferrari, G.R. Lemaitre, S. Mazzanti, P. Lanzoni, F. Derie, VLTI pupil transfer: Variable curvature mirrors [10], Final results and performances, in Astronomical Telescopes and Instrumentation, SPIE Proc., 4006, 104–116 (2000)
M. Ferrari, S. Mazzanti, G.R. Lemaitre, J. Lemerrer, P. Lanzoni, P. Dargent, F. Derie, A. Huxley, A. Wallanders, Variable curvature mirrors - Implementation in the VLTI delay lines for field compensation, in Interferometry for Optical Astronomy II, SPIE Proc., 4838, 1155–1162 (2002)
A. Glindeman et al. The VLT Interferometer, in Interferometry in Optical Astronomy, SPIE Proc., 4006, 2–12 (2000)
E. Hugot, Optique astronomique et élasticité – Ph. D., Université de Provence – Aix Marseille I, Chap. 4 (2007)
P. Jacquinot, C. Dufour, J. Rech. CNRS, Lab. Bellevue (Paris), 6, 91 (1948)
P. Jacquinot, J. Opt. Soc. Amer., 54, 761 (1954)
B. Koehler, C. Flebus, VLT auxiliary telescopes, in Interferometry in Optical Astronomy, SPIE Proc., 4006, 13–24 (2000)
D. Korsch, in Reflective Optics, Academic Press Inc., 173 (1991)
M. Krautter, Aplanatic two-mirror surfaces, in Optical System Design, Analysis, and Production for Advanced Technology Systems, SPIE Proc., 655, 127–137 (1986)
O. von der Lühe, J.M. Beckers, R. Braun, The configuration of the VLTI on the Paranal site, in High Resolution by Interferometry II, ESO Conf. Proc., 959–968 (1991)
O. von der Lühe et al., A new plan for the VLTI, The Messenger, ESO ed., 87, 8–14 (1997)
A. Labeyrie, Stellar interferometry methods, Ann. Rev. Astron. Astrophys., 16, 77–102 (1978)
A. Labeyrie, Interferometry with arrays of large-aperture ground based telescopes, Proc. KPNO Conf. on Optical and Infrared Telescopes for the 1990s, II, 786–796 (1980)
C. Leinert, U. Graser, MIDI – The Mid-Infrared interferometer instrument for the VLTI, in Astronomical Interferometry, SPIE Proc., 3350, 389–402 (1998)
G.R. Lemaitre, Élasticité et miroirs à focale variable, C. R. Acad. Sc. Paris, 282 B, 87–89 (1976)
G.R. Lemaitre, French patent No 2343262 (1976), US patent No 4119 366 (1976)
G.R. Lemaitre, S. Mazzanti, M. Ferrari, P. Montiel, P. Lanzoni, Tulip-form variable curvature mirrors, in Astronomical Interferometry, SPIE Proc., 3350, 373–379 (1998)
G.R. Lemaitre, M. Ferrari, S. Mazzanti, P. Lanzoni, P. Joulié, VLTI pupil transfer: Variable curvature mirrors [2], Plasticity, hysteresis and curvature control, in Astronomical Telescopes and Instrumentation, SPIE Proc., 4006, 192–197 (2000)
G.R. Lemaitre, P. Montiel, P. Joulié, K. Dohlen, P. Lanzoni, Active optics and modified-Rumsey wide-field telescopes: MINITRUST demonstrators with vase- and tulip-form mirrors, Appl. Opt., 44(34), 7322–7332 (2005)
J. Lubliner, in Plasticity Theory, MacMillan Publ. ed., New York (1991)
J.-P. Maillard, Seismology with Fourier transform spectrometer, Appl. Opt., 35, 16, 2734–2746 (1996)
J.-P. Maillard, A super-imaging FTS for the VLTI, in Scientific Drivers for ESO Future VLT/VLTI instrumentation, ESO Conf., 193 (2002)
J.-M. Mariotti et al., The VLTI program: A status report, in Astronomical Interferometry, SPIE Proc., bf 3350, 800–806 (1998)
F. Merkle, Synthetic-aperture imaging with the VLT, Journ. Opt. Soc. Am., A 5(6), 904 (1989)
M. Mersenne, Traité de l’ Harmonie Universelle, Paris (1636)
M. Mersenne, L’Optique et la Catoptrique, posthume publication, in La Perspective Curieuse by J.-F. Niceron, F. Langlois alias Chartres edt., Paris (1652)
L. Mertz, in Transformation in Optics, John Wiley and Sons ed., New York (1965)
A.A. Michelson, On the application of interference methods to astronomical measurements, Ap. J., 51, 257–262 (1920)
D. Mourard et al., The GI2T / REGAIN interferometer, in Astronomical Interferometry, SPIE Proc., 3350, 517–525 (1998)
F. Paresce, F. Delplancke, F. Derie, A. Glindemann, A. Richichi, M. Tarrenghi, Scientific objectives of ESO’s PRIMA facility, in Interferometry for Optical Astronomy I, SPIE Proc., 4838, 486–495 (2002)
M. Paul, Systèmes correcteurs pour réflecteurs astronomiques, Rev. Opt., 14(5), 169–202 (1935)
N.J. Rumsey, A compact three-reflection astronomical camera, in Optical Instruments and Techniques, ICO 8 Meeting, London, Home Dickson edt., Oriel Press Newcastle, 514–520 (1969)
L. Seidel, Astron. Nachr., 43, 289 (1856)
B.C. Smith, in Fundamentals of Fourier Transform Infrared Spectroscopy, CRC Press, Florida ISBN 0849 324 610, (1996)
E. Stephan, Sur les franges d’interférence observées avec de grands instruments, C. R. Acad. Sc., 76, 1008–1010 (1873)
G.W. Stroke and A.T. Funkhauser, Physics Letters, 16, 272 (1965)
A.P. Thorne, in Spectrophysics, Chapman and Hall ed., London (1988)
S.P. Timoshenko, S. Woinowsky-Krieger, Theory of plate and shells, McGraw-Hill ed., 396 (1976)
F. Vakili, I. Percheron, Beam combination and coherence tracking with diluted arrays, in High Resolution by Interferometry II, ESO Conf. Proc., 1247–1256 (1991)
A. Valentin, Fourier spectroscopy with a very long optical path length, Spectrochim. Acta, 51-A(7), 1127–1142 (1995)
A. Valentin, A. Henry, The Fourier infrared spectrometer of Laboratoire de Physique Moléculaire et Applications, Paris-Jussieu, Internal report of LPMA/CNRS, Univ. P. & M. Curie, Paris (2002)
R.N. Wilson, Karl Schwarzschild and Telescope Optics, Karl Schwarzschild Lecture given to the German Astronomical Society, Bochum (1993), published in Review of Modern Astronomy, 7, 1 (1994). See also Reflecting Telescope Optics I, Springer edt., 88 (1996)
L. Woltjer et al., Proposal for the construction of the 16-m VLT, ESO/VLT Report no. 57 (1987)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lemaitre, G. (2009). Dioptrics and Elasticity – Variable Curvature Mirrors (VCMs). In: Astronomical Optics and Elasticity Theory. Astronomy and Astrophysics Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68905-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-540-68905-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68904-1
Online ISBN: 978-3-540-68905-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)