OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 22, Iss. 6 — Jun. 1, 2005
  • pp: 1093–1105

Mach-Zehnder interferometer for piston and tip-tilt sensing in segmented telescopes: theory and analytical treatment

Natalia Yaitskova, Kjetil Dohlen, Philippe Dierickx, and Luzma Montoya  »View Author Affiliations


JOSA A, Vol. 22, Issue 6, pp. 1093-1105 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001093


View Full Text Article

Acrobat PDF (363 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A study is presented of a Mach-Zehnder interferometer for the measurement of phasing errors of the type found in segmented telescopes. We show that with a pinhole much larger than the Airy disk and an optical path difference between the arms equal to a quarter of the wavelength, the interferometric signal is related to the second derivative of the wave front. In this condition the signal is produced mostly by the segmentation errors and is marginally sensitive to other aberrations including atmospheric turbulence. The signal has distinguishable symmetric and antisymmetric properties that are related to segment aberrations. We suggest using the antisymmetric component of the signal to retrieve piston, tip, and tilt. The symmetric component of the signal serves as an estimate of the measurement error. In this way we proceed with a study of the errors associated with the misalignment of the interferometer, the segment edge imperfections, and the nonaveraged atmospheric perturbations. The entire study is performed on a theoretical basis, and numerical simulations are used to cross check the analytical results.

© 2005 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.6110) Fourier optics and signal processing : Spatial filtering
(110.6770) Imaging systems : Telescopes

Citation
Natalia Yaitskova, Kjetil Dohlen, Philippe Dierickx, and Luzma Montoya, "Mach-Zehnder interferometer for piston and tip-tilt sensing in segmented telescopes: theory and analytical treatment," J. Opt. Soc. Am. A 22, 1093-1105 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-6-1093


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. P. Dierickx, J. L. Beckers, E. Brunetto, R. Conan, E. Fedrigo, R. Gilmozzi, N. Hubin, F. Koch, M. Le Louarn, E. Marchetti, G. Monnet, L. Noethe, M. Quattri, M. Sarazin, J. Spyromillo, and N. Yaitskova, "The eye of the beholder: designing the OWL," in Future Giant Telescopes, J. R. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 151-170 (2002).
  2. T. Andersen, A. L. Ardeberg, J. Beckers, A. Goncharov, M. Own-Petersen, H. Riewaldt, R. Snel, and D. Walker, "The Euro50 Extremely Large Telescope," in Future Giant Telescopes, J. R. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 214-225 (2002).
  3. J. Nelson, "Progress of the Californian Extremely Large Telescope (CELT)," in Future Giant Telescopes, J. R. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 47-59 (2002).
  4. S. Strom, L. Stepp, M. Mountain, and B. Gregory, "Giant Segmented Mirror Telescope: a point design based on science drivers," in Future Giant Telescopes, J. R. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 116-128 (2002).
  5. J. Nelson, T. Mast, and S. Faber, "The design of the Keck Observatory and telescope," Keck Observatory Rep. 90 (W. M. Keck Library, Kamuela, Hawaii, 1985), pp. 5-1-5-44.
  6. V. L. Krabbendam, T. A. Sebring, F. B. Ray, and J. R. Fowler, "Development and performance of Hobby-Eberly Telescope 11 meter segmented mirror," in Advanced Technology Optical/IR Telescopes VI, L. Stepp, ed., Proc. SPIE 3352, 436-445 (1998).
  7. F. J. Castro, N. Devaney, L. Jochum, B. Ronquillo, and L. Cavaller, "The status of the design and fabrication of the GTC mirrors," in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE 4003, 24-33 (2000).
  8. G. Chanan and M. Troy, "Strehl ratio and modulation transfer function for segmented mirror telescope as function of segment phase error," Appl. Opt. 38, 6642-6647 (1999).
  9. N. Yaitskova, K. Dohlen, and P. Dierickx, "Analytical study of diffraction effects in extremely large segmented telescopes," J. Opt. Soc. Am. A 20, 1563-1575 (2003).
  10. J. N. Aubrun, K. R. Lorell, T. W. Havas, and W. C. Henninger, "Performance analysis of the segmented alignment control system for the ten-meter telescope," Automatica 24, 437-454 (1988).
  11. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, "Phasing the mirror segments of the Keck telescope: the broadband phasing algorithm," Appl. Opt. 37, 140-155 (1998).
  12. S. Cuevas, V. G. Orlov, F. Garfias, V. Voitsekhovich, and L. Sanchez, "Curvature equation for a segmented telescope," in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE 4003, 291-302 (2000).
  13. S. Esposito, E. Pinna, A. Tozzi, P. Stefenini, and N. Devaney, "Co-phasing of segmented mirrors using pyramid sensor," in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson and M. Lloyd-Hard, eds., Proc. SPIE 5169, 214-225 (2003).
  14. N. Yaitskova, "Performance analysis of Mach-Zehnder interferometer for detection of wavefront discontinuities,"in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, and M. Lloyd-Hard, eds., Proc. SPIE 5169, 62-71 (2003).
  15. L. Montoya, N. Yaitskova, P. Dierickx, and K. Dohlen, "Mach-Zehnder wave front sensor for phasing of segmented telescopes," in Future Giant Telescopes, J. R. Angel and R. Gilmozzi, eds., Proc. SPIE 4840, 564-573 (2002).
  16. D. Malacara, Optical Shop Testing (Wiley, New York, 1992), p. 74.
  17. R. Angel, "Ground-based imaging of extrasolar planets using adaptive optics," Nature (London) 368, 203 (1994). [CrossRef]
  18. M. Langlois, R. Angel, M. Lloyd-Hard, F. Widi, G. Love, and A. Naumov, "High order, reconstructor-free adaptive optics for a 6-8 meter class telescope," in Beyond Conventional Adaptive Optics, E.Vernet, R.Ragazzoni, S.Esposito, and N.Hubin, eds., ESO Conference Workshop Proceedings No. 58 (European Southern Observatory, Garching bei München, Germany, 2002), pp. 113-120 (2002).
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1986).
  20. L. Schwartz, Théorie des Distributions (Hermann, Paris, 1966).
  21. A. SchumacherAchim.Schumacher@iac.es (personal communication).
  22. N. Yaitskova, L. Montoya, K. Dohlen, and P. Dierickx, "A Mach-Zehnder phasing sensor for extremely large segmented telescopes: laboratory results and close loop algorithm," in Ground-Based Telescopes, J. Oschmann and M. Tarenghi, eds., Proc. SPIE 5489, 1139-1151 (2004).
  23. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
  24. K. Dohlen, "Phase masks in astronomy: from the Mach-Zehnder interferometer to coronagraphs," in Astronomy with High Contrast Imaging II, C.Aime and R.Soummer, eds., EAS Publ. Ser. 12 (European Astronomical Society, 2004), pp. 33-44; http://www2.iap.fr/eas.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited