Characterization of the Performance of a 7-Mirror Segmented Reflecting Telescope via the Angular Spectrum Method

  • Mary Angelie AlagaoEmail author
  • Mary Ann Go
  • Maricor Soriano
  • Giovanni Tapang
Part of the Springer Series in Optical Sciences book series (SSOS, volume 218)


A segmented reflecting telescope made of seven 76 mm concave mirrors, each with a focal length of 300 mm, was characterized. Its performance was evaluated by computing the point spread function (PSF) and comparing it to an equivalent monolithic mirror. Aberrations were added and corrected using a phase retrieval technique called the Gerchberg-Saxton (GS) algorithm to obtain the correction phase that serves as the input to the spatial light modulator (SLM). Results revealed an improvement in the telescope angular resolution as a result of the implemented phase correction. It was also shown that the PSF varies depending on the orientation and number of mirrors added.


Point spread function Segmented reflecting telescope Gerchberg-Saxton Phase retrieval 



This work was done at the National Institute of Physics, University of the Philippines, Diliman, Quezon City. It was made possible by the support from the DOST PCIEERD Standards and Testing Automated Modular Platform (STAMP) project (03439), the University of the Philippines Office of the Vice President for Academic Affairs EIDR-VISSER::SM project (C02-001) and the UP System Enhanced Creative Work and Research Grant (ECWRG 2014-11). It was also partly funded by the UP OVPAA ECWRG. GT and MAA would like to thank Dr. Paul Leonard Hilario and Dr. Caesar Saloma for their invaluable advice in this work.


  1. 1.
    I. Ridpath, Norton’s Star Atlas and Reference Handbook (Prentice Hall, 1998)Google Scholar
  2. 2.
    G. Chanan, J. Nelson, T. Mast, Segmented mirror telescopes, in Planets, Stars and Stellar Systems. Volume 1: Telescope and Instrumentation (Springer, 2013), pp. 99–136Google Scholar
  3. 3.
    J. Goodman, Introduction to Fourier Optics, 3rd edn. (Roberts and Compan Publishers, 2005)Google Scholar
  4. 4.
    M. Kasper, R. Davies, Adaptive optics for astronomy. Annu. Rev. Astron. Astrophys. (2012)Google Scholar
  5. 5.
    J. Arines et al., Measurement and compensation of optical aberrations using a spatial light modulator. Opt. Soc. Am. (2007)Google Scholar
  6. 6.
    G. Love, Wavefront correction and production of Zernike modes with a liquid-crystal spatial light modulator. Appl. Opt. 36, 1517–1524 (1997)ADSCrossRefGoogle Scholar
  7. 7.
    K.A. Nugent, T.E. Gureyev, A. Roberts, Phase retrieval with the transport-of-intensity equation: matrix solution with use of Zernike polynomials. J. Opt. Soc. Am. 12, 1932–1941 (1995)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Vyas, B. Ropashree, R.K. Banyal, B. Raghavendra, Spatial light modulator for wavefront correction, in Proceedings of International Conference on Trends in Optics and Photonics (2009), pp. 318–330Google Scholar
  9. 9.
    J. Astola, V. Katkovnik, Phase retrieval via spatial light modulator phase modulation in 4f optical setup: numerical inverse imaging with sparse regularization for phase and amplitude. J. Opt. Soc. Am. 29, 105–116 (2012)Google Scholar
  10. 10.
    C. Kopylow, R.B. Bergmann, C. Falldorf, M. Agour, Phase retrieval by means of a spatial light modulator in the Fourier domain of an imaging system. Appl. Opt. 49, 182601830 (2010)Google Scholar
  11. 11.
    G. Bautista, M.J. Romero, G. Tapang, V.R. Daria, Parallel two-photon photopolymerization of microgear patterns. Opt. Commun. 282, 3746–3750 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    P.L.A. Hilario, M.J. Villangca, G. Tapang, Independent light fields generated using a phase only spatial light modulator. Opt. Lett. 39, 2036–2039 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    E. Wolf, B.R.: Electromagnetic diffraction in optical systems. II. Structure of the image field in the aplanatic system. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 253: 358–379 (1959)Google Scholar
  14. 14.
    V. Mahajan, Zernike circle polynomials and optical aberrations of systems with circular pupils. Suppl. Appl. Opt. 33, 8121–8124 (1994)ADSCrossRefGoogle Scholar
  15. 15.
    M. Born, R. Wolf, Principle of Optics (Cambridge University Press, 1999)Google Scholar
  16. 16.
    R.W. Gerchberg, W.O. Saxton, A practical algorithm for the determination of phase from image and diffraction plane pictures. Optik 35, 237–246 (1972)Google Scholar
  17. 17.
    G. Tapang, C. Saloma, Behavior of the point-spread function in photon-limited confocal microscopy. Appl. Opt. 41, 1534–1540 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    Laser Teaching Center, D.o.P., Astronomy, S.U., An Introduction to Spatial Light ModulatorsGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Mary Angelie Alagao
    • 1
    • 2
    Email author
  • Mary Ann Go
    • 1
    • 3
  • Maricor Soriano
    • 1
  • Giovanni Tapang
    • 1
  1. 1.National Institute of PhysicsUniversity of the PhilippinesQuezon CityPhilippines
  2. 2.National Astronomical Research Institute of ThailandChiang MaiThailand
  3. 3.Department of Biomedical EngineeringImperial College LondonLondonUK

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