Abstract

To achieve the diffraction limit, the segments in a segmented telescope must be correctly aligned to a fraction of a wavelength. This alignment is performed via optical measurements using starlight. We investigate the piston degree of freedom or phasing of the segments and the impact of rolled segment edges on the accuracy of the optical alignment. Three models for edge profiles are developed and fit to data from optic manufacturers. These profiles are then used, along with a simplified model of a Shack–Hartmann optical sensor, to determine their impact on phasing accuracy. The results can help estimate the residual phasing error and set requirements on segment polishing.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Cordero-Dávila, J. González-García, M. Pedrayes-López, L. Alberto Aguilar-Chiu, J. Cuautle-Cortés, and C. Robledo-Sánchez, “Edge effects with the Preston equation for a circular tool and workpiece,” Appl. Opt. 43, 1250–1254 (2004).
    [CrossRef] [PubMed]
  2. P. Guo, H. Fang, and J. Yu, “Edge effect in fluid jet polishing,” Appl. Opt. 45, 6729–6735 (2006).
    [CrossRef] [PubMed]
  3. A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.
  4. J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
    [CrossRef]
  5. 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).
    [CrossRef]
  6. M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
    [CrossRef]
  7. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  8. G. Chanan, C. Ohara, and Mitchell Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]
  9. N. Yaitskova, K. Dohlen, P. Dierickx, and L. 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).
    [CrossRef]
  10. I. Surdej, N. Yaitskova, and F. Gonte, “On-sky performance of the Zernike phase contrast sensor for the phasing of segmented telescopes,” Appl. Opt. 49, 4053–4063 (2010).
    [CrossRef]
  11. J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)
  12. M. Cayrel, ESO, Karl Schwarzschildstrasse 2, D-85748 Garching b. Muenchen, Germany (private communication 2008), mcayrel@eso.org.
  13. E. Ruch, Sagem Défense Sécurité, Avenue de la Tour Maury 91 280, Saint-Pierre-du-Perray, France (private communication 2010), eric.ruch@sagem.com.
  14. R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
    [CrossRef]
  15. F. Gonte, R. Mazzoleni, I. Surdej, and L. Noethe, are preparing a manuscript for Applied Optics to be called “On-sky performance of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes.”
  16. J. H. Hardy, Adaptive Optics for Astronomical Telescopes, 1st ed. (Oxford University, 1998), p. 210.
  17. M. Troy, G. Chanan, E. Sirko, and E. Leffert, “Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics,” Proc. SPIE 3352, 307–317 (1998).
    [CrossRef]

2010 (3)

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

I. Surdej, N. Yaitskova, and F. Gonte, “On-sky performance of the Zernike phase contrast sensor for the phasing of segmented telescopes,” Appl. Opt. 49, 4053–4063 (2010).
[CrossRef]

2008 (1)

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

2006 (1)

2005 (1)

2004 (1)

2003 (1)

2000 (1)

1998 (2)

G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

M. Troy, G. Chanan, E. Sirko, and E. Leffert, “Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics,” Proc. SPIE 3352, 307–317 (1998).
[CrossRef]

Abe, L.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Aguilar-Chiu, L. Alberto

Aller-Carpentier, E.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Antichi, J.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Araujo, C.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Baudoz, P.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Beuzit, J.-L.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Boccaletti, A.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Bonavita, M.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Brast, R.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Cayrel, M.

M. Cayrel, ESO, Karl Schwarzschildstrasse 2, D-85748 Garching b. Muenchen, Germany (private communication 2008), mcayrel@eso.org.

Chanan, G.

Clarkson, A.

J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)

Cordero-Dávila, A.

Cuautle-Cortés, J.

Daniel, J.

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)

Dekens, F.

Derie, F.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Dierickx, P.

Dohlen, K.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, and L. 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).
[CrossRef]

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).
[CrossRef]

Duhoux, P.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Dupuy, C.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Fang, H.

Fedrigo, E.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Frank, C.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Gonte, F.

I. Surdej, N. Yaitskova, and F. Gonte, “On-sky performance of the Zernike phase contrast sensor for the phasing of segmented telescopes,” Appl. Opt. 49, 4053–4063 (2010).
[CrossRef]

F. Gonte, R. Mazzoleni, I. Surdej, and L. Noethe, are preparing a manuscript for Applied Optics to be called “On-sky performance of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes.”

Gonté, F.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

González-García, J.

Gratton, R.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Guo, P.

Hall, C.

A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.

Hanenburg, H.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Hardy, J. H.

J. H. Hardy, Adaptive Optics for Astronomical Telescopes, 1st ed. (Oxford University, 1998), p. 210.

Hubin, N.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Hull, T.

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

Jager, R.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Johnson, J.

J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)

Jones, A.

A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.

Karban, R.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Kasper, M.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Keller, C.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Kerber, F.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Kirkman, D.

Korkiakoski, V.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Leffert, E.

M. Troy, G. Chanan, E. Sirko, and E. Leffert, “Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics,” Proc. SPIE 3352, 307–317 (1998).
[CrossRef]

Martinez, P.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Mast, T.

Mazzoleni, R.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, R. Mazzoleni, I. Surdej, and L. Noethe, are preparing a manuscript for Applied Optics to be called “On-sky performance of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes.”

Mesa, D.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Michaels, S.

Montoya, L.

Mueller, U.

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

Nelson, J.

Noethe, L.

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, R. Mazzoleni, I. Surdej, and L. Noethe, are preparing a manuscript for Applied Optics to be called “On-sky performance of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes.”

O’Donohue, S.

A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.

Ohara, C.

Pedrayes-López, M.

Peters, T.

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

Piche, F.

J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)

Preis, O.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Rabou, P.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Robledo-Sánchez, C.

Roelfsema, R.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Ruch, E.

E. Ruch, Sagem Défense Sécurité, Avenue de la Tour Maury 91 280, Saint-Pierre-du-Perray, France (private communication 2010), eric.ruch@sagem.com.

Salter, G.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Schmid, H. Martin

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Shorey, A.

A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.

Sirko, E.

M. Troy, G. Chanan, E. Sirko, and E. Leffert, “Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics,” Proc. SPIE 3352, 307–317 (1998).
[CrossRef]

Sporer, S.

J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)

Sporer, S. F.

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

Surdej, I.

I. Surdej, N. Yaitskova, and F. Gonte, “On-sky performance of the Zernike phase contrast sensor for the phasing of segmented telescopes,” Appl. Opt. 49, 4053–4063 (2010).
[CrossRef]

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

F. Gonte, R. Mazzoleni, I. Surdej, and L. Noethe, are preparing a manuscript for Applied Optics to be called “On-sky performance of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes.”

Tecza, M.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Thatte, N.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Tricard, M.

A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.

Troy, M.

G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
[CrossRef]

M. Troy, G. Chanan, E. Sirko, and E. Leffert, “Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics,” Proc. SPIE 3352, 307–317 (1998).
[CrossRef]

Troy, Mitchell

Venema, L.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Verinaud, C.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

Yaitskova, N.

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

I. Surdej, N. Yaitskova, and F. Gonte, “On-sky performance of the Zernike phase contrast sensor for the phasing of segmented telescopes,” Appl. Opt. 49, 4053–4063 (2010).
[CrossRef]

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

N. Yaitskova, K. Dohlen, P. Dierickx, and L. 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).
[CrossRef]

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).
[CrossRef]

Yu, J.

Appl. Opt. (5)

J. Opt. Soc. Am. A (2)

Proc. SPIE (3)

M. Kasper, J.-L. Beuzit, C. Verinaud, R. Gratton, F. Kerber, N. Yaitskova, A. Boccaletti, N. Thatte, H. Martin Schmid, C. Keller, P. Baudoz, L. Abe, E. Aller-Carpentier, J. Antichi, M. Bonavita, K. Dohlen, E. Fedrigo, H. Hanenburg, N. Hubin, R. Jager, V. Korkiakoski, P. Martinez, D. Mesa, O. Preis, P. Rabou, R. Roelfsema, G. Salter, M. Tecza, and L. Venema, “EPICS: direct imaging of exoplanets with the E-ELT,” Proc. SPIE 7735, 77352E (2010).
[CrossRef]

R. Mazzoleni, F. Gonté, I. Surdej, C. Araujo, R. Brast, F. Derie, P. Duhoux, C. Dupuy, C. Frank, R. Karban, L. Noethe, and N. Yaitskova, “Design and performances of the Shack–Hartmann sensor within the Active Phasing Experiment,” Proc. SPIE 7012, 70123A (2008).
[CrossRef]

Proc. SPIE (1)

J. Daniel, U. Mueller, T. Peters, S. F. Sporer, and T. Hull, “Tinsley progress on stress mirror polishing (SMP) for the Thirty Meter Telescope (TMT) primary mirror segments II,” Proc. SPIE 7733, 773328 (2010).
[CrossRef]

Proc. SPIE (3)

M. Troy, G. Chanan, E. Sirko, and E. Leffert, “Residual misalignments of the Keck Telescope primary mirror segments: classification of modes and implications for adaptive optics,” Proc. SPIE 3352, 307–317 (1998).
[CrossRef]

Other (6)

F. Gonte, R. Mazzoleni, I. Surdej, and L. Noethe, are preparing a manuscript for Applied Optics to be called “On-sky performance of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes.”

J. H. Hardy, Adaptive Optics for Astronomical Telescopes, 1st ed. (Oxford University, 1998), p. 210.

A. Jones, A. Shorey, C. Hall, S. O’Donohue, and M. Tricard, “Deterministic fabrication of large and astronomical optics using magnetorheological finishing (MRF),” http://optics.nasa.gov/tech_days/tech_days_2006/docs/16 QED Deterministic Fabrication of Large and Astronomical.pdf.

J. Daniel, S. Sporer, J. Johnson, A. Clarkson, and F. Piche, “E-ELT primary mirror segment manufacturing study by Tinsley,” EELT report E-TRE-ESO-300-0496 (2009)

M. Cayrel, ESO, Karl Schwarzschildstrasse 2, D-85748 Garching b. Muenchen, Germany (private communication 2008), mcayrel@eso.org.

E. Ruch, Sagem Défense Sécurité, Avenue de la Tour Maury 91 280, Saint-Pierre-du-Perray, France (private communication 2010), eric.ruch@sagem.com.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Approximation of the residual profile H with a parabolic function h. Parameters: ε = 0.2 μm , R = η = 12.1 mm . Inset, intersection area of a circular tool with a workpiece.

Fig. 2
Fig. 2

Edge profile after MRF and its parabolic fit. Fitting parameters: ε = 0.475 μm , η = 12.1 mm . Here and everywhere else, ε 0 = 1 μm .

Fig. 3
Fig. 3

Residual edge profile and fitted model. a,  Data provided by Company A for the highest edge. Parameters for the model for curve 1: ε = 0.156 μm , α = 0.47 , η = 11.16 mm , η 2 = 6.75 mm and for curve 2: ε = 0.203 μm , α = 0.34 , η = 10.9 mm , η 2 = 4.74 mm . b,  Data provided by Company B for the best edge. Parameters: ε = 0.156 μm , α = 0.12 , η = 12 mm , η 2 = 6 mm .

Fig. 4
Fig. 4

Edge profile by Model 2. Control parameter: 1, α = 0 ; 2, α = 0.08 ; 3, α = 0.16 ; 4, α = 0.28 ; and 5, α = 0.4 . For all curves, ε = 0.2 μm .

Fig. 5
Fig. 5

Residual edge profile and fitted model from Eq. (9). a,  Data from Company A. Curve 1: ε = 0.155 μm , α = 0.23 , η = 11 mm , η 2 = 5.1 mm , β = 0.19 , m = 2.4 ; curve 2: ε = 0.094 μm , α = 0.089 , η = 10.8 mm , η 2 = 4.3 mm , β = 0.21 , m = 2.7 ; and curve 3: ε = 0.167 μm , α = 0.08 , η = 10.3 mm , η 2 = 4.0 mm , β = 0.18 , m = 2.8 . b,  Data from Company B with a positive ε. Curve 1: ε = 0.096 μm , α = 0.12 , η = 65.3 mm , η 2 = 29.6 mm , β = 0.21 , m = 2.7 ; curve 2: ε = 0.12 μm , α = 0.14 , η = 60.6 mm , η 2 = 26.7 mm , β = 0.18 , m = 2.7 ; and curve 3: ε = 0.057 μm , α = 0.054 , η = 67.3 mm , η 2 = 36.1 mm , β = 0.2 , m = 2.5 ; c,  Data from Company B with a negative ε. Curve 1: ε = 0.169 μm , α = 0.164 , η = 59.9 mm , η 2 = 29.9 mm , β = 0.022 , m = 2.8 ; curve 2: ε = 0.112 μm , α = 0.102 , η = 66.5 mm , η 2 = 37.6 mm , β = 0.14 , m = 2.4 ; curve 3: ε = 0.137 μm , α = 0.109 , η = 66.5 mm , η 2 = 33.3 mm , β = 0.042 , m = 2.3 ; and curve 4: ε = 0.081 μm , α = 0.026 , η = 61.75 mm , η 2 = 29.5 mm , β = 0.12 , m = 2.8 .

Fig. 6
Fig. 6

Edge profile by Model 3. Control parameter 1, α = 0 ; 2, α = 0.08 ; 3, α = 0.16 ; 4, α = 0.28 ; and 5, α = 0.4 . For all curves, β = 0.2 , ε = 0.2 μm .

Fig. 7
Fig. 7

a,  Detail of a lenslet design for the Shack–Hartmann sensor used in the APE and b,  the image in the focal plane of the lenses. The elongated lenses measure the relative steps, and the circular lenses measure segment aberrations. Segments are shown as dashed lines along the lenses. Double lines in the elongated signal signify a nonzero step between segments.

Fig. 8
Fig. 8

Profiles of a signal for the Shack–Hartmann phasing sensor for the perfect edge: solid curve, δ = 0 ; dashed curve, δ = π / 2 ; and dotted curve, δ = π .

Fig. 9
Fig. 9

Phasing error due to the rolled down parabolic edges as a function of the intersegment step. Curve 1, edge PtV = 0.06 μm surface; curve 2, PtV = 0.09 μm ; and curve 3, PtV = 0.1 μm . The relative size of the lens is a = 1 . The wavelength is 0.6 μm , here and everywhere in the paper.

Fig. 10
Fig. 10

Phasing error as a function of the edge PtV for three different sizes of the lens. Curves marked with 1, a = 1 ; curves marked with 2, a = 2 ; and curves marked with 3, a = 6 . Solid curve, Model 1; dashed curve, Model 2; and dotted curve, Model 3. In the case of models 2 and 3, the optimal control is chosen for each value of the PtV. The phase step is δ / k = 100 nm .

Fig. 11
Fig. 11

Phasing error as a function of the relative size of the lens, a . Parameters: the phase step is δ / k = 100 nm and the edge profile PtV is ε = 0.1 μm .

Fig. 12
Fig. 12

Phasing error as a function of a control parameter for a fixed PtV: curve 1, PtV = 0.1 μm and curve 2, PtV = 0.15 μm . Phase step δ / k = 100 nm . The minimum of the phasing error corresponds to the minimum of the profile rms value.

Fig. 13
Fig. 13

Phasing error due to rolled-down edges for Model 1 as a function of the intersegment step. The difference in profiles is Δ ε = 10 nm . The mean profile PtV is ε = 0.05 μm . The relative size of the lens is a = 1 .

Fig. 14
Fig. 14

Final error found by fitting: Model 1 (squares) and Model 2 with α = α opt (circles). The solid curve is an approximation from Eq. (19). The difference in profiles is Δ ε = 10 nm . The mean profile PtV is ε = 0 for Model 1 and ε = 0.25 μm for Model 2. The relative size of the lens is a = 1 .

Fig. 15
Fig. 15

Phasing error due to rolled-down parabolic edges as a function of the intersegment step, a = 6 , ε = 0.1 μm . Curve 1: the error when the phasing subimages are recentered using a centroid algorithm. Curve 2: it is assumed that the subimage location is known perfectly.

Fig. 16
Fig. 16

Phasing error as a function of the image shift of the subimage for a = 1 (solid curve), 2 (dashed curve), and 6 (dotted curve). The phasing errors at zero shift correspond to those shown in Fig. 10.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

S ( x ) = π R 2 [ 1 1 π arccos ( x R ) + 1 π x R 1 ( x R ) 2 ] , 0 x R ,
H ( x ) = ε [ π R 2 S ( x ) 1 ] , 0 x R ,
H ( x ) h ( x ) = ε ( 1 x / η ) 2 , 0 x η .
r 1 ( t ) = ε ( 1 t ) 2 , 0 t 1.
c ( x ) = ε 0 α [ 1 1 η 1 2 ( 3 η 2 η 1 ) ( 3 η 2 x 2 x 3 ) ] .
r 2 ( x ) = ε 0 { [ h ( x ) ε 0 + 1 ] [ c ( x ) ε 0 + 1 ] 1 } ,
r 2 ( t ) = ε 0 { [ 1 ε ( 1 t ) 2 ] [ 1 + α ( 1 3 t 2 + 2 t 3 ) ] 1 } , 0 t 1.
α opt = 33 4 112 75 ε 567 ε 2 1595 ε + 1287 ε .
r 3 ( x ) = r 2 ( x ) + ε 0 ε β [ sin ( m π x η ) 1 ] .
r 3 ( t ) = ε 0 { [ 1 ε ( 1 t ) 2 ] [ 1 + α ( 1 3 t 2 + 2 t 3 ) ] 1 + ε β [ sin ( 2.5 π t ) 1 ] } .
α opt [ r 3 ] = α opt [ r 2 ] · ( 1 + β 57 ε 153 75 ε 112 ) ,
f ( w ) = 1 a a / 2 0 exp ( i δ / 2 ) exp ( i k x w ) d x + 1 a 0 a / 2 exp ( i δ / 2 ) exp ( i k x w ) d x = 2 a 0 a / 2 cos ( k x w + δ / 2 ) d x ,
S ( ς ) = | f ( w ) | 2 = ( π ς ) 2 [ sin ( π ς + δ / 2 ) sin ( δ / 2 ) ] 2 ,
f ( w ) = 1 a a / 2 0 exp [ i δ / 2 + i φ 1 ( x ) ] exp ( i k x w ) d x + 1 a 0 a / 2 exp [ i δ / 2 + i φ 2 ( x ) ] exp ( i k x w ) d x ,
S m ( ς ) = | 1 a 0 a exp [ i 2 k r 1 ( t ) ] cos ( π t ς a + δ 2 ) d t | 2 ,
S m sat ( ς ) = | 1 a 1 a cos ( π t ς a + δ 2 ) d t | 2 = ( π ς ) 2 [ sin ( π ς + δ 2 ) sin ( π ς a + δ 2 ) ] 2 .
S m ( ς ) = | 1 a 0 a exp [ i 2 k r q ( t , ε ) ] cos [ π t ς a + δ 2 + k Δ ε r q ( t , ε ) ε ] d t | 2 ,
0 2 [ S m ( ς ) S m ( ς ) ] 2 d ς min .
δ fin 0.42 k Δ ε / a 2 , a 1.

Metrics