Abstract

The Large Synoptic Survey Telescope (LSST) uses a novel, three-mirror, modified Paul-Baker design, with an 8.4-meter primary mirror, a 3.4-m secondary, and a 5.0-m tertiary, along with three refractive corrector lenses to produce a flat focal plane with a field of view of 9.6 square degrees. In order to maintain image quality during operation, the deformations and rigid body motions of the three large mirrors must be actively controlled to minimize optical aberrations, which arise primarily from forces due to gravity and thermal expansion. We describe the methodology for measuring the telescope aberrations using a set of curvature wavefront sensors located in the four corners of the LSST camera focal plane. We present a comprehensive analysis of the wavefront sensing system, including the availability of reference stars, demonstrating that this system will perform to the specifications required to meet the LSST performance goals.

© 2010 OSA

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References

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  1. D. W. Sweeney, “Overview of the Large Synoptic Survey Telescope Project,” Proc. SPIE 6267, 626706 (2006).
    [CrossRef]
  2. Z. Ivezic, J. A. Tyson, T. Axelrod, D. Burke, C. F. Claver, K. H. Cook, S. M. Kahn, R. H. Lupton, D. G. Monet, P. A. Pinto, M. A. Strauss, C. W. Stubbs, L. Jones, A. Saha, R. Scranton, and C. Smith, “LSST: From science drivers to reference design and anticipated data products,” Version 1.0, http://aps.arxiv.org/abs/0805.2366v1 or www.lsst.org , (2008).
  3. D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
    [CrossRef]
  4. S. S. Olivier, L. G. Seppala, and D. K. Gilmore, “Optical Design of the LSST Camera,” Proc. SPIE 7018, 70182G (2008).
    [CrossRef]
  5. M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
    [CrossRef]
  6. K.W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, M. Waterson, “Design of the Pan-STARRS telescopes,” AN 325, No. 6–8, 636–642 (2004).
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    [CrossRef]
  11. A. M. Manuel, S. S. Olivier, D. W. Phillion, M. Warner and K. Arndt are preparing a manuscript to be called “Active Guiding of the Large Synoptic Survey Telescope (LSST).”
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    [CrossRef]
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    [CrossRef]
  17. A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 365(4), 1235–1242 (2006).
    [CrossRef]
  18. D. Mihalas, and J. Binney, Galactic Astronomy: structure and kinematics, Second Edition (W.H. Freeman, 1981).
  19. J. N. Bahcall and R. M. Soneira, “The Universe at Faint Magnitudes: I. Models for the Galaxy and Predicted Star Counts,” Astrophys. J. Suppl. Ser. 44, 73–110 (1980).
    [CrossRef]
  20. Z. Ivezic, University of Washington Astronomy Department, (personal communication, 2009).
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  22. D. Weistrop, “A new upper limit to local population II density,” A.J. 77, 366 (1972)
    [CrossRef]
  23. J. N. Bahcall and R. M. Soneira, “The distribution of stars to V=16th magnitude near the north galactic pole – Normalization, clustering, properties, and counts in various bands,” Ap.J. 246, 122–135 (1981).
    [CrossRef]

2008

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

S. S. Olivier, L. G. Seppala, and D. K. Gilmore, “Optical Design of the LSST Camera,” Proc. SPIE 7018, 70182G (2008).
[CrossRef]

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

2006

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

D. W. Sweeney, “Overview of the Large Synoptic Survey Telescope Project,” Proc. SPIE 6267, 626706 (2006).
[CrossRef]

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 365(4), 1235–1242 (2006).
[CrossRef]

K. L. Baker, “Tomographic reconstruction of high-energy-density plasmas with picosecond temporal resolution,” Opt. Lett. 31(6), 730–732 (2006).
[CrossRef] [PubMed]

2004

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

2003

B. A. Patterson and W. J. Sutherland, “Analysis of Curvature Sensing for VISTA,” Proc. SPIE 4842, 231–241 (2003).
[CrossRef]

1996

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996).
[CrossRef]

1991

1988

1984

1981

J. N. Bahcall and R. M. Soneira, “The distribution of stars to V=16th magnitude near the north galactic pole – Normalization, clustering, properties, and counts in various bands,” Ap.J. 246, 122–135 (1981).
[CrossRef]

1980

J. N. Bahcall and R. M. Soneira, “The Universe at Faint Magnitudes: I. Models for the Galaxy and Predicted Star Counts,” Astrophys. J. Suppl. Ser. 44, 73–110 (1980).
[CrossRef]

1972

D. Weistrop, “A new upper limit to local population II density,” A.J. 77, 366 (1972)
[CrossRef]

Bahcall, J. N.

J. N. Bahcall and R. M. Soneira, “The distribution of stars to V=16th magnitude near the north galactic pole – Normalization, clustering, properties, and counts in various bands,” Ap.J. 246, 122–135 (1981).
[CrossRef]

J. N. Bahcall and R. M. Soneira, “The Universe at Faint Magnitudes: I. Models for the Galaxy and Predicted Star Counts,” Astrophys. J. Suppl. Ser. 44, 73–110 (1980).
[CrossRef]

Baker, K.

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

Baker, K. L.

Bissonauth, N.

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

Bowden, G.

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Chow, W. W.

Clark, P.

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

Dalton, G. B.

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

Doi, M.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Foss, M.

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Fukugita, M.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Gilmore, D. K.

S. S. Olivier, L. G. Seppala, and D. K. Gilmore, “Optical Design of the LSST Camera,” Proc. SPIE 7018, 70182G (2008).
[CrossRef]

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Guiffre, G.

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Gunn, J. E.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Gureyev, T. E.

Hvisc, S.

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

Ichikawa, T.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Kahn, S.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Ku, J.

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Lawrence, G. N.

Myers, R.

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

Nordby, M.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Nugent, K. A.

O’Connor, P.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Oliver, J.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Olivier, S. S.

S. S. Olivier, L. G. Seppala, and D. K. Gilmore, “Optical Design of the LSST Camera,” Proc. SPIE 7018, 70182G (2008).
[CrossRef]

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

Patterson, B. A.

B. A. Patterson and W. J. Sutherland, “Analysis of Curvature Sensing for VISTA,” Proc. SPIE 4842, 231–241 (2003).
[CrossRef]

Phillion, D. W.

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

Radeka, V.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Roddier, C.

Roddier, F.

Schalk, T.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Schindler, R.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Schneider, D. P.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Seppala, L.

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

Seppala, L. G.

S. S. Olivier, L. G. Seppala, and D. K. Gilmore, “Optical Design of the LSST Camera,” Proc. SPIE 7018, 70182G (2008).
[CrossRef]

Shimasaku, K.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Soneira, R. M.

J. N. Bahcall and R. M. Soneira, “The distribution of stars to V=16th magnitude near the north galactic pole – Normalization, clustering, properties, and counts in various bands,” Ap.J. 246, 122–135 (1981).
[CrossRef]

J. N. Bahcall and R. M. Soneira, “The Universe at Faint Magnitudes: I. Models for the Galaxy and Predicted Star Counts,” Astrophys. J. Suppl. Ser. 44, 73–110 (1980).
[CrossRef]

Sutherland, W.

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

Sutherland, W. J.

B. A. Patterson and W. J. Sutherland, “Analysis of Curvature Sensing for VISTA,” Proc. SPIE 4842, 231–241 (2003).
[CrossRef]

Sweeney, D. W.

D. W. Sweeney, “Overview of the Large Synoptic Survey Telescope Project,” Proc. SPIE 6267, 626706 (2006).
[CrossRef]

Tokovinin, A.

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 365(4), 1235–1242 (2006).
[CrossRef]

Travouillon, T.

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 365(4), 1235–1242 (2006).
[CrossRef]

Van Berg, R.

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

Weistrop, D.

D. Weistrop, “A new upper limit to local population II density,” A.J. 77, 366 (1972)
[CrossRef]

A.J.

D. Weistrop, “A new upper limit to local population II density,” A.J. 77, 366 (1972)
[CrossRef]

Ap.J.

J. N. Bahcall and R. M. Soneira, “The distribution of stars to V=16th magnitude near the north galactic pole – Normalization, clustering, properties, and counts in various bands,” Ap.J. 246, 122–135 (1981).
[CrossRef]

Appl. Opt.

Astron. J.

M. Fukugita, T. Ichikawa, J. E. Gunn, M. Doi, K. Shimasaku, and D. P. Schneider, “The Sloan digital sky survey photometric system,” Astron. J. 111, 1748–1756 (1996).
[CrossRef]

Astrophys. J. Suppl. Ser.

J. N. Bahcall and R. M. Soneira, “The Universe at Faint Magnitudes: I. Models for the Galaxy and Predicted Star Counts,” Astrophys. J. Suppl. Ser. 44, 73–110 (1980).
[CrossRef]

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

A. Tokovinin and T. Travouillon, “Model of optical turbulence profile at Cerro Pachón,” Mon. Not. R. Astron. Soc. 365(4), 1235–1242 (2006).
[CrossRef]

Opt. Lett.

Proc. SPIE

D. W. Phillion, S. S. Olivier, K. Baker, L. Seppala, and S. Hvisc, “Tomographic wavefront correction for the LSST,” Proc. SPIE 6272, 627213 (2006).
[CrossRef]

B. A. Patterson and W. J. Sutherland, “Analysis of Curvature Sensing for VISTA,” Proc. SPIE 4842, 231–241 (2003).
[CrossRef]

N. Bissonauth, P. Clark, G. B. Dalton, R. Myers, and W. Sutherland, “Image Analysis Algorithms for Critically Sampled Curvature Wavefront Sensor Images in the Presence of Large Intrinsic Aberrations,” Proc. SPIE 5496, 738–746 (2004).
[CrossRef]

D. W. Sweeney, “Overview of the Large Synoptic Survey Telescope Project,” Proc. SPIE 6267, 626706 (2006).
[CrossRef]

D. K. Gilmore, S. Kahn, M. Nordby, P. O’Connor, J. Oliver, V. Radeka, T. Schalk, R. Schindler, and R. Van Berg, “The LSST camera overview: design and performance,” Proc. SPIE 7014, 70140C (2008).
[CrossRef]

S. S. Olivier, L. G. Seppala, and D. K. Gilmore, “Optical Design of the LSST Camera,” Proc. SPIE 7018, 70182G (2008).
[CrossRef]

M. Nordby, G. Bowden, M. Foss, G. Guiffre, J. Ku, and R. Schindler, “Mechanical Design of the LSST Camera,” Proc. SPIE 7018, 70182H (2008).
[CrossRef]

Other

K.W. Hodapp, N. Kaiser, H. Aussel, W. Burgett, K. C. Chambers, M. Chun, T. Dombeck, A. Douglas, D. Hafner, J. Heasley, J. Hoblitt, C. Hude, S. Isani, R. Jedicke, D. Jewitt, U. Laux, G. A. Luppino, R. Lupton, M. Maberry, E. Magnier, E. Mannery, D. Monet, J. Morgan, P. Onaka, P. Price, A. Ryan, W. Siegmund, I. Szapudi, J. Tonry, R. Wainscoat, M. Waterson, “Design of the Pan-STARRS telescopes,” AN 325, No. 6–8, 636–642 (2004).

Z. Ivezic, J. A. Tyson, T. Axelrod, D. Burke, C. F. Claver, K. H. Cook, S. M. Kahn, R. H. Lupton, D. G. Monet, P. A. Pinto, M. A. Strauss, C. W. Stubbs, L. Jones, A. Saha, R. Scranton, and C. Smith, “LSST: From science drivers to reference design and anticipated data products,” Version 1.0, http://aps.arxiv.org/abs/0805.2366v1 or www.lsst.org , (2008).

A. M. Manuel, S. S. Olivier, D. W. Phillion, M. Warner and K. Arndt are preparing a manuscript to be called “Active Guiding of the Large Synoptic Survey Telescope (LSST).”

D. Mihalas, and J. Binney, Galactic Astronomy: structure and kinematics, Second Edition (W.H. Freeman, 1981).

Z. Ivezic, University of Washington Astronomy Department, (personal communication, 2009).

A. N. Cox, Allen’s Astrophysical Quantities, Fourth Edition, edited by Arthur N. Cox, (Springer AIP Press, 2000).

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Figures (19)

Fig. 1
Fig. 1

Layout of the Large Synoptic Survey Telescope (LSST). The LSST contains three mirrors in a modified Paul-Baker configuration, along with three refractive corrector lenses, to enable a reasonably well corrected 3.5 degree field-of-view across the flat focal plane array.

Fig. 2
Fig. 2

Tomography geometry for LSST (with the telescope mirrors shown schematically as thin lenses). Wavefront data may be collected from stars at different field angles using multiple wavefront sensors.

Fig. 3
Fig. 3

a) Layout of the LSST focal plane array. The focal plane of the telescope is primarily populated with CCD arrays performing the telescope surveys, represented by small blue squares depicting 4096 × 4096 pixel sensors (16.8 Mpixels). There are 189 of these science sensors, assembled 3 × 3 into 21 rafts (outlined in red), for a total count of 3.2 Gpixels. There are four wavefront sensors, located in the corners of the array and eight guide sensors adjacent to the wavefront sensors. b) Schematic of the corner raft tower concept, which includes one wavefront sensor and two guider sensor packages.

Fig. 4
Fig. 4

a) A three-dimensional view and b) a side view of a schematic of the curvature wavefront sensor (CWFS) located on the focal plane array. The extra- and intra- focus CWFS detectors are displaced by Δz below and above the science focal plane.

Fig. 5
Fig. 5

Simulated intra-focal intensity and extra-focal intensity images used to test the curvature wavefront sensor reconstruction. The defocused images are rings due to the annular pupil shape of LSST and appear speckled due to the simulated atmosphere.

Fig. 6
Fig. 6

Additional curvature wavefront sensor errors due to photon and read noise lead to larger image sizes. Each data point shows the resulting spot size (in the i band) after correcting the telescope for arbitrary mirror deformations and rigid body motions in the presence of a set of wavefront sensor error coefficients and simulated atmosphere. The error bars show the resulting range of image sizes for different realizations of the atmospheres.

Fig. 7
Fig. 7

Pairs of curvature WFS images for different magnitude stars are used to reconstruct the applied phase (shown in the upper right). Each of the intra- and extra-focal wavefront sensor CCD images includes the same electronic and sky background noise, which is more apparent for the dimmer source stars (on the left, with larger values of stellar magnitude). The images of dim stars are background limited which causes the applied phase to be poorly reconstructed.

Fig. 8
Fig. 8

Histograms of observations during a ten-year LSST survey period vs. magnitude of sky brightness in two different filter bands. The magnitudes in the graph are the brightness values per square arcsecond in the wavelength band of interest (Left image: u band, Right image: i band). Courtesy of Kem Cook.

Fig. 9
Fig. 9

Phase reconstruction error versus star magnitude for each of the six wavelength bands in LSST. The amount of sky brightness noise added to the images used for the reconstructions corresponds to the mean expected level in each band (values in parentheses) over a 10-year period. Brighter stars (lower stellar magnitude values) have only small amounts of curvature wavefront sensor reconstruction errors. All magnitudes (stellar and background) are specified at the appropriate filter band wavelength.

Fig. 10
Fig. 10

Probability of finding a star brighter than magnitude m, in the six wavelength bands, at the north galactic pole in each of eight 88 sq. arcminute detectors. More stars are found near the red end of the spectrum (y) than the blue end (u) due to the abundance of low-mass, red dwarf type stars.

Fig. 11
Fig. 11

Probability vs. CWFS Error at the north galactic pole, the region of the sky with the fewest stars. The probability curves are similar for each of the middle bands (g, r, i) and there are easily enough stars available in this region to fill each of the eight detector halves for curvature wavefront sensor operate well below the 200nm error goal. However, ~5% of fields in the y band and ~15% of fields in the u band will not meet the 200 nm accuracy requirement.

Fig. 12
Fig. 12

A crowding star (shifted by 50% of the diameter) in one of the intra- or extra- focal detectors causes errors in the phase reconstruction. a) The applied phase representing the telescope aberrations (a combination of the first 36 annular Zernike coefficients), b) the intra-focal image with a neighboring star, shown here one magnitude dimmer, causing crowding c) the extra-focal image, with no crowding, and d) the reconstructed phase and CWFS error for a variety of different crowding star magnitudes. As the fraction of the intensity in the crowding star goes lower, the reconstruction improves.

Fig. 13
Fig. 13

A typical star field in y band at galactic equator seen by one pair of intra- and extra-focal CWFS detectors (with |Δz| = 1 mm defocus). The field shown, which is 176 square arcminutes (4096 × 4096 pixels), represents the most crowded area of the sky in the band with the most stars (reddest band) and there are still usable stars wavefront sensing.

Fig. 14
Fig. 14

The amount of vignetting of the pupil increases toward the edge of the wavefront sensor field. The pupils are shown for the following field angels: a) θ = 1.45° (inside corner of CWFS), b) θ = 1.62° (CWFS area center), c) θ = 1.75° (edge of 3.5° diameter FOV), d) θ = 1.78° (outside corner of CWFS).

Fig. 15
Fig. 15

Reconstruction errors due to vignetting of star images. When there is no correction at all for vignetting (blue dashed curve), the errors will be exceeding large. When there is correction for vignetting, but the amount of vignetting is incorrect (pink solid curve), the errors are manageable.

Fig. 16
Fig. 16

Large defocus distances enable better curvature wavefront sensor reconstructions (ignoring sources of electron and photon noise and crowding). For small defocus distances, the defocused image covers too few pixels to achieve accurate reconstructions. The defocused image of a point source covers about 80 × 80 pixels in this system when the defocus distance is ± 1 mm. (This plot shows the rms errors for reconstructing 36 annular Zernike coefficients with a power law distribution, using simulated defocused images in the i band.)

Fig. 17
Fig. 17

The upper two curves are the average image spot FWHM values for two sets of field points: the four CWFS field point positions and the 24 field point positions defined by using four rings (0.461°, 1.005°, 1.432°, 1.688°) and six spokes. The innermost and outermost rings have half the weighting of the two center rings. The lower two curves have the as-designed telescope 0.14 arcsecond FWHM removed by Gaussian quadrature. Hence the lower two curves give the added GQ image spot FWHM due to the atmosphere.

Fig. 18
Fig. 18

left) u band, no wind, r 0 = 15 cm at λ = 500 nm, z = + 1 mm., right) u band, wind = 3 m/s, r 0 = 15 cm at λ = 500 nm, z = + 1 mm.

Fig. 19
Fig. 19

Comparison of the cumulative star counts per square degree at the NGP in the LSST u g r i z bands between NGPcountsSDSSWeistrop.dat [20] and the corresponding star counts obtained from the model based upon the tables in Mihalas and Binney [18]. The spheroidal component is included in the model. The underscored variables are for the model. The _y curve from the model is also shown. SDSS is saturated at the bright end, so the curves were extended using Weistrop’s counts [22] as tabulated by Bahcall and Soneira [23]. These were for the V band. The extensions for the other bands were done by scaling the V band curve. The measured SDSS counts are used for u > 17.10, g > 15.60, r > 15, i > 14.80 and z > 14.60.

Tables (1)

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Table 1 Comparison of the star densities at the NGP in the visual band between Allen’s Astrophysical Quantities [21] and the model based upon Mihalas and Binney [18]. The model star counts are given for the disk only and also for the two-component disk and spheroidal [19] populations.

Equations (4)

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k I ( r ) z = [ I ( r ) ϕ ( r ) ]
ϕ = R 2 M 1 F
M i j = Ω I ( r ) Z i ( r / R , θ ) Z j ( r / R , θ ) r d r d θ
λ ( f Δ z ) r 0 < < r 0 Δ z f

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