Abstract

In this paper, an opto-thermal analysis of a moderately heated lightweighted solar telescope mirror is carried out using 3D finite element analysis (FEA). A physically realistic heat transfer model is developed to account for the radiative heating and energy exchange of the mirror with surroundings. The numerical simulations show the non-uniform temperature distribution and associated thermo-elastic distortions of the mirror blank clearly mimicking the underlying discrete geometry of the lightweighted substrate. The computed mechanical deformation data is analyzed with surface polynomials and the optical quality of the mirror is evaluated with the help of a ray-tracing software. The thermal print-through distortions are further shown to contribute to optical figure changes and mid-spatial frequency errors of the mirror surface. A comparative study presented for three commonly used substrate materials, namely, Zerodur, Pyrex and Silicon Carbide (SiC) is relevant to vast area of large optics requirements in ground and space applications.

© 2013 OSA

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  1. R. René, “The historical growth of telescope aperture,” Publ. Astron. Soc. Pac.116, 77–83, (2004).
    [CrossRef]
  2. R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
    [CrossRef]
  3. O. von der Lühe, “History of solar telescopes,” Exp. Astron.25, 193–207, (2009).
    [CrossRef]
  4. K. L. Stephen, R. R. Thomas, and W. Jeremy, “Advanced technology solar telescope,” Earth Moon Planets104,77–82, (2009).
    [CrossRef]
  5. C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
    [CrossRef]
  6. S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
    [CrossRef]
  7. W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).
  8. W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
    [CrossRef]
  9. P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
    [CrossRef]
  10. A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).
  11. C. M. Lowne, “An investigation of the effects of mirror temperature upon telescope seeing,” Mon. Not. R. Astron. Soc.188, 249–259 (1979).
  12. B. Bohannan, E. T. Pearson, and D. Hagelbarger, “Thermal control of classical astronomical primary mirrors,” Proc. SPIE4003, 406–416 (2000).
    [CrossRef]
  13. R. J. S. Greenhalgh, L. M. Stepp, and E. R. Hansen, “Gemini primary mirror thermal management system,” Proc. SPIE2199, 911–921 (1994).
    [CrossRef]
  14. A. Ahmad, Handbook of Optomechanical Engineering (CRC Press, 1997), Chap. 5.
  15. T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
    [CrossRef]
  16. J. M. Tamkin, “A study of image artifacts caused by structured mid-spatial frequnecy fabrication errors on optica surfaces,” Ph. D. dissertion (Univesity of Arizona, 2010).
  17. R. N. Youngworth and B. D. Stone, “Simple estimates for the effects of mid-spatial-frequency errors on image quality,” Appl. Opt.39, 2198–2209 (2000).
    [CrossRef]
  18. E. Segato, V. D. Deppo, S. Debei, G. Naletto, G. Cremonese, and E. Flamini, “Method for studying the effects of thermal deformations on optical systems for space application,” Appl. Opt.50, 2836–2845 (2011).
    [CrossRef] [PubMed]
  19. Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
    [CrossRef]
  20. F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2001).
  21. R. K. Banyal and B. Ravindra, “Thermal characteristics of a classical solar telescope primary mirror,” New Astron.16, 328–336 (2011).
    [CrossRef]
  22. F. M. Gottsche and F. S. Olesen, “Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data,” Remote Sens. Environ.76, 337–348 (2001).
    [CrossRef]
  23. M. H. Sadd, Elasticity: Theory, Applications, and Numerics (Academic Press, 2009), Chap. 2.
  24. M. Süß, T. Volkmer, and P. Eisenträger, “GREGOR M1 mirror and cell design: Effect of different mirror substrate on the telescope design,” Proc. SPIE7736, 77391l (2010).
    [CrossRef]
  25. T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
    [CrossRef]
  26. K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis (SPIE Press, 2002), Chap. 4.
    [CrossRef]
  27. R. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am.66, 207–211 (1976).
    [CrossRef]
  28. V. N. Mahajan, “Zernike annular polynomials and optical aberrations of systems with annular pupils,” Appl. Opt.33, 8125–8127 (1994).
    [CrossRef] [PubMed]
  29. We have chsoen the normalization factor and the indexing scheme similar to Noll’s notaion which is also followed in Zemax ray-tracing software.
  30. D. W. Kim, B. J. Lewisa, and J. H. Burgea, “Open-source data analysis and visualization software platform: SAGUARO,” Proc. SPIE8126, 81260B–81260B-10 (2011).
    [CrossRef]
  31. R.A. Applegate, E.J. Sarver, and V. Kemsara, “Are all aberrations equal?,” J. Refract. Surg.18, S556–S562, (2002).
    [PubMed]
  32. Zemax, Optical Design Program (User’s Manual, 2012).

2012

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

2011

R. K. Banyal and B. Ravindra, “Thermal characteristics of a classical solar telescope primary mirror,” New Astron.16, 328–336 (2011).
[CrossRef]

D. W. Kim, B. J. Lewisa, and J. H. Burgea, “Open-source data analysis and visualization software platform: SAGUARO,” Proc. SPIE8126, 81260B–81260B-10 (2011).
[CrossRef]

E. Segato, V. D. Deppo, S. Debei, G. Naletto, G. Cremonese, and E. Flamini, “Method for studying the effects of thermal deformations on optical systems for space application,” Appl. Opt.50, 2836–2845 (2011).
[CrossRef] [PubMed]

2010

M. Süß, T. Volkmer, and P. Eisenträger, “GREGOR M1 mirror and cell design: Effect of different mirror substrate on the telescope design,” Proc. SPIE7736, 77391l (2010).
[CrossRef]

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

2009

O. von der Lühe, “History of solar telescopes,” Exp. Astron.25, 193–207, (2009).
[CrossRef]

K. L. Stephen, R. R. Thomas, and W. Jeremy, “Advanced technology solar telescope,” Earth Moon Planets104,77–82, (2009).
[CrossRef]

T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
[CrossRef]

2004

Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
[CrossRef]

R. René, “The historical growth of telescope aperture,” Publ. Astron. Soc. Pac.116, 77–83, (2004).
[CrossRef]

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
[CrossRef]

P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
[CrossRef]

2003

A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).

2002

R.A. Applegate, E.J. Sarver, and V. Kemsara, “Are all aberrations equal?,” J. Refract. Surg.18, S556–S562, (2002).
[PubMed]

2001

F. M. Gottsche and F. S. Olesen, “Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data,” Remote Sens. Environ.76, 337–348 (2001).
[CrossRef]

2000

B. Bohannan, E. T. Pearson, and D. Hagelbarger, “Thermal control of classical astronomical primary mirrors,” Proc. SPIE4003, 406–416 (2000).
[CrossRef]

R. N. Youngworth and B. D. Stone, “Simple estimates for the effects of mid-spatial-frequency errors on image quality,” Appl. Opt.39, 2198–2209 (2000).
[CrossRef]

1994

V. N. Mahajan, “Zernike annular polynomials and optical aberrations of systems with annular pupils,” Appl. Opt.33, 8125–8127 (1994).
[CrossRef] [PubMed]

R. J. S. Greenhalgh, L. M. Stepp, and E. R. Hansen, “Gemini primary mirror thermal management system,” Proc. SPIE2199, 911–921 (1994).
[CrossRef]

1979

C. M. Lowne, “An investigation of the effects of mirror temperature upon telescope seeing,” Mon. Not. R. Astron. Soc.188, 249–259 (1979).

1976

Ahmad, A.

A. Ahmad, Handbook of Optomechanical Engineering (CRC Press, 1997), Chap. 5.

Ahn, K.

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Applegate, R.A.

R.A. Applegate, E.J. Sarver, and V. Kemsara, “Are all aberrations equal?,” J. Refract. Surg.18, S556–S562, (2002).
[PubMed]

Balthasar, H.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Banyal, R. K.

R. K. Banyal and B. Ravindra, “Thermal characteristics of a classical solar telescope primary mirror,” New Astron.16, 328–336 (2011).
[CrossRef]

Berkefeld, T.

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

Berkefeld, Th.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Bohannan, B.

B. Bohannan, E. T. Pearson, and D. Hagelbarger, “Thermal control of classical astronomical primary mirrors,” Proc. SPIE4003, 406–416 (2000).
[CrossRef]

Bornkessel, T.

P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
[CrossRef]

Burgea, J. H.

D. W. Kim, B. J. Lewisa, and J. H. Burgea, “Open-source data analysis and visualization software platform: SAGUARO,” Proc. SPIE8126, 81260B–81260B-10 (2011).
[CrossRef]

Cao, W.

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Cheng, H.

Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
[CrossRef]

Cohan, L. E.

T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
[CrossRef]

Collados, M.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

Coulter, R.

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Cremonese, G.

Debei, S.

Denker, C.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Deppo, V. D.

DeWitt, D. P.

F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2001).

Ding, Y.

Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
[CrossRef]

Doyle, K. B.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis (SPIE Press, 2002), Chap. 4.
[CrossRef]

Eisenträger, P.

M. Süß, T. Volkmer, and P. Eisenträger, “GREGOR M1 mirror and cell design: Effect of different mirror substrate on the telescope design,” Proc. SPIE7736, 77391l (2010).
[CrossRef]

Emde, P.

P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
[CrossRef]

Fischer, A.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Flamini, E.

Gelly, B.

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

Genberg, V. L.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis (SPIE Press, 2002), Chap. 4.
[CrossRef]

Gilmozzi, R.

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
[CrossRef]

Gonzalez, N. B.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Goode, P. R.

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Gorceix, N.

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Gottsche, F. M.

F. M. Gottsche and F. S. Olesen, “Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data,” Remote Sens. Environ.76, 337–348 (2001).
[CrossRef]

Gray, T. L.

T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
[CrossRef]

Greenhalgh, R. J. S.

R. J. S. Greenhalgh, L. M. Stepp, and E. R. Hansen, “Gemini primary mirror thermal management system,” Proc. SPIE2199, 911–921 (1994).
[CrossRef]

Hagelbarger, D.

B. Bohannan, E. T. Pearson, and D. Hagelbarger, “Thermal control of classical astronomical primary mirrors,” Proc. SPIE4003, 406–416 (2000).
[CrossRef]

Halbgewachs, C.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Hansen, E. R.

R. J. S. Greenhalgh, L. M. Stepp, and E. R. Hansen, “Gemini primary mirror thermal management system,” Proc. SPIE2199, 911–921 (1994).
[CrossRef]

Hasan, S. S.

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

Heidecke, F.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Hofmann, A.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Incropera, F. P.

F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2001).

Itoh, N.

A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).

Jeremy, W.

K. L. Stephen, R. R. Thomas, and W. Jeremy, “Advanced technology solar telescope,” Earth Moon Planets104,77–82, (2009).
[CrossRef]

Kärcher, H.

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

Kemsara, V.

R.A. Applegate, E.J. Sarver, and V. Kemsara, “Are all aberrations equal?,” J. Refract. Surg.18, S556–S562, (2002).
[PubMed]

Kim, D. W.

D. W. Kim, B. J. Lewisa, and J. H. Burgea, “Open-source data analysis and visualization software platform: SAGUARO,” Proc. SPIE8126, 81260B–81260B-10 (2011).
[CrossRef]

Kneer, F.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Kühn, J.

P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
[CrossRef]

Lagg, A.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Lewisa, B. J.

D. W. Kim, B. J. Lewisa, and J. H. Burgea, “Open-source data analysis and visualization software platform: SAGUARO,” Proc. SPIE8126, 81260B–81260B-10 (2011).
[CrossRef]

López, R.

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

Lowne, C. M.

C. M. Lowne, “An investigation of the effects of mirror temperature upon telescope seeing,” Mon. Not. R. Astron. Soc.188, 249–259 (1979).

Lu, E.

Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
[CrossRef]

Macaraya, G.

A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).

Mahajan, V. N.

Michels, G. J.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis (SPIE Press, 2002), Chap. 4.
[CrossRef]

Miller, D. W.

T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
[CrossRef]

Miyashita, A.

A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).

Naletto, G.

Nicklas, H.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Noll, R.

Ogasawara, R.

A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).

Olesen, F. S.

F. M. Gottsche and F. S. Olesen, “Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data,” Remote Sens. Environ.76, 337–348 (2001).
[CrossRef]

Pearson, E. T.

B. Bohannan, E. T. Pearson, and D. Hagelbarger, “Thermal control of classical astronomical primary mirrors,” Proc. SPIE4003, 406–416 (2000).
[CrossRef]

Popow, E.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Puschmann, K.G.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Rasilla, J. L.

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

Ravindra, B.

R. K. Banyal and B. Ravindra, “Thermal characteristics of a classical solar telescope primary mirror,” New Astron.16, 328–336 (2011).
[CrossRef]

René, R.

R. René, “The historical growth of telescope aperture,” Publ. Astron. Soc. Pac.116, 77–83, (2004).
[CrossRef]

Rimmele, T. R.

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Sadd, M. H.

M. H. Sadd, Elasticity: Theory, Applications, and Numerics (Academic Press, 2009), Chap. 2.

Sánchez, C. J.

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

Sarver, E.J.

R.A. Applegate, E.J. Sarver, and V. Kemsara, “Are all aberrations equal?,” J. Refract. Surg.18, S556–S562, (2002).
[PubMed]

Säß, M.

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

Schäfer, M.

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

Schmidt, D.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Schmidt, W.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Segato, E.

Sigwarth, M.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Smith, M. W.

T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
[CrossRef]

Sobotka, M.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Solanki, S. K.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Soltau, D.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

Staude, J.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Stephen, K. L.

K. L. Stephen, R. R. Thomas, and W. Jeremy, “Advanced technology solar telescope,” Earth Moon Planets104,77–82, (2009).
[CrossRef]

Stepp, L. M.

R. J. S. Greenhalgh, L. M. Stepp, and E. R. Hansen, “Gemini primary mirror thermal management system,” Proc. SPIE2199, 911–921 (1994).
[CrossRef]

Stone, B. D.

Strassmeier, K.G.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Süß, M.

M. Süß, T. Volkmer, and P. Eisenträger, “GREGOR M1 mirror and cell design: Effect of different mirror substrate on the telescope design,” Proc. SPIE7736, 77391l (2010).
[CrossRef]

Tamkin, J. M.

J. M. Tamkin, “A study of image artifacts caused by structured mid-spatial frequnecy fabrication errors on optica surfaces,” Ph. D. dissertion (Univesity of Arizona, 2010).

Thomas, A.

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

Thomas, R. R.

K. L. Stephen, R. R. Thomas, and W. Jeremy, “Advanced technology solar telescope,” Earth Moon Planets104,77–82, (2009).
[CrossRef]

Volkmer, R.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Volkmer, T.

M. Süß, T. Volkmer, and P. Eisenträger, “GREGOR M1 mirror and cell design: Effect of different mirror substrate on the telescope design,” Proc. SPIE7736, 77391l (2010).
[CrossRef]

von der Lühe, O.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

O. von der Lühe, “History of solar telescopes,” Exp. Astron.25, 193–207, (2009).
[CrossRef]

Waldmann, T.A.

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

Weis, U.

P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
[CrossRef]

Weissenburger, M.

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

Werner, T.

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

Werz, A.

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

Westerhoff, T.

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

You, Z.

Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
[CrossRef]

Youngworth, R. N.

Appl. Opt.

Astron. Nachr.

S. S. Hasan, D. Soltau, H. Kärcher, M. Säß, and T. Berkefeld, “NLST: India’s National Large Solar Telescope,” Astron. Nachr.331, 628–635 (2010).
[CrossRef]

W. Schmidt, O. von der Lühe, R. Volkmer, C. Denker, S. K. Solanki, H. Balthasar, N. B. Gonzalez, Th. Berkefeld, M. Collados, A. Fischer, C. Halbgewachs, F. Heidecke, A. Hofmann, F. Kneer, A. Lagg, H. Nicklas, E. Popow, K.G. Puschmann, D. Schmidt, M. Sigwarth, M. Sobotka, D. Soltau, J. Staude, K.G. Strassmeier, and T.A. Waldmann, “The 1.5 meter solar telescope GREGOR,” Astron. Nachr.331, 796–809 (2012).

W. Cao, N. Gorceix, R. Coulter, K. Ahn, T. R. Rimmele, and P. R. Goode, “Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear,” Astron. Nachr.333, 636–639 (2010).
[CrossRef]

Earth Moon Planets

K. L. Stephen, R. R. Thomas, and W. Jeremy, “Advanced technology solar telescope,” Earth Moon Planets104,77–82, (2009).
[CrossRef]

Exp. Astron.

O. von der Lühe, “History of solar telescopes,” Exp. Astron.25, 193–207, (2009).
[CrossRef]

J. Opt. Soc. Am.

J. Refract. Surg.

R.A. Applegate, E.J. Sarver, and V. Kemsara, “Are all aberrations equal?,” J. Refract. Surg.18, S556–S562, (2002).
[PubMed]

Mon. Not. R. Astron. Soc.

C. M. Lowne, “An investigation of the effects of mirror temperature upon telescope seeing,” Mon. Not. R. Astron. Soc.188, 249–259 (1979).

New Astron.

R. K. Banyal and B. Ravindra, “Thermal characteristics of a classical solar telescope primary mirror,” New Astron.16, 328–336 (2011).
[CrossRef]

Opt. Eng.

Y. Ding, Z. You, E. Lu, and H. Cheng, “A thermo-optical analysis method for a space optical remote sensor optostructural system,” Opt. Eng.43, 2730–2735 (2004).
[CrossRef]

Proc. SPIE

T. L. Gray, M. W. Smith, L. E. Cohan, and D. W. Miller, “Minimizing high spatial frequency residual in active space telescope mirrors,” Proc. SPIE7436, 74360M (2009.)
[CrossRef]

B. Bohannan, E. T. Pearson, and D. Hagelbarger, “Thermal control of classical astronomical primary mirrors,” Proc. SPIE4003, 406–416 (2000).
[CrossRef]

R. J. S. Greenhalgh, L. M. Stepp, and E. R. Hansen, “Gemini primary mirror thermal management system,” Proc. SPIE2199, 911–921 (1994).
[CrossRef]

C. J. Sánchez, M. Collados, D. Soltau, R. López, J. L. Rasilla, and B. Gelly, “Current concept for the 4m European Solar Telescope (EST) optical design,” Proc. SPIE7652, 76520S (2010).
[CrossRef]

R. Gilmozzi, “Science and technology drivers for future giant telescopes,” Proc. SPIE5489, 1–10 (2004).
[CrossRef]

P. Emde, J. Kühn, U. Weis, and T. Bornkessel, “Thermal design features of the solar telescope GREGOR,” Proc. SPIE5495, 238–246 (2004).
[CrossRef]

D. W. Kim, B. J. Lewisa, and J. H. Burgea, “Open-source data analysis and visualization software platform: SAGUARO,” Proc. SPIE8126, 81260B–81260B-10 (2011).
[CrossRef]

M. Süß, T. Volkmer, and P. Eisenträger, “GREGOR M1 mirror and cell design: Effect of different mirror substrate on the telescope design,” Proc. SPIE7736, 77391l (2010).
[CrossRef]

T. Westerhoff, M. Schäfer, A. Thomas, M. Weissenburger, T. Werner, and A. Werz, “Manufacturing of the ZERODUR 1.5-m primary mirror for the solar telescope GREGOR as preparation of light weighting of blanks up to 4-m diameter,” Proc. SPIE7739, 77390M–77390M-9 (2010).
[CrossRef]

Publ. Astron. Soc. Pac.

R. René, “The historical growth of telescope aperture,” Publ. Astron. Soc. Pac.116, 77–83, (2004).
[CrossRef]

Publ. Nat. Astron. Observ. Jpn

A. Miyashita, R. Ogasawara, G. Macaraya, and N. Itoh, “Temperature control for the primary mirror of Subaru Telescope using the data from ‘Forecast for Mauna Kea observatories’,” Publ. Nat. Astron. Observ. Jpn7, 25–31 (2003).

Remote Sens. Environ.

F. M. Gottsche and F. S. Olesen, “Modelling of diurnal cycles of brightness temperature extracted from METEOSAT data,” Remote Sens. Environ.76, 337–348 (2001).
[CrossRef]

Other

M. H. Sadd, Elasticity: Theory, Applications, and Numerics (Academic Press, 2009), Chap. 2.

K. B. Doyle, V. L. Genberg, and G. J. Michels, Integrated Optomechanical Analysis (SPIE Press, 2002), Chap. 4.
[CrossRef]

We have chsoen the normalization factor and the indexing scheme similar to Noll’s notaion which is also followed in Zemax ray-tracing software.

Zemax, Optical Design Program (User’s Manual, 2012).

A. Ahmad, Handbook of Optomechanical Engineering (CRC Press, 1997), Chap. 5.

J. M. Tamkin, “A study of image artifacts caused by structured mid-spatial frequnecy fabrication errors on optica surfaces,” Ph. D. dissertion (Univesity of Arizona, 2010).

F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, 2001).

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Figures (11)

Fig. 1
Fig. 1

Typical variations in ambient temperature (red curve, scale: vertical–left) and solar flux reaching the mirror surface (blue curve, scale: vertical–right). The peaks of solar flux and ambient temperature are shifted by 2 hrs due to thermal time lag.

Fig. 2
Fig. 2

Mirror geometry: (a) The side view and (b) the CAD model of the mirror with open back lightweighted honeycomb structure and 12 mm thick faceplate on top. Mirror has 6-fold symmetry about the z-axis. The faceplate is shown placed only on one of the 6 sectors of the mirror.

Fig. 3
Fig. 3

The impact of daytime heating on the Zerodur mirror with ambient temperature varying between 20–30°C and h = 5 W/m2. (a) Temperature print-through pattern on the mirror faceplate subjected to daytime radiative heating. (b) Temperature variations along the radial line AA′ of the mirror faceplate at different times.

Fig. 4
Fig. 4

Temperature difference between two reference points located at hexagonal cell-center (C) and cell-edge (E).

Fig. 5
Fig. 5

Thermally induced structural deformation: (a) for the Zerodur mirror and the corresponding z-displacements w (nm) along the radial line AA′ of the mirror faceplate for (b) Zerodur, (c) for Pyrex and (d) for SiC at different times of the day. The ambient temperature range was 20–30°C and h = 5 W/m2.

Fig. 6
Fig. 6

(a) Surface sag for thermally deformed Pyrex mirror at t = 14 hrs and h = 5 W/m2. The variation of RMS surface sag with daytime (b) for Pyrex and SiC and (c) for Zerodur mirror.

Fig. 7
Fig. 7

Zernike expansion coefficients corresponding to (a) defocus, primary, secondary and other higher order spherical aberrations which contribute to overall all figure change and (b) the remaining low-amplitude terms which contribute to mid-frequency surface errors.

Fig. 8
Fig. 8

Residual map obtained by subtracting the reconstructed Zernike surface from the original sag data.

Fig. 9
Fig. 9

Optical model of a Gregorian-type reflecting telescope in Zemax. M1: primary mirror; M2: secondary mirror; F1: primary focus; F2: secondary focus or image plane.

Fig. 10
Fig. 10

The spot diagram showing the telescope performance for a on-axis 0° field point. The blue traces represent the ray distribution in the image plane due to temperature induced surface imperfections in M1. The pattern has an envelop of six-fold symmetry due to hexagonal nature of the elements, as expected. The diffraction limited Airy disc is indicated by the black circle. The specified wavelength is 0.55 μm and the radius of the airy disc is close to 15 μm. Top row (a)–(c), when all the Zernike terms were included. Bottom row (d)–(f), without piston, focus and spherical terms.

Fig. 11
Fig. 11

The system contrast in terms of transverse modulation transfer function at various spatial frequencies for a 0° field angle (a) for Pyrex and (b) for the SiC mirror. For Zerodur (not shown), the ray aberrations are well within the diffraction limits and three MTF curves would overlap.

Tables (5)

Tables Icon

Table 1 Values of material properties used in FEA studies

Tables Icon

Table 2 The temperature difference for different glass material computed for heat transfer coefficient h1 = 5 W/m2 and h2 = 15 W/m2.

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Table 3 Parameters describing the mechanical deformation of the surface.

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Table 4 Low-order radial Zernike aberration terms.

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Table 5 Predominant low-amplitude Zernike terms consisting of azimuth and radial parts.

Equations (13)

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x ( K T x ) + y ( K T y ) + z ( K T z ) = T t + q ( x , y , z ; t )
T ( x , y , z ; t = 0 ) = T i ( x , y , x ) and
k ( T n ) | Ω = [ q 0 h ( T T a ) ε s σ R ( T 4 T a 4 ) ] | Ω
q 0 = γ I and
I = I 0 [ sin ( φ ) sin ( δ ) + cos ( φ ) cos ( δ ) cos ( H ) ]
T D ( t ) = T r + T 0 cos [ π ω ( t τ m ) ] for t < t s
T N ( t ) = T r + T d + { T 0 cos [ π ω ( t τ m ) ] T d } exp [ ( t t s ) / κ ] for t t s
ε th = α ( T T ref )
ε x x = u x ; ε x y = ε y x = 1 2 ( u y + v x ) ε y y = v y ; ε y z = ε z y = 1 2 ( v z + w y ) ε z z = w z ; ε z x = ε x z = 1 2 ( w x + u z )
Δ s = w w ( r 0 ) r u 2 + v 2
[ x y z Δ s ] = [ cos θ sin θ 0 0 sin θ cos θ 0 0 0 0 1 0 0 0 0 1 ] [ x y z Δ s ]
Δ s ( ρ , ϕ ; ε ) = j = 1 a j Z j ( ρ , ϕ ; ε )
Z j ( ρ , ϕ ; ε ) = { 2 ( n + 1 ) R n m ( ρ ; ε ) cos m ϕ m 0 , j even 2 ( n + 1 ) R n m ( ρ ; ε ) sin m ϕ m 0 , j odd n + 1 R n 0 ( ρ ; ε ) m = 0

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