Abstract

Due to the absence of rotational symmetry, off-axis astronomical telescopes with off-set pupil become subject to rotational misalignments. Rotational misalignments of large off-axis mirrors with reference to their geometric center can greatly degrade the imaging quality. This paper presents an in-depth discussion on the net aberration fields of off-axis astronomical telescopes induced by rotational misalignments. Aberration function of off-axis telescopes with rotational misalignments is derived based on the framework of nodal aberration theory. Expressions of several important aberrations are obtained under some approximations. Then the specific field characteristics of these aberrations are presented and explicated. Meanwhile, we demonstrate that rotational misalignments can be converted to a kind of surface decenters; on the other hand, the effects of rotational misalignments have their special features which are different from the effects of general surface decenters. Besides, some other insightful discussions are further presented. This work is also applicable to the rotational misalignments of the off-axis segments of primary mirror in segmented mirror astronomical telescopes.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  24. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2018 (2)

2016 (1)

2015 (1)

2014 (2)

2012 (2)

2011 (1)

2010 (7)

T. Schmid, K. P. Thompson, and J. P. Rolland, “Misalignment-induced nodal aberration fields in two-mirror astronomical telescopes,” Appl. Opt. 49(16), D131–D144 (2010).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations,” J. Opt. Soc. Am. A 27(6), 1490–1504 (2010).
[Crossref] [PubMed]

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18(16), 17433–17447 (2010).
[Crossref] [PubMed]

W. Cao, N. Gorceix, and et al.., “First Light of the 1.6 meter off-axis New Solar Telescope at Big Bear Solar Observatory,” Proc. SPIE 7333, 73330 (2010).

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

R. Upton and T. Rimmele, “Active reconstruction and alignment strategies for the Advanced Technology Solar Telescope,” Proc. SPIE 7793, 77930E (2010).
[Crossref]

2009 (2)

2008 (1)

2007 (1)

2005 (1)

2004 (2)

G. Moretto, M. P. Langlois, and M. Ferrari, “Suitable off-axis space-based telescope designs,” Proc. SPIE 5487(163), 1111–1118 (2004).
[Crossref]

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

2001 (1)

M. Bartelmann and P. Schneider, “Weak gravitational lensing,” Phys. Rep. 340(4–5), 291–472 (2001).
[Crossref]

2000 (1)

1999 (1)

R. J. R. Kuhn and S. L. Hawley, “Some astronomical performance advantages of off-axis telescopes,” Publ. Astron. Soc. Pac. 111(759), 601–620 (1999).
[Crossref]

1991 (1)

M. A. Lundgren and W. L. Wolfe, “Alignment of a three-mirror off-axis telescope by reverse optimization,” Opt. Eng. 30(3), 307–311 (1991).
[Crossref]

1980 (1)

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

Allen, R. G.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

Bartelmann, M.

M. Bartelmann and P. Schneider, “Weak gravitational lensing,” Phys. Rep. 340(4–5), 291–472 (2001).
[Crossref]

Bernstein, R.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Burge, J. H.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

Cakmakci, O.

Cao, W.

W. Cao, N. Gorceix, and et al.., “First Light of the 1.6 meter off-axis New Solar Telescope at Big Bear Solar Observatory,” Proc. SPIE 7333, 73330 (2010).

Clampin, M.

M. Clampin, “Status of the James Webb Space Telescope observatory,” Proc. SPIE 8442, 84422A (2012).
[Crossref]

Cuerden, B.

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

Dalton, G. B.

Davison, W.

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

Fabricant, D. G.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Ferrari, M.

G. Moretto, M. P. Langlois, and M. Ferrari, “Suitable off-axis space-based telescope designs,” Proc. SPIE 5487(163), 1111–1118 (2004).
[Crossref]

Fuerschbach, K.

Gorceix, N.

W. Cao, N. Gorceix, and et al.., “First Light of the 1.6 meter off-axis New Solar Telescope at Big Bear Solar Observatory,” Proc. SPIE 7333, 73330 (2010).

Gu, Z.

Hagen, J.

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

Hawley, S. L.

R. J. R. Kuhn and S. L. Hawley, “Some astronomical performance advantages of off-axis telescopes,” Publ. Astron. Soc. Pac. 111(759), 601–620 (1999).
[Crossref]

Ju, G.

Kim, D. W.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

Kim, S.-W.

Kingsley, J. S.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

Kuhn, J. R.

Kuhn, R. J. R.

R. J. R. Kuhn and S. L. Hawley, “Some astronomical performance advantages of off-axis telescopes,” Publ. Astron. Soc. Pac. 111(759), 601–620 (1999).
[Crossref]

Langlois, M. P.

G. Moretto, M. P. Langlois, and M. Ferrari, “Suitable off-axis space-based telescope designs,” Proc. SPIE 5487(163), 1111–1118 (2004).
[Crossref]

Lee, H.

Lundgren, M. A.

M. A. Lundgren and W. L. Wolfe, “Alignment of a three-mirror off-axis telescope by reverse optimization,” Opt. Eng. 30(3), 307–311 (1991).
[Crossref]

Ma, H.

Martin, H. M.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

Matt, J.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

McCarthy, P.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Moretto, G.

G. Moretto, M. P. Langlois, and M. Ferrari, “Suitable off-axis space-based telescope designs,” Proc. SPIE 5487(163), 1111–1118 (2004).
[Crossref]

G. Moretto and J. R. Kuhn, “Optical performance of the 6.5-m off-axis New Planetary Telescope,” Appl. Opt. 39(16), 2782–2789 (2000).
[Crossref] [PubMed]

Papa, J. C.

Phillips, M.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Qiao, Y.

Rakich, A.

Rimmele, T.

R. Upton and T. Rimmele, “Active reconstruction and alignment strategies for the Advanced Technology Solar Telescope,” Proc. SPIE 7793, 77930E (2010).
[Crossref]

Roger, J. P.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Rolland, J. P.

N. Zhao, J. C. Papa, K. Fuerschbach, Y. Qiao, K. P. Thompson, and J. P. Rolland, “Experimental investigation in nodal aberration theory (NAT) with a customized Ritchey-Chrétien system: third-order coma,” Opt. Express 26(7), 8729–8743 (2018).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Extending nodal aberration theory to include mount-induced aberrations with application to freeform surfaces,” Opt. Express 20(18), 20139–20155 (2012).
[Crossref] [PubMed]

T. Schmid, K. P. Thompson, and J. P. Rolland, “Misalignment-induced nodal aberration fields in two-mirror astronomical telescopes,” Appl. Opt. 49(16), D131–D144 (2010).
[Crossref] [PubMed]

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18(16), 17433–17447 (2010).
[Crossref] [PubMed]

K. P. Thompson, T. Schmid, O. Cakmakci, and J. P. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26(6), 1503–1517 (2009).
[Crossref] [PubMed]

K. P. Thompson, T. Schmid, and J. P. Rolland, “The misalignment induced aberrations of TMA telescopes,” Opt. Express 16(25), 20345–20353 (2008).
[Crossref] [PubMed]

Schmid, T.

Schneider, P.

M. Bartelmann and P. Schneider, “Weak gravitational lensing,” Phys. Rep. 340(4–5), 291–472 (2001).
[Crossref]

Shack, R. V.

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

Shectman, S. A.

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Shi, G.

Thompson, K.

Thompson, K. P.

N. Zhao, J. C. Papa, K. Fuerschbach, Y. Qiao, K. P. Thompson, and J. P. Rolland, “Experimental investigation in nodal aberration theory (NAT) with a customized Ritchey-Chrétien system: third-order coma,” Opt. Express 26(7), 8729–8743 (2018).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Extending nodal aberration theory to include mount-induced aberrations with application to freeform surfaces,” Opt. Express 20(18), 20139–20155 (2012).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the astigmatic aberrations,” J. Opt. Soc. Am. A 28(5), 821–836 (2011).
[Crossref] [PubMed]

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18(16), 17433–17447 (2010).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations,” J. Opt. Soc. Am. A 27(6), 1490–1504 (2010).
[Crossref] [PubMed]

T. Schmid, K. P. Thompson, and J. P. Rolland, “Misalignment-induced nodal aberration fields in two-mirror astronomical telescopes,” Appl. Opt. 49(16), D131–D144 (2010).
[Crossref] [PubMed]

K. P. Thompson, “Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: spherical aberration,” J. Opt. Soc. Am. A 26(5), 1090–1100 (2009).
[Crossref] [PubMed]

K. P. Thompson, T. Schmid, O. Cakmakci, and J. P. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26(6), 1503–1517 (2009).
[Crossref] [PubMed]

K. P. Thompson, T. Schmid, and J. P. Rolland, “The misalignment induced aberrations of TMA telescopes,” Opt. Express 16(25), 20345–20353 (2008).
[Crossref] [PubMed]

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

Tosh, I. A. J.

Tuell, M. T.

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

Upton, R.

R. Upton and T. Rimmele, “Active reconstruction and alignment strategies for the Advanced Technology Solar Telescope,” Proc. SPIE 7793, 77930E (2010).
[Crossref]

Wang, Y.

West, S. C.

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

Wolfe, W. L.

M. A. Lundgren and W. L. Wolfe, “Alignment of a three-mirror off-axis telescope by reverse optimization,” Opt. Eng. 30(3), 307–311 (1991).
[Crossref]

Wu, H.

Yan, C.

Zeng, F.

Zhang, J.

Zhang, X.

Zhao, C.

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

Zhao, N.

Zobrist, T.

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

Appl. Opt. (3)

J. Opt. Soc. Am. A (5)

Opt. Eng. (1)

M. A. Lundgren and W. L. Wolfe, “Alignment of a three-mirror off-axis telescope by reverse optimization,” Opt. Eng. 30(3), 307–311 (1991).
[Crossref]

Opt. Express (9)

H. Lee, G. B. Dalton, I. A. J. Tosh, and S.-W. Kim, “Computer-guided alignment II :Optical system alignment using differential wavefront sampling,” Opt. Express 15(23), 15424–15437 (2007).
[Crossref] [PubMed]

K. P. Thompson, T. Schmid, and J. P. Rolland, “The misalignment induced aberrations of TMA telescopes,” Opt. Express 16(25), 20345–20353 (2008).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Extending nodal aberration theory to include mount-induced aberrations with application to freeform surfaces,” Opt. Express 20(18), 20139–20155 (2012).
[Crossref] [PubMed]

F. Zeng, X. Zhang, J. Zhang, G. Shi, and H. Wu, “Optics ellipticity performance of an unobscured off-axis space telescope,” Opt. Express 22(21), 25277–25285 (2014).
[Crossref] [PubMed]

K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “Theory of aberration fields for general optical systems with freeform surfaces,” Opt. Express 22(22), 26585–26606 (2014).
[Crossref] [PubMed]

Z. Gu, C. Yan, and Y. Wang, “Alignment of a three-mirror anastigmatic telescope using nodal aberration theory,” Opt. Express 23(19), 25182–25201 (2015).
[Crossref] [PubMed]

G. Ju, C. Yan, Z. Gu, and H. Ma, “Aberration fields of off-axis two-mirror astronomical telescopes induced by lateral misalignments,” Opt. Express 24(21), 24665–24703 (2016).
[Crossref] [PubMed]

T. Schmid, J. P. Rolland, A. Rakich, and K. P. Thompson, “Separation of the effects of astigmatic figure error from misalignments using Nodal Aberration Theory (NAT),” Opt. Express 18(16), 17433–17447 (2010).
[Crossref] [PubMed]

N. Zhao, J. C. Papa, K. Fuerschbach, Y. Qiao, K. P. Thompson, and J. P. Rolland, “Experimental investigation in nodal aberration theory (NAT) with a customized Ritchey-Chrétien system: third-order coma,” Opt. Express 26(7), 8729–8743 (2018).
[Crossref] [PubMed]

Phys. Rep. (1)

M. Bartelmann and P. Schneider, “Weak gravitational lensing,” Phys. Rep. 340(4–5), 291–472 (2001).
[Crossref]

Proc. SPIE (8)

W. Cao, N. Gorceix, and et al.., “First Light of the 1.6 meter off-axis New Solar Telescope at Big Bear Solar Observatory,” Proc. SPIE 7333, 73330 (2010).

H. M. Martin, R. G. Allen, J. H. Burge, D. W. Kim, J. S. Kingsley, M. T. Tuell, S. C. West, C. Zhao, and T. Zobrist, “Fabrication and testing of the first 8.4-m off-axis segment for the Giant Magellan Telescope,” Proc. SPIE 7339, 73390A (2010).

S. C. West, J. H. Burge, B. Cuerden, W. Davison, J. Hagen, H. M. Martin, M. T. Tuell, C. Zhao, and T. Zobrist, “Alignment and use of the optical test for the 8.4-m off-axis primary mirrors of the Giant Magellan Telescope,” Proc. SPIE 7339, 73390N (2010).

J. Matt, J. P. Roger, S. A. Shectman, R. Bernstein, D. G. Fabricant, P. McCarthy, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

M. Clampin, “Status of the James Webb Space Telescope observatory,” Proc. SPIE 8442, 84422A (2012).
[Crossref]

R. Upton and T. Rimmele, “Active reconstruction and alignment strategies for the Advanced Technology Solar Telescope,” Proc. SPIE 7793, 77930E (2010).
[Crossref]

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).
[Crossref]

G. Moretto, M. P. Langlois, and M. Ferrari, “Suitable off-axis space-based telescope designs,” Proc. SPIE 5487(163), 1111–1118 (2004).
[Crossref]

Publ. Astron. Soc. Pac. (1)

R. J. R. Kuhn and S. L. Hawley, “Some astronomical performance advantages of off-axis telescopes,” Publ. Astron. Soc. Pac. 111(759), 601–620 (1999).
[Crossref]

Other (2)

K. P. Thompson, “Aberration fields in tilted and decentered optical systems,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1980).

J. M. Sasian, “Imagery of the Bilateral Symmetric Optical System,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1988).

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Figures (7)

Fig. 1
Fig. 1 (a) Coordinate transformation between the pupil of the off-axis system and its rotationally symmetric parent system in the nominal case. (b) Coordinate transformation between the off-axis surface and its rotationally symmetric parent surface when the off-axis surface is rotated about its geometric center.
Fig. 2
Fig. 2 Optical layout of the off-axis SNAP telescope.
Fig. 3
Fig. 3 FFDs for astigmatism in the off-axis SNAP telescope (a) without and (b) with the rotational misalignments presented in Table 1. We can see that a large 45° astigmatism which is nearly constant in the field is introduced by rotationally misalignments.
Fig. 4
Fig. 4 FFDs for coma in the off-axis SNAP telescope (a) without and (b) with the rotational misalignments presented in Table 1. We can see that a field-constant coma in x direction (perpendicular to the direction of pupil offset) is introduced by rotationally misalignments.
Fig. 5
Fig. 5 FFDs for medial focal surface of the off-axis SNAP telescope (a) in the nominal state, (b) in the presence of the rotational misalignments presented in Table 1, and (c) in the presence of some general lateral misalignments (not in the direction perpendicular to the direction of pupil offset). We can see that rotational misalignments do not introduce focal shift while lateral misalignments can generally introduce a large focal shift.
Fig. 6
Fig. 6 FFDs for (a) astigmatism and (b) coma in the off-axis SNAP telescope after introducing lateral misalignment of the secondary mirror to compensate for the effects of rotational misalignments presented in Table 1. Referring to Fig. 3(a) and Fig. 4(a), we can see that both the two kinds of aberrations are nearly corrected to the nominal state.
Fig. 7
Fig. 7 (a) FFD for astigmatism of the off-axis SNAP telescope with the same rotational misalignments as presented in Table 1while the magnitude of pupil offset is reduced by half (i.e. the distance of the center of the actual primary mirror to the center of its parent surface becomes 1325mm). (b) FFD for astigmatism of the off-axis SNAP telescope with the same misalignments presented in Table 2 while the magnitude of pupil offset is reduced by half.

Tables (6)

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Table 1 Introduced rotational misalignments

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Table 2 Equivalent decenters of each mirror obtained with Eq. (4)

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Table 3 Fringe Zernike coefficients (2th-9th) for two field points in the presence of the rotational misalignments presented in Table 1 (Case 1) and the decenter misalignments presented in Table 2 (Case 2)

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Table 4 Basic optics parameters of the off-axis SNAP telescope

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Table 5 Aspheric parameters of the off-axis SNAP telescope

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Table 6 Aberration coefficients for each individual surface

Equations (43)

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W= j p n m W klm j ( H H ) p ( ρ ρ ) n ( H ρ ) m ,
ρ =b ρ '+ s ,
W= j p n m W klm j ( H H ) p [ ( b ρ '+ s )( b ρ '+ s ) ] n [ H ( b ρ '+ s ) ] m ,
V j =[ S j sin δ j S j ( 1cos δ j ) ],
W= j p n m W klm j [ ( H σ j )( H σ j ) ] p ( ρ ρ ) n [ ( H σ j ) ρ ] m .
ρ =b ρ '+ t 0 ,
t 0 = s v 0 ,
| v 0 |=| s || δ 0 |,
W= j p n m W klm j [ ( H σ j )( H σ j ) ] p [ ( ρ + s )( ρ + s ) ] n [ ( H σ j )( ρ + s ) ] m ,
W= C 20 ( ρ ρ )+ C 22 ρ 2 + C 31 ρ ( ρ ρ )+ C 40 ( ρ ρ ) 2 ,
C 20 = W 020 + j W 220Mj ( H σ j )( H σ j ) +2 j W 131j s ( H σ j )+4 W 040 ( s s ),
C 22 = 1 2 j W 222j ( H σ j )( H σ j ) + j W 131j s ( H σ j ) +2 W 040 s 2 ,
C 31 = j W 131j ( H σ j )+4 W 040 s ,
C 40 = W 040 .
W AST =( C 22 (0) + C 22 (1) + C 22 (2) ) ρ 2 ,
C 22 (0) = 1 2 W 222 H 2 + W 131 s H +2 W 040 s 2 ,
C 22 (1) = A 222 H A 131 s ,
C 22 (2) = j W 222 σ j 2 ,
A klm = j W klm σ j .
Δ W AST =( A 222 H A 131 s ) ρ 2 ,
V j =[ S j δ j 0 ].
Δ W AST K 131 e x s ρ 2 ,
ϕ AST = 1 2 [ ξ( s )+ξ( e x )+ψ( K 131 ) ],
W Coma = C 31 (0) ρ ( ρ ρ )+ C 31 (1) ρ ( ρ ρ ),
C 31 (0) = W 131 H +4 W 040 s ,
C 31 (1) = A 131 .
Δ W Coma = A 131 ρ ( ρ ρ ).
Δ W Coma = K 131 e x ρ ( ρ ρ ).
ϕ Coma =ξ( e x )+ψ( K 131 ).
W MFS =( C 20 (0) + C 20 (1) + C 20 (2) )( ρ ρ ),
C 20 (0) = W 020 + W 220M ( H H )+2 W 131 ( s H )+4 W 040 ( s s ),
C 20 (1) =2 A 220M H 2 A 131 s ,
C 20 (2) = j W 220M ( σ j σ j ) .
Δ W MFS =( 2 A 220M H 2 A 131 s )( ρ ρ ),
A 131 s =0.
σ PM sph = 1 u ¯ PM β PM ,
σ SM sph = 2 u ¯ PM β PM + 1 u ¯ PM ( d 1 + r SM ) ( V PM V SM r SM β SM ),
σ TM sph = 2 u ¯ PM β PM + ( 2 d 2 r SM +2 r TM ) V PM ( 2 d 2 +2 r TM )( V SM + r SM β SM ) u ¯ PM ( 2 d 1 d 2 d 1 r SM + d 2 r SM +2 d 1 r TM + r SM r TM ) ,
σ PM asph = 0 ,
σ SM asph = 1 d 1 u ¯ PM ( V PM V SM +2 d 1 β PM ),
σ TM asph = 2 u ¯ PM β PM + ( 2 d 2 r SM ) V PM 2 d 2 ( V SM + r SM β SM ) u ¯ PM ( 2 d 1 d 2 d 1 r SM + d 2 r SM ) ,
{ A 131 = 0 A 222 = 0 .
V j =[ | s | R j ' δ j 0 ],

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