Abstract

We present the aberration field response of Ritchey-Chrétien telescopes, with the aperture stop on the primary mirror, to secondary mirror misalignments. More specifically, we derive a general condition for the geometry of the binodal astigmatic aberration field for a telescope that has been aligned to remove field-constant coma. It has been observed that when the coma caused by secondary mirror misalignments is removed the astigmatic field is typically not symmetric around the periphery, but, significantly, it is always effectively zero on-axis. This observation is a manifestation of binodal astigmatism where one of the astigmatic nodes remains near the field center. Here, we show how the condition to remove field-constant coma simultaneously creates a constraint whereby one of the astigmatic nodes must remain effectively on-axis. This result points to why the alignment of a large telescope based on axial imagery is insufficient and demonstrates exactly the geometry of the remaining misalignment aberration field, which dominates the performance of the telescope, providing insights into more complete alignment approaches.

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References

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  1. H. H. Hopkins, in The Wave Theory of Aberrations (Oxford on Clarendon Press, 1950).
  2. R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, 1976).
  3. R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
  4. K. P. Thompson, “Aberration Fields in Tilted and Decentered Optical Systems,” Ph.D. dissertation (University of Arizona, 1980).
  5. K. P. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. A 22(7), 1389–1401 (2005).
    [CrossRef]
  6. 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]
  7. 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]
  8. B. McLeod, “Collimation of Fast Wide-Field Telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
    [CrossRef]
  9. R. N. Wilson, in Reflecting Telescope Optics II (Springer-Verlag, Berlin, 1999), Chap. 2.
  10. L. Noethe and S. Guisard, “Analytic expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT,” Acta Anat. Suppl. (Basel) 144, 157–167 (2000).
  11. A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
    [CrossRef]
  12. T. Schmid, K. P. Thompson, and J. P. Rolland, “The misalignment induced nodal aberration fields in two mirror astronomical telescopes,” submitted to Appl. Opt. (2009).

2009 (3)

2008 (1)

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

2005 (1)

2000 (1)

L. Noethe and S. Guisard, “Analytic expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT,” Acta Anat. Suppl. (Basel) 144, 157–167 (2000).

1996 (1)

B. McLeod, “Collimation of Fast Wide-Field Telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

1980 (1)

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

Biddick, C. J.

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

Cakmakci, O.

Guisard, S.

L. Noethe and S. Guisard, “Analytic expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT,” Acta Anat. Suppl. (Basel) 144, 157–167 (2000).

Hill, J. M.

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

Leibold, T.

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

McLeod, B.

B. McLeod, “Collimation of Fast Wide-Field Telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

Miller, D. L.

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

Noethe, L.

L. Noethe and S. Guisard, “Analytic expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT,” Acta Anat. Suppl. (Basel) 144, 157–167 (2000).

Rakich, A.

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

Rolland, J. P.

T. Schmid, K. P. Thompson, and J. P. Rolland, “The misalignment induced nodal aberration fields in two mirror astronomical telescopes,” submitted to Appl. Opt. (2009).

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]

Schmid, T.

T. Schmid, K. P. Thompson, and J. P. Rolland, “The misalignment induced nodal aberration fields in two mirror astronomical telescopes,” submitted to Appl. Opt. (2009).

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]

Shack, R. V.

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

Thompson, K.

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

Thompson, K. P.

Acta Anat. Suppl. (Basel) (1)

L. Noethe and S. Guisard, “Analytic expressions for field astigmatism in decentered two mirror telescopes and application to the collimation of the ESO VLT,” Acta Anat. Suppl. (Basel) 144, 157–167 (2000).

Appl. Opt. (1)

T. Schmid, K. P. Thompson, and J. P. Rolland, “The misalignment induced nodal aberration fields in two mirror astronomical telescopes,” submitted to Appl. Opt. (2009).

J. Opt. Soc. Am. A (3)

Proc. SPIE (2)

R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).

A. Rakich, J. M. Hill, C. J. Biddick, D. L. Miller, and T. Leibold, “Use of field aberrations in the alignment of the Large Binocular Telescope optics,” Proc. SPIE 7012, 70121 (2008).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

B. McLeod, “Collimation of Fast Wide-Field Telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[CrossRef]

Other (4)

R. N. Wilson, in Reflecting Telescope Optics II (Springer-Verlag, Berlin, 1999), Chap. 2.

K. P. Thompson, “Aberration Fields in Tilted and Decentered Optical Systems,” Ph.D. dissertation (University of Arizona, 1980).

H. H. Hopkins, in The Wave Theory of Aberrations (Oxford on Clarendon Press, 1950).

R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, 1976).

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Figures (2)

Fig. 1
Fig. 1

(a) The surface-by-surface wave aberration coefficients for coma and astigmatism of a typical RC telescope including the separation of the contribution from the spherical base curve of a conic/aspheric mirror and the contribution from the conic/aspheric departure. (b) Aberration field center vectors for the spherical base curve and conic/aspheric contributions of the secondary mirror of a misaligned RC telescope. The opposing alignment of σ S M ( s p h ) and σ S M ( a s p h ) is a key constraint imposed by the correction of misalignment induced coma.

Fig. 2
Fig. 2

Example of (a) field-quadratic astigmatism (magnitude) in case of an aligned RC telescope, (b) misalignment induced binodal astigmatism (3rd order) of a RC telescope aligned for zero coma.

Equations (11)

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W N O S Y M , R C = ( A 131 ρ ) ( ρ ρ ) + 1 2 W 222 [ ( H a 222 ) 2 + b 222 2 ] ρ 2 .
A 131 = W 131 , S M ( s p h ) σ S M ( s p h ) +     W 131 , S M ( a s p h ) σ S M ( a s p h ) ,
W 131 = W 131 , P M ( s p h ) + W 131 , S M ( s p h ) + W 131 , S M ( a s p h ) = 0 ,
σ SM ( sph ) = 1 / ( u ¯ P M ( c S M d 1 + 1 ) ) ( B D E S M - c S M X D E S M , - ( A D E S M + c S M Y D E S M ) ) ,
σ SM ( asp h ) = - 1 / ( u ¯ P M d 1 ) ( X D E S M , Y D E S M ) ,
b 222 2 B 222 2 W 222 a 222 2 ,
B 222 2 = W 2 2 2 , S M ( s p h ) σ S M 2 ( s p h ) + W 2 2 2 , S M ( a s p h ) σ S M 2 ( a s p h ) ,
a 222 A 222 W 222 = 1 W 222 ( W 2 2 2 , S M ( s p h ) σ S M ( s p h ) + W 2 2 2 , S M ( a s p h ) σ S M ( a s p h ) ) .
W A S T = 1 2 W 2 2 2 [ ( H a 2 2 2 ) 2 + b 2 2 2 2 ] ρ 2 = 0 , ( H a 2 2 2 ) 2 = - b 2 2 2 2 , ( H a 2 2 2 ) = ± ( - b 2 2 2 2 ) , H = + a 2 2 2 ± i b 2 2 2 .
b 222 2 ( a 222 2 ) .
( H a 222 ) 2 = - b 222 2 - ( - a 222 2 ) a 222 2 , ( H a 222 ) ± a 222 2 , H = + a 222 ± a 222 0 , 2 a 222 .

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