Abstract

We present the nodal aberration field response of Ritchey-Chrétien telescopes to a combination of optical component misalignments and astigmatic figure error on the primary mirror. It is shown that both astigmatic figure error and secondary mirror misalignments lead to binodal astigmatism, but that each type has unique, characteristic locations for the astigmatic nodes. Specifically, the characteristic node locations in the presence of astigmatic figure error (at the pupil) in an otherwise aligned telescope exhibit symmetry with respect to the field center, i.e. the midpoint between the astigmatic nodes remains at the field center. For the case of secondary mirror misalignments, one of the astigmatic nodes remains nearly at the field center (in a coma compensated state) as presented in Optics Express 18, 5282-5288 (2010), while the second astigmatic node moves away from the field center. This distinction leads directly to alignment methods that preserve the dynamic range of the active wavefront compensation component.

©2010 Optical Society of America

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References

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  1. 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]
  2. J. R. Rogers, “Techniques and tools for obtaining symmetrical performance from tilted-component systems,” Opt. Eng. 39(7), 1776–1787 (2000).
    [Crossref]
  3. 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]
  4. 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]
  5. H. H. Hopkins, in The Wave Theory of Aberrations (Oxford on Clarendon Press, 1950).
  6. R. A. Buchroeder, “Tilted component optical systems,” Ph.D. dissertation (University of Arizona, 1976).
  7. R. V. Shack and K. Thompson, “Influence of alignment errors of a telescope system on its aberration field,” Proc. SPIE 251, 146–153 (1980).
  8. T. Schmid, K. P. Thompson, and J. P. Rolland, “A unique astigmatic nodal property in misaligned Ritchey-Chrétien telescopes with misalignment coma removed,” Opt. Express 18(5), 5282–5288 (2010).
    [Crossref] [PubMed]
  9. B. McLeod, “Collimation of Fast Wide-Field Telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
    [Crossref]
  10. D. L. Terrett and W. J. Sutherland, “The interaction between pointing and active optics on the VISTA Telescope,” presented at SPIE Astronomical Instrumentation, San Diego, CA, USA, 27 June - 2 July 2010.
  11. R. N. Wilson, in Reflecting Telescope Optics II (Springer-Verlag, Berlin, 1999), Chap. 2.
  12. K. P. Thompson, “Aberration Fields in Unobscured Mirror Systems,” J. Opt. Soc. Am. 70, 1603 (1980).
  13. K. P. Thompson, “The aberration fields of optical systems without symmetry”, PhD dissertation, The University of Arizona, College of Optical Sciences, (1980).
  14. C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc. 103, 159–165 (1942).
  15. J. C. Wyant, and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, Vol. XI, Academic Press (1992), Chap. 1.
  16. K. P. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry: errata,” J. Opt. Soc. Am. A 26(3), 699–699 (2009).
    [Crossref]
  17. 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]

2010 (2)

2009 (2)

2008 (1)

2005 (1)

2000 (1)

J. R. Rogers, “Techniques and tools for obtaining symmetrical performance from tilted-component systems,” Opt. Eng. 39(7), 1776–1787 (2000).
[Crossref]

1996 (1)

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

1980 (2)

K. P. Thompson, “Aberration Fields in Unobscured Mirror Systems,” J. Opt. Soc. Am. 70, 1603 (1980).

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

1942 (1)

C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc. 103, 159–165 (1942).

Burch, C. R.

C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc. 103, 159–165 (1942).

Cakmakci, O.

McLeod, B.

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

Rogers, J. R.

J. R. Rogers, “Techniques and tools for obtaining symmetrical performance from tilted-component systems,” Opt. Eng. 39(7), 1776–1787 (2000).
[Crossref]

Rolland, J. P.

Schmid, T.

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.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

K. P. Thompson, “Aberration Fields in Unobscured Mirror Systems,” J. Opt. Soc. Am. 70, 1603 (1980).

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

Mon. Not. R. Astron. Soc. (1)

C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc. 103, 159–165 (1942).

Opt. Eng. (1)

J. R. Rogers, “Techniques and tools for obtaining symmetrical performance from tilted-component systems,” Opt. Eng. 39(7), 1776–1787 (2000).
[Crossref]

Opt. Express (2)

Proc. SPIE (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).

Publ. Astron. Soc. Pac. (1)

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

Other (6)

D. L. Terrett and W. J. Sutherland, “The interaction between pointing and active optics on the VISTA Telescope,” presented at SPIE Astronomical Instrumentation, San Diego, CA, USA, 27 June - 2 July 2010.

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

K. P. Thompson, “The aberration fields of optical systems without symmetry”, PhD dissertation, The University of Arizona, College of Optical Sciences, (1980).

J. C. Wyant, and K. Creath, “Basic Wavefront Aberration Theory for Optical Metrology,” in Applied Optics and Optical Engineering, Vol. XI, Academic Press (1992), Chap. 1.

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 (11)

Fig. 1
Fig. 1 Aspheric corrector plate with aperture stop positions (a) centered on the optical axis utilizing the full aperture indicating spherical aberration, (b) centered on the optical axis utilizing only a small portion of the aperture, (c,d) shifted aperture stop, causing field-constant astigmatism.

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Fig. 2
Fig. 2 Interferogram characterizing the primary mirror astigmatic figure error.

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Fig. 3
Fig. 3 Coordinate system definition in the exit-pupil, showing (a) the definition for the FRINGE Zernike polynomials, and (b) the coordinate system orientation utilized in nodal aberration theory.

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Fig. 4
Fig. 4 (a) Binodal astigmatism caused by an astigmatic figure error on the primary mirror in the case of a fully aligned Ritchey-Chrétien telescope, and (b) the magnitude of astigmatism corresponding to (b).

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Fig. 5
Fig. 5 (a) Wave aberration contributions for coma (top) and astigmatism (bottom), showing the spherical base curve and conic/aspheric surface contributions, (b) secondary mirror aberration field centers (spherical and aspheric) before (denoted by “*”) and after removing misalignment induced coma. The example used here to demonstrate the theory is equivalent to the Ritchey-Chrétien configuration utilized in [8].

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Fig. 6
Fig. 6 (a) Aberration field centers for the spherical and aspheric aberration field contributions of the secondary mirror after aligning the telescope for zero field-constant coma. (b) Astigmatic primary mirror figure error for a Ritchey-Chrétien telescope.

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Fig. 7
Fig. 7 The vector a 222 that locates the center of biplanar symmetry of the binodal astigmatic field for a Ritchey-Chrétien telescope with secondary misalignment and primary mirror astigmatic figure error. (a) Contribution from secondary mirror misalignments under the condition that field-constant coma has been removed, and (b) the contribution from astigmatic figure error on the primary mirror, as derived in Section 2 and 3, has no a 222 component.

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Fig. 8
Fig. 8 The vector b 222 that points then as ± i b 222 from the endpoint of a 222 to the nodal points for binodal astigmatism, shown here for a Ritchey-Chrétien telescope with secondary misalignment and primary mirror astigmatic figure error, consisting of (a) b ( A L I ) 222 2 , denoting the contribution caused by secondary mirror misalignments, (b) b ( F I G ) 222 2 determined by interferogram data, combined with the knowledge of the total astigmatism in the nominal optical system, resulting in (c) the overall vector b 222 2 and b 222 the final astigmatic node locating vector, when combined with a 222 .

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Fig. 9
Fig. 9 The characteristic node geometry for (a) the nominal astigmatic aberration field, exhibiting purely quadratic astigmatism, (b) misalignment induced binodal astigmatism, (c) astigmatic figure error induced binodal astigmatism, and (d) both contributions, (b) and (c) combined.

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Fig. 10
Fig. 10 Magnitude of astigmatism of (a) the nominal Ritchey-Chrétien telescope, (b) binodal astigmatism in the presence of misalignments after alignment to remove constant coma, (c) an aligned telescope with only astigmatic figure error, (d) combined misalignments (b) and astigmatic figure error (c).

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Fig. 11
Fig. 11 A Real-Ray based verification of the prediction of astigmatic nodal positions by a generalized Coddington close skew ray trace, illustrating the (a) nominal astigmatic aberration field, exhibiting purely quadratic astigmatism with two coincident astigmatic nodes at the field center, (b) node positions for secondary mirror misalignments only, in a configuration that is corrected for zero field-constant coma, (c) node positions corresponding to the astigmatic figure error illustrated in Figs. 8(b), and 8(d) net display including the secondary misalignments and astigmatic figure error.

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Equations (20)

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W = W 040 [ ( ρ + Δ ρ ) • ( ρ + Δ ρ ) ] 2     = W 040 [ ( ρ • ρ ) 2 + 4 ( Δ ρ • ρ ) ( ρ • ρ ) + 4 ( Δ ρ • Δ ρ ) ( ρ • ρ )       + 2 ( Δ ρ 2 • ρ 2 ) + 4 ( Δ ρ • Δ ρ ) ( Δ ρ • ρ ) + ( Δ ρ • Δ ρ ) 2 ] ,
C ( F I G E R R ) 5 , 6 = ( C ( F I G E R R ) 5 ) 2 + ( C ( F I G E R R ) 6 ) 2 ,
ξ ( F I G E R R ) 5 , 6 * = 1 2 A r c T a n ( ( C ( F I G E R R ) 6 ) ( C ( F I G E R R ) 5 ) ) .
Z ( F I G E R R ) 5   = C ( F I G E R R ) 5 ρ 2 cos ( 2 ϕ ) ,
Z ( F I G E R R ) 6   = C ( F I G E R R ) 6 ρ 2 sin ( 2 ϕ ) ,
ρ 2 = ρ 2 ( sin ( 2 ϕ ) cos ( 2 ϕ ) ) ,
ρ = ρ e j ϕ ,
ξ ( F I G E R R ) 5 , 6 = 1 2 A r c T a n ( − ( C ( F I G E R R ) 6 ) ( C ( F I G E R R ) 5 ) ) .
B 222 2 =   B ( M I S A L I G N ) 222 2   +   B ( F I G E R R ) 222 2 ,
B ( F I G E R R ) 222 2 ≡ 2 ( C ( F I G E R R ) 5 , 6 ) exp [ j 2 ( ξ ( F I G E R R ) 5 , 6 ) ] ,
B ( M I S A L I G N ) 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 ) ,
W ( R C , M I S A L I G N , F I G E R R ) = W A S T = 1 2 W 222 [ ( H − a 222 ) 2 + b 222 2 ] · ρ 2 ,
b 222 2 ≡ B 222 2 W 222 − a 222 2 ,
B 222 2 = B ( M I S A L I G N ) 222 2 + B ( F I G E R R ) 222 2 .
a 222 ≡ A 222 W 222 ,
A 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 ( R C , A L I G N , F I G E R R ) = 1 2 [ W 222 H 2 + B ( F I G E R R ) 222 2 ] • ρ 2 .
H 2 = − B ( F I G E R R ) 222 2 W 222 ,
H =   ± i B ( F I G E R R ) 222 W 222 ,
W 1 3 1 , S M ( S P H ) σ S M ( S P H )   +   W 1 3 1 , S M ( A S P H ) σ S M ( A S P H )   =   0 ,

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