Abstract

This paper proposes a systematic design method for two-mirror astronomical telescopes with reduced misalignment sensitivities. The analytic expressions between misalignment sensitivities and optical structure parameters are derived based on the nodal aberration theory (NAT). The sensitivities include coma and astigmatism aberration to lateral misalignments. The inherent relations among different misalignment sensitivities and conditions when optical structure parameters satisfy zero misalignment sensitivities have been summarized. On this basis, the design method is introduced. The design method gives consideration to both reduced misalignment sensitivities and good image quality, which utilizes monotonicity of the misalignment sensitivities functions. To demonstrate further the feasibility of the design method, an example for the Ritchey-Chretien (R-C) telescope is conducted. The results show that misalignment sensitivities can be reduced effectively.

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

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References

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2018 (2)

2017 (1)

2016 (2)

2015 (1)

J. Rogers, “Global optimization and desensitization,” Proc. SPIE 9633, 96330S (2015).
[Crossref]

2013 (2)

L. C. Scaduto, J. Sasian, M. A. Stefani, and J. C. Neto, “Two-mirror telescope design with third-order coma insensitive to decenter misalignment,” Opt. Express 21(6), 6851–6866 (2013).
[Crossref] [PubMed]

V. Costes, D. Laubier, P. Darré, and L. Perret, “Optical design and active optics for next generation space telescopes,” Proc. SPIE 8860, 88600B (2013).
[Crossref]

2011 (1)

2010 (2)

2009 (1)

2008 (1)

2006 (1)

2005 (1)

2004 (1)

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

1996 (1)

B. A. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[Crossref]

1994 (1)

1989 (1)

J. W. Figoski, “Design and tolerance specification of a wide-field, three-mirror unobscured, high-resolution sensor,” Proc. SPIE 1049, 157–165 (1989).
[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]

Bauman, B. J.

Catalan, G.

Costes, V.

V. Costes, D. Laubier, P. Darré, and L. Perret, “Optical design and active optics for next generation space telescopes,” Proc. SPIE 8860, 88600B (2013).
[Crossref]

Darré, P.

V. Costes, D. Laubier, P. Darré, and L. Perret, “Optical design and active optics for next generation space telescopes,” Proc. SPIE 8860, 88600B (2013).
[Crossref]

Ferrari, M.

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

Figoski, J. W.

J. W. Figoski, “Design and tolerance specification of a wide-field, three-mirror unobscured, high-resolution sensor,” Proc. SPIE 1049, 157–165 (1989).
[Crossref]

Gu, Z.

Ju, G.

Langlois, M.

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

Laubier, D.

V. Costes, D. Laubier, P. Darré, and L. Perret, “Optical design and active optics for next generation space telescopes,” Proc. SPIE 8860, 88600B (2013).
[Crossref]

Ma, H.

McLeod, B. A.

B. A. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[Crossref]

Meng, Q.

Moretto, G.

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

Neto, J. C.

Perret, L.

V. Costes, D. Laubier, P. Darré, and L. Perret, “Optical design and active optics for next generation space telescopes,” Proc. SPIE 8860, 88600B (2013).
[Crossref]

Rogers, J.

J. Rogers, “Global optimization and desensitization,” Proc. SPIE 9633, 96330S (2015).
[Crossref]

Rolland, J. P.

Sasian, J.

Scaduto, L. C.

Schmid, T.

Schneider, M. D.

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]

Stefani, M. A.

Thompson, K.

Thompson, K. P.

Upton, R.

Wang, H.

Wang, W.

Xu, S.

Yan, C.

Yan, Z.

Zhang, D.

Zhang, X.

Appl. Opt. (5)

J. Opt. Soc. Am. A (4)

Opt. Express (5)

Proc. SPIE (5)

J. W. Figoski, “Design and tolerance specification of a wide-field, three-mirror unobscured, high-resolution sensor,” Proc. SPIE 1049, 157–165 (1989).
[Crossref]

V. Costes, D. Laubier, P. Darré, and L. Perret, “Optical design and active optics for next generation space telescopes,” Proc. SPIE 8860, 88600B (2013).
[Crossref]

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

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

J. Rogers, “Global optimization and desensitization,” Proc. SPIE 9633, 96330S (2015).
[Crossref]

Publ. Astron. Soc. Pac. (1)

B. A. McLeod, “Collimation of fast wide-field telescopes,” Publ. Astron. Soc. Pac. 108, 217–219 (1996).
[Crossref]

Other (8)

Code V Reference Manual (Synopsys Inc., 2012).

T. Schmid, “Misalignment induced nodal aberration fields and their use in the alignment of astronomical telescopes,” Ph.D. dissertation (University of Central Florida Orlando, Florida, 2010).

R. N. Wilson, Reflecting Telescope Optics Vol. I, Basic Design Theory and its Historical Development, 2nd ed. (Springer, 2003), Chap. 3, pp. 88–111.

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw Hill, 2008), Chap. 18, pp. 508–514.

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

A. M. Manuel, “Field-dependent aberrations for misaligned reflective optical systems,” Ph.D. dissertation (Optical Sciences Center, University of Arizona 2009).

J. Rogers, “Optimization of as-built performance,” EOS Annual Meeting (2014)

D. J. Schroeder, Astronomical Optics (Academic, 1987).

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Figures (4)

Fig. 1
Fig. 1 The Gaussian optics of a two-mirror telescope.
Fig. 2
Fig. 2 Schematic layout of the 1.2m Mt. Hopkins telescope.
Fig. 3
Fig. 3 In the optimization process, the variations of mirror curvature and conic constant when the d and L vary (a) and (b) the variations of mirror curvature and conic constant with the d varies and (c) and (d) the variations of mirror curvature and conic constant with the L varies.
Fig. 4
Fig. 4 Full-Field-Display showing the RMS spot diameter across the field for (a) the initial system and (b) the optimized system.

Tables (8)

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Table 1 The Influence on Misalignment Sensitivities of the Initial System by the Variable of d and L

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Table 2 The Partial Derivatives for the Misalignment Sensitivity Functions to the d and L

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Table 3 Optical Parameters for the Optimized System

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Table 4 The Misalignment Sensitivities of the Initial System and the Optimized System

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Table 5 The Misalignment Sensitivities Influenced by the Variable of d and L

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Table 6 Optical Parameters for the Mt. Hopkins Telescope Based on McLeod

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Table 7 The Misalignment Sensitivities of the Initial System Based on the Numerical Calculations and the Deviation between the Analytic Functions and Numerical Calculations

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Table 8 The Rates of Change for the Misalignment Sensitivities to dand L based on the Numerical Calculations and the Deviation between the Analytic Functions and Numerical Calculations

Equations (29)

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W= j p n m ( W klm ) j [ ( H σ j )( H σ j ) ] p [ ρ ρ ] n [ ( H σ j ) ρ ] m , k=2p+m,l=2n+m,
W AST = 1 2 j W 222j [ ( H σ j ) 2 ρ 2 ] .
W AST = 1 2 [ ( j W 222j ) H 2 2 H ( j W 222j σ j )+( j W 222j σ j 2 ) ] ρ 2 .
Δ W AST = 1 2 [ 2 H A 222 ] ρ 2 ,
{ A 222x = W 222,SM sph σ SM,x sph + W 222,SM asph σ SM,x asph A 222y = W 222,SM sph σ SM,y sph + W 222,SM asph σ SM,y asph ,
[ H x H y H y H x ][ A 222,x A 222,y ]=[ Δ C 5 W 222 Δ C 6 W 222 ],
{ σ SM,x sph = BD E SM c SM XD E SM ( 1+ c SM d ) u ¯ PM σ SM,y sph = AD E SM + c SM YD E SM ( 1+ c SM d ) u ¯ PM σ SM,x asph = XD E SM d u ¯ PM σ SM,y asph = YD E SM d u ¯ PM ,
{ S XD E SM C 5 = C 5 system XD E SM Δ C 5 system XD E SM = H x ( α AST + β AST ) S AD E SM C 5 = C 5 system AD E SM Δ C 5 system AD E SM = H y ( α AST c SM ) H y H x S YD E SM C 6 = S XD E SM C 6 = S YD E SM C 5 = H y H x S XD E SM C 5 H x H y S BD E SM C 6 = S AD E SM C 6 = S BD E SM C 5 = H x H y S AD E SM C 5 α AST = 1 u ¯ PM W 222,SM sph c SM ( 1+ c SM d ) β AST = 1 u ¯ PM W 222,SM asph ( 1 d ) ,
{ W 222,SM sph = 1 2 ( y 1 f ) 2 ξ 0 L [ ( d L EPT f )+ 2 f L( m 2 1) ] 2 u ¯ 2 PM W 222,SM asph = 1 2 ( y 1 f ) 2 ξ L ( d L EPT f ) 2 u ¯ 2 PM ,
{ S XD E SM C 5 = H x 1 8 ( y 1 f ) 2 u ¯ PM ( m 2 +1) 2 ((L+d+ f )+(L+d+ f ) b s2 ) L S AD E SM C 5 = H y 1 4 ( y 1 f ) 2 u ¯ PM ( m 2 +1)L(L+d+ f ) = H y 1 4 ( y 1 f ) 2 u ¯ PM (d+ f ) 2 L 2 d .
W= j W 131j [ ( H σ j ) ρ ]( ρ ρ ) .
W={ [ ( j W 131j ) H ( j W 131j σ j ) ] ρ }( ρ ρ ).
Δ W COMA ={ A 131 ρ }( ρ ρ ),
{ A 131x = W 131,SM sph σ SM,x sph + W 131,SM asph σ SM,x asph A 131y = W 131,SM sph σ SM,y sph + W 131,SM asph σ SM,y asph ,
1 3 [ 1 0 0 1 ][ A 131,x A 131,y ]=[ Δ C 7 W 131 Δ C 8 W 31 ],
{ S XD E SM C 7 = C 7 system XD E SM Δ C 7 system XD E SM = 1 3 ( α coma + β coma ) S BD E SM C 7 = C 7 system BD E SM Δ C 7 system BD E SM = 1 3 α coma c SM S YD E SM C 8 = S XD E SM C 7 S AD E SM C 8 = S BD E SM C 7 S XD E SM C 8 = S BD E SM C 8 = S YD E SM C 7 = S AD E SM C 7 =0 α coma = 1 u ¯ PM W 131,SM sph c SM ( 1+ c SM d ) β coma = 1 u ¯ PM W 131,SM asph ( 1 d ) ,
{ W 131,SM sph = 1 2 ( y 1 f ) 3 ξ 0 [ d L f EPT+ 2 f ( m 2 1) ] u ¯ PM W 131,SM asph = 1 2 ( y 1 f ) 3 ξ [ d L f EPT ] u ¯ PM .
{ S XD E SM C 7 = 1 24 ( y 1 f ) 3 ( m 2 +1) 2 (( m 2 1)( m 2 +1) b s2 ) S BD E SM C 7 = 1 12 ( y 1 f ) 3 ( m 2 1)( m 2 +1)L = 1 12 ( y 1 f ) 3 L( ( f L d ) 2 1 ) .
b s1 = 1 ( c PM ) 3 [2L d 2 (L f ) 2 ] 8 (d) 3 ( f ) 3 ,
b s2 = 1 ( c SM ) 3 [2 f (L f ) 2 +( f (d)L)( f +(d)L)((d) f L)] 8 (d) 3 L 3 ,
c PM = L f 2(d) f .
c SM = L+(d) f 2(d)L .
{ S XD E SM C 7 = 1 12 ( y 1 f ) 3 ( m 2 3 + L d )= 1 12 ( y 1 f ) 3 1 (d) 3 ( (L f ) 3 d 2 L ) S XD E SM C 5 = H x 1 4 ( y 1 f ) 2 u ¯ PM m 2 ( m 2 + 2 f +d L ) = H x 1 4 ( y 1 f ) 2 u ¯ PM (L f ) d 2 L (L(L f )d(2 f +d)) .
S sys = ( Field Misalignment Zernike ( S Misalignment Zernike ) 2 d H x d H y Field d H x d H y ) 1/2 ,
S RMS = ( S XD E SM C 5 ) 2 + ( S AD E SM C 5 ) 2 + ( S XD E SM C 7 ) 2 + ( S BD E SM C 7 ) 2 .
{ S XD E SM C 5 d = H x 1 2 ( y 1 f ) 2 u ¯ PM (Lf) d 3 L (L( f L)+ f d) S XD E SM C 5 L = H x 1 4 ( y 1 f ) 2 u ¯ PM 1 d ( 2(L f ) d (2f+d) f L 2 ) ,
{ S AD E SM C 5 d = H y 1 4 ( y 1 f ) 2 u ¯ PM d 2 ( f ) 2 + L 2 d 2 S AD E SM C 5 L = H y 1 4 ( y 1 f ) 2 u ¯ PM 2L d ,
{ S XD E SM C 7 d = 1 12 ( y 1 f ) 3 1 d 2 ( 3 (Lf) 3 d 2 L) S XD E SM C 7 L = 1 12 ( y 1 f ) 3 (3 (Lf) 2 d 2 ) d 3 ,
{ S BD E SM C 7 d = 1 6 ( y 1 f ) 3 L (L f ) 2 d 3 S BD E SM C 7 L = 1 12 ( y 1 f ) 3 ( ( f L)( f 3L) d 2 1 ) .