Abstract

A significant challenge in the production of Earth observation satellites is the precise alignment of the telescope optical components. We have developed a strategy to perform automated alignment of two-mirror telescopes for use in a realistic factory-based setting. A Ritchey–Chrétien telescope was used as an example. The secondary mirror was mounted on a high precision hexapod and its misalignment inferred from the Zernike coefficients for tilt, defocus, and coma, as measured by a phase-shifting interferometer. The required corrections to the position of the secondary mirror were implemented using an integral controller and alignment was achieved within minutes, compared to within days when using a manual alignment process. The Zernike coefficient for each aberration was reduced to within one standard deviation of the fluctuations due to residual instability (48 nm).

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References

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  1. J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
    [Crossref]
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    [Crossref]
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    [Crossref]
  4. J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2014 (1)

E. Oh, K.-B. Ahn, and S.-W. Kim, “Experimental sensitivity table method for precision alignment of Amon-Ra instrument,” J. Astron. Space Sci. 31, 241–246 (2014).
[Crossref]

2013 (1)

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

2012 (2)

2010 (1)

W. Bin, J. S. Lei, and Q. Tian, “Study on computer-aided alignment method of Cassegrain system,” Proc. SPIE 7654, 765405 (2010).
[Crossref]

2009 (1)

A. M. Manuel and J. H. Burge, “Alignment aberrations of the new solar telescope,” Proc. SPIE 7433, 74330A (2009).
[Crossref]

2008 (1)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[Crossref]

2007 (1)

2005 (1)

2001 (1)

E. Luna, S. Zazueta, and L. Gutiérrez, “An innovative method for the alignment of astronomical telescopes,” Publ. Astron. Soc. Pac. 113, 379–384 (2001).
[Crossref]

1999 (1)

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

1998 (1)

1996 (1)

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

1989 (1)

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

1972 (1)

Aglietti, G.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Ahn, K.-B.

E. Oh, K.-B. Ahn, and S.-W. Kim, “Experimental sensitivity table method for precision alignment of Amon-Ra instrument,” J. Astron. Space Sci. 31, 241–246 (2014).
[Crossref]

An, X.

Bin, W.

W. Bin, J. S. Lei, and Q. Tian, “Study on computer-aided alignment method of Cassegrain system,” Proc. SPIE 7654, 765405 (2010).
[Crossref]

Blanco, D. R.

D. R. Blanco, “Near-perfect collimation of wide-field Cassegrain telescopes,” Publ. Astron. Soc. Pac. 124, 36–41 (2012).
[Crossref]

Bloemhof, E. E.

Blows, R.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Booth, M.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Bortoletto, F.

Burge, J. H.

A. M. Manuel and J. H. Burge, “Alignment aberrations of the new solar telescope,” Proc. SPIE 7433, 74330A (2009).
[Crossref]

Choi, S. C.

Choi, Y.-J.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Choi, Y.-W.

Cordero, A.

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

Figoski, J. W.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Gooding, D.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Gutiérrez, L.

E. Luna, S. Zazueta, and L. Gutiérrez, “An innovative method for the alignment of astronomical telescopes,” Publ. Astron. Soc. Pac. 113, 379–384 (2001).
[Crossref]

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

Hampson, K. M.

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[Crossref]

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Haslehurst, A.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Jin, H.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Kang, M.-S.

Kim, E. D.

Kim, S.

Kim, S.-W.

E. Oh, K.-B. Ahn, and S.-W. Kim, “Experimental sensitivity table method for precision alignment of Amon-Ra instrument,” J. Astron. Space Sci. 31, 241–246 (2014).
[Crossref]

S. Kim, H.-S. Yang, Y.-W. Lee, and S.-W. Kim, “Merit function regression method for efficient alignment control of two-mirror optical systems,” Opt. Express 15, 5059–5068 (2007).
[Crossref]

Kuan, G.

Lee, J. U.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Lee, S.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Lee, Y.-W.

Lei, J. S.

W. Bin, J. S. Lei, and Q. Tian, “Study on computer-aided alignment method of Cassegrain system,” Proc. SPIE 7654, 765405 (2010).
[Crossref]

Lim, J.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Luna, E.

E. Luna, S. Zazueta, and L. Gutiérrez, “An innovative method for the alignment of astronomical telescopes,” Publ. Astron. Soc. Pac. 113, 379–384 (2001).
[Crossref]

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

Mahajan, V. N.

V. N. Mahajan, “Calculation of primary aberrations: perturbed optical systems,” in Optical Imaging and Aberrations: Part 1. Ray Geometrical Optics (SPIE, 1998), pp. 435–460.

Manuel, A. M.

A. M. Manuel and J. H. Burge, “Alignment aberrations of the new solar telescope,” Proc. SPIE 7433, 74330A (2009).
[Crossref]

McLeod, B. A.

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

Moon, I. K.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Moore, D.

Moore, G. F.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

O’Shay, B.

Oh, E.

E. Oh, K.-B. Ahn, and S.-W. Kim, “Experimental sensitivity table method for precision alignment of Amon-Ra instrument,” J. Astron. Space Sci. 31, 241–246 (2014).
[Crossref]

Page, N.

Park, J.-H.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

Pernechele, C.

Reif, K.

Richardson, G.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Rimmer, M. P.

Salas, L.

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

Saunders, C.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Shore, J.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Shrode, T. E.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Smith, D.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

Tang, H.

Tian, Q.

W. Bin, J. S. Lei, and Q. Tian, “Study on computer-aided alignment method of Cassegrain system,” Proc. SPIE 7654, 765405 (2010).
[Crossref]

Valdez, J.

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

Wetherell, W. B.

Yang, H.-S.

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

S. Kim, H.-S. Yang, Y.-W. Lee, and S.-W. Kim, “Merit function regression method for efficient alignment control of two-mirror optical systems,” Opt. Express 15, 5059–5068 (2007).
[Crossref]

Zazueta, S.

E. Luna, S. Zazueta, and L. Gutiérrez, “An innovative method for the alignment of astronomical telescopes,” Publ. Astron. Soc. Pac. 113, 379–384 (2001).
[Crossref]

Appl. Opt. (3)

J. Astron. Space Sci. (1)

E. Oh, K.-B. Ahn, and S.-W. Kim, “Experimental sensitivity table method for precision alignment of Amon-Ra instrument,” J. Astron. Space Sci. 31, 241–246 (2014).
[Crossref]

J. Korean Phys. Soc. (1)

J. Lim, S. Lee, I. K. Moon, H.-S. Yang, J. U. Lee, Y.-J. Choi, J.-H. Park, and H. Jin, “Sensitivity analysis of a wide-field telescope,” J. Korean Phys. Soc. 63, 28–35 (2013).
[Crossref]

J. Mod. Opt. (1)

K. M. Hampson, “Adaptive optics and vision,” J. Mod. Opt. 55, 3425–3467 (2008).
[Crossref]

J. Opt. Soc. Korea (1)

Opt. Express (1)

Proc. SPIE (3)

A. M. Manuel and J. H. Burge, “Alignment aberrations of the new solar telescope,” Proc. SPIE 7433, 74330A (2009).
[Crossref]

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

W. Bin, J. S. Lei, and Q. Tian, “Study on computer-aided alignment method of Cassegrain system,” Proc. SPIE 7654, 765405 (2010).
[Crossref]

Publ. Astron. Soc. Pac. (4)

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

D. R. Blanco, “Near-perfect collimation of wide-field Cassegrain telescopes,” Publ. Astron. Soc. Pac. 124, 36–41 (2012).
[Crossref]

E. Luna, A. Cordero, J. Valdez, L. Gutiérrez, and L. Salas, “Telescope alignment by out‐of‐focus stellar image analysis,” Publ. Astron. Soc. Pac. 111, 104–110 (1999).
[Crossref]

E. Luna, S. Zazueta, and L. Gutiérrez, “An innovative method for the alignment of astronomical telescopes,” Publ. Astron. Soc. Pac. 113, 379–384 (2001).
[Crossref]

Other (2)

V. N. Mahajan, “Calculation of primary aberrations: perturbed optical systems,” in Optical Imaging and Aberrations: Part 1. Ray Geometrical Optics (SPIE, 1998), pp. 435–460.

D. Gooding, G. Richardson, A. Haslehurst, D. Smith, C. Saunders, G. Aglietti, R. Blows, J. Shore, K. M. Hampson, and M. Booth, “A novel deployable telescope to facilitate a low-cost <1m GSD video rapid-revisit small satellite constellation,” in Proceedings of the International Conference on Space Optics (2019).

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Figures (2)

Fig. 1.
Fig. 1. Telescope construction showing the primary mirror, secondary mirror, flat mirror, hexapod, and interferometer.
Fig. 2.
Fig. 2. (a) Procedure for automated alignment. (b) Example data from two different misalignments. Shaded regions show the coupling between horizontal coma and horizontal tilt. When horizontal coma was corrected, horizontal tilt became more negative. (c) Example wavefront map before and after correction.

Tables (2)

Tables Icon

Table 1. Primary and Secondary Mirror Parameters

Tables Icon

Table 2. Sensitivity of the Zernike Coefficients to Movements of the Secondary Mirrora

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

[DecxDecyRotxRoty]i+1=[DecxDecyRotxRoty]ig×[sDx,vTiltsDx,hTiltsDy,vTiltsDy,hTiltsRx,vTiltsRx,hTiltsRy,vTiltsRy,hTilt][cvTiltchTilt]i+1,
s(Move,Zern)=Z+ZMove+Move,
Desi+1=Desig×sDes,Def×cDefi+1,
RCOCxi+1=RvComaig×sxComa×cvComai+1,
RCOCyi+1=RhComaig×syComa×chComai+1.

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