Abstract

In this paper, the Zernike coefficient is analytically expressed as the product of the dependence of aberration field decenter vectors (related with perturbations) and the dependence of fields of view (FOVs), on the frame work of nodal aberration theory (NAT). By expanding and analyzing this expression, an alignment strategy by optical compensation for the perturbed on-axis or off-axis telescope is presented. Specifically, two cases, corresponding to the misalignment of tertiary mirror (TM) and the deformation of primary mirror (PM), respectively, are discussed for the same three mirror anastigmatic (TMA) telescope. Here the misaligned TM and the deformed PM are compensated only by aligning secondary mirror (SM). By analyzing the aberration field after compensation with the nominal, it is found that either PM or TM can be compensated by SM. It is also found TM is more easily compensated than PM. In the end, the NAT method developed here used for optical compensation is compared to merit function regression (MFR) method and sensitivity table method (STM). By comparing NAT method with MFR method, it is shown that the calculated correction values of SM based on NAT method is very close to the referred values obtained from MFR method. It proves the correctness of NAT method developed here. By comparing NAT method with STM, it demonstrates that the computation accuracy of NAT method is much higher in poor conditions and NAT method is less sensitive to measurement errors. It is further illustrated that the theory of optical compensation by SM developed here is correct and applicable.

© 2017 Optical Society of America

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References

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2016 (2)

2015 (2)

2013 (1)

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

2012 (2)

J. Sebag, W. Gressler, T. Schmid, J. P. Rolland, and K. P. Thompson, “LSST Telescope Alignment Plan Based on Nodal Aberration Theory,” Publ. Astron. Soc. Pac. 124(914), 380–390 (2012).

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

2010 (1)

2009 (1)

2008 (1)

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

2007 (3)

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(8), 5059–5068 (2007).

J. M. Howard, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): III. Wavefront aberrations due to alignment and figure compensation,” Proc. SPIE 6675, 667503 (2007).

M. Lampton and M. Sholl, “Comparison of on-axis three-mirror-anastigmat telescopes,” Proc. SPIE 6687, 66870S (2007).

2005 (2)

2004 (1)

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

1995 (1)

J. Robichaud, M. Anapol, L. Gardner, and P. Hadfield, “Ultralightweight off-axis three-mirror anastigmatic SiC visible telescope,” Proc. SPIE 2543, 180–184 (1995).

1987 (1)

R. N. Wilson, F. Franza, and L. Noethe, “Active optics: I. A system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).

1979 (2)

S. G. L. Williams, “On-axis three-mirror anastigmat with an offset field of view,” Proc. SPIE 183, 212–217 (1979).

L. G. Cook, “Three-mirror anastigmat used of-axis in aperture and field,” Proc. SPIE 183, 207–211 (1979).

Anapol, M.

J. Robichaud, M. Anapol, L. Gardner, and P. Hadfield, “Ultralightweight off-axis three-mirror anastigmatic SiC visible telescope,” Proc. SPIE 2543, 180–184 (1995).

Bos, B.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Cakmakci, O.

Chandrasekharan, S.

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

Choi, S. C.

Choi, Y. W.

Claver, C. F.

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

Contreras, J.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Cook, L. G.

L. G. Cook, “Three-mirror anastigmat used of-axis in aperture and field,” Proc. SPIE 183, 207–211 (1979).

Davila, P.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Evans, C.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Franza, F.

R. N. Wilson, F. Franza, and L. Noethe, “Active optics: I. A system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).

Fu, H. Y.

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

Gardner, L.

J. Robichaud, M. Anapol, L. Gardner, and P. Hadfield, “Ultralightweight off-axis three-mirror anastigmatic SiC visible telescope,” Proc. SPIE 2543, 180–184 (1995).

Gray, R. W.

Greenhouse, M.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Gressler, W.

J. Sebag, W. Gressler, T. Schmid, J. P. Rolland, and K. P. Thompson, “LSST Telescope Alignment Plan Based on Nodal Aberration Theory,” Publ. Astron. Soc. Pac. 124(914), 380–390 (2012).

Gu, Z.

Ha, K. Q.

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

Hadfield, P.

J. Robichaud, M. Anapol, L. Gardner, and P. Hadfield, “Ultralightweight off-axis three-mirror anastigmatic SiC visible telescope,” Proc. SPIE 2543, 180–184 (1995).

Hobbs, G.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Holota, W.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Howard, J. M.

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

J. M. Howard, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): III. Wavefront aberrations due to alignment and figure compensation,” Proc. SPIE 6675, 667503 (2007).

Huff, L. W.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Hutchings, J.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Jamieson, T. H.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Jiang, B.

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

Jiang, K.

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

Ju, G.

Kang, M. S.

Kim, E. D.

Kim, S.

Kim, S. W.

Krabbendam, V.

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

Lampton, M.

M. Lampton and M. Sholl, “Comparison of on-axis three-mirror-anastigmat telescopes,” Proc. SPIE 6687, 66870S (2007).

Lee, Y. W.

Liang, M.

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

Lightsey, P.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Ma, H.

Mei, C.

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

Morbey, C.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Mosier, G.

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

Muheim, D.

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

Murowinski, R.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Noethe, L.

R. N. Wilson, F. Franza, and L. Noethe, “Active optics: I. A system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).

Plate, M. T.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Rakich, A.

Rieke, M.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Robichaud, J.

J. Robichaud, M. Anapol, L. Gardner, and P. Hadfield, “Ultralightweight off-axis three-mirror anastigmatic SiC visible telescope,” Proc. SPIE 2543, 180–184 (1995).

Rolland, J. P.

Rowlands, N.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Schmid, T.

Sebag, J.

J. Sebag, W. Gressler, T. Schmid, J. P. Rolland, and K. P. Thompson, “LSST Telescope Alignment Plan Based on Nodal Aberration Theory,” Publ. Astron. Soc. Pac. 124(914), 380–390 (2012).

Shiri, R.

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

Sholl, M.

M. Lampton and M. Sholl, “Comparison of on-axis three-mirror-anastigmat telescopes,” Proc. SPIE 6687, 66870S (2007).

Smith, J. S.

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

Steakley, B.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Thompson, K.

Thompson, K. P.

Wang, Y.

Wells, M.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Williams, S. G. L.

S. G. L. Williams, “On-axis three-mirror anastigmat with an offset field of view,” Proc. SPIE 183, 212–217 (1979).

Wilson, R. N.

R. N. Wilson, F. Franza, and L. Noethe, “Active optics: I. A system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).

Wright, D. G.

P. Davila, B. Bos, J. Contreras, C. Evans, M. Greenhouse, G. Hobbs, W. Holota, L. W. Huff, J. Hutchings, T. H. Jamieson, P. Lightsey, C. Morbey, R. Murowinski, M. Rieke, N. Rowlands, B. Steakley, M. Wells, M. T. Plate, and D. G. Wright, “The James Webb Space Telescope science instrument suite: an overview of optical designs,” Proc. SPIE 5487, 611–627 (2004).

Xin, B.

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

Xu, S.

Yan, C.

Yang, H. S.

Zhang, D.

Zhang, X.

Zhou, S. Z.

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

Appl. Opt. (1)

J. Mod. Opt. (1)

R. N. Wilson, F. Franza, and L. Noethe, “Active optics: I. A system for optimizing the optical quality and reducing the costs of large telescopes,” J. Mod. Opt. 34(4), 485–509 (1987).

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

J. Opt. Soc. Korea (1)

Opt. Express (4)

Proc. SPIE (9)

B. Jiang, S. Z. Zhou, K. Jiang, H. Y. Fu, and C. Mei, “Alignment off-axis optical system using Nodal Aberration Theory,” Proc. SPIE 8910, 89100E (2013).

M. Liang, V. Krabbendam, C. F. Claver, S. Chandrasekharan, and B. Xin, “Active Optics in Large Synoptic Survey Telescope,” Proc. SPIE 8444, 84444Q (2012).

J. M. Howard, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): III. Wavefront aberrations due to alignment and figure compensation,” Proc. SPIE 6675, 667503 (2007).

J. M. Howard, K. Q. Ha, R. Shiri, J. S. Smith, G. Mosier, and D. Muheim, “Optical modeling activities for NASA’s James Webb Space Telescope (JWST): Part V. Operational alignment updates,” Proc. SPIE 7071, 70710X (2008).

S. G. L. Williams, “On-axis three-mirror anastigmat with an offset field of view,” Proc. SPIE 183, 212–217 (1979).

M. Lampton and M. Sholl, “Comparison of on-axis three-mirror-anastigmat telescopes,” Proc. SPIE 6687, 66870S (2007).

L. G. Cook, “Three-mirror anastigmat used of-axis in aperture and field,” Proc. SPIE 183, 207–211 (1979).

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Publ. Astron. Soc. Pac. (1)

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Other (3)

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Figures (13)

Fig. 1
Fig. 1 The optical layout of the selected TMA telescopes (a) the on-axis TMA telescope (b) the off-axis telescope.
Fig. 2
Fig. 2 FFDs of the Fringe Zernike coefficients for the nominal on-axis TMA telescope (a) C 5 / 6 (astigmatism) (average value = 0.0018λ) (b) C 7 / 8 (coma) (average value = 0.0017λ).
Fig. 3
Fig. 3 FFDs of the Fringe Zernike coefficients for the nominal off-axis TMA telescope (a) C 5 / 6 (astigmatism) (average value = 0.1183λ) (b) C 7 / 8 (coma) (average value = 0.0327λ).
Fig. 4
Fig. 4 FFDs of the Fringe Zernike coefficients C 5 / 6 for the on-axis TMA telescope after misalignment and compensation (a) misalignment (average value = 0.0034λ) (b) compensation (average value = 0.0018λ).
Fig. 5
Fig. 5 FFDs of the Fringe Zernike coefficients C 7 / 8 for the on-axis TMA telescope after misalignment and compensation (a) misalignment (average value = 0.0018λ) (b) compensation (average value = 0.0017λ).
Fig. 6
Fig. 6 FFDs of the Fringe Zernike coefficients C 5 / 6 for the off-axis TMA telescope after misalignment and compensation (a) misalignment (average value = 0.1290λ) (b) compensation (average value = 0.1183λ).
Fig. 7
Fig. 7 FFDs of the Fringe Zernike coefficients C 7 / 8 for the off-axis TMA telescope after misalignment and compensation (a) misalignment (average value = 0.0332λ) (b) compensation (average value = 0.0331λ).
Fig. 8
Fig. 8 FFDs of the astigmatic aberration field ( C 5 / 6 ) for the on-axis TMA telescope after deformation and compensation (a) deformation (average value = 0.1341λ) (b) compensation (average value = 0.0707λ).
Fig. 9
Fig. 9 FFDs of the astigmatic aberration field ( C 5 / 6 ) for the off-axis TMA telescope after deformation and compensation (a) deformation (average value = 0.1602λ) (b) compensation (average value = 0.1175λ).
Fig. 10
Fig. 10 Averaged values of astigmatism ( C 5 / 6 ) for the on-axis TMA telescope after misalignment and compensation for different cases based on NAT method. (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4. Note that the pink spots represent the averaged values of astigmatism after misalignment. The blue spots represent the averaged values of astigmatism after compensation.
Fig. 11
Fig. 11 Averaged values of astigmatism ( C 5 / 6 ) for the on-axis TMA telescope after misalignment and compensation for different cases based on STM method. (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4. Note that the pink spots represent the averaged values of astigmatism after misalignment. The blue spots represent the averaged values of astigmatism after compensation. The red spots represent the averaged values of astigmatism in the nominal design.
Fig. 12
Fig. 12 Averaged values of astigmatism ( C 5 / 6 ) for the off-axis TMA telescope after misalignment and compensation for different cases based on NAT method. (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4. Note that the pink spots represent the averaged values of astigmatism after misalignment. The blue spots represent the averaged values of astigmatism after compensation.
Fig. 13
Fig. 13 Averaged values of astigmatism ( C 5 / 6 ) for the off-axis TMA telescope after misalignment and compensation for different cases based on STM method. (a) Case 1 (b) Case 2 (c) Case 3 (d) Case 4. Note that the pink spots represent the averaged values of astigmatism after misalignment. The blue spots represent the averaged values of astigmatism after compensation. The red spots represent the averaged values of astigmatism in the nominal design.

Tables (11)

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Table 1 Optical prescription of the selected on-axis TMA telescope

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Table 2 Optical prescription of the selected off-axis TMA telescope

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Table 3 Wave aberration coefficients of SM and TM for the selected on-axis TMA telescope

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Table 4 Wave aberration coefficients of SM and TM for the selected off-axis TMA telescope

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Table 5 The introduced misalignments of TM for on-axis TMA telescope and off-axis TMA telescope

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Table 6 The calculated correction values of SM for adjusting the misaligned TM of on-axis TMA telescope and off-axis TMA telescope

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Table 7 The introduced astigmatic figure errors of PM for on-axis TMA telescope and off-axis TMA telescope

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Table 8 The calculated correction values of SM for adjusting the deformed PM of on-axis TMA telescope and off-axis TMA telescope

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Table 9 The calculated correction values of SM for the misaligned TM of on-axis TMA telescope and off-axis TMA telescope based on NAT method and MFR method and their relative errors

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Table 10 The calculated correction values of SM for the deformed PM of on-axis TMA telescope and off-axis TMA telescope based on NAT method and MFR method and their relative errors

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Table 11 The four different cases considered in the Monte-Carlo simulations

Equations (21)

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W = j p n m ( W k l m ) j [ ( H σ j ) ( H σ j ) ] p [ ρ ρ ] n [ ( H σ j ) ρ ] m , k = 2 p + m , l = 2 n + m
W = i [ k l m q f k l m q ( H x , H y ) A k l m q ( σ x , σ y ) ] i Z i ( ρ , φ ) ,
k l m q f k l m q ( H x , H y ) A k l m q ( σ x , σ y ) = C ( H x , H y ) ,
C ( H x , H y ) = f k l m 0 ( H x , H y ) A k l m 0 ( σ x , σ y ) + f k l m 1 ( H x , H y ) A k l m 1 ( σ x , σ y ) , + f k l m 2 ( H x , H y ) A k l m 2 ( σ x , σ y ) + e l s e
f k l m 1 ( H x , H y ) A k l m 1 ( σ x , σ y ) + f k l m 2 ( H x , H y ) A k l m 2 ( σ x , σ y ) = 0 ,
f k l m 1 ( H x , H y ) A k l m 1 ( σ x , σ y ) = 0.
A k l m 1 ( σ x , σ y ) = 0.
A k l m 1 ( σ x , σ y ) = { W k l m , S M ( s p h ) σ S M , x ( s p h ) + W k l m , S M ( a s p h ) σ S M , x ( a s p h ) + W k l m , T M ( s p h ) σ T M , x ( s p h ) + W k l m , T M ( a s p h ) σ T M , x ( a s p h ) W k l m , S M ( s p h ) σ S M , y ( s p h ) + W k l m , S M ( a s p h ) σ S M , y ( a s p h ) + W k l m , T M ( s p h ) σ T M , y ( s p h ) + W k l m , T M ( a s p h ) σ T M , y ( a s p h ) ,
{ σ T M , x s p h = F x + C σ S M , x s p h Q σ T M , y s p h = F y + C σ S M , y s p h Q { σ T M , x a s p h = E x + D σ S M , x s p h R σ T M , y a s p h = E y + D σ S M , y s p h R ,
{ Q = [ c T M ( d 2 d 1 ) + 2 c S M ( c T M d 1 d 2 + d 1 ) + 1 ] u ¯ P M R = [ d 2 + d 1 ( 2 c S M d 2 1 ) ] u ¯ P M C = 2 ( 1 + c T M d 2 ) ( 1 + c S M d 1 ) u ¯ P M D = 2 d 2 ( 1 + c S M d 1 ) u ¯ P M ,
{ E x = X D E T M F x = c T M X D E T M B D E T M E y = Y D E T M F y = c T M Y D E T M + A D E T M .
{ ( W k l m , S M ( s p h ) + C Q W k l m , T M ( s p h ) + D R W k l m , T M ( a s p h ) ) σ S M , x ( s p h ) + W k l m , S M ( a s p h ) σ S M , x ( a s p h ) + F x Q W k l m , T M ( s p h ) + E x R W k l m , T M ( a s p h ) = 0 ( W k l m , S M ( s p h ) + C Q W k l m , T M ( s p h ) + D R W k l m , T M ( a s p h ) ) σ S M , y ( s p h ) + W k l m , S M ( a s p h ) σ S M , y ( a s p h ) + F y Q W k l m , T M ( s p h ) + E y R W k l m , T M ( a s p h ) = 0 ,
[ W 222 , S M ( s p h ) + C Q W 222 , T M ( s p h ) + D R W 222 , T M ( a s p h ) W 222 , S M ( a s p h ) W 131 , S M ( s p h ) + C Q W 131 , T M ( s p h ) + D R W 131 , T M ( a s p h ) W 131 , S M ( a s p h ) ] [ σ S M , x ( s p h ) σ S M , x ( a s p h ) ] = [ F x Q W 222 , T M ( s p h ) + E x R W 222 , T M ( a s p h ) F x Q W 131 , T M ( s p h ) + E x R W 131 , T M ( a s p h ) ] ,
[ W 222 , S M ( s p h ) + C Q W 222 , T M ( s p h ) + D R W 222 , T M ( a s p h ) W 222 , S M ( a s p h ) W 131 , S M ( s p h ) + C Q W 131 , T M ( s p h ) + D R W 131 , T M ( a s p h ) W 131 , S M ( a s p h ) ] [ σ S M , y ( s p h ) σ S M , y ( a s p h ) ] = [ F y Q W 222 , T M ( s p h ) + E y R W 222 , T M ( a s p h ) F y Q W 131 , T M ( s p h ) + E y R W 131 , T M ( a s p h ) ] .
{ X D E S M = u ¯ P M d 1 σ S M , x ( a s p h ) Y D E S M = u ¯ P M d 1 σ S M , y ( a s p h ) A D E S M = u ¯ P M ( 1 + c S M d 1 ) σ S M , y ( s p h ) c S M Y D E S M B D E S M = u ¯ P M ( 1 + c S M d 1 ) σ S M , x ( s p h ) + c S M Y D E S M .
f 131 1 ( H x , H y ) A 131 1 ( σ x , σ y ) = 0 ,
f 222 1 ( H x , H y ) A 222 1 ( σ x , σ y ) + f 222 2 ( H x , H y ) A 222 2 ( σ x , σ y ) = 0 ,
[ H x H y H y H x ] [ A 222 , x 1 ( σ x , σ y ) A 222 , y 1 ( σ x , σ y ) ] = 2 B 2 [ C 5 , F i g P M C 6 , F i g P M ] .
[ W 222 , S M ( s p h ) + C Q W 222 , T M ( s p h ) + D R W 222 , T M ( a s p h ) W 222 , S M ( a s p h ) W 131 , S M ( s p h ) + C Q W 131 , T M ( s p h ) + D R W 131 , T M ( a s p h ) W 131 , S M ( a s p h ) ] [ σ S M , x ( s p h ) σ S M , x ( a s p h ) ] = [ A 222 , x 1 ( σ x , σ y ) 0 ] ,
[ W 222 , S M ( s p h ) + C Q W 222 , T M ( s p h ) + D R W 222 , T M ( a s p h ) W 222 , S M ( a s p h ) W 131 , S M ( s p h ) + C Q W 131 , T M ( s p h ) + D R W 131 , T M ( a s p h ) W 131 , S M ( a s p h ) ] [ σ S M , y ( s p h ) σ S M , y ( a s p h ) ] = [ A 222 , y 1 ( σ x , σ y ) 0 ] .
M F 2 = i W i ( V i T i ) 2 i W i ,

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