Abstract

It is well known that derotator is commonly used to compensate for image rotation in astronomical telescopes. The classical derotator, consisting of three mirrors, is named K-mirror. The main disadvantage of the K-mirror is that it has high instrumental polarization, causing a larger polarization measurement error in polarimetry. In the paper, we proposed a new design of the derotator based on the Mueller matrix transformation theory of mirrors in polarized light. The new designed derotator contains five mirrors and is called five-mirror derotator. It has a very small instrumental polarization, overcoming the shortcomings of the classical K-mirror. A novel method is applied to compensate for the beam shift induced by the thickness of the reflector. From the result of numerical polarization analysis, it is showed that the five-mirror derotator has a significant advantage for the telescopes with a small field of view, especially in polarimetry at longer wavelengths.

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

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References

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  1. G. H. Sanders, “The Thirty Meter Telescope (TMT): An International Observatory,” J. Astrophys. Astr. 34(2), 81–86 (2013).
    [Crossref]
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    [Crossref]
  3. M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
    [Crossref]
  4. S. X. Tao, W. Ma, and L. Z. Qian, “Rotation-canceling real time system of color video image,” Proc. SPIE 6279, 627959 (2007).
    [Crossref]
  5. Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).
  6. D. S. L. Durie, “A compact derotator design,” Opt. Eng. 13(1), 19–22 (1973).
  7. H. Z. Sar-EI, “Revised Dove prism formulas,” Appl Opt. 30(4), 375–376 (1991).
    [Crossref]
  8. M. Padgett and J. Paullesso, “Dove prisms and polarized light,” Mod. Opt. 46(2), 175–179 (1999).
    [Crossref]
  9. Z. C. Wang, Y. Z. Zhao, and C. Zhou, “Design of K Mirror for Alt-az Telescope,” Acta Photonica Sinica 41(7), 762–765 (2012).
    [Crossref]
  10. S. C. West, “Polarimetry with multiple mirror telescopes,” Proc. SPIE 628, 50–59 (1986).
    [Crossref]
  11. M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).
  12. D. Goldstein and D. H. Goldstein, Polarized Light, Revised and Expanded (Lasers Optics & Photonics, 2003).
    [Crossref]
  13. J. S. Almeida, V. M. Pillet, and A. D. Wittmann, “The instrumental polarization of a Gregory-Coude telescope,” Solar Phys. 134(1), 1–13 (1991).
    [Crossref]
  14. J. Polasek, “Matrix Analysis of Gimbaled Mirror and Prism System,” J. Opt. Soc. Am. 57(10), 1193–1201 (1967).
    [Crossref]
  15. J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
    [Crossref]

2014 (1)

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

2013 (2)

G. H. Sanders, “The Thirty Meter Telescope (TMT): An International Observatory,” J. Astrophys. Astr. 34(2), 81–86 (2013).
[Crossref]

M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
[Crossref]

2012 (2)

Z. C. Wang, Y. Z. Zhao, and C. Zhou, “Design of K Mirror for Alt-az Telescope,” Acta Photonica Sinica 41(7), 762–765 (2012).
[Crossref]

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

2007 (1)

S. X. Tao, W. Ma, and L. Z. Qian, “Rotation-canceling real time system of color video image,” Proc. SPIE 6279, 627959 (2007).
[Crossref]

2004 (1)

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

1999 (1)

M. Padgett and J. Paullesso, “Dove prisms and polarized light,” Mod. Opt. 46(2), 175–179 (1999).
[Crossref]

1991 (2)

H. Z. Sar-EI, “Revised Dove prism formulas,” Appl Opt. 30(4), 375–376 (1991).
[Crossref]

J. S. Almeida, V. M. Pillet, and A. D. Wittmann, “The instrumental polarization of a Gregory-Coude telescope,” Solar Phys. 134(1), 1–13 (1991).
[Crossref]

1986 (1)

S. C. West, “Polarimetry with multiple mirror telescopes,” Proc. SPIE 628, 50–59 (1986).
[Crossref]

1973 (1)

D. S. L. Durie, “A compact derotator design,” Opt. Eng. 13(1), 19–22 (1973).

1967 (1)

Almeida, J. S.

J. S. Almeida, V. M. Pillet, and A. D. Wittmann, “The instrumental polarization of a Gregory-Coude telescope,” Solar Phys. 134(1), 1–13 (1991).
[Crossref]

Angelb, R.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Bao, M. X.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Berger, T.

M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
[Crossref]

Bernsteind, R.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

Borrero, J. M.

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

Card, G. L.

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

Chen, L. F.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Durie, D. S. L.

D. S. L. Durie, “A compact derotator design,” Opt. Eng. 13(1), 19–22 (1973).

Elmore, D.

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

Fabricantc, D.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Feng, H. R.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Goldstein, D.

D. Goldstein and D. H. Goldstein, Polarized Light, Revised and Expanded (Lasers Optics & Photonics, 2003).
[Crossref]

Goldstein, D. H.

D. Goldstein and D. H. Goldstein, Polarized Light, Revised and Expanded (Lasers Optics & Photonics, 2003).
[Crossref]

Gu, B. Z.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Jin, Z. Y.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Johnsa, M.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Li, Z.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Liu, G. Q.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Liu, Z.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Lou, K.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Lu, R. W.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Ma, W.

S. X. Tao, W. Ma, and L. Z. Qian, “Rotation-canceling real time system of color video image,” Proc. SPIE 6279, 627959 (2007).
[Crossref]

McCarthya, P.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Mcmullin, J.

M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
[Crossref]

Norton, A. A.

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

Padgett, M.

M. Padgett and J. Paullesso, “Dove prisms and polarized light,” Mod. Opt. 46(2), 175–179 (1999).
[Crossref]

Paullesso, J.

M. Padgett and J. Paullesso, “Dove prisms and polarized light,” Mod. Opt. 46(2), 175–179 (1999).
[Crossref]

Phillips, M.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Pillet, V. M.

J. S. Almeida, V. M. Pillet, and A. D. Wittmann, “The instrumental polarization of a Gregory-Coude telescope,” Solar Phys. 134(1), 1–13 (1991).
[Crossref]

Polasek, J.

Qian, L. Z.

S. X. Tao, W. Ma, and L. Z. Qian, “Rotation-canceling real time system of color video image,” Proc. SPIE 6279, 627959 (2007).
[Crossref]

Qian, Q.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Rao, C. H.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Rimmele, T.

M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
[Crossref]

Sanders, G. H.

G. H. Sanders, “The Thirty Meter Telescope (TMT): An International Observatory,” J. Astrophys. Astr. 34(2), 81–86 (2013).
[Crossref]

Sar-EI, H. Z.

H. Z. Sar-EI, “Revised Dove prism formulas,” Appl Opt. 30(4), 375–376 (1991).
[Crossref]

Schou, J.

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

Shectmana, S.

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

Shen, L. X.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Tao, S. X.

S. X. Tao, W. Ma, and L. Z. Qian, “Rotation-canceling real time system of color video image,” Proc. SPIE 6279, 627959 (2007).
[Crossref]

Tomczyk, S.

J. Schou, J. M. Borrero, A. A. Norton, S. Tomczyk, D. Elmore, and G. L. Card, “Polarization Calibration of the Helioseismic and Magnetic Imager (HMI) onborad the Solar Dynamics Observatory (SDO),” Solar Physics 275(1–2), 327–355 (2012).
[Crossref]

Wang, F. F.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Wang, S.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Wang, Z. C.

Z. C. Wang, Y. Z. Zhao, and C. Zhou, “Design of K Mirror for Alt-az Telescope,” Acta Photonica Sinica 41(7), 762–765 (2012).
[Crossref]

Warner, M.

M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
[Crossref]

Wen, L. H.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

West, S. C.

S. C. West, “Polarimetry with multiple mirror telescopes,” Proc. SPIE 628, 50–59 (1986).
[Crossref]

Wittmann, A. D.

J. S. Almeida, V. M. Pillet, and A. D. Wittmann, “The instrumental polarization of a Gregory-Coude telescope,” Solar Phys. 134(1), 1–13 (1991).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1965).

Wu, M. C.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Xu, J.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Xu, Z.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

You, J. Q.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Zhang, B. R.

Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

Zhao, Y. Z.

Z. C. Wang, Y. Z. Zhao, and C. Zhou, “Design of K Mirror for Alt-az Telescope,” Acta Photonica Sinica 41(7), 762–765 (2012).
[Crossref]

Zhou, C.

Z. C. Wang, Y. Z. Zhao, and C. Zhou, “Design of K Mirror for Alt-az Telescope,” Acta Photonica Sinica 41(7), 762–765 (2012).
[Crossref]

Acta Photonica Sinica (1)

Z. C. Wang, Y. Z. Zhao, and C. Zhou, “Design of K Mirror for Alt-az Telescope,” Acta Photonica Sinica 41(7), 762–765 (2012).
[Crossref]

Appl Opt. (1)

H. Z. Sar-EI, “Revised Dove prism formulas,” Appl Opt. 30(4), 375–376 (1991).
[Crossref]

J. Astrophys. Astr. (1)

G. H. Sanders, “The Thirty Meter Telescope (TMT): An International Observatory,” J. Astrophys. Astr. 34(2), 81–86 (2013).
[Crossref]

J. Opt. Soc. Am. (1)

Mod. Opt. (1)

M. Padgett and J. Paullesso, “Dove prisms and polarized light,” Mod. Opt. 46(2), 175–179 (1999).
[Crossref]

Opt. Eng. (1)

D. S. L. Durie, “A compact derotator design,” Opt. Eng. 13(1), 19–22 (1973).

Proc. SPIE (4)

M. Johnsa, R. Angelb, S. Shectmana, R. Bernsteind, D. Fabricantc, P. McCarthya, and M. Phillips, “Status of the Giant Magellan Telescope (GMT) Project,” Proc. SPIE 5489, 441–453 (2004).
[Crossref]

M. Warner, J. Mcmullin, T. Rimmele, and T. Berger, “The Advanced Technology Solar Telescope (ATST) project: a construction update,” Proc. SPIE 8862, 88620D (2013).
[Crossref]

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[Crossref]

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Z. Liu, J. Xu, B. Z. Gu, S. Wang, J. Q. You, L. X. Shen, R. W. Lu, Z. Y. Jin, L. F. Chen, K. Lou, Z. Li, G. Q. Liu, Z. Xu, C. H. Rao, Q. Qian, H. R. Feng, L. H. Wen, F. F. Wang, M. X. Bao, M. C. Wu, and B. R. Zhang, “New vacuum solar telescope and observations with high resolution,” RAA 14(6), 705–718 (2014).

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[Crossref]

Solar Physics (1)

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Figures (7)

Fig. 1
Fig. 1 Simplified diagram of a five-mirror derotator.
Fig. 2
Fig. 2 Relationship of Mueller matrix of five-mirror derotator with the incident angle θ1. x axis is the incident angle θ1 in degree, y axis is each element of Mueller matrix. The blue, green and red lines represent the optimized results in wavelengths 0.525um, 1.083um and 12um respectively.
Fig. 3
Fig. 3 Beam shift and compensation in the five-mirror derotator. The red line indicates a beam shift due to the thickness of the reflector composed of M1 and M5, and the blue dotted line shows the beam shift compensation after a rotation and a translation of M3 and M4.
Fig. 4
Fig. 4 ZEMAX simulation for compensation effect. (a) and (b) are the simulation results without and with beam shift compensation respectively.
Fig. 5
Fig. 5 The contour map of error matrix ΔM at λ = 0.525um. the horizontal coordinate is the field of view (FOV) in degrees, the vertical coordinate is the rotation angle β in degrees, and the colorized subgraph displays variations of each element of ΔM with FOV and β (see colorbar).
Fig. 6
Fig. 6 The contour map of error matrix ΔM at λ = 1.083um, the same as Fig. 5.
Fig. 7
Fig. 7 The contour map of error matrix ΔM at λ = 12um, the same as Fig. 5.

Tables (1)

Tables Icon

Table 1 Linear relationships between FOV and β in different wavelengths.

Equations (37)

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S out = M i S in = R ( ϕ ) M i 0 R ( ϕ ) S in
R ( ϕ ) = [ 1 0 0 0 0 cos 2 ϕ sin 2 ϕ 0 0 sin 2 ϕ cos 2 ϕ 0 0 0 0 1 ]
M i 0 = [ 1 X 2 1 X 2 + 1 0 0 X 2 1 X 2 + 1 1 0 0 0 0 2 X X 2 + 1 cos δ 2 X X 2 + 1 sin δ 0 0 2 X X 2 + 1 sin δ 2 X X 2 + 1 cos δ ]
r s = cos θ i n ˜ 2 sin 2 θ i cos θ i + n ˜ 2 sin 2 θ i
r p = n ˜ 2 cos θ i n ˜ 2 sin 2 θ i n ˜ 2 cos θ i + n ˜ 2 sin 2 θ i
X = | r s | | r p |
δ = arctan ( Imag ( r s ) Real ( r s ) ) arctan ( Imag ( r p ) Real ( r p ) )
M = M m M 2 M 1 = R ( ϕ m ) M m 0 R ( ϕ m ) R ( ϕ 2 ) M 2 0 R ( ϕ 2 ) R ( ϕ 1 ) M 1 0 R ( ϕ 1 )
M = M 2 M 1 = R ( π / 2 ) M 1 0 R ( π / 2 ) M 1 0 = 4 X 2 ( X 2 + 1 ) 2 I
M = M 5 M 4 M 3 M 2 M 1 = R ( ϕ 5 ) M 5 0 R ( ϕ 5 ϕ 4 ) M 4 0 R ( ϕ 4 ϕ 3 ) M 3 0 R ( ϕ 3 ϕ 2 ) M 2 0 R ( ϕ 2 ϕ 1 ) M 1 0 R ( ϕ 1 )
M = M 5 0 R ( π / 2 ) M 4 0 M 3 0 M 2 0 R ( π / 2 ) M 1 0
R = Rot z ( α ) T Rot z ( α ) A
Rot z ( α ) = [ cos α sin α 0 sin α cos α 0 0 0 1 ]
T = T 5 T 4 T 3 T 2 T 1
T i = [ 1 2 N i x 2 2 N i x N i y 2 N i x N i z 2 N i x N i y 1 2 N i y 2 2 N i y N i z 2 N i x N i z 2 N i y N i z 1 2 N i z 2 ] , i = 1 5
N 1 = ( 0 sin θ 1 cos θ 1 ) = N 5
N 2 = Rot x ( 90 ° 2 θ 1 ) ( sin 30 ° cos 30 ° 0 ) = ( sin 30 ° sin 2 θ 1 cos 30 ° cos 2 θ 1 cos 30 ° )
N 3 = Rot x ( 90 ° 2 θ 1 ) ( 1 0 0 ) = ( 1 0 0 )
N 4 = Rot x ( 90 ° 2 θ 1 ) ( sin 30 ° cos 30 ° 0 ) = ( sin 30 ° sin 2 θ 1 cos 30 ° cos 2 θ 1 cos 30 ° )
Rot x ( 90 ° 2 θ 1 ) = [ 1 0 0 0 cos ( 90 ° 2 θ 1 ) sin ( 90 ° 2 θ 1 ) 0 sin ( 90 ° 2 θ 1 ) cos ( 90 ° 2 θ 1 ) ]
T = [ 1 0 0 0 1 0 0 0 1 ]
F = Rot z ( α ) T Rot z ( α ) Rot z ( α 0 ) A 0 = [ cos ( 2 α α 0 ) sin ( 2 α α 0 ) 0 sin ( 2 α α 0 ) cos ( 2 α α 0 ) 0 0 0 1 ] ( A x 0 A y 0 A z 0 )
d = ( b / 2 cos β b / 2 ) tan 60 °
β = arcsin ( h sin 2 θ 1 b cos θ 1 cos 30 ° )
N 4 = Rot x ( 90 ° 2 θ 1 ) Rot y ( β ) ( sin 30 ° cos 30 ° 0 )
Rot y ( β ) = [ cos β 0 sin β 0 1 0 sin β 0 cos β ]
C = Rot x ( 90 ° 2 θ 1 ) ( sin 60 ° cos 60 ° 0 ) , D = Rot x ( 90 ° 2 θ 1 ) Rot y ( β ) ( sin 60 ° cos 60 ° 0 )
N 3 = D C | D C |
θ i = π arccos ( V i i N i | V i i | | N i | )
ϕ i = arccos ( N Π i N Π 1 | N Π i | | N Π 1 | )
N Π i = V i i × N i
V i o = V i i 2 V i i N i | V i i | N i |
V i + 1 i = V i o
Δ M < [ 0.001 0.01 0.01 0.01 0.001 0.01 0.01 0.01 0.001 0.01 0.01 0.01 0.001 0.01 0.01 0.01 ]
Δ M K mirror 0.525 u m = [ 0.0053 0.1357 0 0 0.1357 0.0053 0 0 0 0 0.4565 0.5348 0 0 0.8348 0.4565 ]
Δ M K mirror 1.083 u m = [ 0.0018 0.0782 0 0 0.0782 0.0018 0 0 0 0 0.1830 0.5745 0 0 0.5745 0.1830 ]
Δ M K mirror 12.00 u m = [ 0.0001 0.0207 0 0 0.0207 0.0001 0 0 0 0 0.0040 0.0878 0 0 0.0878 0.0040 ]

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