Abstract

A concept is described for the high-accuracy absolute calibration of the instrumental polarization introduced by the primary mirror of a large-aperture telescope. This procedure requires a small aperture with polarization-calibration optics (e.g., mounted on the dome) followed by a lens that opens the beam to illuminate the entire surface of the mirror. The Jones matrix corresponding to this calibration setup (with a diverging incident beam) is related to that of the normal observing setup (with a collimated incident beam) by an approximate correction term. Numerical models of parabolic on-axis and off-axis mirrors with surface imperfections are used to explore the accuracy of the procedure.

© 2005 Optical Society of America

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References

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  1. A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
    [CrossRef]
  2. J. Trujillo Bueno, F. Moreno-Insertis, F. Sánchez, eds., Astrophysical Spectropolarimetry, XII Canary Islands Winter School of Astrophysics (Cambridge U. Press, Cambridge, UK, 2002).
  3. C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
    [CrossRef]
  4. S. Keil, T. Rimmele, C. Keller , and The ATST Team, “Design and development of the Advanced Technology Solar Telescope,” Astron. Nachr. 324, 303–304 (2003).
    [CrossRef]
  5. A. Gandorfer, “The second solar spectrum in the ultraviolet,” in Solar Polarization Workshop 3, Vol. 307 of Astronomical Society of the Pacific Conference Series, J. Trujillo Bueno, J. Sánchez Almeida, eds. (Astronomical Society of the Pacific, San Francisco, Calif., 2003), pp. 399–406.
  6. H. Socas-Navarro, J. Trujillo Bueno, E. Landi Degl’Innocenti, “Signatures of incomplete Paschen-Back splitting in the polarization profiles of the He I λ 10830 multiplet,” Astrophys. J. 612, 1175–1180 (2004).
    [CrossRef]
  7. J. C. Kemp, J. H. Macek, F. W. Nehring, “Induced atomic orientation, an efficient mechanism for magnetic circular polarization,” Astrophys. J. 278, 863–873 (1984).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 5th ed. (Pergamon, Oxford, U.K., 1975).
  9. E. Landi Degl’Innocenti, “The Physics of Polarization,” in Astrophysical Spectropolarimetry, J. Trujillo Bueno, F. Moreno-Insertis, F. Sánchez, eds., XII Canary Islands Winter School of Astrophysics (Cambridge U. Press, Cambridge, UK, 2002), pp. 1–53.

2004 (1)

H. Socas-Navarro, J. Trujillo Bueno, E. Landi Degl’Innocenti, “Signatures of incomplete Paschen-Back splitting in the polarization profiles of the He I λ 10830 multiplet,” Astrophys. J. 612, 1175–1180 (2004).
[CrossRef]

2003 (1)

S. Keil, T. Rimmele, C. Keller , and The ATST Team, “Design and development of the Advanced Technology Solar Telescope,” Astron. Nachr. 324, 303–304 (2003).
[CrossRef]

2002 (1)

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

1997 (1)

A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
[CrossRef]

1984 (1)

J. C. Kemp, J. H. Macek, F. W. Nehring, “Induced atomic orientation, an efficient mechanism for magnetic circular polarization,” Astrophys. J. 278, 863–873 (1984).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 5th ed. (Pergamon, Oxford, U.K., 1975).

Gandorfer, A.

A. Gandorfer, “The second solar spectrum in the ultraviolet,” in Solar Polarization Workshop 3, Vol. 307 of Astronomical Society of the Pacific Conference Series, J. Trujillo Bueno, J. Sánchez Almeida, eds. (Astronomical Society of the Pacific, San Francisco, Calif., 2003), pp. 399–406.

Hill, F.

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

Keil, S.

S. Keil, T. Rimmele, C. Keller , and The ATST Team, “Design and development of the Advanced Technology Solar Telescope,” Astron. Nachr. 324, 303–304 (2003).
[CrossRef]

Keil, S. L.

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

Keller, C.

S. Keil, T. Rimmele, C. Keller , and The ATST Team, “Design and development of the Advanced Technology Solar Telescope,” Astron. Nachr. 324, 303–304 (2003).
[CrossRef]

Keller, C. U.

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

Kemp, J. C.

J. C. Kemp, J. H. Macek, F. W. Nehring, “Induced atomic orientation, an efficient mechanism for magnetic circular polarization,” Astrophys. J. 278, 863–873 (1984).
[CrossRef]

Landi Degl’Innocenti, E.

H. Socas-Navarro, J. Trujillo Bueno, E. Landi Degl’Innocenti, “Signatures of incomplete Paschen-Back splitting in the polarization profiles of the He I λ 10830 multiplet,” Astrophys. J. 612, 1175–1180 (2004).
[CrossRef]

E. Landi Degl’Innocenti, “The Physics of Polarization,” in Astrophysical Spectropolarimetry, J. Trujillo Bueno, F. Moreno-Insertis, F. Sánchez, eds., XII Canary Islands Winter School of Astrophysics (Cambridge U. Press, Cambridge, UK, 2002), pp. 1–53.

Lites, B. W.

A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
[CrossRef]

Macek, J. H.

J. C. Kemp, J. H. Macek, F. W. Nehring, “Induced atomic orientation, an efficient mechanism for magnetic circular polarization,” Astrophys. J. 278, 863–873 (1984).
[CrossRef]

Marti´nez Pillet, V.

A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
[CrossRef]

Nehring, F. W.

J. C. Kemp, J. H. Macek, F. W. Nehring, “Induced atomic orientation, an efficient mechanism for magnetic circular polarization,” Astrophys. J. 278, 863–873 (1984).
[CrossRef]

Oschmann, J. M.

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

Rimmele, T.

S. Keil, T. Rimmele, C. Keller , and The ATST Team, “Design and development of the Advanced Technology Solar Telescope,” Astron. Nachr. 324, 303–304 (2003).
[CrossRef]

Rimmele, T. R.

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

Seagraves, P.

A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
[CrossRef]

Skumanich, A.

A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
[CrossRef]

Socas-Navarro, H.

H. Socas-Navarro, J. Trujillo Bueno, E. Landi Degl’Innocenti, “Signatures of incomplete Paschen-Back splitting in the polarization profiles of the He I λ 10830 multiplet,” Astrophys. J. 612, 1175–1180 (2004).
[CrossRef]

Trujillo Bueno, J.

H. Socas-Navarro, J. Trujillo Bueno, E. Landi Degl’Innocenti, “Signatures of incomplete Paschen-Back splitting in the polarization profiles of the He I λ 10830 multiplet,” Astrophys. J. 612, 1175–1180 (2004).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 5th ed. (Pergamon, Oxford, U.K., 1975).

Astron. Nachr. (2)

C. U. Keller, T. R. Rimmele, F. Hill, S. L. Keil, J. M. Oschmann, and the ATST Team, “The Advanced Technology Solar Telescope,” Astron. Nachr. 323, 294–298 (2002).
[CrossRef]

S. Keil, T. Rimmele, C. Keller , and The ATST Team, “Design and development of the Advanced Technology Solar Telescope,” Astron. Nachr. 324, 303–304 (2003).
[CrossRef]

Astrophys. J. (2)

H. Socas-Navarro, J. Trujillo Bueno, E. Landi Degl’Innocenti, “Signatures of incomplete Paschen-Back splitting in the polarization profiles of the He I λ 10830 multiplet,” Astrophys. J. 612, 1175–1180 (2004).
[CrossRef]

J. C. Kemp, J. H. Macek, F. W. Nehring, “Induced atomic orientation, an efficient mechanism for magnetic circular polarization,” Astrophys. J. 278, 863–873 (1984).
[CrossRef]

Astrophys. J. Suppl. (1)

A. Skumanich, B. W. Lites, V. Martı́nez Pillet, P. Seagraves, “The calibration of the advanced Stokes polarimeter,” Astrophys. J. Suppl. 110, 357 (1997).
[CrossRef]

Other (4)

J. Trujillo Bueno, F. Moreno-Insertis, F. Sánchez, eds., Astrophysical Spectropolarimetry, XII Canary Islands Winter School of Astrophysics (Cambridge U. Press, Cambridge, UK, 2002).

A. Gandorfer, “The second solar spectrum in the ultraviolet,” in Solar Polarization Workshop 3, Vol. 307 of Astronomical Society of the Pacific Conference Series, J. Trujillo Bueno, J. Sánchez Almeida, eds. (Astronomical Society of the Pacific, San Francisco, Calif., 2003), pp. 399–406.

M. Born, E. Wolf, Principles of Optics. Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 5th ed. (Pergamon, Oxford, U.K., 1975).

E. Landi Degl’Innocenti, “The Physics of Polarization,” in Astrophysical Spectropolarimetry, J. Trujillo Bueno, F. Moreno-Insertis, F. Sánchez, eds., XII Canary Islands Winter School of Astrophysics (Cambridge U. Press, Cambridge, UK, 2002), pp. 1–53.

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Figures (3)

Fig. 1
Fig. 1

Left: normal observing configuration (OS) with a collimated incident beam. Right: calibration configuration (CS) with an inclined (diverging) incident beam.

Fig. 2
Fig. 2

Incidence angles θ and α for the OS (solid lines) and CS (dashed lines), respectively. The dotted line represents the normal to the mirror surface.

Fig. 3
Fig. 3

Schematic representation of the equivalent on-axis mirror. Left, lateral view: The thick line represents the actual off-axis mirror of radius r max and the thin line represents the equivalent on-axis mirror. Right, overhead view: The shaded area is the actual off-axis mirror.

Tables (3)

Tables Icon

Table 1 Simulation of a 4-m On-Axis Mirror

Tables Icon

Table 2 Simulation of a 4-m Off-Axis Mirror

Tables Icon

Table 3 Simulation of a 4-m Off-Axis Mirror with Surface Irregularities

Equations (23)

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M ps = r p 0 0 r s .
r p = ( N 2 - sin 2   θ ) 1 / 2 - N 2 cos θ ( N 2 - sin 2   θ ) 1 / 2 + N 2 cos θ ,
r s = cos θ - ( N 2 - sin 2   θ ) 1 / 2 cos θ + ( N 2 - sin 2   θ ) 1 / 2 ,
M ( ρ ,   ϕ ) = R ( - ϕ ) M ps R ( ϕ ) ,
M ( ρ ,   ϕ ) = r p   cos 2   ϕ + r s   sin 2   ϕ ( r p + r s ) sin ϕ cos ϕ ( r p + r s ) sin ϕ cos ϕ r p   sin 2   ϕ + r s   cos 2   ϕ .
tan θ = ρ / 2 F .
M ( ρ ) = ρ 0 2 π M ( ρ ,   ϕ ) d ϕ = ρ π ( r s + r p ) 0 0 ( r s + r p ) .
r p ( θ CS ) = r p ( θ OS - α ) = r p ( θ OS ) - α   d r p d θ θ OS + α 2 2 d 2 r p d θ 2 θ OS + ,
M OS ( ρ ,   ϕ ) M CS ( ρ ,   ϕ ) - α d 1 , p   cos 2   ϕ + d 1 , s   sin 2   ϕ ( d 1 , p + d 1 , s ) sin ϕ cos ϕ ( d 1 , p + d 1 , s ) sin ϕ cos ϕ d 1 , p   sin 2   ϕ + d 1 , s   cos 2   ϕ + α 2 2   d 2 , p   cos 2   ϕ + d 2 , s   sin 2   ϕ ( d 2 , p + d 2 , s ) sin ϕ cos ϕ ( d 2 , p + d 2 , s ) sin ϕ cos ϕ d 2 , p   sin 2   ϕ + d 2 , s   cos 2   ϕ + ,
d i , p = d i r p d θ i θ OS ,
d i , p = d ˆ i , p + δ d i , p ,
M OS = 0 2 π 0 ρ max ρ M OS ( ρ ,   θ ) d ρ d ϕ = M CS + Δ M + δ M ,
Δ M ( ρ ,   θ ) = - α d ˆ 1 , p   cos 2   ϕ + d ˆ 1 , s   sin 2   ϕ ( d ˆ 1 , p + d ˆ 1 , s ) sin ϕ cos ϕ ( d ˆ 1 , p + d ˆ 1 , s ) sin ϕ cos ϕ d ˆ 1 , p   sin 2   ϕ + d ˆ 1 , s   cos 2   ϕ + α 2 2   d ˆ 2 , p   cos 2   ϕ + d ˆ 2 , s   sin 2   ϕ ( d ˆ 2 , p + d ˆ 2 , s ) sin ϕ cos ϕ ( d ˆ 2 , p + d ˆ 2 , s ) sin ϕ cos ϕ d ˆ 2 , p   sin 2   ϕ + d ˆ 2 , s   cos 2   ϕ + .
M OS = - 0.94 exp ( 0.64 i ) 1 + 0.00 - 0.06 exp ( 1.72 i ) - 0.06 exp ( 1.72 i ) 4.20 × 10 - 5 exp ( 0.40 i ) ,
M CS = M OS + 1.56 × 10 - 5 exp ( 0.78 i ) 1.00 - 0.07 exp ( 0.28 i ) - 0.07 exp ( 0.28 i ) - 0.76 exp ( 0.67 i ) .
M OS = - 0.97 exp ( 0.59 i ) × 1 + 0.00 0.00 0.00 - 3.51 × 10 - 2 exp ( 1.61 i ) ,
M CS = M OS + 1.24 × 10 - 2 exp ( 2.22 i ) × 1.00 0.00 0.00 0.95 exp ( 3.11 i ) .
M CS + Δ M = M OS + 2.22 × 10 - 4 exp ( 2.65 i ) × 1.00 0.00 0.00 0.43 exp ( 0.44 i ) .
M OS = 0.89 - 3.42 × 10 - 5 1.65 × 10 - 2 - 2.19 × 10 - 6 - 3.42 × 10 - 5 0.88 5.49 × 10 - 7 0.11 1.65 × 10 - 2 5.49 × 10 - 7 0.89 - 1.45 × 10 - 5 2.19 × 10 - 6 - 0.11 1.45 × 10 - 5 0.88 .
M CS = M OS + 2.23 × 10 - 5 × 0.30 1.00 - 6.77 × 10 - 2 6.42 × 10 - 2 1.00 0.30 - 1.80 × 10 - 2 5.45 × 10 - 2 - 6.77 × 10 - 2 - 1.80 × 10 - 2 0.30 0.45 - 6.42 × 10 - 2 - 5.45 × 10 - 2 - 0.45 0.30 .
M OS = 0.94 - 1.93 × 10 - 3 2.29 × 10 - 7 0.00 - 1.93 × 10 - 3 0.94 0.00 0.00 2.29 × 10 - 7 0.00 0.94 3.29 × 10 - 2 0.00 0.00 - 3.29 × 10 - 2 0.94 .
M CS = M OS + 2.34 × 10 - 2 × 6.92 × 10 - 3 5.85 × 10 - 2 0.00 0.00 5.85 × 10 - 2 6.92 × 10 - 3 0.00 0.00 0.00 0.00 2.96 × 10 - 2 - 1.00 0.00 0.00 1.00 2.96 × 10 - 2 .
M CS + Δ M = M OS + 1.82 × 10 - 4 × - 0.97 - 0.13 - 1.78 × 10 - 5 0.00 - 0.13 - 0.97 0.00 1.13 × 10 - 5 - 1.78 × 10 - 5 0.00 - 1.00 0.72 0.00 - 1.13 × 10 - 5 - 0.72 - 1.00 .

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