Abstract

The principles of a polarizing atmospheric Michelson interferometer are outlined. The tilt of its reflection mirror results in deflection of the reflected beam and affects the intensities of the observed inteferogram. This effect is systematically analyzed. Both rectangular and circular apertures are considered. The theoretical expression of the modulation depth and phase of the interferogram are derived. These parameters vary with the inclination angle of the mirror and the distance between the deflection center and the optical axis and significantly influence the retrieved temperature and wind speed. If the wind and temperature errors are required to be less than 3m/s and 5 K, the deflection angle must be less than 0.5°. The errors are also dependent on the shape of aperture. If the reflection mirror is deflected in one direction, the temperature error is smaller for a circular aperture (1.3 K) than for a rectangular one (2.6 K), but the wind velocity errors are almost the same (less than 3m/s). If the deflection center and incident light beam are coincident, the temperature errors are 3×104K and 0.45 K for circular and rectangular apertures, respectively. The wind velocity errors are 1.2×103m/s and 0.06m/s. Both are small. The result would be helpful for theoretical research and development of the static polarization wind imaging interferometer.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (2)

2010 (5)

C. Zhang and X. Jian, “Wide-spectrum reconstruction method for a birefringence interference imaging spectrometer,” Opt. Lett. 35, 366–368 (2010).
[CrossRef]

H. Zhu, C. Zhang, and X. Jian, “A wide field wind image interferometer with chromatic and thermal compensation,” Acta Phys. Sin. 59, 893–898 (2010) (in Chinese).

C. Zhang and L. Zhu, “Influence of the polarization direction on the modulation depth and interferential intensity of a new polarizing atmospheric Michelson interferometer,” Acta Phys. Sin. 59, 989–997 (2010) (in Chinese).

J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study on the rule of light transmission through the four-sided pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin. 59, 1631–1637 (2010) (in Chinese).

Q. Yang, “Moving corner-cube mirror interferometer and reflection characteristic of corner-cube mirror,” Appl. Opt. 49, 4088–4095 (2010).
[CrossRef]

2009 (1)

Q. Yang, R. Zhou, and B. Zhao, “Tilt tolerance of the moving mirror in Michelson interferometric spectrometer,” Acta Photon. Sin. 38, 677–680 (2009) (in Chinese).

2008 (1)

2006 (3)

C. Zhang, B. Zhao, B. Xiangli, and Y. Li, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

C. Zhang and J. He, “The generalization of upper atmospheric wind and temperature based on the Voigt line shape profile,” Opt. Express 14, 12561–12567 (2006).
[CrossRef]

C. Zhang, B. Zhao, and B. Xiangli, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

2004 (1)

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

2003 (1)

W. A. Gault, I. C. McDade, Y. J. Rochon, and A. Scott, “Filters and calibration for the SWIFT instrument on GCOM-A1,” Proc. SPIE 4881, 60–66 (2003).
[CrossRef]

2001 (3)

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

W. A. Gault, S. I. Sargoytchev, and S. Brown, “Divided mirror technique for measuring Doppler shifts with a Michelson interferometer,” Proc. SPIE 4306, 266 (2001).
[CrossRef]

W. E. Ward, W. A. Gault, G. G. Shepherd, and N. Rowlands, “The waves Michelson interferometer: a visible/near-IR interferometer for observing middle atmosphere dynamics and constituents,” Proc. SPIE 4540, 100–111 (2001).
[CrossRef]

1998 (1)

1997 (1)

B. Xiang, J. Yang, Z. Gao, and G. Liu, “On the tolerance of the mirror tilting in Fourier transform interferometer,” Acta Photon. Sin. 26, 132–135 (1997) (in Chinese).

1996 (1)

1995 (1)

J. C. Bird, F. Liang, B. H. Solheim, and G. G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6, 1368–1378 (1995).
[CrossRef]

1993 (1)

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

1985 (1)

Alunni, J. M.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy(Academic, 1972), Chapter 1.

Bird, J. C.

J. C. Bird, F. Liang, B. H. Solheim, and G. G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6, 1368–1378 (1995).
[CrossRef]

Brown, S.

W. A. Gault, S. I. Sargoytchev, and S. Brown, “Divided mirror technique for measuring Doppler shifts with a Michelson interferometer,” Proc. SPIE 4306, 266 (2001).
[CrossRef]

W. A. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. G. Shepherd, and J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
[CrossRef]

Brun, J. F.

Brun, J.-F.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Brune, S.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Buttner, G.

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

Charlot, P.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Cogger, L. L.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Desaulniers, D.-L.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Evans, W. F. J.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Gao, Z.

B. Xiang, J. Yang, Z. Gao, and G. Liu, “On the tolerance of the mirror tilting in Fourier transform interferometer,” Acta Photon. Sin. 26, 132–135 (1997) (in Chinese).

Gattinger, R. L.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Gault, W.

Gault, W. A.

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

W. A. Gault, I. C. McDade, Y. J. Rochon, and A. Scott, “Filters and calibration for the SWIFT instrument on GCOM-A1,” Proc. SPIE 4881, 60–66 (2003).
[CrossRef]

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

W. A. Gault, S. I. Sargoytchev, and S. Brown, “Divided mirror technique for measuring Doppler shifts with a Michelson interferometer,” Proc. SPIE 4306, 266 (2001).
[CrossRef]

W. E. Ward, W. A. Gault, G. G. Shepherd, and N. Rowlands, “The waves Michelson interferometer: a visible/near-IR interferometer for observing middle atmosphere dynamics and constituents,” Proc. SPIE 4540, 100–111 (2001).
[CrossRef]

W. A. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. G. Shepherd, and J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
[CrossRef]

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. W. Kendall, and J. R. Wimperis, “WAMDII, wide-angle Michelson Doppler image interferometer for space-lab,” Appl. Opt. 24, 1571–1584 (1985).
[CrossRef]

Girod, F.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Harvie, D.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Haslett, J. W.

He, J.

Herse, M.

Hersom, C.

Hum, R. H.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Jian, X.

C. Zhang and X. Jian, “Wide-spectrum reconstruction method for a birefringence interference imaging spectrometer,” Opt. Lett. 35, 366–368 (2010).
[CrossRef]

H. Zhu, C. Zhang, and X. Jian, “A wide field wind image interferometer with chromatic and thermal compensation,” Acta Phys. Sin. 59, 893–898 (2010) (in Chinese).

Johnston, S. F.

Kendall, D. J. W.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. W. Kendall, and J. R. Wimperis, “WAMDII, wide-angle Michelson Doppler image interferometer for space-lab,” Appl. Opt. 24, 1571–1584 (1985).
[CrossRef]

Kosteniuk, P. R.

Li, Y.

C. Zhang, B. Zhao, B. Xiangli, and Y. Li, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

Liang, D.

Liang, F.

J. C. Bird, F. Liang, B. H. Solheim, and G. G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6, 1368–1378 (1995).
[CrossRef]

Liu, G.

B. Xiang, J. Yang, Z. Gao, and G. Liu, “On the tolerance of the mirror tilting in Fourier transform interferometer,” Acta Photon. Sin. 26, 132–135 (1997) (in Chinese).

Liu, N.

J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study on the rule of light transmission through the four-sided pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin. 59, 1631–1637 (2010) (in Chinese).

Llewellyn, E. J.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Lowe, R. P.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Lukovich, J. V.

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

McDade, I. C.

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

W. A. Gault, I. C. McDade, Y. J. Rochon, and A. Scott, “Filters and calibration for the SWIFT instrument on GCOM-A1,” Proc. SPIE 4881, 60–66 (2003).
[CrossRef]

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

Miller, D. W.

Moise, A.

Mu, T.

Ohrt, J.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Pasternak, F.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Pasturczyk, Z.

Peillet, O.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Powell, I.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Rahnama, P.

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

Rochon, Y.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Rochon, Y. J.

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

W. A. Gault, I. C. McDade, Y. J. Rochon, and A. Scott, “Filters and calibration for the SWIFT instrument on GCOM-A1,” Proc. SPIE 4881, 60–66 (2003).
[CrossRef]

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

Rowlands, N.

W. E. Ward, W. A. Gault, G. G. Shepherd, and N. Rowlands, “The waves Michelson interferometer: a visible/near-IR interferometer for observing middle atmosphere dynamics and constituents,” Proc. SPIE 4540, 100–111 (2001).
[CrossRef]

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

Sargoytchev, S. I.

W. A. Gault, S. I. Sargoytchev, and S. Brown, “Divided mirror technique for measuring Doppler shifts with a Michelson interferometer,” Proc. SPIE 4306, 266 (2001).
[CrossRef]

Scott, A.

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

W. A. Gault, I. C. McDade, Y. J. Rochon, and A. Scott, “Filters and calibration for the SWIFT instrument on GCOM-A1,” Proc. SPIE 4881, 60–66 (2003).
[CrossRef]

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

Sellar, G.

Shepherd, G. G.

W. E. Ward, W. A. Gault, G. G. Shepherd, and N. Rowlands, “The waves Michelson interferometer: a visible/near-IR interferometer for observing middle atmosphere dynamics and constituents,” Proc. SPIE 4540, 100–111 (2001).
[CrossRef]

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

W. A. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. G. Shepherd, and J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
[CrossRef]

J. C. Bird, F. Liang, B. H. Solheim, and G. G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6, 1368–1378 (1995).
[CrossRef]

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

G. G. Shepherd, W. A. Gault, D. W. Miller, Z. Pasturczyk, S. F. Johnston, P. R. Kosteniuk, J. W. Haslett, D. J. W. Kendall, and J. R. Wimperis, “WAMDII, wide-angle Michelson Doppler image interferometer for space-lab,” Appl. Opt. 24, 1571–1584 (1985).
[CrossRef]

Solheim, B. H.

J. C. Bird, F. Liang, B. H. Solheim, and G. G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6, 1368–1378 (1995).
[CrossRef]

Thuillier, G.

G. Thuillier, W. Gault, J. F. Brun, M. Herse, W. Ward, and C. Hersom, “In-flight calibration of the wind imaging interferometer (WINDII) on board the upper atmosphere research satellite,” Appl. Opt. 37, 1356–1369 (1998).
[CrossRef]

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Wang, J.

J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study on the rule of light transmission through the four-sided pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin. 59, 1631–1637 (2010) (in Chinese).

Ward, W.

Ward, W. E.

W. E. Ward, W. A. Gault, G. G. Shepherd, and N. Rowlands, “The waves Michelson interferometer: a visible/near-IR interferometer for observing middle atmosphere dynamics and constituents,” Proc. SPIE 4540, 100–111 (2001).
[CrossRef]

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Wiens, R. H.

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Wimperis, J.

W. A. Gault, S. Brown, A. Moise, D. Liang, G. Sellar, G. G. Shepherd, and J. Wimperis, “ERWIN: an E-region wind interferometer,” Appl. Opt. 35, 2913–2922 (1996).
[CrossRef]

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Wimperis, J. R.

Wu, Q.

Xiang, B.

B. Xiang, J. Yang, Z. Gao, and G. Liu, “On the tolerance of the mirror tilting in Fourier transform interferometer,” Acta Photon. Sin. 26, 132–135 (1997) (in Chinese).

Xiangli, B.

C. Zhang, B. Zhao, B. Xiangli, and Y. Li, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

C. Zhang, B. Zhao, and B. Xiangli, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

Yang, J.

B. Xiang, J. Yang, Z. Gao, and G. Liu, “On the tolerance of the mirror tilting in Fourier transform interferometer,” Acta Photon. Sin. 26, 132–135 (1997) (in Chinese).

Yang, Q.

Zhang, C.

C. Zhang, Q. Wu, and T. Mu, “Influences of pyramid prism deflection on inversion of wind velocity and temperature in a novel static polarization wind imaging interferometer,” Appl. Opt. 50, 6134–6139 (2011).
[CrossRef]

C. Zhang, H. Zhu, and B. Zhao, “The tempo-spatially modulated polarization atmosphere Michelson interferometer,” Opt. Express 19, 9626–9635 (2011).
[CrossRef]

C. Zhang and X. Jian, “Wide-spectrum reconstruction method for a birefringence interference imaging spectrometer,” Opt. Lett. 35, 366–368 (2010).
[CrossRef]

J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study on the rule of light transmission through the four-sided pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin. 59, 1631–1637 (2010) (in Chinese).

H. Zhu, C. Zhang, and X. Jian, “A wide field wind image interferometer with chromatic and thermal compensation,” Acta Phys. Sin. 59, 893–898 (2010) (in Chinese).

C. Zhang and L. Zhu, “Influence of the polarization direction on the modulation depth and interferential intensity of a new polarizing atmospheric Michelson interferometer,” Acta Phys. Sin. 59, 989–997 (2010) (in Chinese).

C. Zhang and J. He, “The generalization of upper atmospheric wind and temperature based on the Voigt line shape profile,” Opt. Express 14, 12561–12567 (2006).
[CrossRef]

C. Zhang, B. Zhao, and B. Xiangli, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

C. Zhang, B. Zhao, B. Xiangli, and Y. Li, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

Zhao, B.

C. Zhang, H. Zhu, and B. Zhao, “The tempo-spatially modulated polarization atmosphere Michelson interferometer,” Opt. Express 19, 9626–9635 (2011).
[CrossRef]

J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study on the rule of light transmission through the four-sided pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin. 59, 1631–1637 (2010) (in Chinese).

Q. Yang, R. Zhou, and B. Zhao, “Tilt tolerance of the moving mirror in Michelson interferometric spectrometer,” Acta Photon. Sin. 38, 677–680 (2009) (in Chinese).

Q. Yang, R. Zhou, and B. Zhao, “Principle of the moving-mirror-pair interferometer and the tilt tolerance of the double moving mirror,” Appl. Opt. 47, 2486–2493 (2008).
[CrossRef]

C. Zhang, B. Zhao, B. Xiangli, and Y. Li, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

C. Zhang, B. Zhao, and B. Xiangli, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

Zhou, R.

Q. Yang, R. Zhou, and B. Zhao, “Tilt tolerance of the moving mirror in Michelson interferometric spectrometer,” Acta Photon. Sin. 38, 677–680 (2009) (in Chinese).

Q. Yang, R. Zhou, and B. Zhao, “Principle of the moving-mirror-pair interferometer and the tilt tolerance of the double moving mirror,” Appl. Opt. 47, 2486–2493 (2008).
[CrossRef]

Zhu, H.

C. Zhang, H. Zhu, and B. Zhao, “The tempo-spatially modulated polarization atmosphere Michelson interferometer,” Opt. Express 19, 9626–9635 (2011).
[CrossRef]

H. Zhu, C. Zhang, and X. Jian, “A wide field wind image interferometer with chromatic and thermal compensation,” Acta Phys. Sin. 59, 893–898 (2010) (in Chinese).

Zhu, L.

C. Zhang and L. Zhu, “Influence of the polarization direction on the modulation depth and interferential intensity of a new polarizing atmospheric Michelson interferometer,” Acta Phys. Sin. 59, 989–997 (2010) (in Chinese).

Acta Photon. Sin. (2)

Q. Yang, R. Zhou, and B. Zhao, “Tilt tolerance of the moving mirror in Michelson interferometric spectrometer,” Acta Photon. Sin. 38, 677–680 (2009) (in Chinese).

B. Xiang, J. Yang, Z. Gao, and G. Liu, “On the tolerance of the mirror tilting in Fourier transform interferometer,” Acta Photon. Sin. 26, 132–135 (1997) (in Chinese).

Acta Phys. Sin. (3)

H. Zhu, C. Zhang, and X. Jian, “A wide field wind image interferometer with chromatic and thermal compensation,” Acta Phys. Sin. 59, 893–898 (2010) (in Chinese).

C. Zhang and L. Zhu, “Influence of the polarization direction on the modulation depth and interferential intensity of a new polarizing atmospheric Michelson interferometer,” Acta Phys. Sin. 59, 989–997 (2010) (in Chinese).

J. Wang, C. Zhang, B. Zhao, and N. Liu, “Study on the rule of light transmission through the four-sided pyramid prism in the static polarization wind imaging interferometer,” Acta Phys. Sin. 59, 1631–1637 (2010) (in Chinese).

Adv. Space Res. (1)

G. G. Shepherd, I. C. McDade, W. A. Gault, Y. J. Rochon, A. Scott, N. Rowlands, and G. Buttner, “The Stratospheric Wind Interferometer For Transport studies (SWIFT),” Adv. Space Res. 4881, 1344–1346 (2001).
[CrossRef]

Appl. Opt. (6)

J. Geophys. Res. (1)

G. G. Shepherd, G. Thuillier, W. A. Gault, J. M. Alunni, J.-F. Brun, S. Brune, P. Charlot, L. L. Cogger, D.-L. Desaulniers, W. F. J. Evans, R. L. Gattinger, F. Girod, D. Harvie, R. H. Hum, D. J. W. Kendall, E. J. Llewellyn, R. P. Lowe, J. Ohrt, F. Pasternak, O. Peillet, I. Powell, Y. Rochon, W. E. Ward, R. H. Wiens, and J. Wimperis, “WINDII, the wind imaging interferometer on the upper atmosphere research satellite,” J. Geophys. Res. 98, 10725–10750 (1993).
[CrossRef]

Meas. Sci. Technol. (1)

J. C. Bird, F. Liang, B. H. Solheim, and G. G. Shepherd, “A polarizing Michelson interferometer for measuring thermospheric winds,” Meas. Sci. Technol. 6, 1368–1378 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Optik (2)

C. Zhang, B. Zhao, and B. Xiangli, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

C. Zhang, B. Zhao, B. Xiangli, and Y. Li, “Interference image spectroscopy for upper atmospheric wind field measurement,” Optik 117, 265–270 (2006).
[CrossRef]

Proc. SPIE (4)

W. A. Gault, S. I. Sargoytchev, and S. Brown, “Divided mirror technique for measuring Doppler shifts with a Michelson interferometer,” Proc. SPIE 4306, 266 (2001).
[CrossRef]

Y. J. Rochon, P. Rahnama, I. C. McDade, A. Scott, W. A. Gault, and J. V. Lukovich, “Data retrieval and error analysis study on the measurement of stratospheric winds with a Michelson interferometer,” Proc. SPIE 5234, 335–346 (2004).
[CrossRef]

W. A. Gault, I. C. McDade, Y. J. Rochon, and A. Scott, “Filters and calibration for the SWIFT instrument on GCOM-A1,” Proc. SPIE 4881, 60–66 (2003).
[CrossRef]

W. E. Ward, W. A. Gault, G. G. Shepherd, and N. Rowlands, “The waves Michelson interferometer: a visible/near-IR interferometer for observing middle atmosphere dynamics and constituents,” Proc. SPIE 4540, 100–111 (2001).
[CrossRef]

Other (1)

R. J. Bell, Introductory Fourier Transform Spectroscopy(Academic, 1972), Chapter 1.

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Figures (11)

Fig. 1.
Fig. 1.

Schematic diagram of NSPWII. There is minimal reflection loss from the input port (past that of the first linear polarizer) due to the multiple passes through the 1/4 wave plates.

Fig. 2.
Fig. 2.

Optical figure of NSPWII, when flat mirror tilted. C is the inclination center, θ is the deflection angle of the mirror with respect to the x axis, and d is the distance between the inclination center and y axis. α is the deflection angle of the mirror with respect to the y axis and d is the distance between inclination center C and y axis. (For convenience, we omit the two 1/4 wave plates.)

Fig. 3.
Fig. 3.

Equivalent light path of NSPWII for the mirror tilted on the x axis. θ is the deflection angle of the mirror, d is the distance between the inclination center and y axis, and θ2 and θ3 are the reflective angles. l1, l2 and l3 are the length of refracted light (for convenience, we omit the two 1/4 wave plates).

Fig. 4.
Fig. 4.

Schematic diagram of deflecting light in beam splitter.

Fig. 5.
Fig. 5.

Schematic diagram of deflecting light intensity integral for rectangular beam. The deflected beam is moved by h and by h along the x and y directions.

Fig. 6.
Fig. 6.

Deflecting light intensity integral schematic of circular beam. The deflected beam is moved by h and by h along the x and y directions.

Fig. 7.
Fig. 7.

Optical intensity map on the CCD with λ=630mm. (a) ideal case, (b) deflection angle is θ=2°, the distance between the inclination center and the central beam of an incident light are d=5mm and d=5mm.

Fig. 8.
Fig. 8.

Variations of the retrieved temperature error with the deflection angle when the mirror is deflected in the x direction: (a) rectangular incident light and (b) circular incident light.

Fig. 9.
Fig. 9.

Variations of the retrieved temperature error with the deflection angle when the deflection center O and incident light center O coincident: (a) rectangular incident light and (b) circular incident light.

Fig. 10.
Fig. 10.

Variations of the retrieved wind velocity error with deflection angle and the distance between deflection center and the optical axis when the mirror is deflected in the x-direction: (a) rectangular incident light and (b) circular incident light.

Fig. 11.
Fig. 11.

The variations of the retrieved wind velocity error with deflection angle and the distance between deflection center and the optical axis when the deflection center O and incident light center O are coincident: (a) rectangular incident light and (b) circular incident light.

Equations (37)

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

I(Δ)=I0[1+Vcos(2πΔσ0+2πΔσ0vc+2ϑ)],
I(Δ)=I0[1+Vcos(φ+2ϑ)].
I1=I0(1+Vcosφ)
I2=I0(1Vsinφ)
I3=I0(1Vcosφ)
I4=I0(1+Vsinφ).
I0=(I1+I3)/2=(I2+I4)/2
V=[(I1I3)2+(I2I4)2]1/2/2I0
tanφ=(I4I2)/(I1I3).
Δcx=n0l1+n2l2+n1l3+n1(h1+h2+h3)(12n1d1+n2d2+n0d0).
Δδx=FD¯+ED¯=FD¯(1+1cos2θ)=(xd)tan2θ,
h=h1+h2+h3,
sin45°l3=sin(180°45°θ3)12d1h1h2,h3=l3sinθ3.
sinθ2=n0n2sin2θ,
sinθ3=n0n1sin2θ.
Δcy=n0l1+n2l2+n1l3+n1(h1+h2+h3)(12n1d1+n2d2+n0d0).
Δδy=(yd)tan2α,
h=h1+h2+h3,
sin45°l3=sin(180°45°α3)12d1h1h2,
h3=l3sinα3,
sinα2=n0n2sin2α,
sinα3=n0n1sin2α.
Δc=Δcx+Δcy=n0l1+n2l2+n1l3+n1(h1+h2+h3)+n0l1+n2l2+n1l3+n1(h1+h2+h3)(n1d1+2n2d2+2n0d0).
Δδ=Δδx+Δδy=(xd)tan2θ+(yd)tan2α.
I(Δ)=1SS1B(σ){1+cos(Δ0+Δc+Δδ)}·dS1+1SS2B(σ)dS2.
Δδ=(xdh)tan2θ+(ydh)tan2α.
I(Δ)=1SEFGHS1B(σ){1+cos[Δ0+Δc+(xdh)tan2θ+(ydh)tan2α]}·dS1+1SEFGHS2B(σ)dS2
I(Δ)=I{1+1D2π2σ2tan2θtan2α·sin[πσ(Dh)tan2θ]·sin[πσ(Dh)tan2α]·cos[2πσ·(Δ0+Δc(d+h2)tan2θ(d+h2)tan2α)]}.
V=1D2π2σ2tan2θtan2α·sin[πσ(Dh)tan2θ]·sin[πσ(Dh)tan2α]
φ=2πσ·[Δ0+Δc(d+h2)tan2θ(d+h2)tan2α].
I(Δ)=1SSB(σ){1+cos(Δ0+Δc+Δδ)}·dS.
Δδ=(Rcosφdh)tan2θ+(Rsinφdh)tan2α.
I(Δ)=I{1{(πcosCBJ1(B)+CπsinC4[6B2J0(B)+2B212B3J1(B)])+tanA·(πsinCBJ1(B)CπcosC4[6B2J0(B)+2B212B3J1(B)])}·cos[2πσ(Δ0+Δc(d+h)tan2θ(d+h)tan2α)]},
V=tanA·(πsinCBJ1(B)CπcosC4[6B2J0(B)+2B212B3J1(B)])(πcosCBJ1(B)+CπsinC4[6B2J0(B)+2B212B3J1(B)])
φ=2πσ(Δ0+Δc(d+h)tan2θ(d+h)tan2α).
I(Δ)=I{1+1Dπσtan2θ·sin[πσ(Dh)tan2θ]·cos[2πσ·(Δ0+Δc(d+h2)tan2θ)]}.
I(Δ)=I{1+(2πJ0(2πσRtan2θ)J1(2πσRtan2θ)πσRtan2θ)cos[2πσ(Δ0+Δc(d+h)tan2θ)]}.

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