Abstract

Basic fan or folded arrangements comprising three identical retarders in cascade between parallel or crossed polarizers are presented for constructing birefringent spectral filters without an internal polarizer. The retarders' axes are oriented with an angle increment of θ or θ preferably with |θ|34.27° such that their orientation angles are, respectively, equal to 45°θ, 45°, and 45°+θ for the fan arrangement, or 45°+θ, 45°+2θ, and 45°+θ for the folded arrangement. A filter in the fan or folded arrangement has the bandwidth of its principal transmission peaks or the amplitude of the sidelobes adjustable by changing the angle increment |θ|. For |θ|=25.91°, the filter exactly produces the transmission spectrum of a standard Lyot two-stage filter. Further, the filter can have the spectral transmission be electrically tunable or switchable, depending on the retarders selected for use. The retarders can be birefringent plates, liquid-crystal variable retarders, or liquid-crystal electrically rotatable retarders. Test measurements and results are presented and discussed.

© 2006 Optical Society of America

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  3. D. Bonaccini and F. Stauffer, "High resolution solar bidimensional spectroscopy with a universal birefringent filter in tandem with a Fabry-Perot interferometer: tests and experimental results," Astron. Astrophys. 229, 272-278 (1990).
  4. C. Bendlin, R. Volkmer, and F. Kneer, "A new instrument for high resolution, two-dimensional solar spectroscopy," Astron. Astrophys. 257, 817-823 (1992).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2006 (1)

2001 (1)

R. Lansford, G. Bearman, and S. E. Fraser, "Resolution of multiple green fluorescent protein color variant and dyes using two-photon microscopy and imaging spectroscopy," J. Biomed. Opt. 6, 311-318 (2001).
[CrossRef] [PubMed]

2000 (1)

G. D. Sharp and K. M. Johnson, "Split-element liquid crystal tunable optical filters," U.S. patent 6,091,462 (18 July 2000).

1998 (1)

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

1997 (3)

G. D. Sharp, S. E. Gilman, and K. M. Johnson, "Progress in field-sequential color shutter technology," in Projection Displays III, M. H. Wu, ed., Proc. SPIE 3013, 107-111 (1997).

S. S. M. Rees, J. Staromlynska, M. P. Gillyon, and J. R. Davy, "Final design and testing of the laser airborne depth sounder filter," Opt. Eng. 36, 1204-1213 (1997).
[CrossRef]

Y. Deng, G. Ai, and J. Wang, "Inhomogeneous distribution of brightness in the split-element filter," Appl. Opt. 36, 1576-1579 (1997).
[CrossRef] [PubMed]

1996 (1)

H. Wright, C. M. Crandall, and P. Miller, "Active filters enable color imaging," Laser Focus World 32(5), 85-90 (1996).

1995 (1)

L. J. November and L. M. Wilkins, "Liquid crystal polarimeter: a solid state imager for solar vector magnetic fields," Opt. Eng. 34, 1659-1668 (1995).
[CrossRef]

1994 (2)

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

H. R. Morris, C. C. Hoyt, and P. J. Treado, "Imaging spectrometers for fluorescence and raman microscopy: acousto-optic and liquid crystal tunable filters," Appl. Spectrosc. 48, 857-866 (1994).
[CrossRef]

1992 (1)

C. Bendlin, R. Volkmer, and F. Kneer, "A new instrument for high resolution, two-dimensional solar spectroscopy," Astron. Astrophys. 257, 817-823 (1992).

1990 (1)

D. Bonaccini and F. Stauffer, "High resolution solar bidimensional spectroscopy with a universal birefringent filter in tandem with a Fabry-Perot interferometer: tests and experimental results," Astron. Astrophys. 229, 272-278 (1990).

1985 (1)

A. Dollfus, F. Colson, D. Crussaire, and F. Launary, "A monochromator for solar quantitative imagery: the instrument FPSS," Astron. Astrophys. 151, 235-253 (1985).

1981 (1)

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

1973 (1)

1965 (1)

1955 (1)

B. Lyot, "Slitless spectrophotometer," U.S. patent 2,718,170 (20 September 1955).

1949 (1)

1933 (1)

B. Lyot, "Optical apparatus with wide field using interference of polarized light," C. R Acad. Sci. (Paris) 197, 1593 (1933).

Ai, G.

Balasubramaniam, K. S.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Bearman, G.

R. Lansford, G. Bearman, and S. E. Fraser, "Resolution of multiple green fluorescent protein color variant and dyes using two-photon microscopy and imaging spectroscopy," J. Biomed. Opt. 6, 311-318 (2001).
[CrossRef] [PubMed]

Bendlin, C.

C. Bendlin, R. Volkmer, and F. Kneer, "A new instrument for high resolution, two-dimensional solar spectroscopy," Astron. Astrophys. 257, 817-823 (1992).

Bertello, L.

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

Bonaccini, D.

D. Bonaccini and F. Stauffer, "High resolution solar bidimensional spectroscopy with a universal birefringent filter in tandem with a Fabry-Perot interferometer: tests and experimental results," Astron. Astrophys. 229, 272-278 (1990).

Cavallini, F.

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

Ceppatelli, G.

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

Colson, F.

A. Dollfus, F. Colson, D. Crussaire, and F. Launary, "A monochromator for solar quantitative imagery: the instrument FPSS," Astron. Astrophys. 151, 235-253 (1985).

Confer, M.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Coulter, R.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Craig, D.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Crandall, C. M.

H. Wright, C. M. Crandall, and P. Miller, "Active filters enable color imaging," Laser Focus World 32(5), 85-90 (1996).

Crussaire, D.

A. Dollfus, F. Colson, D. Crussaire, and F. Launary, "A monochromator for solar quantitative imagery: the instrument FPSS," Astron. Astrophys. 151, 235-253 (1985).

Davy, J. R.

S. S. M. Rees, J. Staromlynska, M. P. Gillyon, and J. R. Davy, "Final design and testing of the laser airborne depth sounder filter," Opt. Eng. 36, 1204-1213 (1997).
[CrossRef]

Deng, Y.

Dollfus, A.

A. Dollfus, F. Colson, D. Crussaire, and F. Launary, "A monochromator for solar quantitative imagery: the instrument FPSS," Astron. Astrophys. 151, 235-253 (1985).

Dunn, R.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Evans, J. W.

Fraser, S. E.

R. Lansford, G. Bearman, and S. E. Fraser, "Resolution of multiple green fluorescent protein color variant and dyes using two-photon microscopy and imaging spectroscopy," J. Biomed. Opt. 6, 311-318 (2001).
[CrossRef] [PubMed]

Gillyon, M. P.

S. S. M. Rees, J. Staromlynska, M. P. Gillyon, and J. R. Davy, "Final design and testing of the laser airborne depth sounder filter," Opt. Eng. 36, 1204-1213 (1997).
[CrossRef]

Gilman, S. E.

G. D. Sharp, S. E. Gilman, and K. M. Johnson, "Progress in field-sequential color shutter technology," in Projection Displays III, M. H. Wu, ed., Proc. SPIE 3013, 107-111 (1997).

Gregory, S.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Gullixson, C.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Haas, B.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Henry, T.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Hoyt, C. C.

Hull, W.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Johnson, K. M.

G. D. Sharp and K. M. Johnson, "Split-element liquid crystal tunable optical filters," U.S. patent 6,091,462 (18 July 2000).

G. D. Sharp, S. E. Gilman, and K. M. Johnson, "Progress in field-sequential color shutter technology," in Projection Displays III, M. H. Wu, ed., Proc. SPIE 3013, 107-111 (1997).

Jones, H.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Kaufman, M.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Keller, C.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Kimura, T.

Kneer, F.

C. Bendlin, R. Volkmer, and F. Kneer, "A new instrument for high resolution, two-dimensional solar spectroscopy," Astron. Astrophys. 257, 817-823 (1992).

Lansford, R.

R. Lansford, G. Bearman, and S. E. Fraser, "Resolution of multiple green fluorescent protein color variant and dyes using two-photon microscopy and imaging spectroscopy," J. Biomed. Opt. 6, 311-318 (2001).
[CrossRef] [PubMed]

Launary, F.

A. Dollfus, F. Colson, D. Crussaire, and F. Launary, "A monochromator for solar quantitative imagery: the instrument FPSS," Astron. Astrophys. 151, 235-253 (1985).

Lyot, B.

B. Lyot, "Slitless spectrophotometer," U.S. patent 2,718,170 (20 September 1955).

B. Lyot, "Optical apparatus with wide field using interference of polarized light," C. R Acad. Sci. (Paris) 197, 1593 (1933).

McGraw, R.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Miller, P.

H. Wright, C. M. Crandall, and P. Miller, "Active filters enable color imaging," Laser Focus World 32(5), 85-90 (1996).

Morris, H. R.

Neidig, D.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

November, L. J.

L. J. November and L. M. Wilkins, "Liquid crystal polarimeter: a solid state imager for solar vector magnetic fields," Opt. Eng. 34, 1659-1668 (1995).
[CrossRef]

Otsuka, K.

Rees, S. S. M.

S. S. M. Rees, J. Staromlynska, M. P. Gillyon, and J. R. Davy, "Final design and testing of the laser airborne depth sounder filter," Opt. Eng. 36, 1204-1213 (1997).
[CrossRef]

Rentschler, R.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Righini, A.

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

Rosenberg, W. J.

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

Salucci, G.

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

Saruwatari, M.

Schimming, R.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Sharp, G. D.

G. D. Sharp and K. M. Johnson, "Split-element liquid crystal tunable optical filters," U.S. patent 6,091,462 (18 July 2000).

G. D. Sharp, S. E. Gilman, and K. M. Johnson, "Progress in field-sequential color shutter technology," in Projection Displays III, M. H. Wu, ed., Proc. SPIE 3013, 107-111 (1997).

Smaga, B.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Solc, I.

Staromlynska, J.

S. S. M. Rees, J. Staromlynska, M. P. Gillyon, and J. R. Davy, "Final design and testing of the laser airborne depth sounder filter," Opt. Eng. 36, 1204-1213 (1997).
[CrossRef]

Stauffer, F.

D. Bonaccini and F. Stauffer, "High resolution solar bidimensional spectroscopy with a universal birefringent filter in tandem with a Fabry-Perot interferometer: tests and experimental results," Astron. Astrophys. 229, 272-278 (1990).

Title, A. M.

A. M. Title and W. J. Rosenberg, "Tunable birefringent filters," Opt. Eng. 20, 815-823 (1981).

Treado, P. J.

Volkmer, R.

C. Bendlin, R. Volkmer, and F. Kneer, "A new instrument for high resolution, two-dimensional solar spectroscopy," Astron. Astrophys. 257, 817-823 (1992).

Wang, J.

Wiborg, P.

D. Neidig, P. Wiborg, M. Confer, B. Haas, R. Dunn, K. S. Balasubramaniam, C. Gullixson, D. Craig, M. Kaufman, W. Hull, R. McGraw, T. Henry, R. Rentschler, C. Keller, H. Jones, R. Coulter, S. Gregory, R. Schimming, and B. Smaga, "The USAF improved solar observing optical network (ISOON) and its impact on solar synoptic data bases," Synoptic Solar Phys. 140, 519-528 (1998).

Wilkins, L. M.

L. J. November and L. M. Wilkins, "Liquid crystal polarimeter: a solid state imager for solar vector magnetic fields," Opt. Eng. 34, 1659-1668 (1995).
[CrossRef]

Wright, H.

H. Wright, C. M. Crandall, and P. Miller, "Active filters enable color imaging," Laser Focus World 32(5), 85-90 (1996).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals, Propagation and Control of Laser Radiation (Wiley, 1984), Chap. 5, pp. 121-154.

Ye, C.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals, Propagation and Control of Laser Radiation (Wiley, 1984), Chap. 5, pp. 121-154.

Appl. Opt. (3)

Appl. Spectrosc. (1)

Astron. Astrophys. (4)

A. Dollfus, F. Colson, D. Crussaire, and F. Launary, "A monochromator for solar quantitative imagery: the instrument FPSS," Astron. Astrophys. 151, 235-253 (1985).

D. Bonaccini and F. Stauffer, "High resolution solar bidimensional spectroscopy with a universal birefringent filter in tandem with a Fabry-Perot interferometer: tests and experimental results," Astron. Astrophys. 229, 272-278 (1990).

C. Bendlin, R. Volkmer, and F. Kneer, "A new instrument for high resolution, two-dimensional solar spectroscopy," Astron. Astrophys. 257, 817-823 (1992).

G. Salucci, L. Bertello, F. Cavallini, G. Ceppatelli, and A. Righini, "The height dependence if intensity and velocity structure in the solar photosphere," Astron. Astrophys. 285, 322-332 (1994).

C. R Acad. Sci. (Paris) (1)

B. Lyot, "Optical apparatus with wide field using interference of polarized light," C. R Acad. Sci. (Paris) 197, 1593 (1933).

J. Biomed. Opt. (1)

R. Lansford, G. Bearman, and S. E. Fraser, "Resolution of multiple green fluorescent protein color variant and dyes using two-photon microscopy and imaging spectroscopy," J. Biomed. Opt. 6, 311-318 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

Laser Focus World (1)

H. Wright, C. M. Crandall, and P. Miller, "Active filters enable color imaging," Laser Focus World 32(5), 85-90 (1996).

Opt. Eng. (3)

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[CrossRef]

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[CrossRef]

Synoptic Solar Phys. (1)

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Figures (6)

Fig. 1
Fig. 1

Schematic of (a) the fan and (b) the folded arrangements of three identical retarders or birefringent plates arranged in series between a pair of polarizers for constructing spectral filters: pl1, pl2, linear polarizers; rt1, rt2, rt3, optical retarders.

Fig. 2
Fig. 2

Calculated transmission profiles (a) T c ( λ ) and (b) T s ( λ ) of spectral filters comprising three quartz plates in accordance with the fan and folded arrangements of Figs. 1(a) and 1(b) for tuning angles | θ | = 34.27 ° , | θ | = 30 ° , | θ | = 25.91 ° , and | θ | = 22 ° versus wavelength λ.

Fig. 3
Fig. 3

Measured transmission profiles T c ( λ ) and T s ( λ ) of spectral filters of three quartz plates constructed according to the fan and the folded arrangements of Figs. 1(a) and 1(b) for tuning angles of (a), (c) | θ | = 26 ° and (b), (d) | θ | = 32 ° versus wavelength λ.

Fig. 4
Fig. 4

Measured overall spectral transmission t low   loss ( λ ) of the constituent elements of the low-loss filter assemblies in Fig. 3 versus wavelength λ, in comparison with the overall transmissions t HN38S ( λ ) , t FPG003 ( λ ) , and t 069 - 1105 ( λ ) of the elements of an equivalent Lyot two-stage filter with different polarizers as the internal polarizers (see text).

Fig. 5
Fig. 5

Measured transmission profiles T c ( λ ) of an electrically wavelength-tunable spectral filter comprising three identical NLC retarders constructed according to the fan arrangement of Fig. 1(a) versus wavelength λ as a function of the tuning voltage such that the NLC retarders have their retardation equal to (a) 360° at λ = 480   nm and λ = 632   nm and (b) λ = 550   nm and λ = 690   nm .

Fig. 6
Fig. 6

Measured transmission profiles T s ( λ ) of an electrically wavelength-tunable spectral filter comprising three identical NLC retarders constructed according to the folded arrangement of Fig. 1(b) versus wavelength λ as a function of the tuning voltage such that the NLC retarders have their retardation equal to (a) 360° at λ = 480   nm and λ = 632   nm and (b) λ = 550   nm and λ = 690   nm .

Equations (13)

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T c ( λ ) = cos 2 Δ ( λ ) 2 { 1 cos 2 θ ( 1 + cos 2 θ ) × [ 1 cos Δ ( λ ) ] } 2 ,
T s ( λ ) = sin 2 Δ ( λ ) 2 { 1 cos 2 θ ( 1 + cos 2 θ ) × [ 1 + cos Δ ( λ ) ] } 2 .
T c ( λ ) = cos 6 Δ ( λ ) 2 ,
T s ( λ ) = sin 6 Δ ( λ ) 2 .
T c ( λ ) = cos 2 Δ ( λ ) 2 cos 2 Δ ( λ ) ,
T s ( λ ) = sin 2 Δ ( λ ) 2 cos 2 Δ ( λ ) .
T c ( λ ) = cos 2 Δ ( λ ) 2 { 1 cos 2 θ ( 1 + cos 2 θ ) [ 1 cos Δ ( λ ) ] } 2 , φ 1 = 45 ° θ , φ 2 = 45 ° , φ 3 = 45 ° + θ ,
T c ( λ ) = 1 sin 2 Δ ( λ ) 2 { 1 cos 2 θ ( 1 + cos 2 θ ) [ 1 + cos Δ ( λ ) ] } 2 , φ 1 = 45 ° + θ , φ 2 = 45 ° + 2 θ , φ 3 = φ 1 ,
T c ( λ ) = 1 , φ 1 , φ 2 , φ 3 = 0 °   or   90 ° ,
T s ( λ ) = sin 2 Δ ( λ ) 2 { 1 cos 2 θ ( 1 + cos 2 θ ) [ 1 + cos Δ ( λ ) ] } 2 , φ 1 = 45 ° + θ , φ 2 = 45 ° + 2 θ , φ 3 = φ 1 ,
T s ( λ ) = 1 cos 2 Δ ( λ ) 2 { 1 cos 2 θ ( 1 + cos 2 θ ) [ 1 cos Δ ( λ ) ] } 2 , φ 1 = 45 ° θ , φ 2 = 45 ° , φ 3 = 45 ° + θ ,
T s ( λ ) = 1 , φ 1 , φ 2 , φ 3 = 0 °   or   90 ° .
n 2 = B 1 + B 2 λ 2 + B 3 λ 2 + C 1 λ 4 + C 2 λ 6 + C 3 λ 8 ,

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