Abstract

We review current synthesis techniques for generating and improving birefringent filters. The relationship between wave-plate orientation and the resulting spectral output is shown to be that of a simple Fourier transform. By using this relationship and starting from the fan Solc configuration, we easily generated plate orientations providing lower sidelobe levels and improved finesse. We outline a method by which filters can be constructed to provide from 0 to 100% of the desired passband in a continuous fashion. Such a filter can be stacked to allow rapid control of any number of passbands and is shown, as an example in a novel design employing super-twisted nematic liquid crystal elements, to control a maximum of three color bands.

© 2002 Optical Society of America

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References

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  1. G. D. Sharp, J. R. Birge, “Retarder stack technology for color manipulation,” in Proceedings of the Society for Information Display (Society for Information Display, San Jose, Calif., 1999), pp. 1072–1075.
  2. I. Solc, “Birefringent chain filters,” J. Opt. Soc. Am. 55, 621–625 (1965).
    [CrossRef]
  3. B. Lyot, “The birefringent filter and its application in solar physics,” Ann. Astrophys. 7, 31–36 (1944).
  4. S. E. Harris, E. O. Amman, I. C. Chang, “Optical net-work synthesis using birefringent crystals. 1. Synthesis of lossless networks of equal-length crystals,” J. Opt. Soc. Am. 54, 1267–1279 (1964).
    [CrossRef]
  5. J. W. Evans, “The birefringent filter,” J. Opt. Soc. Am. 39, 229–242 (1949).
    [CrossRef]
  6. J. W. Evans, “Solc birefringent filter,” J. Opt. Soc. Am. 48, 142–145 (1958).
    [CrossRef]
  7. W. J. Rosenberg, A. M. Title, “Solc filter engineering,” Proc. SPIE 307, 106–111 (1981).
    [CrossRef]
  8. S. A. Schoolman, “Contrast elements in birefringent filters,” Sol. Phys. 30, 255–261 (1973).
    [CrossRef]
  9. S. Saeed, P. J. Bos, Z. Li, “A method of generating full color in a liquid crystal display using birefringent filters,” Jpn. J. Appl. Phys. 40, 3266–3271 (2001).
    [CrossRef]
  10. W. J. Gunning, “Electro-optically tuned spectral filters: a review,” Opt. Eng. 20, 837–845 (1981).
    [CrossRef]
  11. S. Huard, Polarization of Light (Wiley, Chichester, UK, 1997), pp. xii, 333.
  12. B. Bahadur, Liquid Crystals: Applications and Uses, 2nd ed. (World Scientific, Singapore, 1990), Vol. 1, p. v.
  13. A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
    [CrossRef]
  14. S. Saeed, P. J. Bos, “Synthesis of a color image display using birefringent filters,” Opt. Eng. 41, 167–175 (2002).
    [CrossRef]

2002 (1)

S. Saeed, P. J. Bos, “Synthesis of a color image display using birefringent filters,” Opt. Eng. 41, 167–175 (2002).
[CrossRef]

2001 (1)

S. Saeed, P. J. Bos, Z. Li, “A method of generating full color in a liquid crystal display using birefringent filters,” Jpn. J. Appl. Phys. 40, 3266–3271 (2001).
[CrossRef]

1997 (1)

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[CrossRef]

1981 (2)

W. J. Gunning, “Electro-optically tuned spectral filters: a review,” Opt. Eng. 20, 837–845 (1981).
[CrossRef]

W. J. Rosenberg, A. M. Title, “Solc filter engineering,” Proc. SPIE 307, 106–111 (1981).
[CrossRef]

1973 (1)

S. A. Schoolman, “Contrast elements in birefringent filters,” Sol. Phys. 30, 255–261 (1973).
[CrossRef]

1965 (1)

1964 (1)

1958 (1)

1949 (1)

1944 (1)

B. Lyot, “The birefringent filter and its application in solar physics,” Ann. Astrophys. 7, 31–36 (1944).

Amman, E. O.

Bahadur, B.

B. Bahadur, Liquid Crystals: Applications and Uses, 2nd ed. (World Scientific, Singapore, 1990), Vol. 1, p. v.

Birge, J. R.

G. D. Sharp, J. R. Birge, “Retarder stack technology for color manipulation,” in Proceedings of the Society for Information Display (Society for Information Display, San Jose, Calif., 1999), pp. 1072–1075.

Bos, P. J.

S. Saeed, P. J. Bos, “Synthesis of a color image display using birefringent filters,” Opt. Eng. 41, 167–175 (2002).
[CrossRef]

S. Saeed, P. J. Bos, Z. Li, “A method of generating full color in a liquid crystal display using birefringent filters,” Jpn. J. Appl. Phys. 40, 3266–3271 (2001).
[CrossRef]

Chang, I. C.

Evans, J. W.

Gunning, W. J.

W. J. Gunning, “Electro-optically tuned spectral filters: a review,” Opt. Eng. 20, 837–845 (1981).
[CrossRef]

Harris, S. E.

Huard, S.

S. Huard, Polarization of Light (Wiley, Chichester, UK, 1997), pp. xii, 333.

Li, Z.

S. Saeed, P. J. Bos, Z. Li, “A method of generating full color in a liquid crystal display using birefringent filters,” Jpn. J. Appl. Phys. 40, 3266–3271 (2001).
[CrossRef]

Lien, A.

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[CrossRef]

Lyot, B.

B. Lyot, “The birefringent filter and its application in solar physics,” Ann. Astrophys. 7, 31–36 (1944).

Rosenberg, W. J.

W. J. Rosenberg, A. M. Title, “Solc filter engineering,” Proc. SPIE 307, 106–111 (1981).
[CrossRef]

Saeed, S.

S. Saeed, P. J. Bos, “Synthesis of a color image display using birefringent filters,” Opt. Eng. 41, 167–175 (2002).
[CrossRef]

S. Saeed, P. J. Bos, Z. Li, “A method of generating full color in a liquid crystal display using birefringent filters,” Jpn. J. Appl. Phys. 40, 3266–3271 (2001).
[CrossRef]

Schoolman, S. A.

S. A. Schoolman, “Contrast elements in birefringent filters,” Sol. Phys. 30, 255–261 (1973).
[CrossRef]

Sharp, G. D.

G. D. Sharp, J. R. Birge, “Retarder stack technology for color manipulation,” in Proceedings of the Society for Information Display (Society for Information Display, San Jose, Calif., 1999), pp. 1072–1075.

Solc, I.

Title, A. M.

W. J. Rosenberg, A. M. Title, “Solc filter engineering,” Proc. SPIE 307, 106–111 (1981).
[CrossRef]

Ann. Astrophys. (1)

B. Lyot, “The birefringent filter and its application in solar physics,” Ann. Astrophys. 7, 31–36 (1944).

J. Opt. Soc. Am. (4)

Jpn. J. Appl. Phys. (1)

S. Saeed, P. J. Bos, Z. Li, “A method of generating full color in a liquid crystal display using birefringent filters,” Jpn. J. Appl. Phys. 40, 3266–3271 (2001).
[CrossRef]

Liq. Cryst. (1)

A. Lien, “A detailed derivation of extended Jones matrix representation for twisted nematic liquid crystal displays,” Liq. Cryst. 22, 171–175 (1997).
[CrossRef]

Opt. Eng. (2)

S. Saeed, P. J. Bos, “Synthesis of a color image display using birefringent filters,” Opt. Eng. 41, 167–175 (2002).
[CrossRef]

W. J. Gunning, “Electro-optically tuned spectral filters: a review,” Opt. Eng. 20, 837–845 (1981).
[CrossRef]

Proc. SPIE (1)

W. J. Rosenberg, A. M. Title, “Solc filter engineering,” Proc. SPIE 307, 106–111 (1981).
[CrossRef]

Sol. Phys. (1)

S. A. Schoolman, “Contrast elements in birefringent filters,” Sol. Phys. 30, 255–261 (1973).
[CrossRef]

Other (3)

S. Huard, Polarization of Light (Wiley, Chichester, UK, 1997), pp. xii, 333.

B. Bahadur, Liquid Crystals: Applications and Uses, 2nd ed. (World Scientific, Singapore, 1990), Vol. 1, p. v.

G. D. Sharp, J. R. Birge, “Retarder stack technology for color manipulation,” in Proceedings of the Society for Information Display (Society for Information Display, San Jose, Calif., 1999), pp. 1072–1075.

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Figures (14)

Fig. 1
Fig. 1

Single pixel of a spatially driven switchable spectral filter showing the three components and their effect on the polarization state of light passing through them. Input spectra on the left side is white light with known polarization state; output spectra on the right is split into the desired spectra with appropriate states of polarization by components 1–3.

Fig. 2
Fig. 2

Four-stage Lyot filter, with spectral output of each stage and final multiplicative output of the entire filter shown on the right.

Fig. 3
Fig. 3

Top, Solc fan and folded filters between parallel and crossed polarizers; arrows signify orientation of the slow axis of the plates. Bottom, resulting spectral output.

Fig. 4
Fig. 4

Spectral output of an unmodified eight-plate Solc fan filter with relative angle plot of the eight-plate sinusoidal modified Solc fan filter. Points 0 and 10 are not used, as they are parallel to the polarizer and analyzer.

Fig. 5
Fig. 5

Spectral outputs. (a) Comparison of the unmodified eight-plate Solc fan filter with the sinusoidal, triangle, and Gaussian modified versions. (b) Sinc-squared modified Solc fan filter. Note that the spectral output is of triangular shape, which is the Fourier transform of the sinc-squared function.

Fig. 6
Fig. 6

Effect of reducing the FWHM (improving the finesse) of the Gaussian modified Solc fan filter by increasing the plate retardations by integer multiples. Increasing the plate retardations reduces the FWHM at the cost of decreased free spectral range.

Fig. 7
Fig. 7

Switchable filter with part 1 composed of four plates (parts a–d), with slow axis orientations defined by the arrows. Part 2e) is the LC cell, and part 3 is a mirror image of part 1, except that it is orthogonal.

Fig. 8
Fig. 8

Spectral output of a switchable green spectral filter, switched from full-on to full-off (0 V–20 V) state.

Fig. 9
Fig. 9

Switchable green channel filter with two plates for part 1 and 2. Solid arrows in circles denote the polarization vector of the red and blue channels; dashed arrows in circles denote the green channel.

Fig. 10
Fig. 10

Spatially driven three-color switchable filter consisting of three individual stages each of which controls the amplitude of a single color. Combining the stages can individually switch the red, green, and blue channels. R1 through R9 signify the retardations of the individual elements; A1 through A9 signify the angles of the slow axis.  

Fig. 11
Fig. 11

DSTN cell composed of the compensator part (top) with opposite twist and placed orthogonal to the STN part (bottom).

Fig. 12
Fig. 12

Stokes parameters S1 and S2 for the red, green, and blue bands for a two-plate-based switchable filter just before entering and just after exiting the DSTN retarder. The green band ends up orthogonal to the entrance, whereas the R and B bands end up at about the same point. The discrepancy is due to the sidelobes found in those channels since only two plates are used for filtering. Open and solid symbols signify coordinates that reside, respectively, in the upper and lower hemispheres of the Poincaré sphere. Squares denote entrance and circles denote exit polarization states.

Fig. 13
Fig. 13

Relative angle plot of the eight-plate sinusoidal, Gaussian, and sinc-squared modified Solc fan filter. Points 0 and 10 are not used, as they are parallel to the polarizer and analyzer.

Fig. 14
Fig. 14

Relative angle plot of the eight-plate triangular modified Solc fan filter.

Equations (46)

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

T=cos2 Γ/2
T=sin Nχsin χcos χ tan p2,
cos χ=cos p cosπΔndλ.
θ1=ϕ1-ϕP,
θ2=ϕ2-ϕ1,
θN+1=ϕA-ϕN,
i=1i=N+1|θi|=π2,
C(ω)=k=0nCkexp(-ikaω),
C(t)=k=0nCkδ(t-ka),
2Np=X,
θ1=ϕ-0=ϕ,
θ2=3ϕ-ϕ=2ϕ,
θ3=5ϕ-3ϕ=2ϕ,
θN=(2N-1)ϕ-Nϕ=2ϕ,
θN+1=π/2-Nϕ=ϕ.
sinπ10, sin2π10, sin3π10, sin4π10, sin5π10,
sin6π10, sin7π10, sin8π10, sin9π10
sinπ10+sin2π10++sin9π10×F
=π2,
 6.3138F=π2,
 F=π12.6276.
ϕ1=θ1,
ϕ2=θ1+θ2,
ϕN=θ1+θ2++θN,
ϕN+1=ϕA=θ1+θ2++θN+1,
ϕ1=4.4°,ϕ2=12.8°,ϕ3=24.3°,ϕ4=37.9°,
ϕ5=52.1°,ϕ6=65.7°,ϕ7=77.2°,ϕ8=85.6°.
25F=π2,
 F=π50.
ϕ1=3.6°,ϕ2=10.8°,ϕ3=21.6°,ϕ4=36.0°,
ϕ5=54.0°,ϕ6=68.4°,ϕ7=79.2°,ϕ8=86.4°.
0.01832,0.1054,0.3679,0.7788,1,0.7788,
0.3679,0.1054,0.01832.
3.5408F=π2,
 F=0.4436.
ϕ1=0.47°,ϕ2=3.1°,ϕ3=12.5°,ϕ4=32.3°,
ϕ5=57.7°,ϕ6=77.5°,ϕ7=86.9°,ϕ8=89.53°.
sin(x)x2
0.0358, 0.0243, 0.0547, 0.573,
1,0.573,0.0547, 0.0243, 0.0358.
2.3752F=π2,
 F=0.6613.
ϕ1=1.4°,ϕ2=2.3°,ϕ3=4.4°,ϕ4=26.1°,
ϕ5=64.0°,ϕ6=85.7°,ϕ7=87.7°,ϕ8=88.6°.

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