Abstract

This paper presents the achromatization of Savart Polariscope to decrease the lateral-shear dispersion in the lateral displacement. The achromatic Savart Polariscope can be made from two different birefringent crystal materials. The achromatic model for the choices of material is presented. The achievements and performances of different achromatic Savart Polariscopes are demonstrated with numerical simulations and ray tracing program. The chromatic variation in lateral displacement can be reduced by an order of magnitude across the spectral range 0.4μm to 0.9μm.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2013 (4)

2012 (4)

2011 (5)

2010 (4)

2009 (2)

K. Fujita, Y. Itoh, T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[CrossRef]

T. Mu, C. Zhang, B. Zhao, “Principle and analysis of a polarization imaging spectrometer,” Appl. Opt. 48(12), 2333–2339 (2009).
[CrossRef] [PubMed]

2008 (1)

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

2007 (1)

J. Masiero, K. Hodapp, D. Harrington, H. Lin, “Commissioning of the Dual-Beam Imaging Polarimeter for the University of Hawaii 88 inch Telescope,” Publ. Astron. Soc. Pac. 119(860), 1126–1132 (2007).
[CrossRef]

2004 (1)

2002 (1)

C. Zhang, B. Xiangli, B. Zhao, X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002).
[CrossRef]

1997 (1)

1995 (1)

P. Hariharan, “Archromatic retarders using quartz and mica,” Meas. Sci. Technol. 6(7), 1078–1079 (1995).
[CrossRef]

Baba, N.

Cai, Y.

Chen, H.

Courtial, J.

Craven-Jones, J.

Dai, H.

Dereniak, E. L.

Duncan, A. J.

Ebizuka, N.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Fletcher-Holmes, D. W.

Fu, L.

Fujita, K.

K. Fujita, Y. Itoh, T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[CrossRef]

Gorman, A.

Hariharan, P.

P. Hariharan, “Archromatic retarders using quartz and mica,” Meas. Sci. Technol. 6(7), 1078–1079 (1995).
[CrossRef]

Harrington, D.

J. Masiero, K. Hodapp, D. Harrington, H. Lin, “Commissioning of the Dual-Beam Imaging Polarimeter for the University of Hawaii 88 inch Telescope,” Publ. Astron. Soc. Pac. 119(860), 1126–1132 (2007).
[CrossRef]

Harvey, A. R.

Hirst, W.

Hodapp, K.

J. Masiero, K. Hodapp, D. Harrington, H. Lin, “Commissioning of the Dual-Beam Imaging Polarimeter for the University of Hawaii 88 inch Telescope,” Publ. Astron. Soc. Pac. 119(860), 1126–1132 (2007).
[CrossRef]

Hxieh, M.-H.

Itoh, Y.

K. Fujita, Y. Itoh, T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[CrossRef]

Iye, M.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Jia, C.

Jian, X.

T. Mu, C. Zhang, W. Ren, X. Jian, “Static dual-channel polarization imaging spectrometer for simultaneous acquisition of inphase and antiphase interference images,” Meas. Sci. Technol. 22(10), 105302 (2011).
[CrossRef]

C. Zhang, X. Jian, “Wide-spectrum reconstruction method for a birefringence interference imaging spectrometer,” Opt. Lett. 35(3), 366–368 (2010).
[CrossRef] [PubMed]

Kajino, F.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Kawabata, K. S.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Kudenov, M. W.

Li, Q.

Lin, H.

J. Masiero, K. Hodapp, D. Harrington, H. Lin, “Commissioning of the Dual-Beam Imaging Polarimeter for the University of Hawaii 88 inch Telescope,” Publ. Astron. Soc. Pac. 119(860), 1126–1132 (2007).
[CrossRef]

Lin, S.-T.

Liu, J.

Masiero, J.

J. Masiero, K. Hodapp, D. Harrington, H. Lin, “Commissioning of the Dual-Beam Imaging Polarimeter for the University of Hawaii 88 inch Telescope,” Publ. Astron. Soc. Pac. 119(860), 1126–1132 (2007).
[CrossRef]

Mu, T.

C. Zhang, W. Ren, T. Mu, L. Fu, C. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013), http://www.opticsinfobase.org/abstract.cfm?uri=oe-21-8-10207 .
[CrossRef] [PubMed]

W. Ren, C. Zhang, C. Jia, T. Mu, Q. Li, L. Zhang, “Precise spectrum reconstruction of the Fourier transforms imaging spectrometer based on polarization beam splitters,” Opt. Lett. 38(8), 1295–1297 (2013).
[CrossRef] [PubMed]

T. Mu, C. Zhang, “Models for polarization detection with the modified polarization interference imaging spectrometer,” Optik (Stuttg.) 124(7), 661–665 (2013).
[CrossRef]

T. Mu, C. Zhang, C. Jia, W. Ren, “Static hyperspectral imaging polarimeter for full linear Stokes parameters,” Opt. Express 20(16), 18194–18201 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-16-18194 .
[CrossRef] [PubMed]

W. Ren, C. Zhang, T. Mu, H. Dai, “Spectrum reconstruction based on the constrained optimal linear inverse methods,” Opt. Lett. 37(13), 2580–2582 (2012).
[CrossRef] [PubMed]

T. Mu, C. Zhang, W. Ren, C. Jia, “Static polarization-difference interference imaging spectrometer,” Opt. Lett. 37(17), 3507–3509 (2012).
[CrossRef] [PubMed]

T. Mu, C. Zhang, W. Ren, X. Jian, “Static dual-channel polarization imaging spectrometer for simultaneous acquisition of inphase and antiphase interference images,” Meas. Sci. Technol. 22(10), 105302 (2011).
[CrossRef]

T. Mu, C. Zhang, “A novel polarization interferometer for measuring upper atmospheric winds,” Chin. Phys. B 19(6), 060702 (2010).
[CrossRef]

T. Mu, C. Zhang, B. Zhao, “Principle and analysis of a polarization imaging spectrometer,” Appl. Opt. 48(12), 2333–2339 (2009).
[CrossRef] [PubMed]

Mukai, T.

K. Fujita, Y. Itoh, T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[CrossRef]

Murakami, N.

Padgett, M. J.

Patterson, B. A.

Perreault, J. D.

Pilkington, R.

Ren, W.

Sato, S.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Sibbett, W.

Stapelbroek, M. G.

Wong, G.

Xiangli, B.

C. Zhang, B. Xiangli, B. Zhao, X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002).
[CrossRef]

Xu, S.

Yeh, S.-L.

Yokota, H.

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Yuan, X.

C. Zhang, B. Xiangli, B. Zhao, X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002).
[CrossRef]

Zeng, X.

Zhang, C.

C. Zhang, W. Ren, T. Mu, L. Fu, C. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013), http://www.opticsinfobase.org/abstract.cfm?uri=oe-21-8-10207 .
[CrossRef] [PubMed]

W. Ren, C. Zhang, C. Jia, T. Mu, Q. Li, L. Zhang, “Precise spectrum reconstruction of the Fourier transforms imaging spectrometer based on polarization beam splitters,” Opt. Lett. 38(8), 1295–1297 (2013).
[CrossRef] [PubMed]

T. Mu, C. Zhang, “Models for polarization detection with the modified polarization interference imaging spectrometer,” Optik (Stuttg.) 124(7), 661–665 (2013).
[CrossRef]

T. Mu, C. Zhang, C. Jia, W. Ren, “Static hyperspectral imaging polarimeter for full linear Stokes parameters,” Opt. Express 20(16), 18194–18201 (2012), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-20-16-18194 .
[CrossRef] [PubMed]

W. Ren, C. Zhang, T. Mu, H. Dai, “Spectrum reconstruction based on the constrained optimal linear inverse methods,” Opt. Lett. 37(13), 2580–2582 (2012).
[CrossRef] [PubMed]

T. Mu, C. Zhang, W. Ren, C. Jia, “Static polarization-difference interference imaging spectrometer,” Opt. Lett. 37(17), 3507–3509 (2012).
[CrossRef] [PubMed]

T. Mu, C. Zhang, W. Ren, X. Jian, “Static dual-channel polarization imaging spectrometer for simultaneous acquisition of inphase and antiphase interference images,” Meas. Sci. Technol. 22(10), 105302 (2011).
[CrossRef]

C. Zhang, X. Jian, “Wide-spectrum reconstruction method for a birefringence interference imaging spectrometer,” Opt. Lett. 35(3), 366–368 (2010).
[CrossRef] [PubMed]

T. Mu, C. Zhang, “A novel polarization interferometer for measuring upper atmospheric winds,” Chin. Phys. B 19(6), 060702 (2010).
[CrossRef]

T. Mu, C. Zhang, B. Zhao, “Principle and analysis of a polarization imaging spectrometer,” Appl. Opt. 48(12), 2333–2339 (2009).
[CrossRef] [PubMed]

C. Zhang, B. Xiangli, B. Zhao, X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002).
[CrossRef]

Zhang, L.

Zhao, B.

T. Mu, C. Zhang, B. Zhao, “Principle and analysis of a polarization imaging spectrometer,” Appl. Opt. 48(12), 2333–2339 (2009).
[CrossRef] [PubMed]

C. Zhang, B. Xiangli, B. Zhao, X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002).
[CrossRef]

Zou, D.

Adv. Space Res. (1)

K. Fujita, Y. Itoh, T. Mukai, “Development of simultaneous imaging polarimeter for asteroids,” Adv. Space Res. 43(2), 325–327 (2009).
[CrossRef]

Appl. Opt. (4)

Chin. Phys. B (1)

T. Mu, C. Zhang, “A novel polarization interferometer for measuring upper atmospheric winds,” Chin. Phys. B 19(6), 060702 (2010).
[CrossRef]

Meas. Sci. Technol. (2)

T. Mu, C. Zhang, W. Ren, X. Jian, “Static dual-channel polarization imaging spectrometer for simultaneous acquisition of inphase and antiphase interference images,” Meas. Sci. Technol. 22(10), 105302 (2011).
[CrossRef]

P. Hariharan, “Archromatic retarders using quartz and mica,” Meas. Sci. Technol. 6(7), 1078–1079 (1995).
[CrossRef]

Opt. Commun. (1)

C. Zhang, B. Xiangli, B. Zhao, X. Yuan, “A static polarization imaging spectrometer based on a Savart polariscope,” Opt. Commun. 203(1-2), 21–26 (2002).
[CrossRef]

Opt. Express (5)

Opt. Lett. (8)

Optik (Stuttg.) (1)

T. Mu, C. Zhang, “Models for polarization detection with the modified polarization interference imaging spectrometer,” Optik (Stuttg.) 124(7), 661–665 (2013).
[CrossRef]

Proc. SPIE (1)

N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, S. Sato, “Novel Direct Vision Prism and Wollaston Prism Assembly for Diffraction Limit Applications,” Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

J. Masiero, K. Hodapp, D. Harrington, H. Lin, “Commissioning of the Dual-Beam Imaging Polarimeter for the University of Hawaii 88 inch Telescope,” Publ. Astron. Soc. Pac. 119(860), 1126–1132 (2007).
[CrossRef]

Other (3)

M. Françon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, New York, 1971), pp. 19–25, 141–145.

W. J. Tropf, M. E. Thomas, and E. W. Rogala, “Properties of Crystals and Glasses,” in Chapter 2 in Vol. 4 of Handbook of Optics, 3 ed., M. Bass, ed. (McGraw-Hill, New York, 2010), pp. 2.60–66.

L. L. C. Radiant Zemax, http://www.zemax.com/ .

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Figures (7)

Fig. 1
Fig. 1

Optical layout of a simple Savart polariscope.

Fig. 2
Fig. 2

Illustration of achromatization principle. SP1 and SP2 are made of birefringent materials with (a) the opposite sign and (b) the same sign of birefringence, respectively.

Fig. 3
Fig. 3

(a) The chromatic variation in the birefringence of YVO4, CaCO3, α-BaB2O4, and LiNbO3, and (b) the chromatic variation in the lateral displacement (CVLD) for the simple SP that is made of a single birefringent material.

Fig. 4
Fig. 4

The spectral variation of the lateral displacement relative to the nominal value for the ASPs that are made of pairing birefringent materials of (a) opposite sign and (b) same sign.

Fig. 5
Fig. 5

The on-axis ray tracing configurations of two simple SPs and two ASPs with Zemax software (light passing from left to right).

Fig. 6
Fig. 6

The on-axis ray shearing diagrams at the last surface of two simple SPs and two ASPs. For visual purposes, one incident ray is shown. The symbols of red rectangle, green reticle and blue cross are used to illustrate the dispersion of different wavelengths.

Fig. 7
Fig. 7

The off-axis ray shearing diagrams at the last surface of ASPs. For visual purposes, one incident ray is shown. The symbols of red rectangle, green reticle and blue cross are used to illustrate the dispersion of different wavelengths.

Tables (2)

Tables Icon

Table 1 Thickness t and Maximum CVLD Max | Δ d | for the Nominal Lateral Displacement of 1 mm of the Simple SPs that are made from 4 Birefringent Crystals: YVO4, Calcite, α-BBO, and LiNbO3.

Tables Icon

Table 2 Thickness ratio ρ, Individual Thickness t, Individual Lateral Displacement d, and Maximum CVLD Max | Δ d | for the Nominal Lateral Displacement of 1 mm of the ASPs that are Made From Four Birefringent Crystals: YVO4, Calcite, α-BBO, and LiNbO3.

Equations (16)

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

d ( t , i , λ ) = t B ( λ ) + t C ( λ ) sin i + terms in sin 3 i , etc . ,
B ( λ ) = 2 n o 2 ( λ ) n e 2 ( λ ) n o 2 ( λ ) + n e 2 ( λ ) , C ( λ ) = 4 n o ( λ ) n e ( λ ) ( n o 2 ( λ ) + n e 2 ( λ ) ) 3 / 2 2 n o ( λ ) ,
Δ d ( t , i , λ ) = | d ( t , i , λ ) | | d ( t , i , λ 0 ) | ,
d ( t 1 , t 2 , i , λ ) = d ( t 1 , i , λ ) ± d ( t 2 , i , λ ) = ( t 1 B 1 ± t 2 B 2 ) + ( t 1 C 1 ± t 2 C 2 ) sin i ,
Δ d ( t 1 , t 2 , i , λ ) = | d ( t 1 , t 2 , i , λ ) | | d ( t 1 , t 2 , i , λ 0 ) | .
d B 1 d λ ( λ 0 ) t 1 ± d B 2 d λ ( λ 0 ) t 2 = 0 ,
d C 1 d λ ( λ 0 ) t 1 ± d C 2 d λ ( λ 0 ) t 2 = 0.
ρ B ( λ 0 ) = t 1 t 2 = d B 2 d λ ( λ 0 ) d B 1 d λ ( λ 0 ) ,
ρ c ( λ 0 ) = t 1 t 2 = d C 2 d λ ( λ 0 ) d C 1 d λ ( λ 0 ) ,
d ( t 1 , t 2 , λ ) = t 1 B 1 ± t 2 B 2 ,
Δ d ( t 1 , t 2 , λ ) = | d ( t 1 , t 2 , λ ) | | d ( t 1 , t 2 , λ 0 ) | .
Max | Δ d | = Max | | d ( t 1 , t 2 , λ ) | | d ( t 1 , t 2 , λ 0 ) | | .
YVO 4 { n o 2 = 3.77834 + 0.069736 / ( λ 2 0.04724 ) 0.0108133 λ 2 n e 2 = 4.59905 + 0.110534 / ( λ 2 0.04813 ) 0.0122676 λ 2 ,
Calcite { n o 2 = 2.69705 + 0.0192064 / ( λ 2 0.01820 ) 0.0151624 λ 2 n e 2 = 2.18438 + 0.0087309 / ( λ 2 0.01018 ) 0.0024411 λ 2 ,
α-BBO { n o 2 = 2.74710 + 0.01878 / ( λ 2 0.01822 ) 0.01354 λ 2 n e 2 = 2.37530 + 0.01224 / ( λ 2 0.01667 ) 0.01516 λ 2 ,
LiNbO 3 { n o 2 = 4.90480 + 0.11768 / ( λ 2 0.04750 ) 0.027169 λ 2 n e 2 = 4.58200 + 0.099169 / ( λ 2 0.04443 ) 0.021950 λ 2 .

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