Abstract

We describe the achromatization of Wollaston prisms to reduce the angular dispersion in the splitting angle. Anal ytical theory and ray-tracing modeling is presented. In an example application, a sixfold reduction in dispersion is achieved for wavelengths in the region 400nm to 1.7μm. Experimental proof of concept is demonstrated, and in an example application, the spectral dispersion of extended images recorded through cascaded Wollaston prisms is shown to be reduced by an order of magnitude.

© 2011 Optical Society of America

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2010 (2)

G. Wong, A. R. Harvey, R. Pilkington, and R. Rickman, Proc. SPIE 7812, 781204 (2010).
[CrossRef]

A. Gorman, D. W. Fletcher-Holmes, and A. R. Harvey, Opt. Express 18, 5602 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (2)

M. Biss, G. Settles, M. Staymates, and S. Sanderson, Appl. Opt. 47, 328 (2008).
[CrossRef] [PubMed]

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

2007 (2)

2005 (1)

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

2004 (1)

2003 (1)

1999 (1)

1996 (1)

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

1995 (1)

M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
[CrossRef]

1986 (1)

1983 (1)

Alouini, M.

Bartels, R. A.

Bénière, A.

Bernath, R.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Biss, M.

Carriere, J.

Cederquist, J.

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

Cense, B.

Chen, T. C.

De Boer, J. F.

Dolfi, D.

Ebizuka, E. N.

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Eismann, M. T.

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

Fletcher-Holmes, D. W.

Françon, M.

M. Françon and S. Mallick, Polarisation Interferometry (Wiley-Interscience, 1971).

George, S.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Gorman, A.

Goudail, F.

Hackwell, J.

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

Harvey, A. R.

A. Gorman, D. W. Fletcher-Holmes, and A. R. Harvey, Opt. Express 18, 5602 (2010).
[CrossRef] [PubMed]

G. Wong, A. R. Harvey, R. Pilkington, and R. Rickman, Proc. SPIE 7812, 781204 (2010).
[CrossRef]

A. R. Harvey and D. W. Fletcher-Holmes, Opt. Express 12, 5368 (2004).
[CrossRef] [PubMed]

M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
[CrossRef]

Huppi, R.

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

Iye, M.

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Kajino, F.

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Kaneko, T.

Kawabata, K. S.

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Keyser, C.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Koay, C.-S.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Mallick, S.

M. Françon and S. Mallick, Polarisation Interferometry (Wiley-Interscience, 1971).

Mansuripur, M.

Masihzadeh, O.

Mujat, M.

Oka, K.

Padgett, M. J.

M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
[CrossRef]

Park, B. H.

Pilkington, R.

G. Wong, A. R. Harvey, R. Pilkington, and R. Rickman, Proc. SPIE 7812, 781204 (2010).
[CrossRef]

Richardson, M. C.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Rickman, R.

G. Wong, A. R. Harvey, R. Pilkington, and R. Rickman, Proc. SPIE 7812, 781204 (2010).
[CrossRef]

Sanderson, S.

Sato, S.

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Schlup, P.

Schwartz, C.

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

Settles, G.

Simon, M. C.

Staymates, M.

Takenoshita, K.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Teerawattanasook, S.

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

Wong, G.

G. Wong, A. R. Harvey, R. Pilkington, and R. Rickman, Proc. SPIE 7812, 781204 (2010).
[CrossRef]

Yeh, W.-H.

Yokota, H.

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

Appl. Opt. (5)

Opt. Express (5)

Proc. SPIE (4)

E. N. Ebizuka, H. Yokota, F. Kajino, K. S. Kawabata, M. Iye, and S. Sato, Proc. SPIE 7018, 70184S (2008).
[CrossRef]

M. C. Richardson, C.-S. Koay, K. Takenoshita, C. Keyser, R. Bernath, S. Teerawattanasook, and S. George, Proc. SPIE 5580, 434 (2005).
[CrossRef]

G. Wong, A. R. Harvey, R. Pilkington, and R. Rickman, Proc. SPIE 7812, 781204 (2010).
[CrossRef]

M. T. Eismann, C. Schwartz, J. Cederquist, J. Hackwell, and R. Huppi, Proc. SPIE 2819, 91 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
[CrossRef]

Other (1)

M. Françon and S. Mallick, Polarisation Interferometry (Wiley-Interscience, 1971).

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Figures (4)

Fig. 1
Fig. 1

Illustration of achromatization principle.

Fig. 2
Fig. 2

Spectral variation of the ray angles of exitance with respect to the surface normal, for the traditional and achromatized prism (optimized for 400 nm to 700 nm ).

Fig. 3
Fig. 3

Captures of the dispersion from the (a) traditional and (b) achromatized prism over 400 nm to 700 nm .

Fig. 4
Fig. 4

Geometric image analysis (a) before and (b) after three β - BaB 2 O 4 / YVO 4 achromatic prisms for an eight-band snapshot imager. The height of an object letter after prism achromatization is 0.122 mm at the image plane.

Tables (2)

Tables Icon

Table 1 Wedge Angles β, Nominal Splitting Angles θ ( β ) for Single Wollaston Prisms at 625 nm , and Overall Net-Splitting Angle θ ( β 1 , β 2 ) for an Achromatic Prism for 400 nm λ 850 nm

Tables Icon

Table 2 Wedge Angles β, Nominal Splitting Angles θ ( β ) for Single Wollaston Prisms at 700 nm , and Overall Net-Splitting Angle θ ( β 1 , β 2 ) for Each Achromatic Prism Pair within an Eight-Band Snapshot Imager Operating over the Range 400 nm λ 700 nm

Equations (4)

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d b 1 / d λ tan ( β 1 ) + d b 2 / d λ tan ( β 2 ) = 0 ,
θ ( β 1 , β 2 , λ ) ( 2 sin 1 ( n o , 2 ( λ ) n e , 2 ( λ ) 2 n ( λ ) 2 ) { cos ( Ψ ) cos ( sin 1 [ b A ( λ ) tan β 1 ] ) } [ tan ( Ψ ) tan ( β 2 + Ψ ) ] ) + sin 1 [ b A ( λ ) tan β 1 ] ,
Ψ = sin 1 ( n o , 1 ( λ ) + n e , 1 ( λ ) n o , 1 ( λ ) + n ( λ ) b 1 ( λ ) tan β 1 ) ,
n = n e , 2 ( λ ) { 1 ( 1 n o , 2 2 ( λ ) 1 n e , 2 2 ( λ ) ) ( b 1 ( λ ) tan β 1 ) 2 } ,

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