Abstract

The image formation through a Wollaston prism with large split angle is studied. Formulas for the split angle, approximate calculations of aberrations, and ray tracings are used. The most important aberrations found are astigmatism and anamorphic distortion. Tilting the Wollaston with respect to the incident beam may reduce these aberrations, and if the orientation of the optical axis in the first element is varied it is possible to cancel one of the two aberrations for both images simultaneously, while the other one is substantially reduced. With an adequate adjustment of all the construction parameters the images become sharp enough to allow the use of large split angles (∼15°).

© 1986 Optical Society of America

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References

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  1. L. Bergmann, C. Schaefer, Lehrbuch der Experimentalphysik, Tome 3, H. Gobrecht, Ed. (Walter Gruyter, New York, 1974).
  2. J. M. Beckers, “High-Resolution Measurements of Photosphere and Sunspot Velocity and Magnetic Fields Using a Narrow-Band Birefringent Filter,” Sol. Phys. 3, 258 (1968).
    [CrossRef]
  3. J. M. Simon, M. C. Simon, “Wollaston Prism as a Beam Splitter in Convergent Light,”Appl. Opt. 17, 3352 (1978).
    [CrossRef] [PubMed]
  4. M. C. Simon, “Ray Tracing Formulas for Monoaxial Optical Components,” Appl. Opt. 22, 354 (1983).
    [CrossRef] [PubMed]
  5. M. Francon, “Isotropic and Anisotropic Media. Application of Anisotropic Materials to Interferometry,”in Advanced Optical Technique, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967).

1983 (1)

1978 (1)

1968 (1)

J. M. Beckers, “High-Resolution Measurements of Photosphere and Sunspot Velocity and Magnetic Fields Using a Narrow-Band Birefringent Filter,” Sol. Phys. 3, 258 (1968).
[CrossRef]

Beckers, J. M.

J. M. Beckers, “High-Resolution Measurements of Photosphere and Sunspot Velocity and Magnetic Fields Using a Narrow-Band Birefringent Filter,” Sol. Phys. 3, 258 (1968).
[CrossRef]

Bergmann, L.

L. Bergmann, C. Schaefer, Lehrbuch der Experimentalphysik, Tome 3, H. Gobrecht, Ed. (Walter Gruyter, New York, 1974).

Francon, M.

M. Francon, “Isotropic and Anisotropic Media. Application of Anisotropic Materials to Interferometry,”in Advanced Optical Technique, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967).

Schaefer, C.

L. Bergmann, C. Schaefer, Lehrbuch der Experimentalphysik, Tome 3, H. Gobrecht, Ed. (Walter Gruyter, New York, 1974).

Simon, J. M.

Simon, M. C.

Appl. Opt. (2)

Sol. Phys. (1)

J. M. Beckers, “High-Resolution Measurements of Photosphere and Sunspot Velocity and Magnetic Fields Using a Narrow-Band Birefringent Filter,” Sol. Phys. 3, 258 (1968).
[CrossRef]

Other (2)

M. Francon, “Isotropic and Anisotropic Media. Application of Anisotropic Materials to Interferometry,”in Advanced Optical Technique, A. C. S. van Heel, Ed. (North-Holland, Amsterdam, 1967).

L. Bergmann, C. Schaefer, Lehrbuch der Experimentalphysik, Tome 3, H. Gobrecht, Ed. (Walter Gruyter, New York, 1974).

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Figures (13)

Fig. 1
Fig. 1

Wollaston prism; trajectories of the principal rays.

Fig. 2
Fig. 2

Geometrical scheme to derive the approximate formula for the split angle.

Fig. 3
Fig. 3

Split angle as a function of the tilt angle of the Wollaston.

Fig. 4
Fig. 4

Image formation through the Wollaston.

Fig. 5
Fig. 5

Spot diagrams corresponding to the images in Fig. 4: α = 45°, α1 = 0°, α1 = −28.8°, and calcite.

Fig. 6
Fig. 6

Astigmatism as a function of the tilt angles α1 for α = 45° and calcite.

Fig. 7
Fig. 7

Distortion as a function of the tilt angle α1 for α = 45° and calcite.

Fig. 8
Fig. 8

Spot diagrams corresponding to the ordinary images when α = 45°, α1 = −24°, and ϑ = 12°.

Fig. 9
Fig. 9

Spot diagrams corresponding to the extraordinary images when α = 45°, α1 = −24°, and ϑ = 12°.

Fig. 10
Fig. 10

Spot diagrams corresponding to the ordinary images when α = 45°, α1 = −25°, and ϑ = 11°.

Fig. 11
Fig. 11

Spot diagrams corresponding to the extraordinary images when α = 45°, α1 = −25°, and ϑ = 11°.

Fig. 12
Fig. 12

Photographs corresponding to the images in Fig. 4.

Fig. 13
Fig. 13

Experimental setup to obtain the photographs in Fig. 12.

Tables (2)

Tables Icon

Table I Aberrations of Wollaston Quartz and Calcite Prisms with the Same Split Angle

Tables Icon

Table II Split Angle and Aberrations for Calcite Wollaston Prisms of Different Angles α for Normal Incidence and Some α1 Values

Equations (33)

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sin ϑ m = n sin α 1 n e ,
Δ 1 = ( a u 0 + b u e + d u ) c , Δ 2 = ( d u + b u 0 + a u e ) c ,
Δ 1 = ( a u e + b u o + d u ) c , Δ 2 = ( d u + b u e + a u o ) c ,
d = d + ( n e n o ) ( a b ) , d = d + ( n o n e ) ( a b ) .
d = l sin α 1 , d = l sin ω , d = l sin ω , l = l cos β , ( a b ) = l [ tan ( α β ) + tan β ] , }
sin ( δ 2 ) = ( n o n e ) cos β cos α 1 [ tan ( α β ) + tan β ] .
n ̅ = n o + n e 2 ,
sin β = n sin α 1 n ̅ .
n = n e 1 ( 1 n o 2 1 n e 2 ) sin 2 α 1 .
sin ( δ 2 ) = ( n o n e 2 n 2 ) cos β cos α 1 [ tan ( α β ) + tan β ] ,
sin β = n sin α 1 n * ¯ ,
n * ¯ = n o + n 2 .
sin ( δ 2 ) = ( n e n o ) tan α .
A L = S 3 o S 3 o * ,
A L = S 3 e S 3 e * .
S 3 o = [ A o ( S 1 a n o ) b n e ] [ 1 ( n e 2 1 ) ( n o n e ) 2 α 2 n e 2 ] , A o = 1 ( n o n e ) 2 sin 2 α cos 2 α ,
S 3 e = [ A e ( S 1 a n e ) b n o ] [ 1 ( n o 2 1 ) ( n e n o ) 2 α 2 n o 2 ] , A e = 1 ( n e n o ) 2 sin 2 α cos 2 α ,
S 3 o * = S 1 a n o b n e ,
S 3 e = S 1 a n e b n o .
D ( % ) = Z m c ( + l ) Z m c ( l ) z l 2 l × 100 ,
Z m c ( ± l ) = ± l A o ( 1 ( n e 2 1 ) ( n o n e ) 2 α 2 n e 2 ) ,
Z m c ( ± l ) = ± l A e ( 1 ( n o 2 1 ) ( n e n o ) 2 α 2 n o 2 ) .
α 1 = 29.1 ° , A L = A L = 3 mm , α 1 = 28.3 ° , D ( % ) = D ( % ) = 2.1 % .
α 1 = 23.3 ° , A L = A L = 2 m m , α 1 = 22.3 ° , D ( % ) = D ( % ) = 0.5 % .
D ( % ) = 0.11 % , D ( % ) = 0.01 % , A L = 1.1 m m , A L = 0.2 m m ,
D ( % ) = 0.39 % , D ( % ) = 0.23 % , A L = 0 , A L = 0 .
( A L A L ) m = 1.4 ± 0.1 ,
( A L A L ) c = 1.3 .
w 4 A w 2 B + C = 0 ,
A = ( b S z 2 + b S y 2 sin 2 ϑ + 1 ) 2 4 b S z 2 cos 2 ϑ , B = 2 ( b S z 2 + b S y 2 sin 2 ϑ + 1 ) ( b sin 2 ϑ + u e 2 u 2 ) 4 b u e 2 u 2 S z 2 cos 2 ϑ , C = ( b sin 2 ϑ + u e 2 u 2 ) 2 ,
S x = cos α 1 ; S y = 0 ; S z = sin α 1 .
A = ( b sin 2 α + 1 ) 2 4 b sin 2 α 1 , B = 2 ( b sin 2 α 1 + 1 ) u e 2 u 2 4 b u e 2 u 2 sin α 1 , C = ( u e 2 u 2 ) 2 .
n = 1 n e 1 ( 1 n o 2 1 n e 2 ) sin 2 α 1 .

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