Abstract

Details are given of the appearance of the field of view when two wedges of doubly refracting material are placed in arbitrary azimuths between crossed polarizing devices. In general the field of view presents a complex pattern but simple fringe systems appear for suitable orientation of the wedges, one of which is the well-known Babinet fringe system. Theoretical relationships are derived for the intensity distribution in the general case and for the simple cases. Photographs show how the simple fringe systems are formed out of the complex cases. A use of the patterns for detecting if the wedges of a Babinet compensator are correctly mounted is mentioned.

© 1949 Optical Society of America

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References

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  1. G. Szivessy, Handbuch der Physik 19, 924 (1928);H. G. Jerrard, J. Opt. Soc. Am. 38, 37 (1948).
    [Crossref]
  2. For a detailed discussion of the optical defect see H. G. Jerrard, J. Sci. Inst. Phys. Ind. (November, 1949).

1949 (1)

For a detailed discussion of the optical defect see H. G. Jerrard, J. Sci. Inst. Phys. Ind. (November, 1949).

1928 (1)

G. Szivessy, Handbuch der Physik 19, 924 (1928);H. G. Jerrard, J. Opt. Soc. Am. 38, 37 (1948).
[Crossref]

Jerrard, H. G.

For a detailed discussion of the optical defect see H. G. Jerrard, J. Sci. Inst. Phys. Ind. (November, 1949).

Szivessy, G.

G. Szivessy, Handbuch der Physik 19, 924 (1928);H. G. Jerrard, J. Opt. Soc. Am. 38, 37 (1948).
[Crossref]

Handbuch der Physik (1)

G. Szivessy, Handbuch der Physik 19, 924 (1928);H. G. Jerrard, J. Opt. Soc. Am. 38, 37 (1948).
[Crossref]

J. Sci. Inst. Phys. Ind. (1)

For a detailed discussion of the optical defect see H. G. Jerrard, J. Sci. Inst. Phys. Ind. (November, 1949).

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Figures (10)

F. 1
F. 1

Wedges mounted between polarizer P and analyzer A.

F. 2
F. 2

The parameters. Ox, Oy are the coordinate axes. OW1 and OW2 are the directions of the lines of greatest slope of the wedges making azimuth angles ρ1 and ρ2 with Ox. R is any point having polar coordinates (l, θ). RM and RN are the perpendiculars to OW1 and OW2 respectively.

F. 3
F. 3

OP and OA are the vibration directions of the polarizer and analyzer respectively; ν1 and ν2 are the angles measured from OP between the fast vibration directions OX1 and OX2 of the plate 1 and 2.

F. 4
F. 4

Simple Fringe Systems (a) One wedge only (b) Babinet fringes (c) and (d) Pseudo-Babinet fringes, (e) uniform field of view. In each case ρ1 = π/4.

F. 5
F. 5

The formation of the Babinet fringes. ρ1 and ρ2 are the azimuths of the wedges 1 and 2 with respect to the coordinate axis Ox.

F. 6
F. 6

The formation of the horizontal Pseudo-Babinet fringes, ρ1 and ρ2 are the azimuths of the wedges 1 and 2 with respect to the coordinate axis Ox.

F. 7
F. 7

The formation of the vertical Pseudo-Babinet fringes, ρ1 and ρ2 are the azimuths of the wedges 1 and 2 with respect to the coordinate axis Ox.

F. 8
F. 8

The disappearance of the fringe system, ρ1 and ρ2 are the azimuths of the wedges 1 and 2 with respect to the coordinate axis Ox.

F. 9
F. 9

Fringes when the wedges of a Babinet compensator are incorrectly set. Compensator mounted so that the line bisecting the obtuse angle between the azimuths of the wedges is (a) at 45° to the vibration direction of the polarizer, (b) at 90° to the vibration direction of the polarizer. α is the angle between the azimuth of each wedge.

F. 10
F. 10

The experimental arrangement. F, filter; D, diaphragm; P, polarizer; A, analyzer; W1 and W2 are the wedges; L1, L2, and L3 are lenses; S, screen.

Equations (28)

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t 1 = d 1 + l cos ( θ ρ 1 ) tan α
t 2 = d 2 + l cos ( θ ρ 2 ) tan α ,
δ 1 = ( 2 π k / λ ) ( d 1 + l cos ( θ ρ 1 ) tan α )
δ 2 = ( 2 π k / λ ) ( d 2 + l cos ( θ ρ 2 ) tan α ) ,
Δ 1 = ( 2 π k / λ ) d 1 ; Δ 2 = ( 2 π k / λ ) d 2 ; c = ( 2 π k / λ ) tan α
δ 1 = Δ 1 + c l cos ( θ ρ 1 ) δ 2 = Δ 2 + c l cos ( θ ρ 2 ) } .
I = sin 2 ν 1 cos 2 ν 2 sin 2 ( ν 2 ν 1 ) sin 2 δ 1 / 2 + cos 2 ν 1 sin 2 ν 2 sin 2 ( ν 2 ν 1 ) sin 2 δ 2 / 2 + sin 2 ν 1 sin 2 ν 2 cos 2 ( ν 2 ν 1 ) sin 2 [ ( δ 1 + δ 2 ) / 2 ] sin 2 ν 1 sin 2 ν 2 sin 2 ( ν 2 ν 1 ) sin 2 [ ( δ 1 δ 2 ) / 2 ] ,
I = sin 2 2 ν 1 sin 2 δ 1 / 2 ,
Δ 1 + c l cos ( θ ρ 1 ) = ± 2 n π , where n = 0 , 1 , 2
l cos ( θ ρ 1 ) = ( ± 2 n π Δ 1 ) / c = p n , say .
a 1 = p n + 1 p n = 2 π / c .
ν 2 = ν 1 + π / 2 in Eq . ( 2 ) .
I = sin 2 2 ν 1 sin 2 1 2 ( δ 1 δ 2 ) ,
sin 1 2 ( δ 1 δ 2 ) = 0 .
Δ 1 + c l cos ( θ ρ 1 ) Δ 2 c l cos ( θ ρ 1 π ) = ± 2 n π ,
l cos ( θ ρ 1 ) = { ± 2 n π ( Δ 1 Δ 2 ) } / 2 c = q n , say .
a 2 = q n + 1 q n = π / c
I = sin 2 2 ν 1 sin 2 1 2 ( δ 1 + δ 2 )
sin 1 2 ( δ 1 + δ 2 ) = 0
Δ 1 + c l cos ( θ ρ 1 ) + Δ 2 + c l cos ( θ ρ 1 π / 2 ) = ± 2 n π
c l cos ( θ ρ 1 ) + c l sin ( θ ρ 1 ) = ± 2 n π ( Δ 1 + Δ 2 ) .
c l { cos ( θ ρ 1 ) ( 1 / 2 ) + sin ( θ ρ 1 ) ( 1 / 2 ) = ( 1 / 2 ) { ± 2 n π ( Δ 1 + Δ 2 ) } , c l { cos ( θ ρ 1 ) cos π / 4 + sin ( θ ρ 1 ) sin π / 4 } = ( 1 / 2 ) { ± 2 n π ( Δ 1 + Δ 2 ) } ,
l cos { θ ( ρ 1 + π / 4 ) } = { ± 2 n π ( Δ 1 + Δ 2 ) } / 2 c = r n , say .
a 3 = r n + 1 r n = 2 π / c .
l cos { θ ( ρ 1 π / 4 ) } = { ± 2 n π ( Δ 1 + Δ 2 ) } / 2 c = s n , say
ρ 1 = ν 1 ; ρ 2 = ρ 1 ; ν 2 = ν 1 + π / 2
I = sin 2 2 ν 1 sin 2 1 2 ( δ 1 δ 2 ) ,
I = sin 2 2 ν 1 sin 2 1 2 ( Δ 1 Δ 2 ) .