An exact analysis of the working parameters of a modified Wollaston
prism is presented. Parameters include the output splitting angle,
the retardation, and the location of the plane of the interference
fringes (plane of apparent splitting). Results are presented
for the entire range of optical axis inclinations and wedge
angles. Approximate expressions from the literature are
evaluated. An angle of incidence that causes the plane of the
interference fringes to be perpendicular to the axis of the optical
system is found for each configuration analyzed. This is then
applied to the design of modified Wollaston prisms for Nomarski
differential interference contrast microscopy.
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Extrema Angles of Incidence and the Corresponding Optical
Axis Inclination Angles when the PAS is Perpendicular to the
Incident Beama
γ (deg)
α⊥max (deg)
δα⊥max (deg)
α⊥min (deg)
δα⊥min (deg)
45
-6.1413
31.4389
-33.6526
123.6573
50
-2.9395
33.4589
-32.0161
124.6012
60
3.0347
37.2505
-28.7029
126.5651
70
8.4289
40.7495
-25.2678
128.6373
75
10.9074
42.4028
-23.3038
129.6172
80
13.3282
44.2826
-21.5529
133.2024
85
15.6026
44.6413
-19.8100
132.4810
87
16.3890
45.9298
-18.8825
132.5090
88
16.8150
46.1984
-18.4771
132.7615
89
17.2367
46.4669
-18.0677
133.0140
89.4
17.4042
46.5691
-17.9027
133.1182
Prisms are quartz in the case 1
configuration, λ = 555 nm.
Table 2
Extrema Distances of the PAS from the Exit Face of the
Prism and the Corresponding Optical Axis Inclination Angles when the
PAS is Perpendicular to the Incident Beam for w =
3-mm-Thick Prisma
γ (deg)
Dmax (mm)
δDmax (deg)
Dmin (mm)
δDmin (deg)
75
1.5806
40.0140
-4.0989
134.1743
80
2.9632
41.5210
-5.5187
136.6092
85
7.1683
41.5611
-9.7041
136.0140
87
12.6725
42.4108
-15.1961
136.4068
88
19.6274
42.6052
-22.1505
136.6052
89
40.5017
42.8016
-43.0243
136.8016
89.25
54.4197
42.8537
-56.9425
136.8537
89.3
58.3964
42.8617
-60.9191
136.8617
89.35
62.9850
42.8737
-65.5077
136.8737
89.4
68.3383
42.8818
-70.8610
136.8818
89.45
74.6651
42.8898
-77.1877
136.8898
89.5
82.2573
42.9016
-84.7799
136.0018
Prisms are quartz in the case 1
configuration λ = 555 nm.
Table 3
Extrema Distances of the PAS from the Exit Face of the
Prism and the Corresponding Optical Axis Inclination Angles when the
PAS is Perpendicular to the Incident Beam for w =
20-mm-Thick Prism
γ (deg)
Dmax (mm)
δDmax (deg)
Dmin (mm)
δDmin (deg)
45
-1.9982
32.6894
-16.8391
128.1142
50
-1.0538
34.1703
-17.2727
129.1102
60
1.4110
36.7735
-18.9974
131.0902
70
5.9958
39.0020
-23.1305
133.0581
75
10.5374
40.0140
-27.3263
134.7435
Prisms are quartz in the case 1
configuration λ = 555 nm.
Table 4
Bias Retardation when the PAS is Perpendicular to the Axis
of the Optical System
γ (deg)
δ (deg)
α⊥ (deg)
D (mm)
dR/dy
0
(µm/mm)
RBias (µm)
89.25
43
17.2064
18.1478
0.1569
6.8033
89.30
43
17.2261
19.4740
0.1464
6.8013
89.35
43
17.2459
21.0042
0.1359
6.7993
89.40
43
17.2657
22.7895
0.1254
6.7972
89.45
43
17.2856
24.8994
0.1149
6.7952
89.50
43
17.3053
27.4313
0.1044
6.7932
Prism are quartz in the case 1
configuration, λ = 555 nm.
Tables (4)
Table 1
Extrema Angles of Incidence and the Corresponding Optical
Axis Inclination Angles when the PAS is Perpendicular to the
Incident Beama
γ (deg)
α⊥max (deg)
δα⊥max (deg)
α⊥min (deg)
δα⊥min (deg)
45
-6.1413
31.4389
-33.6526
123.6573
50
-2.9395
33.4589
-32.0161
124.6012
60
3.0347
37.2505
-28.7029
126.5651
70
8.4289
40.7495
-25.2678
128.6373
75
10.9074
42.4028
-23.3038
129.6172
80
13.3282
44.2826
-21.5529
133.2024
85
15.6026
44.6413
-19.8100
132.4810
87
16.3890
45.9298
-18.8825
132.5090
88
16.8150
46.1984
-18.4771
132.7615
89
17.2367
46.4669
-18.0677
133.0140
89.4
17.4042
46.5691
-17.9027
133.1182
Prisms are quartz in the case 1
configuration, λ = 555 nm.
Table 2
Extrema Distances of the PAS from the Exit Face of the
Prism and the Corresponding Optical Axis Inclination Angles when the
PAS is Perpendicular to the Incident Beam for w =
3-mm-Thick Prisma
γ (deg)
Dmax (mm)
δDmax (deg)
Dmin (mm)
δDmin (deg)
75
1.5806
40.0140
-4.0989
134.1743
80
2.9632
41.5210
-5.5187
136.6092
85
7.1683
41.5611
-9.7041
136.0140
87
12.6725
42.4108
-15.1961
136.4068
88
19.6274
42.6052
-22.1505
136.6052
89
40.5017
42.8016
-43.0243
136.8016
89.25
54.4197
42.8537
-56.9425
136.8537
89.3
58.3964
42.8617
-60.9191
136.8617
89.35
62.9850
42.8737
-65.5077
136.8737
89.4
68.3383
42.8818
-70.8610
136.8818
89.45
74.6651
42.8898
-77.1877
136.8898
89.5
82.2573
42.9016
-84.7799
136.0018
Prisms are quartz in the case 1
configuration λ = 555 nm.
Table 3
Extrema Distances of the PAS from the Exit Face of the
Prism and the Corresponding Optical Axis Inclination Angles when the
PAS is Perpendicular to the Incident Beam for w =
20-mm-Thick Prism
γ (deg)
Dmax (mm)
δDmax (deg)
Dmin (mm)
δDmin (deg)
45
-1.9982
32.6894
-16.8391
128.1142
50
-1.0538
34.1703
-17.2727
129.1102
60
1.4110
36.7735
-18.9974
131.0902
70
5.9958
39.0020
-23.1305
133.0581
75
10.5374
40.0140
-27.3263
134.7435
Prisms are quartz in the case 1
configuration λ = 555 nm.
Table 4
Bias Retardation when the PAS is Perpendicular to the Axis
of the Optical System
γ (deg)
δ (deg)
α⊥ (deg)
D (mm)
dR/dy
0
(µm/mm)
RBias (µm)
89.25
43
17.2064
18.1478
0.1569
6.8033
89.30
43
17.2261
19.4740
0.1464
6.8013
89.35
43
17.2459
21.0042
0.1359
6.7993
89.40
43
17.2657
22.7895
0.1254
6.7972
89.45
43
17.2856
24.8994
0.1149
6.7952
89.50
43
17.3053
27.4313
0.1044
6.7932
Prism are quartz in the case 1
configuration, λ = 555 nm.