Entanglement and Bell’s Inequalities
David Cruz, Nelson Lee
University of Rochester Institute of Optics
December 11, 2013
Abstract:
The main goal of this experiment was to prove the polarization-entangled state of a pair
of photons. These photon pairs were created using a non-linear optical process known as
spontaneous parametric down conversion (SPDC). We will prove this by using Bell’s
Inequalities, which in the case for entangled photons is violated for some angles of polarizers.
The experimental setup is described in detail in this report, and the results will show that Bell’s
Inequalities were indeed violated for some polarizer angles.
Key words: polarization-entangled photons, spontaneous parametric down conversion, Bell’s
Inequalities
Introduction and Background:
Entangled photons are a pair of photons where measurements performed on one particle
gives reliable information about the state of the second particle, regardless of how far apart these
particles are. Their wave functions cannot be separated nor can they be defined by their
individual wave functions alone. For this lab these photons are produced by a process known as
spontaneous parametric down conversion (SPDC). Using a Type I Beta Barium Borate (BBO)
crystal, when a vertically (or horizontally) polarized photon with a wavelength of λ is incident on
the crystal, two photons with horizontally (or vertically) polarization are produced with a
wavelength that is double that of the original photon, 2λ.
Figure 1: Pump Laser Incident on BBO Crystals with their Resulting Idler and Signal Beams
A quartz plate is used to compensate for the phase difference in these beams that results from the
thicknesses of each crystal. From there the down converted photons will be detected by two
APDs with polarizers placed in front, as well as interference filter to remove any stray light from
the laser. Once we observe and record the coincidence photon counts from each detector for a
given set up angles, we will use the following mathematical expression to determine
entanglement by calculating Bell’s Inequality in the form of Clauser, Horne, Shimony, and Holt
correlation.
𝑆 = 𝐸(𝑎, 𝑏) − 𝐸(𝑎, 𝑏 ′ ) + 𝐸(𝑎′ , 𝑏) + 𝐸(𝑎′ , 𝑏′)
(1)
These values of S will be calculated for:
𝐸(𝛼, 𝛽) =
[𝑁(𝛼,𝛽)+ 𝑁(𝛼⊥ -,𝛽⊥ )− 𝑁(𝛼,𝛽⊥ )− 𝑁(𝛼⊥ ,𝛽)]
[𝑁(𝛼,𝛽)+ 𝑁(𝛼⊥ ,𝛽⊥ )+ 𝑁(𝛼,𝛽⊥ )+ 𝑁(𝛼⊥ ,𝛽)]
(2)
a=-45° , a’=0° , 𝛼⊥ =45° , 𝛼⊥ ’=90°, b= -22.5° , b’ = 22.5° , 𝛽⊥= 67.5° , 𝛽⊥’=112.5°
The maximum value of S in Bell’s Inequality is |2|, therefore we know that obtaining a value of S
greater than |2| will prove that we have violated Bell’s Inequality. Another condition to violate
Bell’s Inequality is we should have a visibility greater than 0.71. We define visibility (V) by the
following equation:
[𝑀𝑎𝑥−𝑀𝑖𝑛]
𝑉 = [𝑀𝑎𝑥+𝑀𝑖𝑛]
(3)
Where “Max” and “Min” are the maximum and minimum number of counts. In this report we
will determine the ideal conditions to violate Bell’s inequalities, this includes polarizer A and B
angles and quartz plate angles, and we will use these angles in our calculations of S.
Experimental Setup:
A laser beam with roughly 25 mW of power and 405.5 nm wavelength passes through a filter
which removes florescence in the beam. The filtered beam reaches the quartz plate, which
induces a phase difference. Next the beam passes through the BBO crystal and experiences
parametric down conversion. This results in two subsequent beams that each pass through an
independent polarizer and eventually reaches two separate APD's where down converted photons
are observed. The following figure depicts the experimental setup described above.
APD B
APD A
Polarizer B
Polarizer A
BBO
Crystal
Quartz
Plate
Filter
Laser
Figure 2: Experimental Setup for Entanglement and Bell’s Inequality Lab
The two photons that result when the initial photon passes through the BBO crystal are called
idler and signal photons. The idler and signal photons that result from the incident photon have
orthogonal polarization.
Procedure:
I. Violate Bell's inequality
1. The polarizers that are in front of the APDs are rotated to different angles to try to find at
which combination of angles is Bell's inequality violated.
2. Determine whether or not Bell's inequalities are violated when setting the polarizers to random
angles.
II. Calculating cos2 dependence
1. Keep the angle of a polarizer constant while changing the angle of the other polarizer by 10
degrees.
III. Aligning Quartz Plate
1. Keep the angles of the polarizers constant.
2. Rotate the quartz wave plate to several angles (relative to the horizontal axis) and then
measure the corresponding coincidence counts.
3. Repeat step 2 but rotate the quartz wave plate to several angles relative to the vertical axis.
Results and Analysis:
Using a laser of 25mW and wavelength 405.5 nm, we recorded the single count of
photons at each detector using a LabView Program. To find the ideal angles for maximum
coincidence counts between the two detectors we will look at the following figures. Tabulating
values from the table in Appendix I allowed us to observe cos2 dependence between polarizer A
Coincidence Count
and polarizer B.
140
120
100
80
60
40
20
0
-20
Polarizer A:
135
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
Polarizer B Angles
Figure 3: Coincidence Counts Between Polarizer A=45°, 135° and Polarizer B Angles
Coincidence Count
V= 0.95 for polarizer A = 45°, V = 0.98 for polarizer A = 135°
100
90
80
70
60
50
40
30
20
10
0
Polarizer
A: 90
Polarizer
A: 0
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
Polarizer B Angles
Figure 4: Coincidence Counts Between Polarizer A=0°, 90° and Polarizer B Angles
V= 0.94 for polarizer A = 0°, V = 0.92 for polarizer A = 90°
340
We can see that coincidence count rates are maximum when the angles for polarizer A and B are
parallel, and a minimum when the angles for both polarizers are orthogonal. For quartz plate
alignment we measured what value gave us maximum coincidence counts when both polarizers
were at parallel angles.
50
45
Coincidence Count
40
35
0,0
30
45,45
25
90,90
135,135
20
15
10
5
0
Quartz Plate Angle
Figure 5: Coincidence Count with Fixed Polarizer Angles and Varying Quartz Plate Angles
However, ultimately we were capable of violating Bell’s Inequalities without the use of a quartz
plate. We tabulated the final results for this experiment for a set of predetermined polarizer
angles and we saw that we did indeed violate Bell’s Inequalities, however when we chose a
random sample set of arbitrary polarizer angles we were not able to meet the conditions to
violate Bell’s Inequalities.
Polarizer
A
Polarizer
B
Singles A
Std. Dev.
Count A
Singles B
Std. Dev.
Count B
-45
-22.5
6096.6
98.7248
6517.1
107.696
-45
22.5
6714.13
88.3682
6202
81.0279
-45
67.5
6670.37
79.6828
5891.23
82.4616
-45
112.5
6621.07
79.104
6718.03
61.2156
0
-22.5
6058.33
165.291
6909
213.101
0
22.5
6120.3
175.463
5927.9
209.193
0
67.5
6198.33
70.3995
6095.17
76.543
0
112.5
6259.07
72.2185
6687.3
70.9051
45
-22.5
5436.43
77.743
7035.77
97.4116
45
22.5
5389.67
86.6186
5927.5
68.213
45
67.5
5436.43
81.092
5683.47
81.5322
45
112.5
5454.23
77.5521
6570.17
100.438
90
-22.5
5784.93
74.0414
7009.9
70.6684
90
22.5
5743.33
88.2982
5956.97
89.8391
90
67.5
5711.6
71.7114
5652.87
71.8369
90
112.5
5739.57
77.4497
6542.67
98.7268
Accident
al
coinciden
ce
2.066071
897
2.165333
782
2.043427
56
2.312988
438
2.176564
102
1.886587
371
1.964553
503
2.176526
498
Average
coinciden
ce
1.988972
497
1.661257
984
1.606684
914
1.863431
353
2.108692
602
1.779067
915
1.678920
479
1.952709
847
Std. Dev.
Ave.
Coincide
nce
125.267
13.5721
30.9333
6.02829
11.8333
4.28376
96.7
8.01357
85.5
8.68113
70.6333
7.84102
4.56667
1.88795
23.0333
4.35877
6.76667
2.84888
46.6
5.59926
53.3667
6.62015
14.4
3.79292
41.6333
7.38817
5.46667
3.22419
50.6333
7.49015
87.8667
9.54746
Net
coinciden
ce
123.2009
281
28.76796
622
9.789872
44
94.38701
156
83.32343
59
68.74671
263
2.602116
497
20.85677
35
4.777697
503
44.93874
202
51.76001
509
12.53656
865
39.52460
74
3.687602
085
48.95437
952
85.91399
015
Std. Dev.
Net
Coincide
nce
13.5721
6.02829
4.28376
8.01357
8.68113
7.84102
1.88795
4.35877
2.84888
5.59926
6.62015
3.79292
7.38817
3.22419
7.49015
9.54746
Table 1: 16 Measurements for Combinations of Polarizer A=-45°, 0°, 45°, 90° and Polarizer
B=-22.5°, 22.5°, 67.5°, 112.5°
ab
E
0.846276
Std. Dev. of E
0.05159
a'b'
0.726075
0.05553
a'b
0.516908
0.05367485
ab'
-0.54266
0.06567
S
2.631921
Std. Dev. of S
0.12436
Table 2: Calculation of S for the Polarization Angles Contained in Table 1
The value for S is greater than 2, therefore we did violate Bell’s Inequalities for these sets of
polarizer angles by 5.08 standard deviations
Polarizer
A
Polarizer
B
Singles A
Std. Dev.
Count A
Singles B
Std. Dev.
Count B
0
22.5
6151.23
75.7367
5950.33
70.1876
0
67.5
6220.53
92.462
5684.67
92.255
0
112.5
6123.9
95.275
6518.27
77.8061
0
157.5
6227.97
99.1354
7078.73
85.9222
45
22.5
5431.23
83.3434
5949.9
73.382
45
67.5
5414.5
74.4774
5668.97
65.4199
45
112.5
5380.87
72.2886
6500.53
96.6846
45
157.5
5333.1
66.7695
6965.1
106.284
90
22.5
5699.13
69.3501
5880.93
75.9346
90
67.5
5773.4
85.7316
5687.93
103.854
90
112.5
5723.4
75.0184
6504.1
89.1559
90
157.5
5737.7
84.4925
7051.13
77.9486
135
22.5
6430.2
83.1598
5912.77
89.7974
135
67.5
6425.83
80.2896
5605.67
92.473
135
112.5
6397.7
92.3345
6462.2
95.4905
135
157.5
6435.83
79.149
7009.1
103.716
Accident
al
coinciden
ce
1.903296
117
1.838806
334
2.075696
15
2.292478
14
1.680394
32
1.596121
179
1.818882
357
1.931569
89
Average
coinciden
ce
1.742841
599
1.707612
143
1.935729
429
2.103777
967
1.977055
27
1.873096
288
2.149847
281
2.345687
555
Std. Dev.
Ave.
Coincide
nce
70.6667
9.4735
10.6333
2.69717
23.1333
4.96702
88.2
9.3823
44.6
7.54572
53
6.77215
14.8
4.14729
6.86667
2.45979
5.83333
2.43655
51.9667
6.63576
87.9
10.9618
44.8667
6.95172
29.9333
5.88354
10.5
2.4879
90.2
10.2264
118.8
11.409
Net
coinciden
ce
68.76340
388
8.794493
666
21.05760
385
85.90752
186
42.91960
568
51.40387
882
12.98111
764
4.935100
11
4.090488
401
50.25908
786
85.96427
057
42.76292
203
27.95624
473
8.626903
712
88.05015
272
116.4543
124
Std. Dev.
Net
Coincide
nce
9.4735
2.69717
4.96702
9.3823
7.54572
6.77215
4.14729
2.45979
2.43655
6.63576
10.9618
6.95172
5.88354
2.4879
10.2264
11.409
Table 3: 16 Measurements for Combinations of Polarizer A=0°, 45°, 90°, 135° and
Polarizer B=22.5°, 67.5°, 112.5°, 157.5°
ab
E
0.720384
Std. Dev. of E
0.057508
a'b'
0.850491
0.037323
a'b
0.523727
0.072874
ab'
-0.45071
0.066717
S
2.545312
Std. Dev. of S
0.120258
Table 4: Calculation of S for the Polarization Angles Contained in Table 3
The value for S is greater than 2, therefore we did violate Bell’s Inequalities for these sets of
polarizer angles by 4.53 standard deviations
Polarizer
A
Polarizer
B
Singles A
Std. Dev.
Count A
Singles B
Std. Dev.
Count B
-40
0
6402.67
82.5158
6387.93
113.212
-40
20
6259.03
171.386
5790.03
173.998
-40
40
6439.67
73.7846
5599.6
96.2653
-40
60
6410.4
91.6833
5517.2
77.3939
10
-30
5868.87
94.3397
7021.9
77.475
10
-10
5811.53
70.8158
6589.53
85.5911
10
10
5795.7
72.0475
6100.6
74.6586
10
30
5884.2
87.382
5675.97
76.205
60
60
5250.07
58.9932
5463.73
66.716
60
100
5207.57
83.3988
6066.07
80.6054
60
130
5230.63
85.8083
6743.5
88.4361
60
160
5243.4
61.855
6855.3
73.5528
110
-100
5979.2
87.1556
6169.17
84.9942
110
50
5889.87
84.4114
5365.57
63.4626
110
100
5868.67
73.7603
6019.4
73.1977
110
150
5940.3
97.9145
6863.07
107.11
Accident
al
coincide
nce
2.126790
004
1.884478
516
1.875097
959
1.839107
862
2.142952
149
1.991353
067
1.838576
866
1.736724
219
Average
coincide
nce
1.491618
178
1.642653
176
1.834183
177
1.869144
161
1.918108
466
1.643330
508
1.836945
354
2.119972
125
Std. Dev.
Ave.
Coincide
nce
85.7
8.36722
40.9667
6.84046
10.1667
3.20649
3.16667
1.80198
58.9
7.48493
74.4
7.24259
79
8.17059
65.7
8.30932
56.2333
7.66399
46.5
7.68676
20.1
3.42758
3.1
2.13913
65.5
7.17635
12.2667
2.94704
89.1333
7.70013
93.1333
8.88134
Net
coincide
nce
83.57321
39.08222
148
8.291602
041
1.327562
138
56.75704
785
72.40864
693
77.16142
313
63.96327
578
54.74168
182
44.85734
682
18.26581
682
1.230855
839
63.58189
153
10.62336
949
87.29635
465
91.01332
787
Std. Dev.
Net
Coincide
nce
8.36722
6.84046
3.20649
1.80198
7.48493
7.24259
8.17059
8.30932
7.66399
7.68676
3.42758
2.13913
7.17635
2.94704
7.70013
8.88134
Table 5: 16 Measurements for Arbitrary Polarizer A and Polarizer B Arbitrary Angles
ab
E
0.235368467
Std. Dev. of E
0.075056078
a'b'
0.373244169
0.059146663
a'b
0.011622633
0.05367485
ab'
-0.067884027
0.122751274
S
0.688119296
Std. Dev. of S
0.164561865
Table 6: Calculation of S for the Polarization Angles Contained in Table 5
The value for S is less than 2; therefore we did not violate Bell’s Inequalities for these sets of
polarizer angles.
Conclusion:
In this experiment, quantum entanglement in photon pairs was observed using a
Spontaneous Parametric Down Conversion. The experimental setup as well as the results show
that there are effects on quantum entanglement behavior when there are changes in the angles of
the polarizer and quartz plate. At certain angles of the polarizer, Bell's inequalities for quantum
experiments
are
violated
and
this
was
seen
by
performing
coincidence
count
measurements. These experiments also showed that rotating the polarizer to random angles
wouldn't be sufficient to violate Bell's inequalities. Experiments that yielded an S value greater
than 2, Bell’s Inequalities for that particular combination of polarizer angles were not
violated. The maximum S measured was 2.63. By measuring coincidence counts for the
polarizer rotated by 10 degrees each way, we observed the cos2 dependence of the probability
that two photons will have the same polarization.
References:
1. Lukishova, Svetlana. Lab 1 Manual, Web. Fall 2013.
http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/op
t253_08_lab1_entangl_manual.pdf
2. J. Eberly, Bell Inequalities and Quantum Mechanics. Amer. J. Phys., 70 (3), 276 (2002)
http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/eb
erlybellsineq.pdf
3. P.G. Kwiat et. al., Ultrabright Source of Polarization-entangled Photons. Phys. Rev. A.
60, R773 (1999)
http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/ty
pe_i_kwiat_physrev_99.pdf
Contributions:
Special thanks to Dr. Svetlana Lukishova. Under her guidance, all members contributed equally
during lab to collect and analyze data.
Nelson Lee wrote the “Experimental Setup”, “Procedure” and “Conclusions” sections.
David Cruz wrote the “Abstract”, “Introduction and Background”, and “Results and Analysis”
sections.
Appendix I: Cos2 Dependence
Polarizer
A
Polarizer
B
Singles
A
Std.
Dev.
Count A
Singles
B
45
0
4760
86.5794
5760.27
45
20
4838.1
147.929
45
40
4786
85.5638
45
60
4753.1
45
80
45
Std.
Dev.
Count B
Accidental
coincidence
Average
coincidence
Std. Dev. Ave.
Coincidence
Net
coincidence
76.7472
1.42578203
22.7667
5.46262
21.34091797
5372.17
129.41
1.351536975
44.6667
7.29824
43.31516302
4964.23
65.7722
1.235457849
56.3
9.04834
55.06454215
104.463
4892.33
89.1699
1.209194154
55.4333
8.77175
54.22410585
4798.6
75.7517
5137.13
89.2504
1.281853665
41.5333
5.46925
40.25144634
100
4867.17
110.418
5681.4
113.509
1.437921661
24.2
4.61183
22.76207834
45
120
5115
87.2286
6366.4
86.3472
1.693335072
9.2333
2.97905
7.539964928
45
140
5052.5
114.308
6607.33
169.052
1.735943811
2.3
1.78403
0.564056189
45
160
5068.07
82.4382
6658.57
94.3357
1.754797141
8.3333
3.25188
6.578502859
45
180
5108.1
82.0766
6431.3
81.0769
1.708289624
28.6667
5.30669
26.95841038
45
200
5088.37
66.8815
6016.53
71.198
1.591945199
47.4
7.28532
45.8080548
45
220
5180.67
95.441
5837.43
83.3301
1.572573521
61.4
7.56398
59.82742648
45
240
5101.7
83.8135
5704.93
79.6228
1.513451752
63.4667
7.80245
61.95324825
45
260
5786.27
102.228
6057.47
110.745
1.822608161
49.4333
7.14714
47.61069184
45
280
5065.83
59.0424
6366.53
73.1893
1.677091451
28.9
3.51695
27.22290855
45
300
5054.63
60.226
6726.57
70.8382
1.768016771
10.0333
3.0341
8.265283229
45
320
5098.1
77.8656
6820.27
60.8282
1.808061761
1.8
1.34933
-0.008061761
45
340
5087.2
86.3998
6616.33
66.4573
1.750246887
7.7
2.86657
5.949753113
90
0
5449.9
88.7085
6167
106.408
1.747695732
12.3
3.43561
10.55230427
90
20
5423.43
67.8175
5352.57
67.9273
1.509523013
5.46667
2.27025
3.957146987
90
40
5400.3
75.4395
5313.47
68.3151
1.492105266
15.9667
3.64345
14.47459473
90
60
5402
68.9232
5236.13
72.7929
1.470849862
42.5667
7.65048
41.09585014
90
80
5374.03
90.8396
5464.83
78.2393
1.527144339
65.9333
7.20121
64.40615566
90
100
5404.07
80.2547
5888.83
91.1214
1.654829776
81.3667
9.83128
79.71187022
90
120
5392.87
81.4454
6306.93
83.8845
1.768647587
85.5
10.2478
83.73135241
90
140
5467.53
97.1982
6656.17
109.388
1.892426076
63.0667
9.07795
61.17427392
90
160
5369.93
75.2673
6615.7
67.4149
1.847343987
38.3333
4.99885
36.48595601
90
180
5356.67
80.2304
6392
77.6873
1.780471401
14.4333
3.08146
12.6528286
90
200
5350.03
64.3125
6005.67
77.5399
1.670786763
5.5333
2.04658
3.862513237
90
220
5379.87
75.6014
5684.7
70.8764
1.590313243
18.5667
3.99727
16.97638676
90
240
5384.2
86.3643
5633.6
65.7244
1.577286314
46.6667
5.94998
45.08941369
90
260
5400.5
72.5566
5911.47
73.2081
1.660094474
75.9333
8.55382
74.27320553
90
280
5354.87
79.0943
6275.4
80.5963
1.747405462
94.0667
9.73771
92.31929454
90
300
5388.47
77.8047
6617.73
79.699
1.854290858
91.8
11.3241
89.94570914
90
320
5377.03
83.1921
6751.73
77.752
1.887821248
69.1333
7.65071
67.24547875
90
340
5380.13
92.4079
6551.4
90.1025
1.832863951
37.6333
5.12925
35.80043605
135
0
6099.33
111.747
6143.33
99.2744
1.948450242
75.6333
9.29027
73.68484976
135
20
6116
108.279
5692.33
79.5046
1.810343095
35.4
5.3922
33.58965691
135
40
6170.27
101.581
5372.43
83.7516
1.72376587
6.86667
2.31537
5.14290413
135
60
6097.47
94.0982
5256.27
109.593
1.666597329
4.2
1.901
2.533402671
23.21756061
135
80
6169.6
77.1213
5555.9
92.9135
1.782439393
25
5.42663
135
100
6184.87
80.725
5939.97
106.579
1.910372997
67.9667
7.95887
66.056327
135
120
6161.43
103.107
6393.13
96.9169
2.048322795
102.567
9.23144
100.5186772
135
140
6181.43
105.934
6737.33
95.6965
2.165609357
125.5
10.3115
123.3343906
135
160
6066.47
110.182
6647.93
93.8142
2.097132331
114.833
12.4349
112.7358677
135
180
6157.27
89.3447
6456.3
69.645
2.06716548
81.3333
8.04013
79.26613452
135
200
6166.17
73.2427
6110.47
91.6804
1.959266234
40.3333
6.37524
38.37403377
135
220
6145.77
97.0377
5770.83
96.797
1.844242082
7.76667
3.01357
5.922427918
135
240
6140.97
111.256
5748.07
117.503
1.835533722
5.06667
2.61209
3.231136278
135
260
6121.9
120.015
5943.3
127.564
1.89198299
32.1333
5.09722
30.24131701
135
280
6191.83
94.63
6429.3
101.238
2.070074896
77.2333
7.33759
75.1632251
135
300
6202.2
104.967
6798.47
118.107
2.192604473
117.433
11.9299
115.2403955
135
320
6172.2
91.9357
6880.93
100.645
2.20846476
131.733
11.8378
129.5245352
135
340
6193.17
87.3886
6713.6
87.894
2.162080238
118.833
10.1066
116.6709198
0
0
5925.57
74.3281
6213.3
93.5363
1.914501892
90.0333
9.28656
88.11879811
0
20
5868.2
75.6277
5759.57
74.9799
1.757512051
72.4667
8.41892
70.70918795
0
40
5850.83
91.9727
5376.87
84.6126
1.63587592
46.7333
6.36766
45.09742408
0
60
5870.8
91.3668
5344.7
97.1622
1.631638568
20.4
5.50611
18.76836143
0
80
5905.43
80.3684
5541.43
85.1371
1.701675402
4.53333
2.09652
2.831654598
0
100
5887.37
76.109
5923.87
82.1432
1.813552755
10.3
3.10894
8.486447245
0
120
5843.4
96.1215
6348.4
75.8213
1.929004509
33.8667
6.1741
31.93769549
0
140
5861.93
92.4266
6707.77
90.4158
2.044664866
60.4
7.30423
58.35533513
0
160
5850.63
107.303
6727.3
102.605
2.046665046
88.5333
8.7286
86.48663495
0
180
5865.13
89.4561
6461.83
78.8858
1.970772595
95.4333
11.425
93.4625274
0
200
5894.1
97.5759
6093.53
92.2959
1.867625509
81.2333
7.24299
79.36567449
0
220
5767.3
150.319
5688.97
161.803
1.706119827
50.7667
6.89669
49.06058017
0
240
5900.7
84.4484
5780.83
84.6119
1.773769066
20.5
4.0322
18.72623093
0
260
5875.1
75.6162
5976.03
75.6213
1.82570824
4.56667
2.31462
2.74096176
0
280
5868.93
92.0311
6377.6
75.9612
1.946343774
12.0333
3.6529
10.08695623
0
300
5880.5
88.2296
6754.2
75.7147
2.065339801
37.7667
5.00815
35.7013602
0
320
5833.9
98.3769
6835
107.933
2.073484738
66.7333
7.2869
64.65981526
0
340
5851.07
97.9254
6648.3
93.3274
2.022782771
89.5667
8.43508
87.54391723
Table A1: Measurements for Polarizer A=0°, 45°, 90°, 135° and Polarizer B= 0°-360°
Incremented by 10°