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Optical Ray Trace Analysis
This analysis treats the geometric optics for the cartridge in a single plane. Although the rays propagate in three dimensions, the worst aberrations will occur in this plane, since it is where rays entering the lens are furthest from the optical axis.
The lines labeled 1, 2 and 3 in the lower left corner of the diagram each represent a bundle of three rays, all of which enter at the same point. They will be designated a, b and c in each bundle; a enters at -2.5 milliradians (-.1432 degrees) from horizontal, b enters horizontally and c enters +2.5 milliradians (.1432 degrees) from horizontal. Rays that pass through a boundary between two materials of differing refractive index, obey Snell's Law, which states that: n1*sin(a1)=n2*sin(a2), where n1 and n2 are the refractive indices of the first and second material, respectively and a1 and a2 are the angles between the ray and the surface normal before and after passing through the surface.
At the input side of surface A, the following conditions prevail (angles in radians):
Angle of Ray Above Horizontal
Position of Ray Above Centerline
Input ID's
1
2
3
Input ID's
1
2
3
n1
1
a
-0.0025
-0.0025
-0.0025
a
-0.09252
-0.17126
-0.25
n2
1.5067
b
0
0
0
b
-0.09252
-0.17126
-0.25
c
0.0025
0.0025
0.0025
c
-0.09252
-0.17126
-0.25
Angle of Surface Normal to Horizontal
Angle of Ray to Surface Normal
Input ID's
1
2
3
Input ID's
1
2
3
a
0.25413
0.48406
0.74687
a
0.256639
0.486564
0.749373
b
0.25413
0.48406
0.74687
b
0.254139
0.484064
0.746873
c
0.25413
0.48406
0.74687
c
0.251639
0.481564
0.744373
At the output side of surface A, the following conditions prevail (angles in radians):
Angle of Ray to Surface Normal
Angle of Ray Above Horizontal
Input ID's
1
2
3
Input ID's
1
2
3
a
0.16927
0.31555
0.46911
a
0.084863
0.168511
0.277754
b
0.16764
0.31400
0.46775
b
0.086492
0.170055
0.279117
c
0.16601
0.31246
0.46639
c
0.088121
0.171600
0.280482
Horizontal Distance to Surface B
Vertical Rise on the Way to Surface B
Input ID's
1
2
3
Input ID's
1
2
3
a
0.21217
0.18172
0.12604
a
0.018049
0.030915
0.035938
b
0.21217
0.18172
0.12604
b
0.018397
0.031203
0.036124
c
0.21217
0.18172
0.12604
c
0.018746
0.031493
0.036310
At the input side of surface B, the following conditions prevail (normal is horizontal):
Angle of Ray Above Horizontal
Position of Ray Above Centerline
Input ID's
1
2
3
Input ID's
1
2
3
n1
1.5067
a
0.08486
0.16851
0.27775
a
-0.074470
-0.140344
-0.214061
n2
1
b
0.08649
0.17005
0.27911
b
-0.074122
-0.140056
-0.213875
c
0.08812
0.17160
0.28048
c
-0.073773
-0.139766
-0.213689
At the output side of surface B, the following conditions prevail:
Angle of Ray Above Horizontal
Vertical Rise on the Way to Surface C
Input ID's
1
2
3
Input ID's
1
2
3
delta x
0.203
a
0.12806
0.25546
0.42589
a
0.026139
0.053018
0.092092
b
0.13052
0.25783
0.42806
b
0.026648
0.053532
0.092623
c
0.13299
0.26020
0.43023
c
0.027157
0.054047
0.093157
At the input side of surface C, the following conditions prevail:
Angle of Ray Above Horizontal
Position of Ray Above Centerline
Input ID's
1
2
3
Input ID's
1
2
3
n1
1
a
0.12806
0.25546
0.42589
a
-0.048330
-0.087326
-0.121969
n2
1.7574
b
0.13052
0.25783
0.42806
b
-0.047473
-0.086523
-0.121251
c
0.13299
0.26020
0.43023
c
-0.046616
-0.085719
-0.120531
At the output side of surface C, the following conditions prevail:
Angle of Ray Above Horizontal
Vertical Rise on the Way to Surface D
Input ID's
1
2
3
Input ID's
1
2
3
delta x
0.177
a
0.07273
0.14429
0.23730
a
0.012896
0.025718
0.042809
b
0.07412
0.14560
0.23845
b
0.013144
0.025956
0.043025
c
0.07552
0.14692
0.23961
c
0.013393
0.026195
0.043242
At the input side of surface D, the following conditions prevail (surface normal is horizontal):
Angle of Ray Above Horizontal
Position of Ray Above Centerline
Input ID's
1
2
3
Input ID's
1
2
3
n1
1.7574
a
0.07273
0.14429
0.23730
a
-0.035434
-0.061608
-0.079160
n2
1
b
0.07412
0.14560
0.23845
b
-0.034328
-0.060567
-0.078226
c
0.07552
0.14692
0.23961
c
-0.033222
-0.059524
-0.077288
At the output side of surface D, the following conditions prevail:
Angle of Ray Above Horizontal
Vertical Rise on the Way to Surface E
Input ID's
1
2
3
Input ID's
1
2
3
delta x
0.159
a
0.12806
0.25546
0.42589
a
0.020473
0.041526
0.072131
b
0.13052
0.25783
0.42806
b
0.020872
0.041929
0.072547
c
0.13299
0.26020
0.43023
c
0.021271
0.042333
0.072965
At the input side of surface E, the following conditions prevail:
Angle of Ray Above Horizontal
Position of Ray Above Centerline
Input ID's
1
2
3
Input ID's
1
2
3
n1
1
a
0.12806
0.25546
0.42589
a
-0.014960
-0.020081
-0.007028
n2
1.48
b
0.13052
0.25783
0.42806
b
-0.013456
-0.018637
-0.005678
c
0.13299
0.26020
0.43023
c
-0.011951
-0.017190
-0.004323
At the output side of surface E, the following conditions prevail:
Angle of Ray Above Horizontal
Vertical Rise on the Way to Surface F
Input ID's
1
2
3
Input ID's
1
2
3
delta x
0.177
a
0.08639
0.17158
0.28290
a
0.015330
0.030671
0.051453
b
0.08805
0.17315
0.28429
b
0.015626
0.030958
0.051720
c
0.08971
0.17472
0.28568
c
0.015922
0.031245
0.051988
At the input side of surface F, the following conditions prevail:
Angle of Ray Above Horizontal
Position of Ray Above Centerline
Input ID's
1
2
3
Input ID's
1
2
3
a
0.08639
0.17158
0.28290
a
3.70278
0.010589
0.044425
b
0.08805
0.17315
0.28429
b
0.002169
0.012320
0.046042
c
0.08971
0.17472
0.28568
c
0.003970
0.014054
0.047665
Bottom
Top
Height
3.70278E
0.04766
0.04729