Claudio Rivolta, "Intensity and resolution at the diffraction focus of optical systems with rotationally symmetric aberration functions," Appl. Opt. 31, 4444-4452 (1992)
The intensities and resolutions at the diffraction focus of optical systems with rotationally symmetric minimum-variance aberration functions as well as functions with slight variations from this shape and a prescribed fixed maximum deviation value at the edge of the exit pupil are calculated for circular and annular exit pupils. The results for the intensity at the diffraction focus obtained either by numerical integration of the diffraction integral or by using the Maréchal formula show that the maxima of these intensities are achieved for optical systems with wave aberration functions of minimum variance, thus verifying the Maréchal criterion. The resolutions (first zeros of the intensities in the radial direction) at this diffraction focus are also presented.
Claudio Rivolta, "Intensity and resolution at the diffraction focus of optical systems with rotationally symmetric aberration functions: erratum," Appl. Opt. 32, 2273-2273 (1993) https://opg.optica.org/ao/abstract.cfm?uri=ao-32-13-2273
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Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
3.752
−9.337
5.835
0.1894
88.485
88.180
1.7845
100
0.2
3.748
−9.155
5.657
0.1554
82.762
82.549
2.6949
92.16
0.3
3.735
−8.867
5.382
0.1174
76.019
75.898
3.7377
82.81
0.4
3.677
−8.333
4.906
0.0782
66.778
66.734
4.7851
70.56
0.5
3.505
−7.449
4.194
0.0428
54.814
54.806
5.3001
56.25
0.6
3.180
−6.243
3.313
0.0171
40.637
40.637
4.8903
40.96
0.707
2.705
−4.821
2.367
0.0241
24.986
24.986
3.5139
25.02
The W2n coefficients of the spherical aberration polynomials are the values that minimize the variance for W(1) = λ/4. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 2
Intensity (INI) at the Diffraction Focus (UDE) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
7.505
−18.675
11.670
0.2340
60.241
57.179
2.0939
100
0.2
7.496
−18.310
11.314
0.1576
59.175
56.892
2.5282
92.16
0.3
7.470
−17.733
10.763
0.1019
58.374
56.973
3.2571
82.81
0.4
7.354
−16.665
9.811
0.0738
56.449
55.898
4.2341
70.56
0.5
7.009
−14.898
8.388
0.0527
50.693
50.585
4.9597
56.25
0.6
6.360
−12.486
6.626
0.0273
39.683
39.675
4.7847
40.96
0.707
5.409
−9.642
4.733
0.0069
24.898
24.898
3.5020
25.02
The W2n coefficients of the spherical aberration polynomials are the values that minimize the variance for W(1) = λ/2. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFs) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 3
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
11.257
−28.012
17.505
18.4146
34.251
20.374
0.4683
100
0.2
11.244
−27.465
16.971
−0.3502
32.268
24.711
2.5786
92.16
0.3
11.205
−26.601
16.146
−0.3245
36.635
31.444
2.7610
82.81
0.4
11.031
−24.999
14.718
−0.1523
42.267
39.965
3.4975
70.56
0.5
10.515
−22.347
12.582
−0.0103
44.421
43.926
4.4433
56.25
0.6
9.540
−18.729
9.939
0.0235
38.137
38.098
4.6136
40.96
0.707
8.115
−14.463
7.101
0.0701
24.751
24.750
3.4822
25.02
The W2n coefficients of the spherical aberration polynomials are the values that minimize the variance for W(1) = 3λ/4. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 4
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
2.752
−8.337
5.835
−1.2733
82.510
78.892
1.3347
100
0.2
2.748
−8.155
5.657
−1.1756
77.247
74.519
2.2854
92.16
0.3
2.735
−7.867
5.382
−0.9901
71.086
69.380
3.3744
82.81
0.4
2.677
−7.333
4.906
−0.6143
62.723
62.063
4.4672
70.56
0.5
2.505
−6.449
4.194
0.0425
51.921
51.759
5.0331
56.25
0.6
2.180
−5.243
3.313
1.0944
39.033
38.565
4.7089
40.96
0.707
1.705
−3.821
2.367
2.8395
24.449
23.410
3.4412
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 1 are, respectively, ΔW4 = −1 and ΔW6 = +1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 5
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
4.752
−10.337
5.835
1.4409
83.278
78.862
2.4720
100
0.2
4.748
−10.155
5.657
1.2761
77.655
74.536
3.1492
92.16
0.3
4.735
−9.867
5.382
1.0270
71.202
69.411
3.9369
82.81
0.4
4.677
−9.333
4.906
0.6076
62.628
62.045
4.7292
70.56
0.5
4.505
−8.449
4.194
−0.0648
51.821
51.753
5.1078
56.25
0.6
4.180
−7.243
3.313
−1.1116
38.998
38.573
4.7196
40.96
0.707
3.705
−5.821
2.367
−2.8049
24.451
23.448
3.4424
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 1 are, respectively, ΔW4 = +1 and ΔW6 = −1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 6
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
6.505
−17.675
11.670
−1.6084
57.789
49.777
1.6102
100
0.2
6.496
−17.310
11.314
−1.5102
56.588
50.252
2.1024
92.16
0.3
6.470
−16.733
10.763
−1.2716
55.563
51.340
2.8849
82.81
0.4
6.354
−15.665
9.811
−0.7875
53.548
51.644
3.9196
70.56
0.5
6.009
−13.898
8.388
−0.0470
48.205
47.670
4.6998
56.25
0.6
5.360
−11.486
6.626
1.0726
38.154
37.625
4.6059
40.96
0.707
4.409
−8.642
4.733
2.8149
24.365
23.339
3.4295
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 2 are, respectively, ΔW4 = −1 and ΔW6 = +1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 7
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
8.505
−19.675
11.670
1.5790
56.561
49.699
2.9635
100
0.2
8.496
−19.310
11.314
1.3310
55.437
50.282
3.1706
92.16
0.3
8.470
−18.733
10.763
1.0195
54.656
51.378
3.6513
82.81
0.4
8.354
−17.665
9.811
0.5752
52.948
51.601
4.3252
70.56
0.5
8.009
−15.898
8.388
−0.0892
47.928
47.643
4.8297
56.25
0.6
7.360
−13.486
6.626
−1.1224
38.077
37.640
4.6257
40.96
0.707
6.409
−10.642
4.733
−2.8283
24.363
23.348
3.4310
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 2 are, respectively, ΔW4 = +1 and ΔW6 = −1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 8
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
10.257
−27.012
17.505
−2.7092
31.598
16.066
2.9402
100
0.2
10.244
−26.465
16.971
−2.6241
33.659
20.400
2.5550
92.16
0.3
10.205
−25.601
16.146
−2.1793
36.917
27.281
2.6485
82.81
0.4
10.031
−23.999
14.718
−1.2925
41.132
36.382
3.3034
70.56
0.5
9.515
−21.347
12.582
−0.2112
42.561
41.209
4.2260
56.25
0.6
8.540
−17.729
9.939
1.0312
36.721
36.086
4.4429
40.96
0.707
7.115
−13.463
7.101
2.8701
24.219
23.145
3.4093
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 3 are, respectively, ΔW4 = −1 and ΔW6 = +1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 9
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
12.257
−29.012
17.505
19.4870
37.994
16.008
0.3794
100
0.2
12.244
−28.465
16.971
20.1466
33.810
20.428
0.1442
92.16
0.3
12.205
−27.601
16.146
0.6607
33.787
27.340
3.1294
82.81
0.4
12.031
−25.999
14.718
0.3410
39.499
36.342
3.6751
70.56
0.5
11.515
−23.347
12.582
−0.1796
41.983
41.192
4.3761
56.25
0.6
10.540
−19.729
9.939
−1.1449
36.593
36.108
4.4695
40.96
0.707
9.115
−15.463
7.101
−2.7708
24.226
23.258
3.4130
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 3 are, respectively, ΔW4 = +1 and ΔW6 = −1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 10
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
A
0
4.758
−11.840
7.399
0.2237
82.032
81.357
0.317
0.2
5.112
−12.488
7.716
0.1727
75.312
74.703
0.341
0.3
5.707
−13.548
8.223
0.1373
67.686
67.144
0.382
0.4
7.001
−15.865
9.340
0.0808
57.660
57.200
0.476
0.5
9.730
−20.679
11.643
0.0125
45.974
45.603
0.694
0.6
15.964
−31.340
16.631
−0.0646
33.485
33.209
1.255
0.707
35.168
−62.690
30.774
−0.1440
20.458
20.285
3.251
The W2n polynomial coefficients were calculated for the edge polynomial values of W(1) = Aλ listed in the last column to obtain the constant variance value of
for each obscuration ratio, i.e., its upper permissible limit for calculating the intensity with the Maréchal formula.
Table 11
Resolution (VR) and Intensity (IR) at the Diffraction Focus Plane (u = uDF) for Optical Systems with the Spherical Aberration Coefficients Listed in Tables 1, 4, and 5a
The second column lists the resolution at the paraxial image plane for a diffraction-limited (DL) system.
Table 12
Resolution (VR) and Intensity (IR) at the Diffraction Focus Plane (U = UDF) for Optical Systems with the Spherical Aberration Coefficients Listed in Tables 2, 6, and 7a
The second column lists the resolution at the paraxial image plane for a diffraction-limited (DL) system.
Table 13
Resolution (VR) and Intensity (IR) at the Diffraction Focus Plane (U = UDF) for Optical Systems with the Spherical Aberration Coefficients Listed in Tables 3, 8, and 9a
The second column lists the resolution at the paraxial image plane for a diffraction-limited (DL) system.
Tables (13)
Table 1
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
3.752
−9.337
5.835
0.1894
88.485
88.180
1.7845
100
0.2
3.748
−9.155
5.657
0.1554
82.762
82.549
2.6949
92.16
0.3
3.735
−8.867
5.382
0.1174
76.019
75.898
3.7377
82.81
0.4
3.677
−8.333
4.906
0.0782
66.778
66.734
4.7851
70.56
0.5
3.505
−7.449
4.194
0.0428
54.814
54.806
5.3001
56.25
0.6
3.180
−6.243
3.313
0.0171
40.637
40.637
4.8903
40.96
0.707
2.705
−4.821
2.367
0.0241
24.986
24.986
3.5139
25.02
The W2n coefficients of the spherical aberration polynomials are the values that minimize the variance for W(1) = λ/4. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 2
Intensity (INI) at the Diffraction Focus (UDE) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
7.505
−18.675
11.670
0.2340
60.241
57.179
2.0939
100
0.2
7.496
−18.310
11.314
0.1576
59.175
56.892
2.5282
92.16
0.3
7.470
−17.733
10.763
0.1019
58.374
56.973
3.2571
82.81
0.4
7.354
−16.665
9.811
0.0738
56.449
55.898
4.2341
70.56
0.5
7.009
−14.898
8.388
0.0527
50.693
50.585
4.9597
56.25
0.6
6.360
−12.486
6.626
0.0273
39.683
39.675
4.7847
40.96
0.707
5.409
−9.642
4.733
0.0069
24.898
24.898
3.5020
25.02
The W2n coefficients of the spherical aberration polynomials are the values that minimize the variance for W(1) = λ/2. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFs) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 3
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
11.257
−28.012
17.505
18.4146
34.251
20.374
0.4683
100
0.2
11.244
−27.465
16.971
−0.3502
32.268
24.711
2.5786
92.16
0.3
11.205
−26.601
16.146
−0.3245
36.635
31.444
2.7610
82.81
0.4
11.031
−24.999
14.718
−0.1523
42.267
39.965
3.4975
70.56
0.5
10.515
−22.347
12.582
−0.0103
44.421
43.926
4.4433
56.25
0.6
9.540
−18.729
9.939
0.0235
38.137
38.098
4.6136
40.96
0.707
8.115
−14.463
7.101
0.0701
24.751
24.750
3.4822
25.02
The W2n coefficients of the spherical aberration polynomials are the values that minimize the variance for W(1) = 3λ/4. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 4
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
2.752
−8.337
5.835
−1.2733
82.510
78.892
1.3347
100
0.2
2.748
−8.155
5.657
−1.1756
77.247
74.519
2.2854
92.16
0.3
2.735
−7.867
5.382
−0.9901
71.086
69.380
3.3744
82.81
0.4
2.677
−7.333
4.906
−0.6143
62.723
62.063
4.4672
70.56
0.5
2.505
−6.449
4.194
0.0425
51.921
51.759
5.0331
56.25
0.6
2.180
−5.243
3.313
1.0944
39.033
38.565
4.7089
40.96
0.707
1.705
−3.821
2.367
2.8395
24.449
23.410
3.4412
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 1 are, respectively, ΔW4 = −1 and ΔW6 = +1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 5
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
4.752
−10.337
5.835
1.4409
83.278
78.862
2.4720
100
0.2
4.748
−10.155
5.657
1.2761
77.655
74.536
3.1492
92.16
0.3
4.735
−9.867
5.382
1.0270
71.202
69.411
3.9369
82.81
0.4
4.677
−9.333
4.906
0.6076
62.628
62.045
4.7292
70.56
0.5
4.505
−8.449
4.194
−0.0648
51.821
51.753
5.1078
56.25
0.6
4.180
−7.243
3.313
−1.1116
38.998
38.573
4.7196
40.96
0.707
3.705
−5.821
2.367
−2.8049
24.451
23.448
3.4424
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 1 are, respectively, ΔW4 = +1 and ΔW6 = −1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 6
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
6.505
−17.675
11.670
−1.6084
57.789
49.777
1.6102
100
0.2
6.496
−17.310
11.314
−1.5102
56.588
50.252
2.1024
92.16
0.3
6.470
−16.733
10.763
−1.2716
55.563
51.340
2.8849
82.81
0.4
6.354
−15.665
9.811
−0.7875
53.548
51.644
3.9196
70.56
0.5
6.009
−13.898
8.388
−0.0470
48.205
47.670
4.6998
56.25
0.6
5.360
−11.486
6.626
1.0726
38.154
37.625
4.6059
40.96
0.707
4.409
−8.642
4.733
2.8149
24.365
23.339
3.4295
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 2 are, respectively, ΔW4 = −1 and ΔW6 = +1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 7
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
8.505
−19.675
11.670
1.5790
56.561
49.699
2.9635
100
0.2
8.496
−19.310
11.314
1.3310
55.437
50.282
3.1706
92.16
0.3
8.470
−18.733
10.763
1.0195
54.656
51.378
3.6513
82.81
0.4
8.354
−17.665
9.811
0.5752
52.948
51.601
4.3252
70.56
0.5
8.009
−15.898
8.388
−0.0892
47.928
47.643
4.8297
56.25
0.6
7.360
−13.486
6.626
−1.1224
38.077
37.640
4.6257
40.96
0.707
6.409
−10.642
4.733
−2.8283
24.363
23.348
3.4310
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 2 are, respectively, ΔW4 = +1 and ΔW6 = −1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 8
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
10.257
−27.012
17.505
−2.7092
31.598
16.066
2.9402
100
0.2
10.244
−26.465
16.971
−2.6241
33.659
20.400
2.5550
92.16
0.3
10.205
−25.601
16.146
−2.1793
36.917
27.281
2.6485
82.81
0.4
10.031
−23.999
14.718
−1.2925
41.132
36.382
3.3034
70.56
0.5
9.515
−21.347
12.582
−0.2112
42.561
41.209
4.2260
56.25
0.6
8.540
−17.729
9.939
1.0312
36.721
36.086
4.4429
40.96
0.707
7.115
−13.463
7.101
2.8701
24.219
23.145
3.4093
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 3 are, respectively, ΔW4 = −1 and ΔW6 = +1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 9
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
IFS
IDL
0
12.257
−29.012
17.505
19.4870
37.994
16.008
0.3794
100
0.2
12.244
−28.465
16.971
20.1466
33.810
20.428
0.1442
92.16
0.3
12.205
−27.601
16.146
0.6607
33.787
27.340
3.1294
82.81
0.4
12.031
−25.999
14.718
0.3410
39.499
36.342
3.6751
70.56
0.5
11.515
−23.347
12.582
−0.1796
41.983
41.192
4.3761
56.25
0.6
10.540
−19.729
9.939
−1.1449
36.593
36.108
4.4695
40.96
0.707
9.115
−15.463
7.101
−2.7708
24.226
23.258
3.4130
25.02
The W4 and W6 coefficients with respect to the coefficients in Table 3 are, respectively, ΔW4 = +1 and ΔW6 = −1. The last two columns list the intensities at the first secondary maximum in the diffraction focus plane (IFS) and at the paraxial image focus for a diffraction-limited system (IDL).
Table 10
Intensity (INI) at the Diffraction Focus (UDF) Calculated with a Numerical Integration of the Diffraction Integral and Using the Approximate Maréchal Formula (IMF)a
∊
W4
W6
W8
uDF
INI
IMF
A
0
4.758
−11.840
7.399
0.2237
82.032
81.357
0.317
0.2
5.112
−12.488
7.716
0.1727
75.312
74.703
0.341
0.3
5.707
−13.548
8.223
0.1373
67.686
67.144
0.382
0.4
7.001
−15.865
9.340
0.0808
57.660
57.200
0.476
0.5
9.730
−20.679
11.643
0.0125
45.974
45.603
0.694
0.6
15.964
−31.340
16.631
−0.0646
33.485
33.209
1.255
0.707
35.168
−62.690
30.774
−0.1440
20.458
20.285
3.251
The W2n polynomial coefficients were calculated for the edge polynomial values of W(1) = Aλ listed in the last column to obtain the constant variance value of
for each obscuration ratio, i.e., its upper permissible limit for calculating the intensity with the Maréchal formula.
Table 11
Resolution (VR) and Intensity (IR) at the Diffraction Focus Plane (u = uDF) for Optical Systems with the Spherical Aberration Coefficients Listed in Tables 1, 4, and 5a
The second column lists the resolution at the paraxial image plane for a diffraction-limited (DL) system.
Table 12
Resolution (VR) and Intensity (IR) at the Diffraction Focus Plane (U = UDF) for Optical Systems with the Spherical Aberration Coefficients Listed in Tables 2, 6, and 7a
The second column lists the resolution at the paraxial image plane for a diffraction-limited (DL) system.
Table 13
Resolution (VR) and Intensity (IR) at the Diffraction Focus Plane (U = UDF) for Optical Systems with the Spherical Aberration Coefficients Listed in Tables 3, 8, and 9a