J.-M. Yang (moon@csie.ntu.edu.tw) and C.-Y. Kao (cykao@csie.ntu.edu.tw) are with the Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan.
Jinn-Moon Yang and Cheng-Yan Kao, "Efficient evolutionary algorithm for the thin-film synthesis of inhomogeneous optical coatings," Appl. Opt. 40, 3256-3267 (2001)
We propose an efficient evolutionary approach for the thin-film
synthesis of inhomogeneous optical coatings. The proposed approach
consists of global and local strategies by integration of
decreasing-based mutations and self-adaptive mutations by means of
family competition and adaptive rules. Numerical results indicate
that the proposed approach performs robustly and is competitive with
other approaches. Our approach, although somewhat slower, is
flexible and can easily be adopted to other application
domains. Our approach is also able to generate homogeneous
solutions with two materials available.
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Methods include those such as dumped
least square and golden section and a real-coded genetic algorithm
(RCGA)8 on the beam splitter with inhomgeneous coating
and 31 equispaced points in the region of interest 0.4 ≤ λ
≤ 1.0 µm. See Ref. 4.
Table 3
Comparison of the FCEA with the Needle Method on the Beam
Splitter with Refractive Indices of ηh = 2.35
and ηl = 1.35 as well as 301 Equispaced
Points in the Region of Interest 0.4 ≤ λ ≤ 1.0 µm
Construction Parameters of the Solutions Found by FCEA for
the Narrow-Band Reflector, the Beam Splitter, and the
CIEx̅λ Filter in Both Inhomogeneous
Coatings and Homogeneous Coatings
Beam Splitter
Narrow-Band Reflector
Inhomogeneous Coating
Homogeneous Coating
Inhomogeneous Coating
Homogeneous Coating
CIEx̅λ
Layer
η
ηd
η
ηd
η
ηd
η
ηd
η
ηd
η
ηd
ηs
1.52
1.52
1.52
1.52
1.52
1.52
1
2.0830
0.0176
2.35
0.020105
2.35
0.0055
1.3899
1.3361
2.35
0.2535
2.323
0.28000
2
1.4807
0.0687
1.35
0.086979
1.35
0.0200
1.5192
1.2387
1.35
0.2284
1.468
0.05073
3
1.8831
0.1606
2.35
0.067596
2.35
0.0868
1.6022
0.4550
2.35
0.2462
2.323
0.26493
4
2.3196
0.2778
1.35
0.063868
1.35
0.0633
1.7678
0.7085
1.35
0.1993
1.468
0.14911
5
1.8542
0.0766
2.35
0.131038
2.35
0.0607
1.7124
0.7324
2.35
0.2046
2.323
0.19554
6
1.8031
0.0433
1.35
0.030119
1.35
0.1116
1.8742
0.4877
1.35
0.2301
1.468
0.14458
7
2.1438
0.0050
2.35
0.127506
2.35
0.0130
1.4340
0.3018
2.35
0.5720
2.323
0.02406
8
1.5058
0.0981
1.35
0.026858
1.35
0.2826
1.5751
0.8744
1.35
0.2490
1.468
0.06198
9
1.4988
0.1405
2.35
0.058282
2.35
0.0610
1.3899
0.1357
2.35
0.4155
2.323
0.14630
10
1.7621
0.1972
1.35
0.092693
1.35
0.1130
1.7167
0.7216
1.35
0.2534
1.468
0.13510
11
1.9163
0.0499
2.35
0.077635
2.35
0.1076
2.1689
0.3051
2.35
0.6011
2.323
0.18503
12
1.4736
0.0801
1.35
0.125771
1.35
0.1999
1.6512
0.4059
1.35
0.2300
1.468
0.01468
13
1.4257
0.2186
2.35
0.194430
2.35
0.1705
1.8065
1.1073
2.35
0.4479
2.323
0.02323
14
2.3499
0.0259
1.35
0.166489
1.35
0.2368
1.8583
0.2180
1.35
0.2541
1.468
0.13814
15
2.0426
0.0601
2.35
0.233750
2.35
0.1208
1.4356
0.7107
2.35
0.2834
2.323
0.28285
16
2.3500
0.2048
1.35
0.120351
1.5672
0.3301
1.35
0.2204
1.468
0.11565
17
1.3500
0.1406
2.1881
1.0271
2.35
1.0605
2.323
0.12761
18
2.3499
0.1394
1.3711
0.1660
1.35
0.0867
1.468
0.12572
19
1.5873
0.6364
2.35
0.3216
2.323
0.12302
20
2.0727
0.3734
1.35
0.3287
1.468
0.05928
21
1.4496
0.4837
2.35
0.3072
2.323
0.11123
22
2.0855
0.7603
1.35
0.2497
1.468
0.10741
23
1.3590
0.1174
2.35
0.2010
2.323
0.22387
24
1.5807
0.8820
1.35
0.2575
1.468
0.12111
25
2.1127
0.2098
2.35
0.8326
2.323
0.12553
26
1.4254
0.7286
1.35
0.2735
1.468
0.05310
27
1.8438
0.7653
2.35
0.5299
2.323
0.10685
28
1.4880
0.4099
1.35
0.2313
1.468
0.10992
29
1.7227
0.6673
2.35
0.2364
2.323
0.06186
30
2.1583
1.6515
1.35
0.2522
1.468
0.04284
31
1.7872
0.5340
2.35
0.2796
2.323
0.12914
32
2.1362
1.2458
1.35
0.3276
1.468
0.09496
33
1.4724
0.1298
2.35
0.3110
2.323
0.20447
34
1.35
0.1712
1.468
0.01468
35
2.323
0.09042
36
1.468
0.01468
37
2.323
0.33694
ηm
1.0
1.0
1.0
1.0
1.0
1.52
Σηd
2.0
1.62
1.65
20.86
11.14
4.597
MF(%)
0.06
0.0281
0.031
0.381
0.399
0.587
Table 5
Comparison of FCEA with the Needle Method on the
CIEx̅λ Filter for the Tristimulus
Colorimeters in the Region 380–780 nm
Methods include those such as dumped
least square and golden section and a real-coded genetic algorithm
(RCGA)8 on the beam splitter with inhomgeneous coating
and 31 equispaced points in the region of interest 0.4 ≤ λ
≤ 1.0 µm. See Ref. 4.
Table 3
Comparison of the FCEA with the Needle Method on the Beam
Splitter with Refractive Indices of ηh = 2.35
and ηl = 1.35 as well as 301 Equispaced
Points in the Region of Interest 0.4 ≤ λ ≤ 1.0 µm
Construction Parameters of the Solutions Found by FCEA for
the Narrow-Band Reflector, the Beam Splitter, and the
CIEx̅λ Filter in Both Inhomogeneous
Coatings and Homogeneous Coatings
Beam Splitter
Narrow-Band Reflector
Inhomogeneous Coating
Homogeneous Coating
Inhomogeneous Coating
Homogeneous Coating
CIEx̅λ
Layer
η
ηd
η
ηd
η
ηd
η
ηd
η
ηd
η
ηd
ηs
1.52
1.52
1.52
1.52
1.52
1.52
1
2.0830
0.0176
2.35
0.020105
2.35
0.0055
1.3899
1.3361
2.35
0.2535
2.323
0.28000
2
1.4807
0.0687
1.35
0.086979
1.35
0.0200
1.5192
1.2387
1.35
0.2284
1.468
0.05073
3
1.8831
0.1606
2.35
0.067596
2.35
0.0868
1.6022
0.4550
2.35
0.2462
2.323
0.26493
4
2.3196
0.2778
1.35
0.063868
1.35
0.0633
1.7678
0.7085
1.35
0.1993
1.468
0.14911
5
1.8542
0.0766
2.35
0.131038
2.35
0.0607
1.7124
0.7324
2.35
0.2046
2.323
0.19554
6
1.8031
0.0433
1.35
0.030119
1.35
0.1116
1.8742
0.4877
1.35
0.2301
1.468
0.14458
7
2.1438
0.0050
2.35
0.127506
2.35
0.0130
1.4340
0.3018
2.35
0.5720
2.323
0.02406
8
1.5058
0.0981
1.35
0.026858
1.35
0.2826
1.5751
0.8744
1.35
0.2490
1.468
0.06198
9
1.4988
0.1405
2.35
0.058282
2.35
0.0610
1.3899
0.1357
2.35
0.4155
2.323
0.14630
10
1.7621
0.1972
1.35
0.092693
1.35
0.1130
1.7167
0.7216
1.35
0.2534
1.468
0.13510
11
1.9163
0.0499
2.35
0.077635
2.35
0.1076
2.1689
0.3051
2.35
0.6011
2.323
0.18503
12
1.4736
0.0801
1.35
0.125771
1.35
0.1999
1.6512
0.4059
1.35
0.2300
1.468
0.01468
13
1.4257
0.2186
2.35
0.194430
2.35
0.1705
1.8065
1.1073
2.35
0.4479
2.323
0.02323
14
2.3499
0.0259
1.35
0.166489
1.35
0.2368
1.8583
0.2180
1.35
0.2541
1.468
0.13814
15
2.0426
0.0601
2.35
0.233750
2.35
0.1208
1.4356
0.7107
2.35
0.2834
2.323
0.28285
16
2.3500
0.2048
1.35
0.120351
1.5672
0.3301
1.35
0.2204
1.468
0.11565
17
1.3500
0.1406
2.1881
1.0271
2.35
1.0605
2.323
0.12761
18
2.3499
0.1394
1.3711
0.1660
1.35
0.0867
1.468
0.12572
19
1.5873
0.6364
2.35
0.3216
2.323
0.12302
20
2.0727
0.3734
1.35
0.3287
1.468
0.05928
21
1.4496
0.4837
2.35
0.3072
2.323
0.11123
22
2.0855
0.7603
1.35
0.2497
1.468
0.10741
23
1.3590
0.1174
2.35
0.2010
2.323
0.22387
24
1.5807
0.8820
1.35
0.2575
1.468
0.12111
25
2.1127
0.2098
2.35
0.8326
2.323
0.12553
26
1.4254
0.7286
1.35
0.2735
1.468
0.05310
27
1.8438
0.7653
2.35
0.5299
2.323
0.10685
28
1.4880
0.4099
1.35
0.2313
1.468
0.10992
29
1.7227
0.6673
2.35
0.2364
2.323
0.06186
30
2.1583
1.6515
1.35
0.2522
1.468
0.04284
31
1.7872
0.5340
2.35
0.2796
2.323
0.12914
32
2.1362
1.2458
1.35
0.3276
1.468
0.09496
33
1.4724
0.1298
2.35
0.3110
2.323
0.20447
34
1.35
0.1712
1.468
0.01468
35
2.323
0.09042
36
1.468
0.01468
37
2.323
0.33694
ηm
1.0
1.0
1.0
1.0
1.0
1.52
Σηd
2.0
1.62
1.65
20.86
11.14
4.597
MF(%)
0.06
0.0281
0.031
0.381
0.399
0.587
Table 5
Comparison of FCEA with the Needle Method on the
CIEx̅λ Filter for the Tristimulus
Colorimeters in the Region 380–780 nm