Max Herzberger and Calvin D. Salzberg, "Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses*," J. Opt. Soc. Am. 52, 420-427 (1962)
The senior author’s interpolation formula for computing the dispersion of glass has been appropriately modified and applied to infrared materials. Indices of refraction for 14 optical materials that are suitable for practical refracting systems have been fitted by the modified formula and have been tabulated at increments of 0.5 μ for the useful transmittance range of each material. The method of applying the dispersion formula is discussed and is illustrated by the design of two three-element superachromats corrected for the region of 2.0–5.0 μ.
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List of materials. Except where noted, the index data were obtained at Eastman Kodak Company by using the method described in reference 2.
No.
Material
Reference and Remarks
1
Fused quartz
Sample having low water content supplied by General Electric Company.
2
Calcium aluminate
Data are for a typical sample supplied by Bausch and Lomb. The remarks made about As2S3 (No. 12) apply except that the variations between the many samples measured by us have been smaller than the variations between As2S3 samples.
3
IR-20
Sample supplied by Bausch and Lomb.
4
Strontium titanate
Birefringent—axis of sample unknown.
5
Magnesium oxide
R. E. Stephens, I. H. Malitson, [J. Research Natl. Bur. Standards 49, 249 (1952)]. We have measured several samples of this material and found no significant differences from the NBS data.
6
Sapphire
I. H. Malitson, F. V. Murphy, Jr., W. S. Rodney, J. Opt. Soc. Am. 48, 72 (1958).
7
Lithium fluoride
L. W. Tilton, E. K. Plyler, J. Research Natl. Bur. Standards 47, 25 (1951).
8
Irtran 1
Variation between samples has been less than our experimental error.
9
Calcium fluoride
W. W. Coblentz, J. Opt. Soc. Am. 4, 432 (1920).
10
Barium fluoride
Reference 4. The authors quote preliminary data measured at the National Bureau of Standards by I. H. Malitson.
11
Silicon
Measurements made on a single-crystal sample.
12
Arsenic trisulfide
Reference 3. Measurements in our laboratories of samples supplied by different manufacturers have shown variations in index value as large as 5×10−2. However, measurements on different samples from the same melt have been within our experimental error of ±2×10−4. Accordingly, the index values presented here should serve only as a guide, and the prospective user of the material should work with data from samples of the melt to be used.
13
Irtran 2
Variation between samples has been less than our experimental error.
14
Germanium
Variation between single and polycrystalline samples has been less than our experimental error.
Table II
Constants to be used with the interpolation formula, Eq. (1).
Wavelength range (μ)
Constant
No.
Material
from
to
A
B
C
D
E
1
Fused quartz
0.5
4.3
1.44902
0.004604
−0.000381
−0.0025268
−0.00007722
2
Calcium aluminate
0.6
4.3
1.64289
0.007860
−0.000231
−0.0022133
−0.00001598
3
IR-20
0.5
5.0
1.83450
0.011834
−0.000100
−0.0022268
−0.00001267
4
Strontium titanate
1.0
5.3
2.28355
0.035906
+0.001666
−0.0061335
−0.00001502
5
Magnesium oxide
0.5
5.5
1.71960
0.006305
−0.000090
−0.0031356
−0.00000770
6
Sapphire
1.0
5.6
1.75458
0.007149
−0.001577
−0.0045380
−0.00002808
7
Lithium fluoride
0.5
6.0
1.38761
0.001796
−0.000041
−0.0023045
−0.00000557
8
Irtran 1
1.0
6.7
1.37770
0.001348
+0.000216
−0.0015041
−0.00000441
9
Calcium fluoride
0.6
8.3
1.42780
0.002267
−0.000069
−0.0011157
−0.00000162
10
Barium fluoride
0.5
11.0
1.46629
0.002867
+0.000064
−0.0006035
−0.000000465
11
Silicon
1.3
11.0
3.41696
0.138497
+0.013924
−0.0000209
+0.000000148
12
Arsenic trisulfide
0.6
12.0
2.41326
0.055720
+0.006177
−0.0003044
−0.000000232
13
Irtran 2
1.0
13.5
2.25698
0.032586
+0.000679
−0.0005272
−0.000000604
14
Germanium
2.0
13.5
3.99931
0.391707
+0.163492
−0.0000060
+0.000000053
Table III
Differences in the fourth decimal place between the measured indices for silicon and the values computed from the dispersion formula
λ
n0
n−n0
1.3570
3.4975
0×10−4
1.3673
3.4962
0
1.3951
3.4929
0
1.5295
3.4795
−1
1.6606
3.4696
−1
1.7092
3.4664
0
1.8131
3.4608
−1
1.9701
3.4537
+1
2.1526
3.4476
0
2.3254
3.4430
+1
2.4373
3.4408
−1
2.7144
3.4358
+1
3.00
3.4320
+4
3.3033
3.4297
−1
3.4188
3.4286
+1
3.50
3.4284
−2
4.00
3.4255
−1
4.258
3.4242
+1
4.50
3.4236
−1
5.00
3.4223
−2
5.50
3.3213
−2
6.00
3.4202
+1
6.50
3.4195
+1
7.00
3.4189
+2
7.50
3.4186
+1
8.00
3.4184
0
8.50
3.4182
−1
10.00
3.4179
−2
10.50
3.4178
−1
11.04
3.4176
+1
Table IV
Differences in the fourth decimal place between the measured indices n0 for arsenic trisulfide and the values computed from the following dispersion formulas:
λ
n0
n0−n1
n0−n2
n0−n3
0.576960
2.6632
−9×10−4
0.579066
2.6605
−7
0.587562
2.6501
1
0.643847
2.5976
10
0.667815
2.5808
10
0.690750
2.5670
8
0.706519
2.5586
6
0.85212
2.5061
−6
0.89440
2.4963
−8
1.01398
2.4757
−9
1.12866
2.4623
−7
1.39505
2.4438
−4
1.5295
2.4380
−2
0×10−4
1.7006
2.4326
0
1
1.81308
2.4300
−1
−1
1.9701
2.4268
1
0
3.4188
2.4137
8
0
4.258
2.4101
6
0
5.138
2.4067
5
0
6.238
2.4022
3
0×10−4
6.692
2.4004
1
0
8.662
2.3904
−5
−1
9.724
2.3834
−4
2
11.035
2.3737
−5
−2
11.475
2.3694
2
1
11.862
2.3658
5
0
Table V
Physical constants and index of refraction computed from interpolation formula, Eq. (1).
No.
Material
Specific gravity
Knoop hardness
Thermal coeff. of expansion deg−1 C
Melting or softening point (S) deg C
INDEX OF REFRACTION
Wavelength (μ)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
1
Fused quartz
2.202
461
0.5×10−6
1700
1.4614
1.4508
1.4449
1.4388
1.4309
1.4205
1.4069
1.3891
1.3664
2
Calcium aluminate
3.07
594
8.1
770S
1.6731
1.6485
1.6413
1.6357
1.6297
1.6225
1.6140
1.6039
1.5919
3
IR-20
5.18
542
9
760
1.8852
1.8443
1.8347
1.8284
1.8220
1.8147
1.8063
1.7964
1.7848
1.7714
4
Strontium titanate
5.122
595
9.4
2080
2.4776
2.3161
2.2862
2.2679
2.2504
2.2312
2.2091
2.1838
2.1550
2.1223
5
Magnesium oxide
3.576
692
13.8
2800
1.7454
1.7229
1.7153
1.7085
1.7007
1.6915
1.6806
1.6679
1.6533
1.6367
1.6179
6
Sapphire
3.98
1370
6.7
2030
⋯
1.7557
1.7471
1.7377
1.7262
1.7122
1.6953
1.6752
1.6515
1.6239
1.5918
1.5550
7
Lithium fluoride
2.639
110
37
870
1.3943
1.3871
1.3832
1.3788
1.3733
1.3666
1.3587
1.3494
1.3388
1.3266
1.3129
1.2975
8
Irtran 1
3.18
576
12
1396
1.3778
1.3749
1.3720
1.3683
1.3640
1.3587
1.3526
1.3455
1.3374
1.3282
1.3179
9
Calcium fluoride
3.179
158
24
1360
1.4363
1.4289
1.4263
1.4239
1.4211
1.4179
1.4141
1.4097
1.4047
1.3990
1.3927
1.3856
10
Barium fluoride
4.83
82
18.4
1280
1.4778
1.4686
1.4662
1.4646
1.4630
1.4611
1.4591
1.4567
1.4540
1.4510
1.4477
1.4440
11
Silicon
2.329
1150
4.15
1420
⋯
⋯
3.4821
3.4526
3.4395
3.4324
3.4282
3.4254
3.4235
3.4221
3.4211
3.4203
12
Arsenic trisulfide
3.198
109
24.6
210S
⋯
2.4768
2.4389
2.4265
2.4205
2.4168
2.4141
2.4118
2.4098
2.4077
2.4057
2.4036
13
Irtran 2
4.102
325
7.4
1020
2.4174
2.2907
2.2706
2.2631
2.2589
2.2558
2.2531
2.2504
2.2477
2.2447
2.2416
2.2381
14
Germanium
5.327
850
6.1
936
4.1083
4.0664
4.0449
4.0324
4.0244
4.0190
4.0151
4.0123
4.0102
INDEX OF REFRACTION
Wavelength (μ)
No.
Material
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
9
Calcium fluoride
1.3778
1.3693
1.3600
1.3498
1.3388
10
Barium fluoride
1.4400
1.4357
1.4309
1.4258
1.4203
1.4144
1.4080
1.4013
1.3941
11
Silicon
3.4196
3.4191
3.4187
3.4184
3.4181
3.4180
3.4178
3.4177
3.4177
3.4177
12
Arsenic trisulfide
2.4013
2.3989
2.3964
2.3937
2.3908
2.3878
2.3845
2.3811
2.3774
2.3735
2.3694
2.3650
13
Irtran 2
2.2344
2.2304
2.2260
2.2213
2.2162
2.2107
2.2049
2.1986
2.1919
2.1847
2.1770
2.1689
2.1602
2.1509
14
Germanium
4.0085
4.0072
4.0062
4.0053
4.0046
4.0040
4.0036
4.0032
4.0029
4.0026
4.0024
4.0023
4.0022
4.0021
4.0021
Table VI
Universal coefficients. Matrix of aik in Eq. (3) for the five wavelengths λ=1.5, 2.5, 3.5, 4.0, and 5.0 μ.
aik
a1k
a2k
a3k
a4k
a5k
ai1
+0.486027
−8.990805
+39.562797
−35.767242
+5.709224
ai2
−4.13135
+60.643808
−204.844076
+174.297648
−25.966032
ai3
+11.968199
−95.574445
+287.12993
−237.90693
+34.383249
ai4
−0.023456
+0.489212
−2.574574
+2.576301
−0.467484
ai5
+0.000395
−0.008824
+0.052071
−0.056382
+0.01274
Table VII
Universal functions ai(λ) calculated for eight wavelengths (λ) from 1.5 μ to 5.0 μ, at intervals of 0.5 μ.
List of materials. Except where noted, the index data were obtained at Eastman Kodak Company by using the method described in reference 2.
No.
Material
Reference and Remarks
1
Fused quartz
Sample having low water content supplied by General Electric Company.
2
Calcium aluminate
Data are for a typical sample supplied by Bausch and Lomb. The remarks made about As2S3 (No. 12) apply except that the variations between the many samples measured by us have been smaller than the variations between As2S3 samples.
3
IR-20
Sample supplied by Bausch and Lomb.
4
Strontium titanate
Birefringent—axis of sample unknown.
5
Magnesium oxide
R. E. Stephens, I. H. Malitson, [J. Research Natl. Bur. Standards 49, 249 (1952)]. We have measured several samples of this material and found no significant differences from the NBS data.
6
Sapphire
I. H. Malitson, F. V. Murphy, Jr., W. S. Rodney, J. Opt. Soc. Am. 48, 72 (1958).
7
Lithium fluoride
L. W. Tilton, E. K. Plyler, J. Research Natl. Bur. Standards 47, 25 (1951).
8
Irtran 1
Variation between samples has been less than our experimental error.
9
Calcium fluoride
W. W. Coblentz, J. Opt. Soc. Am. 4, 432 (1920).
10
Barium fluoride
Reference 4. The authors quote preliminary data measured at the National Bureau of Standards by I. H. Malitson.
11
Silicon
Measurements made on a single-crystal sample.
12
Arsenic trisulfide
Reference 3. Measurements in our laboratories of samples supplied by different manufacturers have shown variations in index value as large as 5×10−2. However, measurements on different samples from the same melt have been within our experimental error of ±2×10−4. Accordingly, the index values presented here should serve only as a guide, and the prospective user of the material should work with data from samples of the melt to be used.
13
Irtran 2
Variation between samples has been less than our experimental error.
14
Germanium
Variation between single and polycrystalline samples has been less than our experimental error.
Table II
Constants to be used with the interpolation formula, Eq. (1).
Wavelength range (μ)
Constant
No.
Material
from
to
A
B
C
D
E
1
Fused quartz
0.5
4.3
1.44902
0.004604
−0.000381
−0.0025268
−0.00007722
2
Calcium aluminate
0.6
4.3
1.64289
0.007860
−0.000231
−0.0022133
−0.00001598
3
IR-20
0.5
5.0
1.83450
0.011834
−0.000100
−0.0022268
−0.00001267
4
Strontium titanate
1.0
5.3
2.28355
0.035906
+0.001666
−0.0061335
−0.00001502
5
Magnesium oxide
0.5
5.5
1.71960
0.006305
−0.000090
−0.0031356
−0.00000770
6
Sapphire
1.0
5.6
1.75458
0.007149
−0.001577
−0.0045380
−0.00002808
7
Lithium fluoride
0.5
6.0
1.38761
0.001796
−0.000041
−0.0023045
−0.00000557
8
Irtran 1
1.0
6.7
1.37770
0.001348
+0.000216
−0.0015041
−0.00000441
9
Calcium fluoride
0.6
8.3
1.42780
0.002267
−0.000069
−0.0011157
−0.00000162
10
Barium fluoride
0.5
11.0
1.46629
0.002867
+0.000064
−0.0006035
−0.000000465
11
Silicon
1.3
11.0
3.41696
0.138497
+0.013924
−0.0000209
+0.000000148
12
Arsenic trisulfide
0.6
12.0
2.41326
0.055720
+0.006177
−0.0003044
−0.000000232
13
Irtran 2
1.0
13.5
2.25698
0.032586
+0.000679
−0.0005272
−0.000000604
14
Germanium
2.0
13.5
3.99931
0.391707
+0.163492
−0.0000060
+0.000000053
Table III
Differences in the fourth decimal place between the measured indices for silicon and the values computed from the dispersion formula
λ
n0
n−n0
1.3570
3.4975
0×10−4
1.3673
3.4962
0
1.3951
3.4929
0
1.5295
3.4795
−1
1.6606
3.4696
−1
1.7092
3.4664
0
1.8131
3.4608
−1
1.9701
3.4537
+1
2.1526
3.4476
0
2.3254
3.4430
+1
2.4373
3.4408
−1
2.7144
3.4358
+1
3.00
3.4320
+4
3.3033
3.4297
−1
3.4188
3.4286
+1
3.50
3.4284
−2
4.00
3.4255
−1
4.258
3.4242
+1
4.50
3.4236
−1
5.00
3.4223
−2
5.50
3.3213
−2
6.00
3.4202
+1
6.50
3.4195
+1
7.00
3.4189
+2
7.50
3.4186
+1
8.00
3.4184
0
8.50
3.4182
−1
10.00
3.4179
−2
10.50
3.4178
−1
11.04
3.4176
+1
Table IV
Differences in the fourth decimal place between the measured indices n0 for arsenic trisulfide and the values computed from the following dispersion formulas:
λ
n0
n0−n1
n0−n2
n0−n3
0.576960
2.6632
−9×10−4
0.579066
2.6605
−7
0.587562
2.6501
1
0.643847
2.5976
10
0.667815
2.5808
10
0.690750
2.5670
8
0.706519
2.5586
6
0.85212
2.5061
−6
0.89440
2.4963
−8
1.01398
2.4757
−9
1.12866
2.4623
−7
1.39505
2.4438
−4
1.5295
2.4380
−2
0×10−4
1.7006
2.4326
0
1
1.81308
2.4300
−1
−1
1.9701
2.4268
1
0
3.4188
2.4137
8
0
4.258
2.4101
6
0
5.138
2.4067
5
0
6.238
2.4022
3
0×10−4
6.692
2.4004
1
0
8.662
2.3904
−5
−1
9.724
2.3834
−4
2
11.035
2.3737
−5
−2
11.475
2.3694
2
1
11.862
2.3658
5
0
Table V
Physical constants and index of refraction computed from interpolation formula, Eq. (1).
No.
Material
Specific gravity
Knoop hardness
Thermal coeff. of expansion deg−1 C
Melting or softening point (S) deg C
INDEX OF REFRACTION
Wavelength (μ)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
1
Fused quartz
2.202
461
0.5×10−6
1700
1.4614
1.4508
1.4449
1.4388
1.4309
1.4205
1.4069
1.3891
1.3664
2
Calcium aluminate
3.07
594
8.1
770S
1.6731
1.6485
1.6413
1.6357
1.6297
1.6225
1.6140
1.6039
1.5919
3
IR-20
5.18
542
9
760
1.8852
1.8443
1.8347
1.8284
1.8220
1.8147
1.8063
1.7964
1.7848
1.7714
4
Strontium titanate
5.122
595
9.4
2080
2.4776
2.3161
2.2862
2.2679
2.2504
2.2312
2.2091
2.1838
2.1550
2.1223
5
Magnesium oxide
3.576
692
13.8
2800
1.7454
1.7229
1.7153
1.7085
1.7007
1.6915
1.6806
1.6679
1.6533
1.6367
1.6179
6
Sapphire
3.98
1370
6.7
2030
⋯
1.7557
1.7471
1.7377
1.7262
1.7122
1.6953
1.6752
1.6515
1.6239
1.5918
1.5550
7
Lithium fluoride
2.639
110
37
870
1.3943
1.3871
1.3832
1.3788
1.3733
1.3666
1.3587
1.3494
1.3388
1.3266
1.3129
1.2975
8
Irtran 1
3.18
576
12
1396
1.3778
1.3749
1.3720
1.3683
1.3640
1.3587
1.3526
1.3455
1.3374
1.3282
1.3179
9
Calcium fluoride
3.179
158
24
1360
1.4363
1.4289
1.4263
1.4239
1.4211
1.4179
1.4141
1.4097
1.4047
1.3990
1.3927
1.3856
10
Barium fluoride
4.83
82
18.4
1280
1.4778
1.4686
1.4662
1.4646
1.4630
1.4611
1.4591
1.4567
1.4540
1.4510
1.4477
1.4440
11
Silicon
2.329
1150
4.15
1420
⋯
⋯
3.4821
3.4526
3.4395
3.4324
3.4282
3.4254
3.4235
3.4221
3.4211
3.4203
12
Arsenic trisulfide
3.198
109
24.6
210S
⋯
2.4768
2.4389
2.4265
2.4205
2.4168
2.4141
2.4118
2.4098
2.4077
2.4057
2.4036
13
Irtran 2
4.102
325
7.4
1020
2.4174
2.2907
2.2706
2.2631
2.2589
2.2558
2.2531
2.2504
2.2477
2.2447
2.2416
2.2381
14
Germanium
5.327
850
6.1
936
4.1083
4.0664
4.0449
4.0324
4.0244
4.0190
4.0151
4.0123
4.0102
INDEX OF REFRACTION
Wavelength (μ)
No.
Material
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
9
Calcium fluoride
1.3778
1.3693
1.3600
1.3498
1.3388
10
Barium fluoride
1.4400
1.4357
1.4309
1.4258
1.4203
1.4144
1.4080
1.4013
1.3941
11
Silicon
3.4196
3.4191
3.4187
3.4184
3.4181
3.4180
3.4178
3.4177
3.4177
3.4177
12
Arsenic trisulfide
2.4013
2.3989
2.3964
2.3937
2.3908
2.3878
2.3845
2.3811
2.3774
2.3735
2.3694
2.3650
13
Irtran 2
2.2344
2.2304
2.2260
2.2213
2.2162
2.2107
2.2049
2.1986
2.1919
2.1847
2.1770
2.1689
2.1602
2.1509
14
Germanium
4.0085
4.0072
4.0062
4.0053
4.0046
4.0040
4.0036
4.0032
4.0029
4.0026
4.0024
4.0023
4.0022
4.0021
4.0021
Table VI
Universal coefficients. Matrix of aik in Eq. (3) for the five wavelengths λ=1.5, 2.5, 3.5, 4.0, and 5.0 μ.
aik
a1k
a2k
a3k
a4k
a5k
ai1
+0.486027
−8.990805
+39.562797
−35.767242
+5.709224
ai2
−4.13135
+60.643808
−204.844076
+174.297648
−25.966032
ai3
+11.968199
−95.574445
+287.12993
−237.90693
+34.383249
ai4
−0.023456
+0.489212
−2.574574
+2.576301
−0.467484
ai5
+0.000395
−0.008824
+0.052071
−0.056382
+0.01274
Table VII
Universal functions ai(λ) calculated for eight wavelengths (λ) from 1.5 μ to 5.0 μ, at intervals of 0.5 μ.
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