The history of achromatic lenses is briefly reviewed. The latest development is the superachromat, which is corrected for four colors. Since the dispersion of glass can be represented by an equation containing four constants, the superachromat is practically corrected for all colors. The application of the superachromatic principle to thick lenses is described and it is shown that a compound lens can be made superachromatic by making each of its separate components superachromatic.
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Values of Universal Functions Appearing in Eq. (1) for Twelve Selected Wavelengths
λ (μ)
Line
a1
a2
a3
a4
1.0140
*
+1.000000
0.000000
0.000000
0.000000
0.7682
A′
+0.192687
+1.051955
−0.276197
+0.031555
0.6563
C
0.000000
+1.000000
0.000000
0.000000
0.6438
C′
−0.012813
+0.966511
+0.051075
−0.004774
0.5893
D
−0.045919
+0.744598
+0.326272
−0.024952
0.5876
d
−0.046326
+0.735480
+0.336338
−0.025492
0.5461
e
−0.043764
+0.479049
+0.597795
−0.033080
0.4861
F
0.000000
0.000000
+1.000000
0.000000
0.4800
F′
+0.006659
−0.052699
+1.036699
+0.009340
0.4358
g
+0.057036
−0.394569
+1.193553
+0.143980
0.4047
h
+0.075791
−0.487634
+1.045064
+0.366779
0.3650
**
0.000000
0.000000
0.000000
+1.000000
Table II
Glass Constants of Ten Thin Superachromatic Triplets of Unit Powera
Comb.
Element
μF
νC
P*
P**
ϕ
Without Fluorite
A
1
0.52242
70.31
1.87887
−1.71332
+4.286179
2
0.64576
44.57
1.80193
−1.86680
−4.484745
3
0.73463
30.22
1.68367
−2.10366
+1.198566
B
1
0.49230
70.73
1.89655
−1.69397
+4.353835
2
0.64576
44.57
1.80193
−1.86680
−5.466357
3
0.66122
34.58
1.70659
−2.04132
+2.112522
C
1
0.52242
70.31
1.87887
−1.71332
+4.489267
2
0.62319
44.61
1.78382
−1.88762
−6.413435
3
0.67756
36.59
1.70788
−2.02484
+2.924168
D
1
0.52242
70.31
1.87887
−1.71332
+4.821587
2
0.62319
44.61
1.78382
−1.88762
−7.028265
3
0.64908
36.06
1.71056
−2.02167
+3.206678
E
1
0.52242
70.31
1.87887
−1.71332
+4.717009
2
0.62319
44.61
1.78382
−1.88762
−6.871062
3
0.63777
36.28
1.71047
−2.02218
+3.154053
With Fluorite
F
1
0.43705
95.84
1.80482
−1.72807
+2.015105
2
0.89563
41.81
1.75117
−1.88562
−1.968550
3
0.67756
36.59
1.70788
−2.02484
+0.953445
G
1
0.43705
95.84
1.80482
−1.72807
+2.097892
2
0.89563
41.81
1.75117
−1.88562
−1.960115
3
0.66817
34.50
1.70418
−2.03872
+0.862223
H
1
0.43705
95.84
1.80482
−1.72807
+2.064021
2
0.89563
41.81
1.75117
−1.88562
−2.089979
3
0.64908
36.06
1.71056
−2.02167
+1.025958
I
1
0.43705
95.84
1.80482
−1.72807
+2.050473
2
0.89563
41.81
1.75117
−1.88562
−2.073647
3
0.63777
36.28
1.71047
−2.02218
+1.023174
J
1
0.43705
95.84
1.80482
−1.72807
+2.380189
2
0.57008
45.94
1.76210
−1.90887
−1.968007
3
0.62914
32.65
1.70317
−2.15361
+0.587818
Many other combinations are possible but these have especially low powers (shown in the last column) for their individual elements.
Table III
Glass Constants for Thin Color-Corrected Lenses of Unit Power, Powers of Individual Elements, and Sums of Absolute Values of These Powersa
Element
μF
νC
P*
P**
ϕ
∑ |ϕ|
Apochromats
1
0.56982
51.66
1.77879
−1.84950
10.050584
2
0.75603
46.52
1.77846
−1.88062
−9.050584
19.101168
1
0.53584
52.33
1.78711
−1.83203
8.635314
2
0.75607
46.27
1.78825
−1.84700
−7.635314
16.270628
1
0.53239
55.34
1.80249
−1.81081
13.732010
2
0.76351
51.31
1.80175
−1.81116
−12.732010
26.464020
1
0.53239
55.34
1.80249
−1.81081
5.138347
2
0.64576
44.57
1.80193
−1.86680
−4.138347
9.276694
Superachromats
1
0.52242
70.31
1.87887
−1.71332
+4.286179
2
0.64576
44.57
1.80193
−1.86680
−4.484745
3
0.73463
30.22
1.68367
−2.10366
+1.198566
9.969490
1
0.49230
70.73
1.89655
−1.69397
+4.353835
2
0.64576
44.57
1.80193
−1.86680
−5.466357
3
0.66122
34.58
1.70659
−2.04132
+2.112522
11.932714
1
0.43705
95.84
1.80482
−1.72807
+2.015105
2
0.89563
41.81
1.75117
−1.88562
−1.968550
3
0.67756
36.59
1.70788
−2.02484
+0.953445
4.937100
The requirement for apochromats is that P1* = P2*; for superachromats, that Pi** = a + bPi*, where i represents each of the a elements and a and b are constants for a given lens.
Tables (3)
Table I
Values of Universal Functions Appearing in Eq. (1) for Twelve Selected Wavelengths
λ (μ)
Line
a1
a2
a3
a4
1.0140
*
+1.000000
0.000000
0.000000
0.000000
0.7682
A′
+0.192687
+1.051955
−0.276197
+0.031555
0.6563
C
0.000000
+1.000000
0.000000
0.000000
0.6438
C′
−0.012813
+0.966511
+0.051075
−0.004774
0.5893
D
−0.045919
+0.744598
+0.326272
−0.024952
0.5876
d
−0.046326
+0.735480
+0.336338
−0.025492
0.5461
e
−0.043764
+0.479049
+0.597795
−0.033080
0.4861
F
0.000000
0.000000
+1.000000
0.000000
0.4800
F′
+0.006659
−0.052699
+1.036699
+0.009340
0.4358
g
+0.057036
−0.394569
+1.193553
+0.143980
0.4047
h
+0.075791
−0.487634
+1.045064
+0.366779
0.3650
**
0.000000
0.000000
0.000000
+1.000000
Table II
Glass Constants of Ten Thin Superachromatic Triplets of Unit Powera
Comb.
Element
μF
νC
P*
P**
ϕ
Without Fluorite
A
1
0.52242
70.31
1.87887
−1.71332
+4.286179
2
0.64576
44.57
1.80193
−1.86680
−4.484745
3
0.73463
30.22
1.68367
−2.10366
+1.198566
B
1
0.49230
70.73
1.89655
−1.69397
+4.353835
2
0.64576
44.57
1.80193
−1.86680
−5.466357
3
0.66122
34.58
1.70659
−2.04132
+2.112522
C
1
0.52242
70.31
1.87887
−1.71332
+4.489267
2
0.62319
44.61
1.78382
−1.88762
−6.413435
3
0.67756
36.59
1.70788
−2.02484
+2.924168
D
1
0.52242
70.31
1.87887
−1.71332
+4.821587
2
0.62319
44.61
1.78382
−1.88762
−7.028265
3
0.64908
36.06
1.71056
−2.02167
+3.206678
E
1
0.52242
70.31
1.87887
−1.71332
+4.717009
2
0.62319
44.61
1.78382
−1.88762
−6.871062
3
0.63777
36.28
1.71047
−2.02218
+3.154053
With Fluorite
F
1
0.43705
95.84
1.80482
−1.72807
+2.015105
2
0.89563
41.81
1.75117
−1.88562
−1.968550
3
0.67756
36.59
1.70788
−2.02484
+0.953445
G
1
0.43705
95.84
1.80482
−1.72807
+2.097892
2
0.89563
41.81
1.75117
−1.88562
−1.960115
3
0.66817
34.50
1.70418
−2.03872
+0.862223
H
1
0.43705
95.84
1.80482
−1.72807
+2.064021
2
0.89563
41.81
1.75117
−1.88562
−2.089979
3
0.64908
36.06
1.71056
−2.02167
+1.025958
I
1
0.43705
95.84
1.80482
−1.72807
+2.050473
2
0.89563
41.81
1.75117
−1.88562
−2.073647
3
0.63777
36.28
1.71047
−2.02218
+1.023174
J
1
0.43705
95.84
1.80482
−1.72807
+2.380189
2
0.57008
45.94
1.76210
−1.90887
−1.968007
3
0.62914
32.65
1.70317
−2.15361
+0.587818
Many other combinations are possible but these have especially low powers (shown in the last column) for their individual elements.
Table III
Glass Constants for Thin Color-Corrected Lenses of Unit Power, Powers of Individual Elements, and Sums of Absolute Values of These Powersa
Element
μF
νC
P*
P**
ϕ
∑ |ϕ|
Apochromats
1
0.56982
51.66
1.77879
−1.84950
10.050584
2
0.75603
46.52
1.77846
−1.88062
−9.050584
19.101168
1
0.53584
52.33
1.78711
−1.83203
8.635314
2
0.75607
46.27
1.78825
−1.84700
−7.635314
16.270628
1
0.53239
55.34
1.80249
−1.81081
13.732010
2
0.76351
51.31
1.80175
−1.81116
−12.732010
26.464020
1
0.53239
55.34
1.80249
−1.81081
5.138347
2
0.64576
44.57
1.80193
−1.86680
−4.138347
9.276694
Superachromats
1
0.52242
70.31
1.87887
−1.71332
+4.286179
2
0.64576
44.57
1.80193
−1.86680
−4.484745
3
0.73463
30.22
1.68367
−2.10366
+1.198566
9.969490
1
0.49230
70.73
1.89655
−1.69397
+4.353835
2
0.64576
44.57
1.80193
−1.86680
−5.466357
3
0.66122
34.58
1.70659
−2.04132
+2.112522
11.932714
1
0.43705
95.84
1.80482
−1.72807
+2.015105
2
0.89563
41.81
1.75117
−1.88562
−1.968550
3
0.67756
36.59
1.70788
−2.02484
+0.953445
4.937100
The requirement for apochromats is that P1* = P2*; for superachromats, that Pi** = a + bPi*, where i represents each of the a elements and a and b are constants for a given lens.