Prisms have been needlessly neglected as components used in modern optical design. In optical throughput, stray light, flexibility, and in their ability to be used in direct-view geometry, they excel over gratings. Here we show that even their well-known weak dispersion relative to gratings has been overrated by designing doublet and double Amici direct-vision compound prisms that have and of dispersion across the visible spectrum, equivalent to 800 and gratings. By taking advantage of the multiple degrees of freedom available in a compound prism design, we also show prisms whose angular dispersion shows improved linearity in wavelength. In order to achieve these designs, we exploit the well-behaved nature of prism design space to write customized algorithms that optimize directly in the nonlinear design space. Using these algorithms, we showcase a number of prism designs that illustrate a performance and flexibility that goes beyond what has often been considered possible with prisms.
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Best Performing Doublet Prisms for Design Targets and (, )a
Glass 1
Glass 2
(deg)
(deg)
(deg)
Δ (deg)
NL ()
SSR
1a
N-PK51
N-BK10
124.14
0.000
1.000
0.182
2.99
2a
N-BAF4
N-KZFS11
104.49
0.000
1.000
0.193
2.71
3a
N-BAF52
N-KZFS4
112.39
0.000
1.000
0.195
2.49
4a
N-KZFS4
N-BAF52
110.73
0.000
1.000
0.205
2.53
5a
N-KZFS11
N-BAF4
99.32
0.000
1.000
0.223
2.40
6a
N-LAK33A
N-BALF5
65.07
1.000
0.323
4.70
7a
N-LASF31A
N-BAF4
56.17
0.000
1.000
0.324
5.22
8a
LAFN7
N-BASF2
82.49
0.000
1.000
0.327
4.72
9a
N-LASF44
N-BAF10
76.74
0.000
1.000
0.328
4.56
10a
N-LAF34
N-SSK5
79.81
0.000
1.000
0.335
4.45
1b
N-SF66
N-LAK34
13.62
0.000
1.000
0.742
11.25
2b
N-SF66
N-LAK33A
13.97
0.000
1.000
0.748
11.34
3b
N-LAK34
N-SF66
13.74
0.000
1.000
0.742
11.25
4b
N-LAK33A
N-SF66
14.08
0.000
1.000
0.749
11.34
5b
N-SF66
N-LAK14
13.47
0.000
1.000
0.740
11.24
Rows 1a–10a list the designs in order of dispersion linearity (1a–5a are unconstrained, while 6a–10a are constrained to incidence angles ); 1b–5b list the designs ordered by thickness. Prisms 1a and 1b are illustrated in Fig. 7.
Table 2
Achromatic Beam Deviation: the Best Performing Doublet Prisms (for ), Listed in Order of (a) Compactness or (b) Dispersion Chromaticity, Where Chromaticity C is Defined by Eq. (13)a
Glass 1
Glass 2
(deg)
(deg)
(deg)
C ()
merit func.: , λ, ,
1a
SF68
LAK34
51.61
30.000
55.554
2a
SF68
LAK33A
51.23
30.000
57.250
3a
SF68
PSK53A
55.42
30.000
45.752
4a
SF68
LAK14
53.08
30.000
55.694
5a
SF66
LAK34
51.46
30.000
55.118
merit func.: , λ, ,
1b
SK5
CAF2
93.20
30.000
0.210
2b
SK57
CAF2
91.88
30.000
0.248
3b
SK11
CAF2
92.76
30.000
0.251
4b
LAK21
CAF2
92.39
30.000
0.253
5b
SK16
CAF2
92.51
30.000
0.259
The dispersions of prisms 1d–5d are illustrated in Fig. 9.
Table 3
Best Performing Double Amici Prisms for Design Targets and (, )a
Glass 1
Glass 2
(deg)
(deg)
(deg)
Δ (deg)
NL ()
SSR
λ range: , , sorted by linearity
1a
N-BAF4
P-LASF47
106.98
0.006
0.903
0.239
4.31
2a
N-BAF4
N-LASF31A
97.68
0.000
1.000
0.269
4.54
3a
N-BAF52
N-LASF41
103.91
0.000
1.000
0.302
4.79
4a
N-BALF5
N-LAF34
104.26
0.002
0.929
0.336
5.55
5a
LITH-CAF2
N-FK5
121.63
0.002
0.951
0.339
4.04
λ range: , , sorted by linearity
1b
LITH-CAF2
N-LAK33A
94.37
0.000
4.000
1.770
5.74
2b
LITH-CAF2
N-LAF34
90.50
0.000
4.000
1.814
5.97
3b
LITH-CAF2
N-LAF35
93.38
0.000
4.000
1.830
6.03
4b
LITH-CAF2
N-LAF21
87.24
0.001
4.000
1.859
6.13
5b
LITH-CAF2
N-LASF44
84.87
0.000
4.000
1.860
6.21
λ range: , , sorted by thickness
1c
N-LAK34
N-SF66
50.29
0.000
4.000
2.995
11.35
2c
N-SF66
N-LAK34
25.09
0.000
4.000
2.937
11.09
3c
N-LAK33A
N-SF66
51.55
0.000
4.000
3.019
11.45
4c
N-SF66
N-LAK33A
25.77
0.000
4.000
2.962
11.18
5c
N-LAK14
N-SF66
49.57
0.000
4.000
2.984
11.33
Sections (a) and (b) of the table list the designs in order of dispersion linearity; section (c) lists the designs ordered by thickness. All of the designs are constrained to angles of incidence . The layout and dispersions for prisms 1a and 1b are illustrated in Fig. 13.
Tables (3)
Table 1
Best Performing Doublet Prisms for Design Targets and (, )a
Glass 1
Glass 2
(deg)
(deg)
(deg)
Δ (deg)
NL ()
SSR
1a
N-PK51
N-BK10
124.14
0.000
1.000
0.182
2.99
2a
N-BAF4
N-KZFS11
104.49
0.000
1.000
0.193
2.71
3a
N-BAF52
N-KZFS4
112.39
0.000
1.000
0.195
2.49
4a
N-KZFS4
N-BAF52
110.73
0.000
1.000
0.205
2.53
5a
N-KZFS11
N-BAF4
99.32
0.000
1.000
0.223
2.40
6a
N-LAK33A
N-BALF5
65.07
1.000
0.323
4.70
7a
N-LASF31A
N-BAF4
56.17
0.000
1.000
0.324
5.22
8a
LAFN7
N-BASF2
82.49
0.000
1.000
0.327
4.72
9a
N-LASF44
N-BAF10
76.74
0.000
1.000
0.328
4.56
10a
N-LAF34
N-SSK5
79.81
0.000
1.000
0.335
4.45
1b
N-SF66
N-LAK34
13.62
0.000
1.000
0.742
11.25
2b
N-SF66
N-LAK33A
13.97
0.000
1.000
0.748
11.34
3b
N-LAK34
N-SF66
13.74
0.000
1.000
0.742
11.25
4b
N-LAK33A
N-SF66
14.08
0.000
1.000
0.749
11.34
5b
N-SF66
N-LAK14
13.47
0.000
1.000
0.740
11.24
Rows 1a–10a list the designs in order of dispersion linearity (1a–5a are unconstrained, while 6a–10a are constrained to incidence angles ); 1b–5b list the designs ordered by thickness. Prisms 1a and 1b are illustrated in Fig. 7.
Table 2
Achromatic Beam Deviation: the Best Performing Doublet Prisms (for ), Listed in Order of (a) Compactness or (b) Dispersion Chromaticity, Where Chromaticity C is Defined by Eq. (13)a
Glass 1
Glass 2
(deg)
(deg)
(deg)
C ()
merit func.: , λ, ,
1a
SF68
LAK34
51.61
30.000
55.554
2a
SF68
LAK33A
51.23
30.000
57.250
3a
SF68
PSK53A
55.42
30.000
45.752
4a
SF68
LAK14
53.08
30.000
55.694
5a
SF66
LAK34
51.46
30.000
55.118
merit func.: , λ, ,
1b
SK5
CAF2
93.20
30.000
0.210
2b
SK57
CAF2
91.88
30.000
0.248
3b
SK11
CAF2
92.76
30.000
0.251
4b
LAK21
CAF2
92.39
30.000
0.253
5b
SK16
CAF2
92.51
30.000
0.259
The dispersions of prisms 1d–5d are illustrated in Fig. 9.
Table 3
Best Performing Double Amici Prisms for Design Targets and (, )a
Glass 1
Glass 2
(deg)
(deg)
(deg)
Δ (deg)
NL ()
SSR
λ range: , , sorted by linearity
1a
N-BAF4
P-LASF47
106.98
0.006
0.903
0.239
4.31
2a
N-BAF4
N-LASF31A
97.68
0.000
1.000
0.269
4.54
3a
N-BAF52
N-LASF41
103.91
0.000
1.000
0.302
4.79
4a
N-BALF5
N-LAF34
104.26
0.002
0.929
0.336
5.55
5a
LITH-CAF2
N-FK5
121.63
0.002
0.951
0.339
4.04
λ range: , , sorted by linearity
1b
LITH-CAF2
N-LAK33A
94.37
0.000
4.000
1.770
5.74
2b
LITH-CAF2
N-LAF34
90.50
0.000
4.000
1.814
5.97
3b
LITH-CAF2
N-LAF35
93.38
0.000
4.000
1.830
6.03
4b
LITH-CAF2
N-LAF21
87.24
0.001
4.000
1.859
6.13
5b
LITH-CAF2
N-LASF44
84.87
0.000
4.000
1.860
6.21
λ range: , , sorted by thickness
1c
N-LAK34
N-SF66
50.29
0.000
4.000
2.995
11.35
2c
N-SF66
N-LAK34
25.09
0.000
4.000
2.937
11.09
3c
N-LAK33A
N-SF66
51.55
0.000
4.000
3.019
11.45
4c
N-SF66
N-LAK33A
25.77
0.000
4.000
2.962
11.18
5c
N-LAK14
N-SF66
49.57
0.000
4.000
2.984
11.33
Sections (a) and (b) of the table list the designs in order of dispersion linearity; section (c) lists the designs ordered by thickness. All of the designs are constrained to angles of incidence . The layout and dispersions for prisms 1a and 1b are illustrated in Fig. 13.