We extend the work of the first two papers in this series [Appl. Opt. 50, 4998–5011 (2011)APOPAI0003-6935, Appl. Opt. 50, 5012–5022 (2011)APOPAI0003-6935] to design compound prisms for linear-in-wavenumber dispersion, especially for application in spectral domain optical coherence tomography (OCT). These dispersive prism designs are believed to be the first to meet the requirements of high resolution OCT systems in direct-view geometry, where they can be used to shrink system size, to improve light throughput, to reduce stray light, and to reduce errors resulting from interpolating between wavelength- and wavenumber-sampled domains. We show prism designs that can be used for thermal sources or for wideband superluminescent diodes centered around wavelengths 850, 900, 1300, and .
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Linear-in-Wavenumber Dispersive Prisms for Wideband Visible Wavelength Spectral Interferometry: the Best Performing Prisms are Listed in Order of Dispersion Linearity in the Wavenumber Domain and Optimized over the Schott Glass Catalog a
Prism Type
Glass 1
Glass 2
Glass 3
(deg)
(deg)
(deg)
(deg)
Δ (deg)
SSR
K
merit func: , λ range: ,
1a.
Doublet
LAF34
SSK5
79.79
0.000
1.000
0.069
1.47
0.49
2a.
Doublet
LITHQ
CAF2
93.15
0.001
0.990
0.071
1.38
0.84
3a.
Doublet
LAK14
BAK4
77.86
0.000
1.000
0.071
1.43
0.40
4a.
Doublet
LASF44
BAF10
76.73
0.000
1.000
0.072
1.50
0.47
5a.
Doublet
FK5
CAF2
87.23
0.000
1.000
0.076
1.41
0.72
Merit func: , λ range: ,
1b.
d-Amici
CAF2
LAK33A
95.25
0.000
4.000
0.479
1.89
1.00
2b.
d-Amici
CAF2
LAF34
92.27
0.000
4.000
0.506
1.97
1.00
3b.
d-Amici
CAF2
LAF35
92.32
0.000
4.000
0.513
1.99
1.00
4b.
d-Amici
CAF2
LAK10
93.73
0.000
4.000
0.524
1.98
1.00
5b.
d-Amici
CAF2
LAF21
89.69
0.000
4.000
0.528
2.02
1.00
Merit func: , λ range: ,
1c.
Triplet
LASF41
SK11
PSK53A
81.20
0.016
3.957
0.411
1.79
0.59
2c.
Triplet
CAF2
LAK34
CAF2
95.55
97.39
3.901
0.452
1.84
0.95
3c.
Triplet
CAF2
LAK33A
CAF2
95.22
95.22
0.000
3.997
0.478
1.89
1.00
4c.
Triplet
FK51A
LAK33A
CAF2
93.00
94.99
3.901
0.487
1.95
0.95
5c.
Triplet
CAF2
LAK33A
PK51
92.90
95.91
3.906
0.494
1.96
0.95
All of the designs are nondeviating (), assume axial illumination (), and are constrained to angles of interface . The dispersion gradient curves of all 10 prisms are illustrated in Fig. 3 together with the layouts of prisms and .
Table 2
OCT Prism Designs: the Best Performing Three-Element Prisms Listed in Order of Dispersion σ-Linearity, for and , and optimized (for sections (a)–(c)) over the ZEMAX Infrared Glass Catalog. Section (d) Optimizes over the Combined Schott Catalog and Infrared Catalog a
Prism Type
Glass 1
Glass 2
Glass 3
(deg)
(deg)
(deg)
(deg)
Δ (deg)
()
SSR
K
Merit func: , λ range: ,
1a.
d-Amici
ZBLA
ZNSE
103.26
0.018
5.889
0.031
1.01
1.00
2a.
d-Amici
BAF2
KRS5
100.03
0.000
5.999
0.032
1.02
1.00
3a.
d-Amici
KCL
KRS5
101.02
0.001
6.000
0.034
1.02
1.00
4a.
d-Amici
F_SILICA
KRS5
100.80
0.039
5.789
0.034
1.03
1.00
5a.
d-Amici
ZBLAN
KRS5
100.59
0.001
6.000
0.034
1.02
1.00
6a.
Triplet
CAF2
KRS5
IRG9
100.67
99.93
5.985
0.031
1.02
0.99
7a.
Triplet
CAF2
KRS5
ZBLAN
100.61
100.20
5.971
0.031
1.01
0.97
8a.
Triplet
IRG9
ZNSE
IRG15
102.58
103.23
0.003
5.907
0.031
1.01
0.91
9a.
Triplet
SRF2
KRS5
F_SILICA
100.25
100.74
5.945
0.032
1.01
0.95
10a.
Triplet
BAF2
KRS5
BAF2
100.03
100.03
0.000
6.000
0.032
1.02
1.00
Merit func: , λ range: ,
1b.
d-Amici
IRGN6
KRS5
103.23
0.002
8.000
0.068
1.03
1.00
2b.
d-Amici
GEO2
KRS5
103.59
7.998
0.073
1.03
1.00
3b.
d-Amici
IRG7
KRS5
104.33
0.001
8.000
0.083
1.03
1.00
4b.
d-Amici
IRGN6
ZNSE
106.35
0.049
7.795
0.107
1.05
1.00
5b.
d-Amici
IRG15
KRS5
104.27
7.999
0.112
1.06
1.00
6b.
Triplet
BAF2
ZNSE
BEO
106.30
103.83
7.931
0.068
1.02
0.92
7b.
Triplet
BEO
KRS5
IRG9
100.56
104.03
0.000
8.000
0.068
1.02
1.00
8b.
Triplet
IRG9
KRS5
CALCITE
105.00
102.37
8.001
0.069
1.03
1.00
9b.
Triplet
IRG9
ZNSE
MGO
106.89
104.32
0.005
7.929
0.069
1.03
0.92
10b.
Triplet
CALCITE
KRS5
IRG15
102.63
104.48
0.000
8.000
0.069
1.03
1.00
Merit func: , λ range: ,
1c.
d-Amici
CAF2
SRTIO3
102.58
0.001
9.999
0.218
1.07
0.97
2c.
d-Amici
CAF2
SRTIO3
102.59
0.000
10.001
0.218
1.08
0.97
3c.
d-Amici
SRF2
SRTIO3
102.58
9.999
0.220
1.08
0.97
4c.
d-Amici
KCL
SRTIO3
103.50
0.002
9.999
0.246
1.10
0.97
5c.
d-Amici
BAF2
SRTIO3
101.81
10.000
0.262
1.08
0.97
6c.
Triplet
CAF2
CLEAR
SRF2
103.86
106.39
9.909
0.184
1.09
0.84
7c.
Triplet
LIF
SRTIO3
CAF2
101.66
102.86
9.931
0.200
1.07
0.88
8c.
Triplet
BAF2
ZNSBR
LIF
103.94
107.87
9.916
0.201
1.10
0.85
9c.
Triplet
CAF2
SRTIO3
LIF
101.79
103.71
9.960
0.208
1.06
0.94
10c.
Triplet
CAF2
CLEAR
KCL
105.06
106.67
9.914
0.215
1.10
0.84
Merit func: , λ range: ,
1d.
d-Amici
MGF2
LAK33A
109.63
0.000
9.998
1.682
2.16
1.00
2d.
d-Amici
MGF2
LAF34
107.90
0.002
10.000
1.770
2.33
1.00
3d.
d-Amici
MGF2
LAF21
106.30
10.001
1.825
2.38
1.00
4d.
d-Amici
MGF2
LAF35
108.26
10.000
1.844
2.40
1.00
5d.
d-Amici
MGF2
LAK10
108.92
9.872
1.850
2.29
1.00
6d.
triplet
GEO2
SAPPHIRE
MGF2
79.45
0.014
9.868
0.726
1.43
0.53
7d.
Triplet
F5
LAK9
MGF2
83.83
0.019
9.857
0.853
1.55
0.57
8d.
Triplet
F5
ALON
IRG9
67.62
4.75
0.031
9.845
0.869
1.39
0.52
9d.
Triplet
F5
LAK14
MGF2
83.45
0.022
9.854
0.874
1.58
0.57
10d.
Triplet
LASF44
BAF2
SAPPHIRE
76.56
9.840
0.878
1.60
0.52
All designs have been constrained to angles of incidence .
Table 3
OCT Prism Designs: the Best Performing Double-Amici Prisms Listed in Order of Dispersion σ-Linearity, for and Optimized over the ZEMAX Infrared Glass Catalog a
Prism Type
Glass 1
Glass 2
Glass 3
(deg)
(deg)
(deg)
(deg)
Δ (deg)
()
SSR
K
Merit func: , λ range: ,
1a.
d-Amici
KCL
CDSE
100.72
0.139
0.570
1.14
1.00
2a.
d-Amici
BAF2
CDSE
100.51
0.001
0.157
0.587
1.16
1.00
3a.
d-Amici
KBR
AMTIR1
101.94
0.000
0.170
0.601
1.17
1.00
4a.
d-Amici
NACL
AMTIR1
101.69
0.000
0.172
0.604
1.17
1.00
5a.
d-Amici
KBR
CDSE
100.10
0.000
0.190
0.624
1.19
1.00
6a.
Triplet
IRG9
KRS5
KCL
103.98
108.82
6.029
0.034
1.03
0.69
7a.
Triplet
IRG9
KRS5
BAF2
103.71
108.51
5.928
0.052
1.05
0.70
8a.
Triplet
F_SILICA
SRTIO3
IRG11
110.54
111.38
5.946
0.055
1.03
0.68
9a.
triplet
NACL
AMTIR1
MGF2
99.61
104.38
0.096
5.915
0.098
1.10
0.87
10a.
triplet
KBR
KRS5
CSBR
107.02
105.89
0.006
5.908
0.126
1.13
0.94
Merit func: , λ range: ,
1b.
d-Amici
NACL
CDSE
103.83
0.001
6.001
0.074
1.06
1.00
2b.
d-Amici
KBR
CDSE
104.00
0.000
6.001
0.076
1.07
1.00
3b.
d-Amici
CSBR
AMTIR1
102.80
0.015
5.871
0.160
1.16
1.00
4b.
d-Amici
CSBR
CDSE
101.22
0.002
6.000
0.175
1.18
1.00
5b.
d-Amici
GEO2
AMTIR1
105.61
0.033
5.824
0.198
1.21
1.00
6b.
Triplet
KBR
CDSE
CAF2
102.21
105.49
5.904
0.040
1.02
0.91
7b.
Triplet
KBR
CDSE
SRF2
102.29
105.45
5.908
0.040
1.03
0.91
8b.
Triplet
KCL
CDSE
IRG9
101.87
104.97
0.050
6.081
0.044
1.03
0.80
9b.
Triplet
CSBR
CDSE
MGF2
102.02
107.09
6.000
0.045
1.03
1.00
10b.
triplet
CSBR
AMTIR1
SRF2
103.29
107.14
0.001
6.001
0.048
1.03
1.00
Merit func: , λ range: ,
1c.
d-Amici
KBR
CDSE
103.26
0.000
6.001
0.124
1.12
1.00
2c.
d-Amici
NACL
CDSE
103.12
0.001
6.000
0.129
1.13
1.00
3c.
d-Amici
CSBR
AMTIR1
102.39
0.000
6.001
0.210
1.22
1.00
4c.
d-Amici
CSBR
CDSE
100.35
0.002
6.000
0.221
1.23
1.00
5c.
d-Amici
GEO2
AMTIR1
105.64
0.016
5.886
0.304
1.33
1.00
6b.
Triplet
SRF2
KRS5
ZBLA
104.03
110.40
0.061
5.976
0.024
1.02
0.53
7b.
Triplet
KBR
CDSE
MGF2
101.21
106.41
5.987
0.049
1.04
0.85
8b.
Triplet
IRG9
SRTIO3
BEO
108.40
111.38
6.061
0.050
1.02
0.58
9b.
Triplet
KCL
CDSE
KCL
101.80
103.79
6.011
0.067
1.05
0.87
10b.
Triplet
CSBR
AMTIR1
MGF2
103.07
108.01
0.000
6.000
0.072
1.07
1.00
All designs have been constrained to angles of incidence .
Tables (3)
Table 1
Linear-in-Wavenumber Dispersive Prisms for Wideband Visible Wavelength Spectral Interferometry: the Best Performing Prisms are Listed in Order of Dispersion Linearity in the Wavenumber Domain and Optimized over the Schott Glass Catalog a
Prism Type
Glass 1
Glass 2
Glass 3
(deg)
(deg)
(deg)
(deg)
Δ (deg)
SSR
K
merit func: , λ range: ,
1a.
Doublet
LAF34
SSK5
79.79
0.000
1.000
0.069
1.47
0.49
2a.
Doublet
LITHQ
CAF2
93.15
0.001
0.990
0.071
1.38
0.84
3a.
Doublet
LAK14
BAK4
77.86
0.000
1.000
0.071
1.43
0.40
4a.
Doublet
LASF44
BAF10
76.73
0.000
1.000
0.072
1.50
0.47
5a.
Doublet
FK5
CAF2
87.23
0.000
1.000
0.076
1.41
0.72
Merit func: , λ range: ,
1b.
d-Amici
CAF2
LAK33A
95.25
0.000
4.000
0.479
1.89
1.00
2b.
d-Amici
CAF2
LAF34
92.27
0.000
4.000
0.506
1.97
1.00
3b.
d-Amici
CAF2
LAF35
92.32
0.000
4.000
0.513
1.99
1.00
4b.
d-Amici
CAF2
LAK10
93.73
0.000
4.000
0.524
1.98
1.00
5b.
d-Amici
CAF2
LAF21
89.69
0.000
4.000
0.528
2.02
1.00
Merit func: , λ range: ,
1c.
Triplet
LASF41
SK11
PSK53A
81.20
0.016
3.957
0.411
1.79
0.59
2c.
Triplet
CAF2
LAK34
CAF2
95.55
97.39
3.901
0.452
1.84
0.95
3c.
Triplet
CAF2
LAK33A
CAF2
95.22
95.22
0.000
3.997
0.478
1.89
1.00
4c.
Triplet
FK51A
LAK33A
CAF2
93.00
94.99
3.901
0.487
1.95
0.95
5c.
Triplet
CAF2
LAK33A
PK51
92.90
95.91
3.906
0.494
1.96
0.95
All of the designs are nondeviating (), assume axial illumination (), and are constrained to angles of interface . The dispersion gradient curves of all 10 prisms are illustrated in Fig. 3 together with the layouts of prisms and .
Table 2
OCT Prism Designs: the Best Performing Three-Element Prisms Listed in Order of Dispersion σ-Linearity, for and , and optimized (for sections (a)–(c)) over the ZEMAX Infrared Glass Catalog. Section (d) Optimizes over the Combined Schott Catalog and Infrared Catalog a
Prism Type
Glass 1
Glass 2
Glass 3
(deg)
(deg)
(deg)
(deg)
Δ (deg)
()
SSR
K
Merit func: , λ range: ,
1a.
d-Amici
ZBLA
ZNSE
103.26
0.018
5.889
0.031
1.01
1.00
2a.
d-Amici
BAF2
KRS5
100.03
0.000
5.999
0.032
1.02
1.00
3a.
d-Amici
KCL
KRS5
101.02
0.001
6.000
0.034
1.02
1.00
4a.
d-Amici
F_SILICA
KRS5
100.80
0.039
5.789
0.034
1.03
1.00
5a.
d-Amici
ZBLAN
KRS5
100.59
0.001
6.000
0.034
1.02
1.00
6a.
Triplet
CAF2
KRS5
IRG9
100.67
99.93
5.985
0.031
1.02
0.99
7a.
Triplet
CAF2
KRS5
ZBLAN
100.61
100.20
5.971
0.031
1.01
0.97
8a.
Triplet
IRG9
ZNSE
IRG15
102.58
103.23
0.003
5.907
0.031
1.01
0.91
9a.
Triplet
SRF2
KRS5
F_SILICA
100.25
100.74
5.945
0.032
1.01
0.95
10a.
Triplet
BAF2
KRS5
BAF2
100.03
100.03
0.000
6.000
0.032
1.02
1.00
Merit func: , λ range: ,
1b.
d-Amici
IRGN6
KRS5
103.23
0.002
8.000
0.068
1.03
1.00
2b.
d-Amici
GEO2
KRS5
103.59
7.998
0.073
1.03
1.00
3b.
d-Amici
IRG7
KRS5
104.33
0.001
8.000
0.083
1.03
1.00
4b.
d-Amici
IRGN6
ZNSE
106.35
0.049
7.795
0.107
1.05
1.00
5b.
d-Amici
IRG15
KRS5
104.27
7.999
0.112
1.06
1.00
6b.
Triplet
BAF2
ZNSE
BEO
106.30
103.83
7.931
0.068
1.02
0.92
7b.
Triplet
BEO
KRS5
IRG9
100.56
104.03
0.000
8.000
0.068
1.02
1.00
8b.
Triplet
IRG9
KRS5
CALCITE
105.00
102.37
8.001
0.069
1.03
1.00
9b.
Triplet
IRG9
ZNSE
MGO
106.89
104.32
0.005
7.929
0.069
1.03
0.92
10b.
Triplet
CALCITE
KRS5
IRG15
102.63
104.48
0.000
8.000
0.069
1.03
1.00
Merit func: , λ range: ,
1c.
d-Amici
CAF2
SRTIO3
102.58
0.001
9.999
0.218
1.07
0.97
2c.
d-Amici
CAF2
SRTIO3
102.59
0.000
10.001
0.218
1.08
0.97
3c.
d-Amici
SRF2
SRTIO3
102.58
9.999
0.220
1.08
0.97
4c.
d-Amici
KCL
SRTIO3
103.50
0.002
9.999
0.246
1.10
0.97
5c.
d-Amici
BAF2
SRTIO3
101.81
10.000
0.262
1.08
0.97
6c.
Triplet
CAF2
CLEAR
SRF2
103.86
106.39
9.909
0.184
1.09
0.84
7c.
Triplet
LIF
SRTIO3
CAF2
101.66
102.86
9.931
0.200
1.07
0.88
8c.
Triplet
BAF2
ZNSBR
LIF
103.94
107.87
9.916
0.201
1.10
0.85
9c.
Triplet
CAF2
SRTIO3
LIF
101.79
103.71
9.960
0.208
1.06
0.94
10c.
Triplet
CAF2
CLEAR
KCL
105.06
106.67
9.914
0.215
1.10
0.84
Merit func: , λ range: ,
1d.
d-Amici
MGF2
LAK33A
109.63
0.000
9.998
1.682
2.16
1.00
2d.
d-Amici
MGF2
LAF34
107.90
0.002
10.000
1.770
2.33
1.00
3d.
d-Amici
MGF2
LAF21
106.30
10.001
1.825
2.38
1.00
4d.
d-Amici
MGF2
LAF35
108.26
10.000
1.844
2.40
1.00
5d.
d-Amici
MGF2
LAK10
108.92
9.872
1.850
2.29
1.00
6d.
triplet
GEO2
SAPPHIRE
MGF2
79.45
0.014
9.868
0.726
1.43
0.53
7d.
Triplet
F5
LAK9
MGF2
83.83
0.019
9.857
0.853
1.55
0.57
8d.
Triplet
F5
ALON
IRG9
67.62
4.75
0.031
9.845
0.869
1.39
0.52
9d.
Triplet
F5
LAK14
MGF2
83.45
0.022
9.854
0.874
1.58
0.57
10d.
Triplet
LASF44
BAF2
SAPPHIRE
76.56
9.840
0.878
1.60
0.52
All designs have been constrained to angles of incidence .
Table 3
OCT Prism Designs: the Best Performing Double-Amici Prisms Listed in Order of Dispersion σ-Linearity, for and Optimized over the ZEMAX Infrared Glass Catalog a
Prism Type
Glass 1
Glass 2
Glass 3
(deg)
(deg)
(deg)
(deg)
Δ (deg)
()
SSR
K
Merit func: , λ range: ,
1a.
d-Amici
KCL
CDSE
100.72
0.139
0.570
1.14
1.00
2a.
d-Amici
BAF2
CDSE
100.51
0.001
0.157
0.587
1.16
1.00
3a.
d-Amici
KBR
AMTIR1
101.94
0.000
0.170
0.601
1.17
1.00
4a.
d-Amici
NACL
AMTIR1
101.69
0.000
0.172
0.604
1.17
1.00
5a.
d-Amici
KBR
CDSE
100.10
0.000
0.190
0.624
1.19
1.00
6a.
Triplet
IRG9
KRS5
KCL
103.98
108.82
6.029
0.034
1.03
0.69
7a.
Triplet
IRG9
KRS5
BAF2
103.71
108.51
5.928
0.052
1.05
0.70
8a.
Triplet
F_SILICA
SRTIO3
IRG11
110.54
111.38
5.946
0.055
1.03
0.68
9a.
triplet
NACL
AMTIR1
MGF2
99.61
104.38
0.096
5.915
0.098
1.10
0.87
10a.
triplet
KBR
KRS5
CSBR
107.02
105.89
0.006
5.908
0.126
1.13
0.94
Merit func: , λ range: ,
1b.
d-Amici
NACL
CDSE
103.83
0.001
6.001
0.074
1.06
1.00
2b.
d-Amici
KBR
CDSE
104.00
0.000
6.001
0.076
1.07
1.00
3b.
d-Amici
CSBR
AMTIR1
102.80
0.015
5.871
0.160
1.16
1.00
4b.
d-Amici
CSBR
CDSE
101.22
0.002
6.000
0.175
1.18
1.00
5b.
d-Amici
GEO2
AMTIR1
105.61
0.033
5.824
0.198
1.21
1.00
6b.
Triplet
KBR
CDSE
CAF2
102.21
105.49
5.904
0.040
1.02
0.91
7b.
Triplet
KBR
CDSE
SRF2
102.29
105.45
5.908
0.040
1.03
0.91
8b.
Triplet
KCL
CDSE
IRG9
101.87
104.97
0.050
6.081
0.044
1.03
0.80
9b.
Triplet
CSBR
CDSE
MGF2
102.02
107.09
6.000
0.045
1.03
1.00
10b.
triplet
CSBR
AMTIR1
SRF2
103.29
107.14
0.001
6.001
0.048
1.03
1.00
Merit func: , λ range: ,
1c.
d-Amici
KBR
CDSE
103.26
0.000
6.001
0.124
1.12
1.00
2c.
d-Amici
NACL
CDSE
103.12
0.001
6.000
0.129
1.13
1.00
3c.
d-Amici
CSBR
AMTIR1
102.39
0.000
6.001
0.210
1.22
1.00
4c.
d-Amici
CSBR
CDSE
100.35
0.002
6.000
0.221
1.23
1.00
5c.
d-Amici
GEO2
AMTIR1
105.64
0.016
5.886
0.304
1.33
1.00
6b.
Triplet
SRF2
KRS5
ZBLA
104.03
110.40
0.061
5.976
0.024
1.02
0.53
7b.
Triplet
KBR
CDSE
MGF2
101.21
106.41
5.987
0.049
1.04
0.85
8b.
Triplet
IRG9
SRTIO3
BEO
108.40
111.38
6.061
0.050
1.02
0.58
9b.
Triplet
KCL
CDSE
KCL
101.80
103.79
6.011
0.067
1.05
0.87
10b.
Triplet
CSBR
AMTIR1
MGF2
103.07
108.01
0.000
6.000
0.072
1.07
1.00
All designs have been constrained to angles of incidence .