Jin Choi,1
T. H. Kim,1
H. J. Kong,1
and Jong Ung Lee2
1J. Choi (jinchoi@kaist.ac.kr), T. H. Kim, and H. J. Kong are with the Department of Physics and Image Information Research Center, Korea Advanced Institute of Science and Technology, Deajeon 305-701, South Korea.
2J. U. Lee is with the Department of Optical Engineering, Chongju University, Chongju 360-764, South Korea.
Jin Choi, T. H. Kim, H. J. Kong, and Jong Ung Lee, "Zoom lens design for a novel imaging spectrometer that controls spatial and spectral resolution individually," Appl. Opt. 45, 3430-3441 (2006)
A novel imaging spectrometer can individually control spatial and spectral resolution by using zoom lenses as the foreoptics of the system and a focusing lens. By varying the focal length we can use the focusing lens to change the spatial and spectral dimensions; with the foreoptics, however, we can change only the spatial dimension. Therefore the spectral resolution and the spectral range are affected by the zoom ratio of the focusing lens, whereas the spatial resolution and the field of view are affected by the multiplication of the zoom ratios of the foreoptics and the focusing lens. By properly combining two zoom ratios, we can control the spectral resolution with a fixed spatial resolution or the spatial resolution with a fixed spectral resolution. For an imaging spectrometer with this novel zooming function, we used the lens module method and third-order aberration theory to design an initial four-group zoom system with an external entrance pupil for the focusing lens. Furthermore, using the optical design software CODE V, we obtained an optimized zoom lens with a focal-length range of 50 to
. Finally, the zoom system with its transmission grating in the Littrow configuration performs satisfactorily as the focusing lens of an imaging spectrometer in the wavelength range 450–900 nm.
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Zoom Ratios of Foreoptics and Focusing Lens, and Resultant Wavelength Range Δλ and FOV of the Imaging Spectrometer
Configuration
Zoom Ratio of Foreoptics
Zoom Ratio of Focusing Lens
Wavelength Range, Δλ (nm)
FOV (°)
Type 1
1 ×
1 ×
450
12
Type 2
1 ×
3 ×
150
4
Type 3
1∕3 ×
3 ×
150
12
Type 4
3 ×
1 ×
450
4
Table 2
Specifications of the Imaging Spectrometer Described in This Paper
FOV
12° (4° for spatial zooming)
Entrance pupil diameter
20 mm
Focal length of focusing lens
50 mm (150 mm for zooming)
Image size
10 mm (spatial dimension) × 7 mm (spectral dimension)
CCD pixel size
12 μm × 12 μm
Spectral coverage
From 450 nm to 900 nm
Spectral bandwidth
450 nm (150 nm for spectral zooming)
Spectral channel
150
Spectral resolution
3 nm (1 nm for spectral zooming)
Table 3
Descriptions of the Lens Modules with a P-N–P-N Arrangement (millimeters)
Measurand
Module 1
Module 2
Module 3
Module 4
EFL
201.25409
−139.02836
64.99072
−179.10648
BFL
192.39370
−185.65545
50.59721
−160.15861
FFL
−204.04616
114.94379
−67.83553
206.66741
MUI
0.0
−0.02484
0.01205
−0.09501
MUT
−0.02484
0.01205
−0.09501
−0.10000
MHI
5.0
4.53143
6.99236
1.72411
MHT
4.77987
5.69180
5.59055
1.00041
PUI
0.04014
0.03870
0.03933
−0.05380
PUT
0.03870
0.03933
−0.05380
−0.04484
PHI
0.40140
1.01926
6.16455
3.08874
PHT
0.63224
1.92092
5.27827
2.45545
SI
−0.0000621
0.0000788
−0.0001688
0.0000142
SII
−0.0000300
−0.0003137
0.0001553
0.0000543
SIII
−0.0001970
0.0003645
−0.0002547
−0.0000632
Table 4
Descriptions of the Lens Modules with a N-P–P-P Arrangement (millimeters)
Measurand
Module 1
Module 2
Module 3
Module 4
EFL
−250.47481
116.21267
71.67249
262.47352
BFL
−256.75380
59.06369
86.05710
221.55422
FFL
249.18656
−146.25008
−45.98844
−304.80762
MUI
0.0
0.01996
−0.03637
−0.08060
MUT
0.01996
−0.03637
−0.08060
−0.10000
MHI
5.0
7.14599
4.10424
1.68005
MHT
5.12534
4.46793
4.32954
1.00022
PUI
0.04015
0.04155
0.01084
−0.05299
PUT
0.04155
0.01084
−0.05299
−0.07524
PHI
0.40153
4.81653
4.29659
3.59544
PHT
0.61069
4.18817
5.33733
2.76016
SI
0.0000463
−0.0004774
0.0007909
−0.0003599
SII
−0.0002145
0.0000952
0.0004222
−0.0003030
SIII
0.0001238
−0.0000002
0.0001604
−0.0002840
Table 5
Design Data of the P-N–P-N Zoom System Obtained from the Thick Lens Transformationa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
79.205
5.0
Schott SF4
3
52.399
5.0
Schott N-BK7
4
3533.080
10.0
Air
5
−15.618
6.0
Schott SF4
6
−15.209
3.654
Air
7
−20.843
6.0
Schott N-FK5
8
−13.517
6.0
Schott N-LaF2
9
−30.578
107.9
Air
10
352.466
6.0
Schott N-LaF2
11
−82.964
2.162
Air
12
30.214
6.0
Schott N-FK5
13
−96.398
6.0
Schott SF4
14
66.304
40.695
Air
15
31.203
4.66
Schott N-BK7
16
55.435
4.66
Schott SF4
17
25.748
Air
All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 6
Design Data of the N-P–P-P Zoom System Obtained from the Thick Lenses Transformationa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
−89.868
4.042
Schott N-BK7
3
159.323
4.042
Schott SF4
4
−3239.872
101.224
Air
5
121.468
6.0
Schott N-LaF2
6
−179.301
34.233
Air
7
43.981
6.0
Schott N-FK5
8
−85.333
6.0
Schott SF4
9
56.383
10.0
Air
10
186.909
6.0
Schott SF4
11
21.080
6.0
Schott N-FK5
12
16.447
4.726
Air
13
22.655
6.0
Schott N-LaF2
14
−67.883
32.872
Air
15
24.818
4.215
Schott SF4
16
352.188
4.215
Schott N-BK7
17
16.783
Air
All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 7
Design Data Optimized from the P-N–P-N Zoom System of Table 5 with Specific Requirementsa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
69.313
5.0
Schott SF4
3
52.480
5.0
Schott N-BK7
4
401.862
3.069–141.833
Air
5
−33.866
8.0
Schott SF4
6
158.536
6.868
Air
7
−69.908
8.0
Schott N-FK5
8
119.949
10.0
Schott N-LaF2
9
−44.314
83.140–1.0
Air
10
82.096
10.445
Schott N-LaF2
11
−222.395
1.0
Air
12
76.673
12.0
Schott N-FK5
13
−79.511
5.0
Schott SF4
14
112.476
57.624–1.0
Air
15
14.264
8.0
Schott N-BK7
16
25.206
5.0
Schott SF4
17
9.369
Air
Entrance pupil diameter, 20 mm; image size, 10 mm; wavelength range 450–900 nm. All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 8
Design Data Optimized from the N-P–P-P Zoom System of Table 6 with Specific Requirementsa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
−215.204
4.0
Schott N-BK7
3
165.594
4.0
Schott SF4
4
455.607
99.590–1.0
Air
5
78.922
10.0
Schott N-LaF2
6
−5243.401
36.626
Air
7
46.663
10.718
Schott N-FK5
8
−58.765
5.739
Schott SF4
9
51.798
5.270–127.545
Air
10
−129.315
6.0
Schott SF4
11
41.701
9.722
Schott N-FK5
12
−74.509
1.0
Air
13
46.353
8.136
Schott N-LaF2
14
−328.460
24.685–1.0
Air
15
19.077
7.5081
Schott SF4
16
−114.165
4.0
Schott N-BK7
17
10.878
Air
Entrance pupil diameter, 20 mm; image size, 10 mm; wavelength range, 450–900 nm. All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 9
Design Data Optimized from the N-P–P-P Zoom System of Table 8 with Two CaF2 Elements and Two Aspheric Surfacesa
The thickness refers to the thickness after the surface of the same number. Ai is the ith aspheric coefficient of the aspheric surface.
Surface 6 asphere data: A4, −1.1590 × 10−7; A6, −5.3385 × 10−10; A8, 1.3985 × 10−12; A10, −1.7862 × 10−15; A12, 8.9605 × 10−19.
Surface 16 asphere data: A4, −1.5320 × 10−5; A6, 7.7928 × 10−8; A8, 2.1700 × 10−9; A10, 1.6074 × 10−11; A12, −4.4304 × 10−14.
Tables (10)
Table 1
Zoom Ratios of Foreoptics and Focusing Lens, and Resultant Wavelength Range Δλ and FOV of the Imaging Spectrometer
Configuration
Zoom Ratio of Foreoptics
Zoom Ratio of Focusing Lens
Wavelength Range, Δλ (nm)
FOV (°)
Type 1
1 ×
1 ×
450
12
Type 2
1 ×
3 ×
150
4
Type 3
1∕3 ×
3 ×
150
12
Type 4
3 ×
1 ×
450
4
Table 2
Specifications of the Imaging Spectrometer Described in This Paper
FOV
12° (4° for spatial zooming)
Entrance pupil diameter
20 mm
Focal length of focusing lens
50 mm (150 mm for zooming)
Image size
10 mm (spatial dimension) × 7 mm (spectral dimension)
CCD pixel size
12 μm × 12 μm
Spectral coverage
From 450 nm to 900 nm
Spectral bandwidth
450 nm (150 nm for spectral zooming)
Spectral channel
150
Spectral resolution
3 nm (1 nm for spectral zooming)
Table 3
Descriptions of the Lens Modules with a P-N–P-N Arrangement (millimeters)
Measurand
Module 1
Module 2
Module 3
Module 4
EFL
201.25409
−139.02836
64.99072
−179.10648
BFL
192.39370
−185.65545
50.59721
−160.15861
FFL
−204.04616
114.94379
−67.83553
206.66741
MUI
0.0
−0.02484
0.01205
−0.09501
MUT
−0.02484
0.01205
−0.09501
−0.10000
MHI
5.0
4.53143
6.99236
1.72411
MHT
4.77987
5.69180
5.59055
1.00041
PUI
0.04014
0.03870
0.03933
−0.05380
PUT
0.03870
0.03933
−0.05380
−0.04484
PHI
0.40140
1.01926
6.16455
3.08874
PHT
0.63224
1.92092
5.27827
2.45545
SI
−0.0000621
0.0000788
−0.0001688
0.0000142
SII
−0.0000300
−0.0003137
0.0001553
0.0000543
SIII
−0.0001970
0.0003645
−0.0002547
−0.0000632
Table 4
Descriptions of the Lens Modules with a N-P–P-P Arrangement (millimeters)
Measurand
Module 1
Module 2
Module 3
Module 4
EFL
−250.47481
116.21267
71.67249
262.47352
BFL
−256.75380
59.06369
86.05710
221.55422
FFL
249.18656
−146.25008
−45.98844
−304.80762
MUI
0.0
0.01996
−0.03637
−0.08060
MUT
0.01996
−0.03637
−0.08060
−0.10000
MHI
5.0
7.14599
4.10424
1.68005
MHT
5.12534
4.46793
4.32954
1.00022
PUI
0.04015
0.04155
0.01084
−0.05299
PUT
0.04155
0.01084
−0.05299
−0.07524
PHI
0.40153
4.81653
4.29659
3.59544
PHT
0.61069
4.18817
5.33733
2.76016
SI
0.0000463
−0.0004774
0.0007909
−0.0003599
SII
−0.0002145
0.0000952
0.0004222
−0.0003030
SIII
0.0001238
−0.0000002
0.0001604
−0.0002840
Table 5
Design Data of the P-N–P-N Zoom System Obtained from the Thick Lens Transformationa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
79.205
5.0
Schott SF4
3
52.399
5.0
Schott N-BK7
4
3533.080
10.0
Air
5
−15.618
6.0
Schott SF4
6
−15.209
3.654
Air
7
−20.843
6.0
Schott N-FK5
8
−13.517
6.0
Schott N-LaF2
9
−30.578
107.9
Air
10
352.466
6.0
Schott N-LaF2
11
−82.964
2.162
Air
12
30.214
6.0
Schott N-FK5
13
−96.398
6.0
Schott SF4
14
66.304
40.695
Air
15
31.203
4.66
Schott N-BK7
16
55.435
4.66
Schott SF4
17
25.748
Air
All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 6
Design Data of the N-P–P-P Zoom System Obtained from the Thick Lenses Transformationa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
−89.868
4.042
Schott N-BK7
3
159.323
4.042
Schott SF4
4
−3239.872
101.224
Air
5
121.468
6.0
Schott N-LaF2
6
−179.301
34.233
Air
7
43.981
6.0
Schott N-FK5
8
−85.333
6.0
Schott SF4
9
56.383
10.0
Air
10
186.909
6.0
Schott SF4
11
21.080
6.0
Schott N-FK5
12
16.447
4.726
Air
13
22.655
6.0
Schott N-LaF2
14
−67.883
32.872
Air
15
24.818
4.215
Schott SF4
16
352.188
4.215
Schott N-BK7
17
16.783
Air
All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 7
Design Data Optimized from the P-N–P-N Zoom System of Table 5 with Specific Requirementsa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
69.313
5.0
Schott SF4
3
52.480
5.0
Schott N-BK7
4
401.862
3.069–141.833
Air
5
−33.866
8.0
Schott SF4
6
158.536
6.868
Air
7
−69.908
8.0
Schott N-FK5
8
119.949
10.0
Schott N-LaF2
9
−44.314
83.140–1.0
Air
10
82.096
10.445
Schott N-LaF2
11
−222.395
1.0
Air
12
76.673
12.0
Schott N-FK5
13
−79.511
5.0
Schott SF4
14
112.476
57.624–1.0
Air
15
14.264
8.0
Schott N-BK7
16
25.206
5.0
Schott SF4
17
9.369
Air
Entrance pupil diameter, 20 mm; image size, 10 mm; wavelength range 450–900 nm. All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 8
Design Data Optimized from the N-P–P-P Zoom System of Table 6 with Specific Requirementsa
Surface Number
Radius of Curvature (mm)
Thickness (mm)
Glass Type
1, stop
10.0
Air
2
−215.204
4.0
Schott N-BK7
3
165.594
4.0
Schott SF4
4
455.607
99.590–1.0
Air
5
78.922
10.0
Schott N-LaF2
6
−5243.401
36.626
Air
7
46.663
10.718
Schott N-FK5
8
−58.765
5.739
Schott SF4
9
51.798
5.270–127.545
Air
10
−129.315
6.0
Schott SF4
11
41.701
9.722
Schott N-FK5
12
−74.509
1.0
Air
13
46.353
8.136
Schott N-LaF2
14
−328.460
24.685–1.0
Air
15
19.077
7.5081
Schott SF4
16
−114.165
4.0
Schott N-BK7
17
10.878
Air
Entrance pupil diameter, 20 mm; image size, 10 mm; wavelength range, 450–900 nm. All surfaces are spherical. The thickness refers to the thickness after the surface of the same number.
Table 9
Design Data Optimized from the N-P–P-P Zoom System of Table 8 with Two CaF2 Elements and Two Aspheric Surfacesa