William T. Plummer, James G. Baker, and Jon Van Tassell, "Photographic optical systems with nonrotational aspheric surfaces," Appl. Opt. 38, 3572-3592 (1999)
Sections of nonrotational aspheric surfaces can be useful in a
variety of optical situations. In several examples, image-forming
objectives, as for photographic or electronic camera products, are
described in which suitably located asymmetric pairs of refractive
surfaces are devised, such that relative rotation about a displaced
axis of one with respect to the other can be used to produce a focusing
effect that is satisfactory for imaging purposes over reasonable fields
of view and for practicable apertures and achromatic
corrections. Taylor expansions about assignable reference points in
any given surface of a sequence, together with suitable coordinate
systems, can be employed to relate performance to shape
parameters.
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SPE, Surface requiring special data for definition; SRF, Surface
identification within the lens design; OBJ, The object plane location;
AST, The aperture stop location and size; IMS, The image plane
location.
Table 2
Computed Design Coefficients of a Contrarotating
Pair—Case A
Two contrarotating Quintic plates, both rotated. Optimized polynomial shapes of 11th and 12th surfaces are given in Table 2. In this case the field locations 16–19 were temporarily moved to the tip corners of the format.
B.1.a
0.0051
5586
Two plane-parallel plates are present, but without polynomial terms yet on the 11th or 12th surfaces. Single (null) object distance only: 1/s = 0.100.
B.1.b
0.1049
27,930
Same as case B.1.a, but evaluated over the five object distances with no change in focus. This large blur illustrates the need for focus adjustment.
B.2
0.0197
27,930
Identical Quintic polynomial shapes introduced on the 11th and 12th surfaces, calculated algebraically from Eq. (25). Only the first Quintic plate is rotated.
B.3
0.0187
27,930
Identical Quintic shapes on 11th and 12th surfaces, but computer optimized with the same sets of seven polynomial coefficients. Only the first Quintic plate is rotated.
B.4
0.0175
27,690
Same as B.3, but reoptimized after moving field points 16–19 temporarily to the tip corners of the format, with slight vignetting. Only the first plate is rotated.
B.5
0.0161
27,930
The same set of polynomial terms, but computer optimized independently on surfaces 11 and 12. Only the first Quintic plate is rotated.
B.6
0.0100
27,930
Quintic shapes optimized independently on surfaces 11 and 12, using all polynomial terms through the fifth order: 40 coefficients in all. These computed values are in Table 3. Only the first Quintic plate is rotated.
C
0.0110
27,796
The fixed Quintic plate has been deleted and its function transferred to surface six, superimposed on its basic rotational aspheric terms. The 20 polynomial coefficients of the fifth-order moving quintic tenth surface were optimized simultaneously with the resulting 44 polynomial coefficients (through the eighth order) on the sixth surface; the values are listed in Table 4.
Table 6
Summary of Spectra Camera Focus Performance, rms Blur
Diametera
(mm)
Object Distance
12.2 m
1.74 m
0.94 m
0.64 m
Field Point
1
0.123
0.027
0.135
0.234
2
0.116
0.031
0.134
0.223
3
0.158
0.094
0.123
0.160
4
0.356
0.192
0.152
0.236
5
0.130
0.027
0.139
0.233
6
0.165
0.048
0.126
0.201
7
0.194
0.102
0.111
0.127
8
0.105
0.058
0.106
0.150
9
0.168
0.163
0.219
0.366
10
0.152
0.092
0.117
0.173
11
0.310
0.206
0.239
0.328
12
0.207
0.143
0.120
0.135
13
0.145
0.080
0.096
0.129
14
0.159
0.091
0.095
0.149
15
0.246
0.133
0.114
0.123
16
0.348
0.256
0.341
0.571
17
0.232
0.216
0.259
0.407
18
0.275
0.210
0.272
0.379
19
0.389
0.203
0.337
0.552
Mean rms diameter (monochromatic)
0.239
0.155
0.194
0.296
Mean rms diameter (four wavelengths, blue to red)
0.308
0.254
0.288
0.374
125 mm, f/10, for 74 mm
× 91 mm format.
Tables (6)
Table 1
Basic Optical System for Quintic Focus Studies
*Lens Data
SRF
Radius
Thickness
Aperture Radius
Glass Spe
OBJ
—
143.441495
35.079155
Air
1
23.575717
1.434415
5.453646 K
F2 C
2
-27.943440
0.135567
5.350368
Air
3
-75.290656
0.430324
5.142378
BACRYLIC C*
4
7.243996
33.290850
4.525579
Air*
5
-275.229770
0.430324
1.506136
BPOLYC C
6
7.259189
1.384612
1.477447
Air*
7
9.839358
0.717207
1.556340
SK2 C
8
-10.498313
0.286883
1.549168
Air
AST
—
0.014344
1.506136 A
Air
10
—
0.430324
4.000000
BPOLYC C
11
—
0.143441
4.000000
Air
12
—
0.430324
4.000000
BPOLYC C
13
—
29.001203
4.000000
Air
14
—
—
3.179948 S
Air
IMS
—
—
3.179948 S
*Conic and Polynomial Aspheric Data
SRF
CC
AD
AE
AF
AG
3
—
-0.000185
1.1402 × 10-6
-9.4176 × 10-10
—
4
-0.578345
—
7.2990 × 10-7
-1.1134 × 10-9
—
6
0.366044
—
3.2242 × 10-6
1.2701 × 10-9
—
*Apertures
Srf
Type
Aperture Radius
0
SPC
35.079155
1
SPC
5.453646 CHK
2
SPC
5.350368
3
SPC
5.142378
4
SPC
4.525579
5
SPC
1.506136
6
SPC
1.477447
7
SPC
1.556340
8
SPC
1.549168
9
SPC
1.506136
10
SPC
4.000000
11
SPC
4.000000
12
SPC
4.000000
13
SPC
4.000000
14
CMP
3.179948
15
CMP
3.179948
*Wavelenghs
Current
WV1/WW1
WV2/WW2
WV3/WW3
1
0.546070
0.486130
0.656270
1.000000
1.000000
1.000000
*Refractive Indices
SRF
Glass
RN1
RN2
RN3
VNBR
TCE
1
F2
1.624081
1.632082
1.615032
36.602872
82.000000
3
BACRYLIC
1.494062
1.497801
1.489200
57.447710
674.000000
5
BPOLYC
1.590804
1.599700
1.580100
30.143025
700.000000
7
SK2
1.609937
1.614857
1.604136
56.887629
60.000000
10
BPOLYC
1.590804
1.599700
1.580100
30.143025
700.000000
12
BPOLYC
1.590804
1.599700
1.580100
30.143025
700.000000
15
Image Surface
*Paraxial Constants
Effective focal length:
14.343647
Lateral magnification:
-0.090652
Numerical aperture:
0.050000
Gaussian image height:
3.180000
Working F number:
10.000000
Petzval radius:
-478.266740
Lagrange invariant:
-0.159002
SPE, Surface requiring special data for definition; SRF, Surface
identification within the lens design; OBJ, The object plane location;
AST, The aperture stop location and size; IMS, The image plane
location.
Table 2
Computed Design Coefficients of a Contrarotating
Pair—Case A
Two contrarotating Quintic plates, both rotated. Optimized polynomial shapes of 11th and 12th surfaces are given in Table 2. In this case the field locations 16–19 were temporarily moved to the tip corners of the format.
B.1.a
0.0051
5586
Two plane-parallel plates are present, but without polynomial terms yet on the 11th or 12th surfaces. Single (null) object distance only: 1/s = 0.100.
B.1.b
0.1049
27,930
Same as case B.1.a, but evaluated over the five object distances with no change in focus. This large blur illustrates the need for focus adjustment.
B.2
0.0197
27,930
Identical Quintic polynomial shapes introduced on the 11th and 12th surfaces, calculated algebraically from Eq. (25). Only the first Quintic plate is rotated.
B.3
0.0187
27,930
Identical Quintic shapes on 11th and 12th surfaces, but computer optimized with the same sets of seven polynomial coefficients. Only the first Quintic plate is rotated.
B.4
0.0175
27,690
Same as B.3, but reoptimized after moving field points 16–19 temporarily to the tip corners of the format, with slight vignetting. Only the first plate is rotated.
B.5
0.0161
27,930
The same set of polynomial terms, but computer optimized independently on surfaces 11 and 12. Only the first Quintic plate is rotated.
B.6
0.0100
27,930
Quintic shapes optimized independently on surfaces 11 and 12, using all polynomial terms through the fifth order: 40 coefficients in all. These computed values are in Table 3. Only the first Quintic plate is rotated.
C
0.0110
27,796
The fixed Quintic plate has been deleted and its function transferred to surface six, superimposed on its basic rotational aspheric terms. The 20 polynomial coefficients of the fifth-order moving quintic tenth surface were optimized simultaneously with the resulting 44 polynomial coefficients (through the eighth order) on the sixth surface; the values are listed in Table 4.
Table 6
Summary of Spectra Camera Focus Performance, rms Blur
Diametera
(mm)