The authors are with the Optics Section, Blackett Laboratory, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BZ, UK.
J. Maxwell and C. C. Hull, "Multidimensional quadratic extrapolation method for the correction of aberrations in lens systems," Appl. Opt. 31, 2234-2240 (1992)
An interactive optical design tool that is based on multidimensional quadratic extrapolation is described. This technique extends the radius of convergence of the aberration manipulation process, provides strategic information about the correctability of the aberrations at each stage in iteration, and is computationally simple. A quadratic approximation to each of the nonlinearly varying aberrations, which are initially based on one relatively remote linearly predicted point in solution space, allows the step length of this differential improvement method to be extended over that which is possible with local derivative techniques. The basic mathematical method works with an equal number of defects and variables, and to involve all the relevant constructional parameters of an optical system these are grouped or linked together on the basis of an assumption about their combined ability to correct the chosen aberrations. Examples are given.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
(Step s = 1.0) to reduce the Petzval sum and control other aberrations.
(Step s = 1.0) to reduce SI and SII.
(Step s = 1.0) to finally include SII.
(Step s = 1.0) to correct SI and SII by using bending.
Indicates that a vertex solution has been taken.
Table III
Initial Design Data for the Engineering Profile Projection Lens (Example B)a
Radius
Separation
Index
Glass
Clear Diameter
1
−473.90
36.000
14.9900
1.51680
BK7
2
−53.32
37.200
8.6000
1.71736
SF1
3
−83.0300
39.000
4.3200
Air
4
92.6700
38.500
15.8400
1.51680
BK7
5
−164.9800
36.100
0.4100
Air
6
−132.8200
36.000
10.2800
1.71736
SF1
7
−433.3400
35.000
94.8700
Air
8
plano
16.500
89.9200
Air
9
−43.6800
26.000
8.8700
1.51680
BK7
10
−915.9800
29.000
13.7800
Air
11
205.8800
35.000
7.2300
1.71736
SF1
12
2567.6000
36.000
Effective focal length 69.014 mm, numerical aperture 0.075, magnitude 25×, object height 10 mm, object distance 147.12 mm.
Tables (3)
Table I
Initial Design Data for the f/3 Tessar Lens (Example A)a
(Step s = 1.0) to reduce the Petzval sum and control other aberrations.
(Step s = 1.0) to reduce SI and SII.
(Step s = 1.0) to finally include SII.
(Step s = 1.0) to correct SI and SII by using bending.
Indicates that a vertex solution has been taken.
Table III
Initial Design Data for the Engineering Profile Projection Lens (Example B)a
Radius
Separation
Index
Glass
Clear Diameter
1
−473.90
36.000
14.9900
1.51680
BK7
2
−53.32
37.200
8.6000
1.71736
SF1
3
−83.0300
39.000
4.3200
Air
4
92.6700
38.500
15.8400
1.51680
BK7
5
−164.9800
36.100
0.4100
Air
6
−132.8200
36.000
10.2800
1.71736
SF1
7
−433.3400
35.000
94.8700
Air
8
plano
16.500
89.9200
Air
9
−43.6800
26.000
8.8700
1.51680
BK7
10
−915.9800
29.000
13.7800
Air
11
205.8800
35.000
7.2300
1.71736
SF1
12
2567.6000
36.000
Effective focal length 69.014 mm, numerical aperture 0.075, magnitude 25×, object height 10 mm, object distance 147.12 mm.