A relationship between longitudinal spherical and longitudinal chromatic aberration and resolving power is discussed and an experiment using this relationship to predict resolving power from design data is described. The results show a high degree of correlation between resolving power predicted by this method and that obtained by measurement on real lenses.
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.
The first row shows the correlation coefficients for the comparison between the predicted and measured values of resolving power from Table I; the two next rows show correlation coefficients for comparisons between the three sets of measured values.
Tables (10)
Table I
0° Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens #2
Lens #3
Nearest to lens
18.0
7.5
7.5
7.5
21.0
10.7
9.1
9.1
30.0
15.0
12.8
10.7
36.0
18.0
21.0
18.0
51.0
36.0
30.0
30.0
60.0
43.0
51.0
43.0
Gaussian focus
60.0
51.0
51.0
51.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
60.0
43.0
51.0
51.0
36.0
30.0
36.0
43.0
26.0
15.0
26.0
26.0
21.0
9.1
18.0
15.0
Furthest from lens
15.0
7.5
7.5
7.5
Correlation coefficient
γ =
0.96
0.94
0.91
Table II
10° Radial. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens 2
Lens #3
Nearest to lens
14.0
10.5
18.0
14.0
14.0
14.0
21.0
21.0
26.0
21.0
26.0
30.0
30.0
30.0
30.0
35.0
42.0
30.0
42.0
42.0
42.0
35.0
59.0
50.0
50.0
42.0
Gaussian focus
59.0
59.0
50.0
50.0
59.0
59.0
50.0
50.0
59.0
50.0
50.0
50.0
59.0
42.0
42.0
42.0
42.0
42.0
35.0
35.0
30.0
30.0
30.0
30.0
21.0
26.0
26.0
26.0
18.0
26.0
21.0
21.0
Furthest from lens
14.0
14.0
14.0
Correlation coefficient
γ =
0.94
0.93
0.96
Table III
10° Tangential. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens #2
Lens #3
Nearest to lens
17.4
7.3
20.0
12.4
12.4
10.4
29.0
25.0
25.0
25.0
35.0
42.0
35.0
25.0
49.0
49.0
42.0
35.0
Gaussian focus
58.0
58.0
42.0
49.0
58.0
58.0
49.0
49.0
58.0
58.0
49.0
49.0
58.0
58.0
49.0
49.0
58.0
49.0
42.0
49.0
29.0
20.0
35.0
35.0
20.0
12.4
25.0
20.0
17.4
8.8
8.8
10.4
14.5
7.3
7.3
7.3
12.4
7.3
6.2
Furthest from lens
10.4
7.3
Correlation coefficient
γ =
0.98
0.95
0.97
Table IV
20° Radial. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens #2
Lens #3
Nearest to lens
14.0
24.0
14.0
28.0
24.0
17.0
28.0
28.0
28.0
20.0
34.0
28.0
28.0
28.0
35.0
34.0
34.0
Gaussian focus
40.0
40.0
40.0
40.0
56.0
48.0
40.0
40.0
56.0
40.0
40.0
40.0
56.0
40.0
40.0
40.0
56.0
40.0
40.0
40.0
56.0
40.0
34.0
34.0
56.0
40.0
34.0
28.0
28.0
28.0
28.0
28.0
20.0
28.0
28.0
24.0
17.0
24.0
24.0
20.0
14.0
20.0
17.0
Furthest from lens
12.0
17.0
Correlation coefficient
γ =
0.90
0.87
0.81
Table V
20° Tangential. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens 2
Lens #3
Nearest to lens
18.5
38.0
23.0
38.0
32.0
32.0
32.0
38.0
32.0
32.0
Gaussian focus
38.0
38.0
32.0
32.0
45.0
38.0
32.0
32.0
45.0
45.0
38.0
32.0
45.0
45.0
45.0
38.0
45.0
45.0
38.0
45.0
45.0
32.0
32.0
38.0
18.5
13.2
23.0
23.0
13.2
9.4
23.0
9.4
11.3
8.0
6.6
6.6
9.4
6.6
5.7
5.7
Furthest from lens
8.0
6.6
5.7
5.7
Correlation coefficient
7
0.85
0.89
0.92
Table VI
30° Radial. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens #2
Lens #3
Nearest to lens
9.3
26.0
9.3
26.0
22.0
26.0
11.1
26.0
26.0
26.0
13.0
26.0
31.0
26.0
15.6
31.0
31.0
44.0
18.0
37.0
37.0
37.0
Gaussian focus
26.0
44.0
44.0
37.0
44.0
52.0
44.0
44.0
52.0
52.0
44.0
44.0
52.0
52.0
44.0
52.0
52.0
52.0
44.0
52.0
52.0
52.0
44.0
44.0
44.0
44.0
44.0
44.0
26.0
44.0
37.0
37.0
18.0
37.0
37.0
Furthest from lens
15.6
37.0
37.0
Correlation coefficient
γ =
0.95
0.85
0.83
Table VII
30° Tangential. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens #2
Lens #3
Nearest to lens
20.0
38.0
23.0
38.0
38.0
45.0
27.0
38.0
38.0
45.0
32.0
38.0
38.0
45.0
32.0
38.0
45.0
45.0
32.0
45.0
45.0
38.0
Gaussian focus
32.0
45.0
45.0
38.0
32.0
38.0
38.0
38.0
9.6
27.0
32.0
32.0
8.0
20.0
20.0
20.0
6.8
11.2
9.6
11.2
5.6
8.0
6.8
8.0
5.6
5.6
5.6
5.6
Furthest from lens
4.8
5.6
4.8
5.6
Correlation coefficient
γ =
0.93
0.92
0.89
Table VIII
40° Radial. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
Resolving power, lines/mm
Predicted
Lens #1
Lens #2
Lens #3
Nearest to lens
7.0
46.0
8.2
46.0
9.8
46.0
11.0
46.0
14.0
46.0
Gaussian focus
20.0
55.0
46.0
46.0
39.0
55.0
55.0
55.0
39.0
55.0
55.0
46.0
39.0
55.0
55.0
46.0
39.0
55.0
55.0
46.0
33.0
55.0
55.0
46.0
23.0
55.0
46.0
46.0
16.0
46.0
46.0
46.0
14.0
46.0
46.0
46.0
11.0
46.0
46.0
46.0
9.8
46.0
46.0
8.2
46.0
46.0
7.0
39.0
46.0
7.0
39.0
46.0
Furthest from lens
5.7
39.0
46.0
Correlation coefficient
γ =
0.89
0.93
0.38
Table IX
40° Tangential. Comparison between Predicted and Measured Resolving Power. Focal Planes Separated by 0.15 mm; E = 0.35
The first row shows the correlation coefficients for the comparison between the predicted and measured values of resolving power from Table I; the two next rows show correlation coefficients for comparisons between the three sets of measured values.