Kiyosumi Fujii, Syuya Ogi, and Noboru Akazawa, "Gradient-index rod lens with a high acceptance angle for color use by Na+ for Li+ exchange," Appl. Opt. 33, 8087-8093 (1994)
The relationship between the characteristics of gradient-index rod lenses obtained by ion exchange and their mother glass compositions is studied. It is observed that Li2O content, R2O (Li2O + Na2O) content, and the Li2O/Na2O ratio are important factors in attaining a high acceptance angle and a small field curvature. Thus the gradient-index lens array is fabricated by the use of a newly developed glass composition and its optical performance; the modulation transfer function, luminous intensity, and chromatic aberration are precisely evaluated. The array is found to have a sufficiently high performance to be applicable for color use.
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.
Compositions of Typical Mother Glasses that Contain Li+ for the Ion Exchange with NaNO3 Molten Salt and the Resulting Maximum Acceptance Angles (θmax) of the GRIN Rod Lenses
Glass Code
Glass Composition (mol. %)
θmax (deg)
SiO2
MgO
BaO
PbO
TiO2
Li2O
Na2O
Li1
58.0
12.0
—
6.0
4.0
8.0
12.0
9.0
Li2
57.0
12.5
2.0
6.0
4.0
9.0
9.5
10.3
Li3
57.0
14.0
2.0
6.0
4.0
9.0
8.0
10.9
Li4
56.0
14.0
2.0
6.0
3.5
9.5
9.0
11.8
Li5
56.0
14.0
2.0
6.0
4.0
10.0
8.0
12.5
Li6
52.0
16.0
—
4.0
8.0
16.0
4.0
12.0
Table 2
Compositions of Mother Glasses Investigated in the Ion-Exchange Experiment with NaNO3 Molten Salt and the Resulting Optical Properties, θmax and ΔF, of the GRIN Rod Lenses
Glass Number
Glass Composition (mol. %)
R2O (mol. %)
Li2O/Na2O
θmax (deg.)
ΔF (μm)
SiO2
MgO
BaO
PbO
TiO2
Li2O
Na2O
a
56.0
7.5
2.0
6.0
5.5
11.5
11.5
23.0
1.000
13.2
−25
b
56.0
10.0
2.0
6.0
5.5
11.5
9.0
20.5
1.278
14.1
−50
c
56.0
12.0
2.0
6.0
5.5
11.5
7.0
18.5
1.643
14.6
−100
d
56.0
14.0
2.0
6.0
5.5
11.5
5.0
16.5
2.300
15.3
−150
Table 3
Parameters or Dimensions for GRIN Lens Arrays at the 570-nm Wavelengtha
Parameter or Dimension
Notation
NEW
EX(Li)
EX(Tl)
Lens diameter
2r0 (mm)
0.860
0.895
0.912
Refractive index on axis
n0
1.633
1.614
1.639
Gradient constant
0.327
0.283
0.547
Periodic length
P (mm)
19.20
22.18
11.49
Maximum acceptance angle
θmax (deg)
13.2
11.7
23.4
Number of rows
N
2
2
1
Total conjugate length
TC (mm)
22.0
25.5
14.4
Lens length
Z0 (mm)
11.74
13.57
6.79
Working distance
l0 (mm)
5.13
5.97
3.81
View radius
X0 (mm)
1.25
1.31
1.62
Overlapping degree
m
1.43
1.43
1.75
NEW denotes the lens array newly developed in this work, and EX(Li) and EX(Tl) denote the commercially available lens arrays made of Li-containing glass and Tl-containing glass, respectively.
Table 4
F-Numbers and Brightness Ratios of the GRIN Lens Arrays
Sample
F-Number
Brightness Ratio
EX(Li)
1.72
1
NEW
1.54
1.25
EX(Tl)
1.29
1.78
Table 5
Periodic Lengths P at Different Wavelengths and Chromatic Aberrations ΔP/P of the GRIN Lens Arraysa
Sample
P(F) (mm)
P(D) (mm)
P(C) (mm)
P(C) − P(F) (mm)
ΔP/P
EX(Li)
22.26
22.28
22.29
0.021
1.0 × 10−3
NEW
19.18
19.21
19.25
0.070
3.7 × 10−3
EX(T1)
11.20
11.55
11.67
0.477
4.13 × 10−2
P(C), P(D), and P(F) represent the periodic lengths at C (656.6 nm), D (587.6 nm), and F (486.1 nm) lights, respectively. ΔP/P is defined as ΔP/P = {[P(C) − P(F)]/[P(D)]}.
Tables (5)
Table 1
Compositions of Typical Mother Glasses that Contain Li+ for the Ion Exchange with NaNO3 Molten Salt and the Resulting Maximum Acceptance Angles (θmax) of the GRIN Rod Lenses
Glass Code
Glass Composition (mol. %)
θmax (deg)
SiO2
MgO
BaO
PbO
TiO2
Li2O
Na2O
Li1
58.0
12.0
—
6.0
4.0
8.0
12.0
9.0
Li2
57.0
12.5
2.0
6.0
4.0
9.0
9.5
10.3
Li3
57.0
14.0
2.0
6.0
4.0
9.0
8.0
10.9
Li4
56.0
14.0
2.0
6.0
3.5
9.5
9.0
11.8
Li5
56.0
14.0
2.0
6.0
4.0
10.0
8.0
12.5
Li6
52.0
16.0
—
4.0
8.0
16.0
4.0
12.0
Table 2
Compositions of Mother Glasses Investigated in the Ion-Exchange Experiment with NaNO3 Molten Salt and the Resulting Optical Properties, θmax and ΔF, of the GRIN Rod Lenses
Glass Number
Glass Composition (mol. %)
R2O (mol. %)
Li2O/Na2O
θmax (deg.)
ΔF (μm)
SiO2
MgO
BaO
PbO
TiO2
Li2O
Na2O
a
56.0
7.5
2.0
6.0
5.5
11.5
11.5
23.0
1.000
13.2
−25
b
56.0
10.0
2.0
6.0
5.5
11.5
9.0
20.5
1.278
14.1
−50
c
56.0
12.0
2.0
6.0
5.5
11.5
7.0
18.5
1.643
14.6
−100
d
56.0
14.0
2.0
6.0
5.5
11.5
5.0
16.5
2.300
15.3
−150
Table 3
Parameters or Dimensions for GRIN Lens Arrays at the 570-nm Wavelengtha
Parameter or Dimension
Notation
NEW
EX(Li)
EX(Tl)
Lens diameter
2r0 (mm)
0.860
0.895
0.912
Refractive index on axis
n0
1.633
1.614
1.639
Gradient constant
0.327
0.283
0.547
Periodic length
P (mm)
19.20
22.18
11.49
Maximum acceptance angle
θmax (deg)
13.2
11.7
23.4
Number of rows
N
2
2
1
Total conjugate length
TC (mm)
22.0
25.5
14.4
Lens length
Z0 (mm)
11.74
13.57
6.79
Working distance
l0 (mm)
5.13
5.97
3.81
View radius
X0 (mm)
1.25
1.31
1.62
Overlapping degree
m
1.43
1.43
1.75
NEW denotes the lens array newly developed in this work, and EX(Li) and EX(Tl) denote the commercially available lens arrays made of Li-containing glass and Tl-containing glass, respectively.
Table 4
F-Numbers and Brightness Ratios of the GRIN Lens Arrays
Sample
F-Number
Brightness Ratio
EX(Li)
1.72
1
NEW
1.54
1.25
EX(Tl)
1.29
1.78
Table 5
Periodic Lengths P at Different Wavelengths and Chromatic Aberrations ΔP/P of the GRIN Lens Arraysa
Sample
P(F) (mm)
P(D) (mm)
P(C) (mm)
P(C) − P(F) (mm)
ΔP/P
EX(Li)
22.26
22.28
22.29
0.021
1.0 × 10−3
NEW
19.18
19.21
19.25
0.070
3.7 × 10−3
EX(T1)
11.20
11.55
11.67
0.477
4.13 × 10−2
P(C), P(D), and P(F) represent the periodic lengths at C (656.6 nm), D (587.6 nm), and F (486.1 nm) lights, respectively. ΔP/P is defined as ΔP/P = {[P(C) − P(F)]/[P(D)]}.