SELFOC® Lens Arrays for Line Scanning Applications

INTELLIGENT OPTO SENSOR
DESIGNER’S
NOTEBOOK
Number 2
SELFOC® Lens Arrays for Line Scanning Applications
Revision B
Contributed by NSG America, Inc.
Design Problem What type of SELFOC Lens Array is best for a particular scanning application?
Solution
A SELFOC® Lens Array (SLA) is a compact image transfer device that is ideal for
use with Texas Advanced Optoelectronic Solutions linear sensor arrays. In scanning
applications, the SLA is used to form a real, erect image directly onto the linear
sensor array with unit magnification.
Figure 1: SLA Dimensional Parameters
Texas Advanced Optoelectronic Solutions (TAOS) provides customer support in varied technical areas. Since TAOS does not possess full access
to data concerning all of the uses a and applications of customers’ products, TAOS assumes no responsibility for customer product design or the
use or application of customers’ products or for any infringements of patents or rights of others which may result from TAOS assistance.
(972) 673-0759
www.taosinc.com
An SLA is typically constructed from one or two rows of SELFOC gradient-index
microlenses which are aligned and secured between two fiberglass-reinforced plates.
These gradient-index (GRIN) microlenses are cylindrically shaped and have flat end
surfaces. Their imaging ability is due to a graded refractive index which is formed
by an ion-exchange process in the glass host material. The resulting index profile has
a maximum at the center of the lens (on axis) and decreases quadratically towards
the outer edge. This smoothly varying index of refraction causes incident rays of
light to refract within the lens and converge towards a point of focus. When
assembled in an array each microlens, or “lenslet”, forms its own image so that the
images from adjacent lenslets overlap and form a continuous image across the width
of the SLA.
Figure 1 illustrates the dimensional parameters used to select and specify an array.
Notice that the heights, X, of the object and image planes are identical. This is
because the SLA is a one-to-one image transfer device and, as such, it operates with
unit magnification. The maximum height of this field that the SLA will “see” is
determined by the numerical aperture of the individual lenslets and by the number
of rows of lenslets in the array. For line scanning applications, the SLA’s field of
view need not be large (perhaps 1 millimeter). For applications other than line
scanning (eg., copiers, printers, etc.), it is necessary to determine the maximum
height of the object field for your application, remembering that shorter field heights
will generally result in greater depth of focus and higher resolution. The maximum
object height currently viewable by a standard SLA is 7.8mm (SLA type 12B-495).
Another aspect of the SLA’s one-to-one imaging ability is conjugate symmetry.
Referring again to Figure 1, the working distance L0 is shown to be identical on
each side of the lens (object distance = image distance). By adding the working
distances to the lenslet length (Z) we obtain the Total Conjugate, or “TC”, of the
optical system (TC=Z+2L0). The TC represents the total separation of the object and
image planes and is a key identifier in the specification of an SLA. A wide range of
TCs are available, from 9.1mm (SLA-20D) to 74mm (SLA-06A), with different TCs
being suitable for different applications. In a contact image sensor (CIS), for
example, the SLA-20D is extremely convenient because it allows the SLA and the
sensor array to be packaged together in a very small unit. For other types of imaging
applications, longer TCs may be needed due to mechanical constraints or optical
requirements. As with the field height specification, there are trade-offs between TC
and depth of focus. The positioning of a “short-TC” lens may be more critical than
for a lens with a longer total conjugate.
Once the total conjugate and the field height requirements are known for your
optical system, the choice of an appropriate SLA becomes much clearer. The table in
the appendix gives a complete list of the standard SLA types and their major optical
parameters. The numeral in the SLA type code corresponds roughly to the
acceptance angle of the lenslets in the array. For example, in an SLA type 09A, each
lenslet has an acceptance angle of about 9 degrees (ie., a lenslet will accept light
from a 9-degree cone). The letter in the type designation is a code corresponding to
the lenslet diameter. Type “A” lenslets are the largest (about 1.1mm), while type “D”
are the smallest (0.56mm). Larger lenslet diameters result in a more massive lens
array and provide a larger viewing angle for field scanning applications.
It is important to remember that the optical properties of an SLA depend upon the
wavelength at which it is used. For example, the values of the total conjugate and the
working distance are specified for a particular wavelength as indicated in the
appendix. But if the SLA is used at a different wavelength, a positioning adjustment
will be required to achieve the best performance. The general rule is that longer
wavelengths require larger working distances and result in greater total conjugates.
Finally, we must determine the width of the entire lens array. Recall that an SLA
creates a continuous image from the overlapping images formed by adjacent groups
of lenslets. A large amount of overlap will result in better image uniformity, higher
brightness, and greater resolution. Consider, however, the lenslets lying at the ends
of the array. Because the degree of overlap is small at the edges of the SLA, the
image quality at the extremities will be correspondingly lower than at the center. For
this reason it is necessary to oversize the SLA width such that this “edge effect” does
not appear in the transmitted image. The following equation shows how to calculate
the SLA lens width WL for a particular image width Wi:
WL = Wi + 2[X0-(D/2)]
X0 is the view radius of a lenslet and D is the lenslet diameter. The values of X0 and
D are tabulated in the appendix for each SLA type. Table 1 lists the required WL of
common SLA types for use with TAOS linear arrays.
In most SLA products there is a small section at each end of the SLA which contains
no lenslets. The total SLA width WT may, therefore, be larger than the width of the
active lens portion WL. See Figure 1 for an illustration.
For order placements and technical inquiries, a unique coding system is used to
specify SELFOC Lens Arrays. The part code is composed of essential identifying
information in the following order: SLA type, total conjugate, wavelength, number
of rows, and array size. Here is an example of a typical SLA part code:
SLA-12A-380-570-2-226/256
The above code indicates an SLA type 12A with a 38.0mm total conjugate at a
wavelength of 570nm and containing 2 rows of lenslets. The final section of the
code represents WL/WT. In this case the lenslet array is 226mm wide and the total
unit is 256mm wide. If special positioning notches, grooves, or holes are required in
the SLA, the coding information for these features is included at the very end of the
part code.
To place an order for a SELFOC Lens Array, or to receive more information about
SELFOC products, contact an applications engineer at NSG America Inc. There are
two regional sales offices in the United States to assist you.
Eastern Regional Office
Western Regional Office
28 Worlds Fair Drive
19200 Von Karman Avenue, Suite 400
Somerset, NJ 08873
Irvine, CA 92715
tel 908-469-9650
tel 714-261-6212
fax 908-469-9654
fax 714-261-6704
Table 1. Required width of common SLA types for use with TAOS Linear Arrays
* Minimum Lens Array Width WL (mm)
Linear
Sensor
Array
Sensor
Resolution
(LP/mm)
Active
Width
(mm)
SLA04D TC
49.0
SLA-06A
TC 64.0
SLA-12A
TC 43.0
SLA-20A
TC 18.0
SLA-20D
TC 9.1
TSL201
3.9
8.13
12
15
17
15
13
TSL202
3.9
16.26
21
23
25
23
21
TSL208
3.9
65.02
69
72
74
72
70
TSL1401
7.9
8.13
12
15
17
15
13
TSL1301 /
5.9
8.64
13
16
18
16
13
7.9
16.26
21
23
25
23
21
TSL2301
TSL1402
Appendix - Mechanical and Optical Parameters of SLA
SLA
Type
No. of
Rows
TC
(mm)
D
(mm)
Z
(mm)
L0
(mm)
X0
(mm)
X
(mm)
MTF@6LP/mm (%)
Avg.
Min.
DOF*
(mm)
Wavelength
(nm)
04D
2
49.0
0.563
23.4 ± 1.5
12.8
0.90
2.29
60
35
±1.3
570
06A
2
2
2
2
2
2
1
2
2
2
1
2
2
2
2
2
2
1
1
1
1
2
2
2
2
2
2
1
74.0
70.0
64.0
54.0
48.0
40.0
58.0
43.0
38.0
32.0
44.2
43.2
43.0
32.1
32.0
25.6
25.5
49.5
40.6
33.4
18.3
22.25
22.2
22.0
18.7
18.0
16.9
17.6
1.070
28.21 ± 1.3
28.56 ± 1.3
29.25 ± 1.3
19.85 ± 1.3
20.40 ± 1.3
21.71 ± 1.6
19.60 ± 0.5
15.12 ± 0.7
15.50 ± 0.7
16.32 ± 0.7
15.05 ± 0.4
15.13 ± 0.7
15.13 ± 0.7
16.32 ± 0.7
16.32 ± 0.7
13.57 ± 0.4
13.57 ± 0.4
11.90 ± 0.3
12.16 ± 0.3
7.86 ± 0.2
8.71 ± 0.2
11.74 ± 0.45
11.74 ± 0.45
11.74 ± 0.45
8.41 ± 0.5
8.41 ± 0.5
8.42 ± 0.5
8.30 ± 0.4
22.90
20.72
17.38
17.05
13.80
9.15
19.20
13.94
11.25
7.84
14.58
14.04
13.94
7.89
7.84
6.02
5.97
18.80
14.22
12.77
4.80
5.26
5.23
5.13
5.15
4.80
4.24
4.65
2.46
2.23
1.90
2.62
2.14
1.47
2.94
2.90
2.36
1.69
3.02
2.90
2.89
1.69
1.69
1.32
1.31
3.91
2.97
2.43
0.97
1.27
1.27
1.25
2.11
2.00
1.82
1.98
5.85
5.39
4.73
6.14
5.18
3.84
5.88
6.74
5.66
4.32
6.04
6.74
6.72
4.32
4.32
3.41
3.40
7.82
5.94
4.86
1.94
3.28
3.28
3.24
5.19
4.97
4.61
3.96
45
48
50
53
55
60
50
60
65
70
60
70
70
73
73
70
60
50
65
55
70
60
60
60
50
50
50
50
25
28
30
28
30
40
25
30
40
50
30
45
45
50
50
50
50
30
35
30
55
45
45
45
35
35
35
35
±0.8
510
510
510
510
510/570
570
510
510
570
570
510
660
570
660
570
660
570
510
510
545
570
740
660
570
740
660
570
570
2
2
2
1
1
15.1
14.6
13.8
14.4
9.1
6.89 ± 0.4
6.89 ± 0.4
6.89 ± 0.4
6.79 ± 0.33
4.30 ± 0.05
4.10
3.86
3.46
3.81
2.40
1.70
1.62
1.48
1.62
0.98
4.18
4.03
3.75
3.24
1.96
55
55
55
55
60
45
45
45
45
50
09A
12A
12A
(HR)
12B
12D
15B
20A
20B
20D
1.045
1.085
1.085
0.895
0.563
0.860
1.115
0.912
0.563
* DOF is based on 10% MTF @ 6LP/mm and is for reference only, not inspected.
** Consult SELFOC® Lens Array Reference Book for complete design and application data.
±0.6
±0.4
±0.45
±0.4
±0.4
±0.35
±0.3
±0.3
±0.3
740
660
570
570
570