A new type of microlens for data storage applications that has improved off-axis performance is described. The lens consists of a micro Fresnel pattern on a curved substrate. The radius of the substrate is equal to the focal length of the lens. If the pattern and substrate are thin, the combination satisfies the Abbe sine condition. Therefore, the lens is free of coma. We analyze a 0.5 numerical aperture, 0.50 mm focal length lens in detail. A 0.16 numerical aperture lens was fabricated holographically, and results are presented

Erwin, J. Kevin

Froehlich, F. F.

Milster, T. D.

Trusty, R. M.

Wang, M. S.

English

NASA Technical Reports Server

Appendix J " 193
Micro-optic lens for data storage
N92-}4 12
T.D. Milster. R.M. Trusty, M.S. Wang, F.F. Froehlich. and J.K. E:--vin
Optical Sciences Center. University of Arizona, Tucson. Arizona 85721 ,i
Abstract _ _/''" _'_21}_ i! i -'
We describe a new type of microlens for data storage applications that has improved
off-axis performance. The lens consists of a micro-Fresnel pattern on a curved substrate.
The radius of the substrate is equal to the focal length of the lens. If the pattern and
substrate are thin, the combination satisfies the Abbe sine condition. Therefore, the lens is
free of coma. We analyze a 0.5 numerical aperture, 0.50 mm focal length lens in detail. A
0.16 numerical aperture lens was fabricated holographically, and results are presented.
2. Introduction
There are several types of microlenses commonly used in optical data storage systems.
The most common are molded glass and molded plastic lenses. Molded optics weigh less
than conventional multiple-element designs. Typical apertures are 3.5 mm to 4.5 mm in
diameter, and numerical apertures (NAs) range from 0.45 to 0.55. For optical data storage
applications, the smallest molded microlenses commercially available have an entrance pupil
diameter of 3.0 mm (I). There are at least two reasons to use smaller optics. If a smaller
microlens is used as an objective lens, the same number of disks can fit into a smaller stack
height, and volumetric storage density will increase. Secondly, if all hardware dimensions
scale linearly with optics size, a reduction in lens size by some factor will allow a reduction
in moving mass by that factor to the third power, since mass scales with volume. The result
will be an improvement in access time.
A serious problem observed with microlens components is a limited field of view. For
applications like multiple beams and galvanometric tracking servos, the spatial area that
must be in focus on the disk encompasses many track widths. The required focal area does
not change as the objective lens focal length becomes smaller, which implies that the angular
field of view increases, as shown in Figure 1. For example, consider a system that must
focus over _. 30 tracks with a 0.5 numerical
aperture (NA) lens. A diffraction-limited
lens with a focal length of 4.5 mm requires
a _0.61" angular field. A lens with a 1.0
mm focal length would require a _.2.8"
angular field. The limiting aberration in
these systems is coma. Coma is also the
limiting aberration in waveguides using
focused grating couplers (_2). In this paper,
we outline a technique that eili-rninates coma
and dramatically improves off-axis
Preprint_m SPIE Proceedings Volume 1499
Ions I
1y
!
NA, = NA.
y,=y,
a, < !1,
Ions 2
IY
Figure 1. Angular
smaller lenses.
field increases with
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https://ntrs.nasa.gov/search.jsp?R=19920005694 2020-03-17T14:13:45+00:00Z
194 Appendix J
performance of these devices. A 160 _m
diameter 0.16 NA microlens has been
fabricated.
3. Microlens properties
There are several microlens techniques
which have been proposed. These include
graded-index lenses (3), holographic lenses
and zone plates (_), and micro-Fresnel lenses
(MFLs) (5). Each of these techniques has the
potential for very small apertures (-100 gm)
and high NA (0.5). Graded-index lenses
depend on the refraction of light rays.
Holographic lenses and zone plates utilize
diffraction properties. In the MFL, the center
planar
zone
plate
/
image
plane
Figure
angle _,.
Planar MFL illuminated at
portion acts like a refractive element, and the edges (where the zone spacing is on the order
of a wavelength) act like a diffractive element. The advantage of the Fresnel lens is that it
does not become significantly thicker and heavier as the NA increases. We now examine
the focal properties of very small (< 1 mm) focal length MFI_,s.
Off-axis performance of planar Fresnel lenses has been described by Young (fi).
Consider the geometry of Figure 2, where a planar MFL is illuminated with a plane wave
at angle _. The radius of the nt_ zone is given by rn. Coma, astigmatism and field
curvature aberrations are described by: Wt3 t --e.r3J2_.j e, Wzzz=a:_/2_.f, and
W2:0 = o['_/4_.f, respectively. These aberrations are plotted as a function of field angle, _,
in Figure 3 for the following parameters: f = 1.0 mm, NA = 0.50 and _. = 0.785 _m. This
lens cannot be used at more than a 0.13" field without coma contributing _./4 departure
(Rayleigh limit) to the ideal wavefront. If the coma could be eliminated, the limiting
aberration is astigmatism, which does not cross the Rayleigh limit until a = 2.1". A factor
of 16 improvement in the field angle would be realized.
Coma can be eliminated by forcing the MFL to satisfy the classical Abbe sine
condition (7). One way to satisfy the
Abbe sine condition is make the zonal
focal lengths equal when the lens is
used at infinite conjugates. As shown in
Figure 4, a planar MFL converts an
incident plane-wave phase distribution
into a converging spherical wave. The
zonal focal lengths, fz,, increase with
radius. To become compatible with the
Abbe sine condition, the optical power
of the element can be placed on a
spherical surface (8), as shown in
Figure 5. The zonal focal lengths are
now equal, and the Abbe sine condition
is satisfied. A simple extension of
Young's treatment verifies that coma is
[
z|
7 ,q ., .... , ......
, , . . , . . . , .... ]
l •A$1il_llt tllm • I
s•s • "_
•J
3
,,e,
2 ,.s"
,¢
s
,¢,¢ As_, ,,m,t
0 05
............. =... !'r_'7? ,
'TO _5 20 25 30
AIIm* I_11
Figure 3. Off-axis aberrations of a 0.50 NA
f = 1.0 mm planar MFL.
_\_j _-r_
Appendix J 195
Figure 4.
focal lengths, fz,, are not equal.
Planar-substrate MFL. Zonal Figure 5. Curved-substrate MFL.'
Zonal focal lengths, f=, are equal.
eliminated. Delano (9) has also shown that coma is zero in this type of design.
In our treatment we neglect effects of the disk cover plate. Spherical aberration
introduced by the cover plate can be corrected by modifying the MFL pattern on either the
flat or curved-substrate designs. Coma due to the cover plate is small compared to coma
from the flat MFL if a thin cover plate is used.
So far we have discussed properties of MFLs with the exact phase distribution
required to form a converging spherical wave. The index variation is similar to a blazed and
chirped diffraction grating. Blazing increases the diffraction efficiency of the MFL.
Theoretically, 100% diffraction efficiency can be obtained with proper blazing (10). For the
planar geometry of Figure 4, the required phase distribution is
O_(r,,) = - f_ _2+ + nn [1]
For the curved geometry of Figure 5, the analogous expression to Equation 1 is
2r_ f /'Tr---'_l
,.(r) = [,_]
It is not necessary to form the exact phase distribution of Equation 1 or Equation 2 in order
to evaluate the optical performance of the lens. Instead, a rectangular profile can be used
at modulo _r phase shifts. The result is a binary-type MFL with a lower diffraction efficiency
but identical optical properties. The binary-type MFLs are desirable in the initial part of
the work because they are easier to fabricate.
4. Experiment
To date, our efforts have focused on making a micro Fresnel lens on a curved
substrate. The necessary substrate must be a thin spherical shell of the proper radius and
high optical quality. We modify microspheres made for laser fusion research, which have
the necessary characteristics. The microspheres are available with radii in the 500 _m -
196 Appendix J
HeCd
I t
Shack Cube
Set-up
Obj. lens
Relayed
pinhole
\
r'-
t,,'
300 gm
microsphere tItollmo t
CCD camera
and display
\ Turning mirror
Shutter
beamsplitter U HeNe
/
Turning mirror
Figure 6. Experimental setup for exposing the hologram.
1000 um range. The shells are 1 _m to 3 _m thick. We have measured quality of two
microspheres using a ZYGO intefferometer. Initial tests have shown that the parallelism
between the inner and outer surfaces is better than a fraction of a fringe. The wavefront
quality of the surfaces varies dramatically. One sphere tested with the ZYGO was of
sufficient quality to use as a substrate, and the other was not. We visually inspect the
surface before each attempt at making a lens.
Our construction procedure consists of making a holographic exposure from a
converging beam and a planar wavefront. A modified Mach-Zehnder arrangement was used,
which is similar in principle to one described by Nishihara and Suhara (11). The
experimental setup is shown in Figure 6. A HeCd laser was used to expose the photoresist.
and a HeNe laser was used for alignment. Both lasers were aligned to be coaxial. A shutter
controlled light from the HeCd laser. One arm of the interferometer passed through a
Shack-cube beam splitter that provided the object point for a finite-conjugate objective lens.
The objective lens was focused at the center of curvature of the microsphere. The second
arm of the interferometer was reflected off a turning mirror and a pellicle beam splitter to
provide the plane-wave component for the hologram. Fringes were observed by a CCD
camera behind the microsphere mount. Reflections off the rnicrosphere that passed back
through the Shack cube were used to align the substrate axially and transversely. After
aligning with the HeNe laser, the substrate was translated axially the proper distance to
compensate for focal shift caused by the blue HeCd laser.
Tolerance of the construction process is an important part of this study. We used
CODEV, an optical design program, to study tolerances for f-- 0.50 mm, NA -" 0.50 and _. =
0.442 _m. Transverse displacement and axial defocus errors during the construction process
_\tt.SrE_L --
Appendix J 197
'Z:
m
3 l:
r'C
-530 -4 O0 -20¢ _,0 2.00 400 6.30
Field Angle (de S )
14
_J
4 X ....
-60Q -400 -L_8 O QO 200 +.0_
Field Angle (des)
60C _0
Figure 7.
error.
Strehl ratio and rms wavefront error for an 11_m transverse alignment
were studied. The Strehl ratio and rms wavefront error are displayed in Figure 7 for an
11 _,m transverse alignment error. The useful field angle is __.2.6° centered about 1.3 °. The
rms waveffont aberration indicates that there are two fields angles for which aberration is
essentially zero. Figure 8 displays astigmatic line images versus field angle. Since there is
no coma in this system, the line image plot is a good indicator of how the device would
actually perform. There are two points in the field where the astigmatism is zero. This
indicates that the system behaves with binodal astigmatism. The transverse displacement can
be compensated by tilting the lens to the
appropriate bias angle. Strehl ratio and
..... .. \ \
//'////-" _...\\
//// / .- .
.5.m
/ / / / / _ ....... \/ , \
,' t l j ,
? / l
r [ I i
i / I ,
\\ \ '\ \ x ........ , /
\\ \ \ -, ......... /
\\\\-.-- ,.,ii
4._ j_
Figure 8. Astigmatic line images versus
field angle.
i: ,L
m
"" :"5
1
\,
\
_Z; Axial rnisali_mmen¢(__m)
Figure 9. Strehl ratio versus axial
alignment error.
OF _OOR QbAL_'iY
_vt_L_TE r2..
198 Appendix J
Figure 10. SEM photograph of a microlens
exposed on a curved substrate.
Figure 11. Enlargement of the central
portion of Figure 10.
ver.sus axial alignment error is shown in Figure 9. The allowable defocus is in the range of
=30 _m, which is quite easy to control.
5. Results
A standard photoresist solution was used to coat a microsphere. The microsphere
was cut in half and mounted on a holder. Figure 10 shows an SEM photograph of a
microlens that has been exposed on the curved surface. Wewere only able to expose a 0.16
NA lens due to a conflict between the finite working distance of the objective lens and the
pellicle beam splitter. Figure 11 shows the same lens under higher magnification. A rough
appearance is observed in the holographic pattern.
We tried to test the optical quality of the microlens, but, due to the large amount of
scatter, strong zero-order beam, and small size, we were not able to get consistent results.
We did test diffraction efficiency and lens NA, which were 11.8% and 0.16, respectively.
6. Conclusions
We have shown that, in order for micro optics to be used effectively in advanced data
storage systems, off-axis aberrations must be considered. One solution for improving off-axis
performance is to curve the substrate of a MFL so that its radius of curvature is equal to
its focal length. This satisfies the Abbe sine condition, and effectively eliminates coma. We
tried a proof-of-principle experiment in which a microsphere substrate was coated with
photoresist and exposed in a modified Mach-Zehnder interferometer. We were successful
in exposing a 0.16 NA photoresist pattern. The pattern was mottled, so we were not able
to test the lens quality due to scattering and physical constraints. The holographic method
was instructive, but the NA is limited to rather low values (<0.20). Our group is pursuing
I_tLSTF_/L
A/_:ndbr J _
other methods of writing the patterns, which include electron-beam writing and binary, optics.
7. Acknowledgements
This work was supported by the Optical Data Storage Center and the Joint Services
Optical Program. Bob Trusty, who received his master's degree from this project, was
supported by a graduate fellowship from Lawrence Livermore National Laboratories.
8. References
1. Corning, Inc., commercial literature describing model 350160 aspheric lens.
2. G.L. Lawrence and P.J. Cronkite, "Waveguide grating with broad spectral response
using gradient-effective index,'! University, of Arizona patent disclosure submitted
June 6¢ L988. " .-:. -. _ ' ......
K. Iga, Y. Kokuban, M. Oikawa, Fundamentals of Microoptics, Academic Press, New
York, 1984.
G.T. Sincerbox, "Miniature optics for optical recording, "Proceedings of the SPIE, vol.
935, Gradient-Index Optics and Miniature Optics, pp. 63-76 (1988).
H. Nishihara and T. Suhara, "Micro Fresnel Lenses," in Progress in Optics Vol XXIH,
E. Wolf, ed., North-Holland Physics Publishing, New York, pp. 3-36 (1987)
M. Young, "Zone plates and their aberrations," JOSA, vol. 62, No. 8, pp. 972-976
(1972)
R. Kingslake, Lens Design Fundamentals, Academic Press, Inc., San Diego, p. 158
(1978)
W.T. Welford, "Aplana!ic hologram lenses on spherical surfaces," Opt. Com., vol. 9,
no. 3, p. 268-269 (1973).
E. Delano, "Primary aberrations of meniscus Fresne/lenses," JOSA, vol. 66, No. 12,
pp 1317-1320 (1976).
10. H. Dammann, "Blazed Synthetic Phase-Only Holograms," Optik, vol 31, pp. 95-104
• (1970) .. " , , .... . • • _ ' ....
• • . , . _ . , ' . ',. , ,',_ [. .. '_, , ,'," ).,*, .' , ,.. , ..
t L "/Ni Nishthara',and T: S_dhffta; :'_Mier0 FresneI" _:ns;eS,!: _Ptaogi,.esS in Optic. V: XXIV, E.
Wolf, editor, North-Holland Physics Publishing, New York, pp. 3-35 (1987).
.
4.
5.
6.
7.
8.
9.
20o ,_m_ J


Micro-optic lens for data storage

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