Aspheric lenses with arbitrary phase functions can be fabricated on thin light weight substrates via the binary optics fabrication technique. However, it is difficult and costly to fabricate a fast lens (f/number less than 1) for use as the shorter wavelengths. The pitch of the masks and the alignment accuracy must be very fine. For a large lens, the space-bandwidth product of the element can also become impractically large. In this paper, two alternate approaches for the fabrication of fast aspheric diffractive lenses are described. The first approach fabricates the diffractive lens interferometrically, utilizing a spherical wavefront to provide the optical power of the lens and a computer generated hologram to create the aspheric components. The second approach fabricates the aspheric diffractive lens in the form if a higher order kinoform which trades groove profile fidelity for coarser feature size. The design and implementation issues for these two fabrication techniques are discussed

Marron, Joseph C.

Tai, Anthony M.

English

NASA Technical Reports Server

N94-17345
Fabrication Techniques for Very Fast Diffractive Lenses
Anthony M. Tai and Joseph C. Marron
Environmental Research Institute of Michigan
P.O. Box 134001
Ann Arbor, MI 48113-4001
Abstract
Aspheric lenses with arbitrary phase functions can be fabricated on thin light
weight substrates via the binary optics fabrication technique. However, it is difficult and
costly to fabricate a fast lens (f/number < 1)for use at the shorter wavelengths. The pitch
of the masks and the alignment accuracy must be very fine. For a large lens, the space-
bandwidth product of the element can also become impractically large. In this paper, two
alternate approaches for the fabrication of fast aspheric diffractive lenses are described.
The first approach fabricates the diffractive lens interferometrically, utilizing a spherical
wavefront to provide the optical power of the lens and a computer generated hologram
to create the aspheric components. The second approach fabricates the aspheric
diffractive lens in the form of a higher order kinoform which trades groove profile fidelity
for coarser feature size. The design and implementation issues for these two fabrication
techniques are discussed
1.0 Introduction
The advantages offered by diffractive lenses are well known. A lens with an
arbitrary aspheric phase function can be easily implemented on a thin and light weight
substrate. However, if the lens is very fast (f/number <1) and the operating wavelength
is short, the groove spacing at the edge of the lens becomes very narrow. For example,
with a f/1 lens designed for 0.51.tm operation, the zone or groove spacing at the edge is
only 1.1t.tm. Fabricating the lens via the binary optics technique [1], the pitch of the
binary masks for a 4-level lens will be about 0.25tam. In addition, the masks must be
aligned with an accuracy much better than 0.251am. If the size of the lens is also large
(>25mm diameter), a substantial amount writing time with an electron beam machine will
be required. Making the matter worse is the need to lower the beam intensity in order
to achieve the fine pitch which further lengthen the writing time. Therefore, the
fabrication of a large and fast diffractive lens with the binary optics technique is a very
expensive proposition.
2.0 Computer-Originated-Hologram
To reduce the demand on the writer, optical interferometric recording can be
combined with computer generated holography. Instead of generating the aspheric lens
function directly as a computer generated diffractive optical element, the lens is fabricated
Conf. on Binary Optics, 1993
179
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by interfering a spherical wavefront produced by a refractive lens (e.g. a microscope
objeCtiVe) with the aspheric Wavefront produced by a computer generated hologram [2]
as illustrated in Figure 1. Let the desired phase function of an aspheric lens with focal
length f be OH(X,y), and
0s(X'Y) = -_rclfil+(x2+y2)f2
be the spherical phase function that matches the optical power of the asphefic lens. A
holographic lens with the desired phase function is obtained by interfering ihe spherical
wavefront with _ aspheric wavefront having a phase function of 0A(x,y ) where _0A(x,y)
= 0s(x,y ) - 0H(x,y ).
To achieve high diffraction efficiency, the hologram has to be recorded in the form
of an off-axis volume Bragg hologram [3]. Special design considerations must be taken
to produce an on-axis lens with uniformly high diffraction efficiency across the entire
lens.
An on-axis lens can be created by bonding two off-axis holographic lenses
together which share a common reference beam as shown in Figure 2. The desired phase
function of the lens is once again decomposed into spherical and aspherical components.
The spherical component, 0s(X,y), is recorded on the first hologram using a diverging
spherical object wavefront and the aspheric component, 0A(x,y ) = 0 n (x,y) - 0s(X,y), is
recorded on the second hologram with an aspheric wavefront produced by a computer
generated hologram.
In the example, the spherical phase function is placed in the first hologram and
the aspherical phase function is put in the second. It does not have to be the case. The
choice of the recording wavefronts is dependent on the operating geometry for which the
lens is designed. To assure diffraction efficiencies that are uniformly high across the
entire lens, the rays in the object wavefronts used to record the two holograms must
match as closely as possible the ray directions of the input and output fields in the
playback geometry. A wide angle diffractive lens had been fabricated using this approach
[4]. The f/0.7 lens was designed to detect and determine the angle of arrival of 850nm
laser radiation. The rms spot size and the diffraction efficiency of the diffractive lens
were both uniform to within 10% over a field of view of 45 ° x 45 °.
Using a microscope objective to provide the optical power, the slope of the
remaining aspheric term will not be very steep. The computer generated hologram can be
fabricated by a variety of writing machines, including the laser writer described in the
following section.
180
2.0 Higher Order Kinoform
Kinoform [5] and Fresnel lens are both collapsed versions of a refractive lens.
With a Fresnel lens, the optical path differences (OPDs) at the transitions between zones
are many wavelength. The OPDs between zones can vary slightly and they are not
exactly integer number of wavelengths. In other words, the zones of a Fresnel lens are
not phased to produce diffraction limited performance. The optical path difference at the
transitions between the zones of a kinoform, on the other hand, is exactly one wavelength.
The angle of the first order diffraction of a kinoform matches the refraction angle of the
wedge shape groove and a diffraction efficiency near 100% can be obtained.
A higher order kinoform resides between a Fresnel lens and a conventional, or first
order, kinoform. The optical path difference between zones of an nth order kinoform is
exactly equal to n wavelengths where n is an integer number greater than one. The zone
spacing of an nth order kinoform is n times wider than its 1st order counterpart as
illustrated in Figure 3. With a higher order kinoform, the angle of the nth order
diffraction matches the refraction angle and a diffraction efficiency near 100% can also
be achieved.
Higher order kinoforms are attractive because they can be fabricated very
efficiently with a laser writer. A laser writer uses a focussed laser beam to expose a
photo-sensitive recording material such as photographic film or photoresist. The scanning
of the laser spot over the recording material can be accomplished by moving the recording
material under the beam using a translator or a rotating drum, or by scanning the beam
with a polygon, holographic or acousto-optics scanner. The spot size of a laser writer is
typically >lpm which is much larger than available with e-beam writing machines.
However, a laser writer is capable of postioning resolutions that are much finer than the
spot size. In addition, they can provide gray scale writing capability with up to 8-bit of
dynamic range.
To achieve high diffraction efficiency, the profile of the zones of a kinoform lens
must be produced with high fidelity. It can be accomplished only if the spot size of the
writing beam is smaller than the zone spacing. A 1st order kinoform with a zone spacing
of 1 pro, for example, cannot be fabricated with a laser writer whose spot size equals to
or larger than lpm. The laser writer, however, can be used to fabricate a higher order
kinoform of the same lens function as illustrated in Figure 4. The laser writer cannot
produce the sharp transition between zones but its effect on diffraction efficiency becomes
less and less significant as n becomes larger. We should emphasize, however, that the
fabrication of higher order kinoform does not reduce the resolution requirement in the
positioning of the writing beam.
While using a larger n will place less demand on the spot size, it will also require
a larger dynamic range, more linear recording and better control of the coating thickness.
The rms phase error introduced should be < 1/8 of a wave to provide diffraction limited
performance. As the zone becomes larger and higher, it will be increasingly more
difficult to achieve the required profile fidelity.
181
In Figure 5, we show the normalized film thickness of a linear photoresist coating
after processing as a function of exposure energy. The recording can be linearized by
using a lookup table to adjust the exposure energy accordingly. Figure 6 shows the
profilometer trace of linear grooves fabricated on a 5gm coating. They correspond to
zones of a 5th order kinoform designed for 500nm operation. The rms phase error was
less than 1/Sth of a wave.
4.0 Concluding Remarks
It is difficult and expensive to fabricate a fast diffractive lens of appreciable size
using the bin_ optics fabrication technique. We have described two alternate
approaches that can be Used¼o fabricate very fast diffractive lenses with arbitrary aspheric
phase :functions at much lower cost. The computer-originated hologram combines the
strengths of optical holographic recording and computer generated hologram. The higher
order kinoform trades profile fidelity for coarser feature size. Both approaches can be
implemented using a laser writer with a spot size > 1Bm. The use of laser writer is
attractive for the following reasons, i) Laser writers are much less expensive to acquire
and operate than e-beam writing machines. 2) The spot size is independent of the laser
power which allows very high writing speed by using a high power laser. 3) With gray
scale writing capability and beam positioning resolution much finer than the spot size, a
computer generated hologram can be written directly from its phase description without
special coding or formatting. 4) By writing first onto a photographic film to form a gray
scale mask, copies can be made on linear photoresist or other materials by simple contact
printing.
The work reported in this paper was supported by ERIM Internal Research and
Development funds.
=
References
1) G.J. Swanson and W.B. Veldkamp, "Binary Lenses for Use at 10.6 Microns," Opt.
Eng. _ 791 (1985).
2) R.C. Fairchild and J.R. Fienup, "Computer-Originated Aspheric Holographic Optical
Elements," Opt. Eng. 21. 133 (1982).
3) H. Kogelnik, "Coupled Wave Theory for Thick Hologram Gratings," Bell Syst. Tech.
J., _ 2909 (1969).
4) A. Tai, M. Eismann and B. Neagle, Holographic Lens for Wide Field of View Laser
Communication Receiver," Final Technical Reprot to AF WRDCIAAAI-2, ERIM
Report No. 213325-3-F, March 1990.
5) J.A. Jordan et al., "Kinoform Lenses," Appl. Opt., 9_, 1883 (1970).
182
L2
t//
&" " _ne-to-One
Telescope
HOE
LI
Figure 1. Fabrication of a computer-originated hologram.
0
0 A
OH
Desired phase function 0I_I = 0 s + 0 A
Figure 2. Fabrication of an on-axis lens by bonding two off-axis volume holograms
183
Higher order kinoforms
• OPD between zones: m waves
m X OPD Desired Outgoing
_JL_.. / Wavefronl
_"-"-- _ Incoming Wavefronl
Substrale
First order kinoform
• ©PD between zones: 1 wave
_. OPD
T-_--__ _ De"_ refrd°nO!u' g° ing
_W___-2RltT-'°"°°_av.,roo,
Figure 3. First order and higher order kinoforms
First order kinoform
° Small dynamic range and fine spot size
_L
Required spot size -"'-_ OPD=k
L../ _,.j,- L,/ T
Available spot size --..-
Higher order kinoform
• Large dynamic range and coarse spot size
Required spot size = _ _'/¢_ "_ ,//"'_ / I
Available spol size Lf '
_t_
OPD=mX
Figure 4. Fabricating kinoforms with a laser writer
184
or'l-
°-
t_
.--
10
tA
U
wm
t- m
E
m
wm N
"O
N
BI
"d
E
O
Z
Linear Photoresist
nt HPR-207)
0 _ .2 t .4 _, .6 4_.8 2.0 .2 2.d
Log exposure energy
Figure 5. Normalized film thickness of photoresist after processing as a function of
exposure energy
Figure 6.
5pm /
I
/
r // ///j.l
100pm
Profilometer trace of linear blaze fabricated on linear photoresist.
(Corresponds to 5th order kinoform designed for 0.51am operation)
185



Fabrication techniques for very fast diffractive lenses

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