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Diffractive optical elements: fabrication and application
A.G. Poleshchuk, V.P.Korolkov, R.K.Nasyrov
Institute of Automation and Electrometry SB RAS,
Koptyuga avenue, 1, Novosibirsk, Russia 630090;
ABSTRACT
We review our recent progress on development of the methods for fabrication of precision binary and as well as high-
efficiency continuous-relief diffractive optical elements (DOEs) by combining complementary advantages of circular
laser writing system (CLWS), direct laser beam writing in thermal and photo-sensitive materials and analog lithography.
The main limitation and tolerances of writing methods are identified, and their influence on optical performance of DOEs
is investigated. The latest results of fabrication and practical applications of DOEs with more than 200 mm diameter and
a minimum feature size of 0.5 micrometer for testing large aspheric surfaces with a Fizeau-type interferometer are
presented.
Keywords: Diffractive optical elements, computer-synthesized holograms, circular laser writing system, analog
lithography, optical testing.
1. INTRODUCTION
Design and fabrication of diffractive optical elements with high precision and diffraction efficiency is until now one of
the most promising trends in development of optics. These elements are thin relief phase structures and have been already
widely used in optical metrology, displays, sensors, laser technology etc. Their potentialities depend in many respects on
the fabrication technology which should ensure desired technical parameters. Until recently, DOEs were fabricated by
means of image pattern generators designed for tasks of semiconductor industry. However the existing variety of
diffractive and microoptical elements creates a stimulus for development of technologies and equipment specialized for
optical tasks. Such manufacturing equipment for optical microstructures should have high precision and reproducibility
while being a cost effective solution. Laser technologies and the equipment on the basis of use of thermostructural,
thermochemical and photosensitive materials allow manufacturing of a whole spectrum of the microstructured optical
elements. Thermostructural and thermochemical materials are used for manufacturing of binary
1
and grayscale masks
2
,
3
.
Photosensitive materials (mostly positive photoresists) allow manufacturing of the binary and multi-level phase
diffractive elements and binary amplitude masks by developing the masking layer through the windows in the
photoresist. Usually the photosensitive material is exposed by low power UV radiation. Some other technologies using
heat-sensitive recording materials normally require laser radiation with much higher intensity in visible spectrum. The
resistless technology have definite advantages for fabrication of binary holograms on thick and large high-precision
substrates
4
.
Besides variety of recording materials there are different types of laser writers. There are some types of DOEs for whose
description the polar coordinate system is more preferred than the Cartesian one. For example, CGHs designed to test and
certify aspheric wavefronts of the primary mirrors in modern telescopes must have the circular diffractive structure
fabricated with an accuracy of about tens nanometers on thick and large substrates with diameter of up to several
hundred millimeters and thickness of up to 25 mm. Such elements are mainly fabricated with the desired precision
and quality only by means of writers with circular scanning of focused laser beam. In the present paper we consider the
two-laser circular writing system providing a realization of photo- and thermo-processes for diffractive optics fabrication
developed in IAE SB RAS and results of its application for different types of DOEs. Besides that we consider some way
to improve performance of continuous-relief DOEs.
2. LASER LITHOGRAPHY
IAE SB RAS developed several generations of circular laser writing systems (CLWS) starting from 1979 (Figure 1, a)
till up to now (Figure 1, b). Prof., Dr. V.P. Koronkevich led the development almost 30 years. Commercialized versions
of the systems were developed jointly with TDI SIE SB RAS (Novosibirsk, Russia). They are now working in scientific
institutions of Russia, Europe and China.
Figure 1: First and last versions of circular laser writing systems developed in IAE SB RAS from 1979 till 2014.
First generations of CLWS has Ar+ laser with adjustable wavelength it allowed us to use thermo- and photo-process for
DOE fabrication after some not so complicated readjustment. However, development of highly stable DPSS and diode
lasers emitting light at only one wavelength made actual to develop a CLWS with two lasers: low power UV diode laser
and powerful 532 nm laser. Such system more fully realizes the advantages of each of the two lasers and allows one
quickly to switch over to another technology and even combine them. Figure 2 depicts simplified diagram of our two-
laser circular writing system (TLCWS). It is based on following design principles:
The use of two lasers with a significant difference in wavelength and beam power,
UV laser diode module generates tightly focused output beam,
Spatial alignment of both beams focused by output microscope objective in the same plane,
Separate control of intensity modulation along radial and angular coordinates for each laser with single-stage
modulation along angular coordinate and multistage control of beam intensity along radial coordinate.
Using the calibration photodetector (CPD) to ensure reproducibility of exposure dose;
Using the writing test photodetector (WTPD) for synchronized photoelectric measurements of alignment and
test structures (for example when searching rotation center and measuring the beam trajectory at spindle rotation).
Control of the intensity of the two laser beams depending on the radial and angular coordinates is performed by
controlling computer through specially developed PCI board of vector function generator (VFG). Vector pattern
generator which generates fast angular analog modulation signals AAM1 and AAM2 is main part of VFG. It is clocked
by MSY clock pulses formed by frequency multiplier with phase locking from pulses SY generated by angular encoder.
VFG contains also PID regulator using feedback signal from FBPD which controls AOM1 in channel 532. Signal of
digital-analog converter (DAC) is used as reference for the feedback or directly feeds to analog modulation input of
diode laser module of channel 405 operating without external feedback. AOM2 and AOM3 have 200 MHz carrier
frequency.
The multistage control of beam intensity along radial coordinate is made by analog and pulse modulation as well by use
of motorized diffractive attenuator with variable transmission. It is necessary to compensate change of linear scanning
speed in range of more than 1:100000 for writing of photosensitive recording materials. VFG also generates radius
dependent pulse modulation (RPM) signal which is superimposed with AAM2 with delay equal to delay in AOM3 (time
diagram in Figure 3). Pulse period of RPM signal is proportional to constant step between points of switching on UV
radiation. To minimize stitching defect between beginning and end of circular track it is necessary to make track length
multiple to . This is possible to select equal to
4s
or
3s
, where s - radial increment. Circular laser writing
systems designed in IA&E SB RAS use special polar coordinate data format (psc-format) in which a linear pixel size is
constant along each ring and equal to
4s
. To avoid the formation of moire between two sampling systems the value
should be also equal to
4s
. Duration Tpulse of RPM pulses is constant and chosen so that the movement of the
beam relative to the substrate during the pulse is not expanded by a single pulse exposure area more than a quarter of
beam diameter. Pulse writing mode is used to expose area around substrate rotation center.
AOM1
AOM2
VHF
Driver 1
VHF
Driver 1
L3
AOM3
Laser
405 nm
MDA
L1
Laser
532
nm
PID
Regula-
tor DAC
AF
controller AF
sensor
Vector
pattern
generator
Focusing lens
L2
Actuator
Film
Substrate
Radial analog
modulation without feedback
RPM
AAM1
Radial analog
modulation with feedback Controlling
computer
WTPD
Channel 532
Channel 405
BS2
BS3
D2
L4
Pinhole
-
+
AAM2
PCI bus
controller
VFG
SY ZL
Carriage of radial
displacement
01
02
FBPD
D1
BS1 2
PCI
BS4
CPD
Shutter
M1
FM with
PL
VHF
Driver 3
MSY
ZL
Angular
encoder
LED
Spindle
Rotation
motor
USB
camera
Center
adjust-
ment unit
Deflector
USB
Ethernet
USB
USB
BS5
M2
Figure 2: Simplified functional diagram of TLCWS:
AOM1-AOM3 – acousto-optical modulators, VHF Drivers 1-3 – VHF drivers for controlling AOM, D1-D2 – diaphragms
for separation of first diffraction order after AOM, L1-L4 – lenses, BS1-BS5 – beam splitters, M1-M2 – mirrors, WTPD – writing
testing photodetector, CPD – calibration photodetector, FBPD – feedback photodetector, Shutter with LED – switchable illuminator
with yellow LED fixed on electromagnetic shutter, MDA – motorized diffractive attenuator.
Figure 3: Time diagram of pulse modulation mode.
Finding of the substrate rotation center is critical point of writing process at circular scanning. The error of
origin of polar coordinates distorts fabricated structure in both coordinates
5
. To measure relative position of spindle
rotation axis and writing spot center at the time of DOE writing we burn a small ring with radius of 10-50µm around
rotation center and align it with the writing beam center by photoelectrical scanning measurement. It is made radial
scanning of the writing beam with small power and measurement of WTPD signal proportional to surface reflection.
Measurement of left and right radial coordinate allows us to find out center of segment between points of crossing the
ring by writing beam. It can be a rotation center if trajectory of the beam in radial direction crosses the rotation center. In
common case it is not true. It is necessary to make the same procedure of center search rotation in direction
perpendicular to air-bearing direction of radial displacement stage. It is made with center adjustment unit (Figure 2)
which turns beamsplitter BS4 around axis of the beam incident from mirror M2. As result focal position of the writing
beam can be scanned in direction perpendicular to radial one. Application of the center adjustment unit allows us to
fabricate non-axially symmetric DOEs with high accuracy which can be estimated as R, where - angular error or
angular encoder, R – radial coordinate.
Commercial version of the TLCWS was created by the joint efforts of TDI SIE and IA&E SB RAS. It is also
produced as single laser version with UV laser module and fully mobile optical channel assembled on stage or radial
displacement. This system allows one to form diffractive elements, computer-synthesized holograms, gratings, limbs,
and different masks with arbitrary topology on plane and axially symmetric curvilinear surfaces. Main specifications are
the following: spatial resolution is up to 1000 lineas/mm, resolution on radial coordinate is no worse than 1 nm, angular
coordinate measurement resolution is up to 0.25”, displacement range on vertical coordinate is up to 25 mm,
autofocusing error is 0.05 µm. Maximum tilt of curved surface is 10º.
3. FABRICATION AND APPLICATION OF DIFFRACTIVE OPTICAL ELEMENTS FOR
NON-TYPICAL SURFACES TESTING
Fabrication of high-quality optics is defined by its testing methods. Spherical and plane wavefronts can be formed in
the optics with extremely high precision. Interferometry ensures quality of fabricated surfaces up to nanometers using
these wavefronts. However, surfaces with shape that differs from spherical and plane are needed for various applications.
Nowadays, the generation of aspherical wavefronts by both refractive and diffractive optical elements (DOE) or
computer-generated holograms (CGH)
6
,
7
is widely used. These elements transform the initial flat or spherical wavefront
into an aspherical one, i.e. they operate as wavefront correctors. The development of the direct laser and e-beam writing
systems allowed the production of diffractive patterns providing wavefront formation with nanometer accuracy
8
,
9
.
Such surfaces as conical, cylindrical, and freeform needs in corresponding wavefronts for testing. In this paper we
have described design, fabrication and alignment issues for these optical elements. In this paper the DOE patterns were
fabricated using a circular laser writing system CLWS-300IAE 3,
10
with a thermochemical method based on laser heating
of the chromium films.
3.1 DOE for cylindrical surface testing
The main problem for testing cylinder surfaces is the necessity to fabricate non-symmetrical diffractive patterns and
to filter out retro-reflecting ghosts. The radius of curvature of the cylinder surface Rcyl determines an appropriate optical
test layout. In a simple case with small numerical apertures there are well-known layout using transmission flats
11
(Figure 4, a,b). For elimination of retro-reflections, the DOE is tilted by a small angle of 0.5 to 1 degree to optical axis.
To test cylinder surfaces with higher numerical apertures we propose to use a Fizeau interferometer with a
Transmission Sphere (Figure 4, c). In this case the DOE operates in a convergent beam. To align the DOE against the
interferometer, auxiliary reflective holograms are used. The advantage of this layout is, that the diffractive pattern
becomes twice as large, and the setup is completely positioned on-axis for all optical components and the lens under test.
This layout can be simplified and the measurement precision can be increased using a combined DOE
12
. For testing
cylinder surfaces, a combined DOE that simultaneously generates a test and a reference beam was developed (Figure 4,
e,f). This diffractive element is consisting of a combination of a DOE that operates with a plane wavefront (Figure 4, a)
and a diffractive grating that generates the reference wavefront in reflection mode. In this case there is no need to use a
Transmission Flat. The contrast of the interferogram can be adapted by varying the duty cycle of this linear grating. High
contrasts can be obtained even for cylinder surfaces with low reflectivity. The DOE substrate is placed inside the Fizeau
cavity and its defects are not affecting the measurement results.
For testing cylinder surfaces with higher numerical apertures we propose to use a Fizeau interferometer with a
Transmission Sphere (Figure 4, c). In this case the DOE operates in a convergent beam. To align the DOE against the
interferometer, auxiliary reflective holograms are used. The advantage of this layout is, that the diffractive pattern
becomes twice as large, and the setup is completely positioned on-axis for all optical components and the lens under test.
This layout can be simplified and the measurement precision can be increased using a combined DOE12. For testing
cylinder surfaces, a combined DOE that simultaneously generates a test and a reference beam was developed (Figure 4,
e,f). This diffractive element is consisting of a combination of a DOE that operates with a plane wavefront (Figure 4, a)
and a diffractive grating that generates the reference wavefront in reflection mode. In this case there is no need to use a
Transmission Flat. The contrast of the interferogram can be adapted by varying the duty cycle of this linear grating. High
contrasts can be obtained even for cylinder surfaces with low reflectivity. The DOE substrate is placed inside the Fizeau
cavity and its defects are not affecting the measurement results.
We fabricated a phase DOE and investigated cylindrical surfaces using an Intellium Z100 interferometer and a diffractive
cylinder imitator as cylinder test sample. We have introduced 1 degree tilt of the optical axis by tilting of cylindrical
surface. In this case there was no ghost line. However, additional alignment was needed. We have added amplitude
grating with period 18µm. This grating reflected and diffracted light back to interferometer when DOE was tilted on
correct angle (Figure 5). It is shown that the auxiliary DOEs allow a precise positioning of the main DOE with few
angular seconds in tilt and few micrometer lateral positioning precision.
Figure 4: Optical layouts for cylinder surfaces testing (a, c, e) and DOE diffractive pattern (b, d, f).
(a) (b)
Figure 5: CGH for cylinder surface testing (a). Interferogram of cylindrical surface (b).
3.2 Measurement of conical surface
We have tested conical surface (metal axicon) with 45 degree angle. In a case if DOE designed to convert plane
wavefront into such conical wave, period of diffractive structure will be 0.9 µm. It is close to the fabrication limit. DOE
which operates with transmission sphere was designed. In this case period will be about 3 µm. Auxiliary hologram was
placed near the center of DOE. This hologram reflected and diffracted light when DOE was settled in correct position
against interferometer (Figure6).
Also in this optical layout there was a problem with ghosts which had a geometry of rings. We have calculated its
position and removed these areas from diffractive pattern. These areas were removed from analyzed area. However, there
were no bright ghosts and therefore contrast of the whole interferogram was improved.
(a) (b)
Figure 6: Optical layout for conical surface testing (а). Interferogram of 45o conical surface (b).
3.3 DOE for freeform surface testing
Freeform surfaces often have no axis of symmetry. Therefore, there is a problem with alignment of optical layout.
We have developed DOE with auxiliary diffractive lenses for focusing light in predefined positions (Figure 7).
Correspondingly, there were small spherical mirrors fabricated on the surface under test. These spherical mirrors
reflected light back into interferometer.
This method was also used for alignment of off-axis parabolic mirrors for large telescopes. In these cases auxiliary
lenses forms spots and crosses on predefined positions.
(a)
(b) Figure 7: Optical layout for freeform surface testing (а). CGH with alignment holograms (b).
4. ENHANCING OF DIFFRACTION EFFICIENCY OF CONTINUOUS-RELIEF DOES
The application of diffractive optics in areas requiring long-term use in demanding conditions (high temperature
extremes, humidity, high-power laser beams) stimulates the development of cost-effective methods to fabricate
continuous-relief diffractive optical elements (DOEs) on a surface of
optical materials such as fused silica. In recent years, analog
technologies based on halftone
13
and grayscale3 masks have been
developed. Methods of direct laser writing
14
,
15
with analog control of
writing beam power P according to calculated profile shape in the resist
are also widely used for manufacturing the high-efficiency DOEs. All
of the analog techniques allow avoiding the numerous operations of
mask alignment inherent to multi-mask technique. However, a limited
spatial resolution of optical setup results in smoothing of the total
exposure dose distribution. Besides that one needs to use a low contrast
photoresist and a developer to get quite linear dependence of the
photoresist thickness on exposure dose. It also results in smoothing a
real surface profile in resist. As a consequence a 1st order diffraction
efficiency (DE1) for narrow zones with wide backward slopes (BWS)
reduces significantly. Very popular way to solve the problem is
optimization of exposure data set15,
16
,
17
. Figure 8 demonstrates optimized diffractive structure fabricated by such method.
The increase of the diffraction efficiency depends in that case on writing spot and zone period.
Figure 9: a – combining the binary and analog technologies with vertical contour mask [6],
b – fabrication process with surface contour mask.
Another way is based on combining vertical walls of the diffractive zones boundaries formed by the dry etching
through a metal mask, and a slanting profile shaped with the grayscale technology. Several variants of the process have
been suggested in work
18
. One of them with vertical contour mask ensures the form of the blazed diffractive structure
Figure 8: AFM profilogram of optimized
diffractive structure with 6.5 m period.
sufficiently close to the ideal one. Sequence of technological steps depicted in Figure 9, a includes the following steps:
(1) formation of openings in the resist layer at the boundaries; (2) reactive ion etching of the substrate to form grooves
along the boundaries; (3) sputtering of Al layer and following chemical-mechanical planarization (CMP) to form the
vertical contour mask; (4) formation of the blazed profile in the resist by means of the grayscale mask aligned with the
vertical contour mask; (5) transfer of the blazed profile from the resist to the substrate using dry etching, and then
removing the aluminum contour mask in liquid etchant.
The complex process requires not only the aligned set of two masks (grayscale and binary) but twice repeating the
dry etching and performing the CMP. We offer a simpler combination of the binary and analog processes with surface
contour mask (SCM) and demonstrate that considerable improvement in the diffraction efficiency can be obtained only
for certain range of linewidth of the mask and etch depth through it
19
.
Considered method of manufacturing of the continuous-relief DOE includes the following basic operations depicted
in Figure 9, b: (1) formation of the SCM on the substrate; (2) spinning of the resist on the contour mask; (3) aligning the
SCM and alignment marks of a system creating the grayscale exposure dose distribution E(x) and the subsequent
exposing the resist to the exposure distribution; (4) liquid development of the photoresist; (5) reactive ion etching
(RIE) of the substrate through the resist profile and removing the SCM. The distribution E(x) forming a given angle of
the diffractive zones profile can be created using one of following technologies: photolithography with grayscale or
halftone mask, direct laser or electron-beam writing. The equipment forming E(x) should have an optical alignment sub-
system. It is standard feature for systems of projection lithography and most of modern e-beam writers. Thus, the
considered optimized contour mask method (OCMM) has only one step of dry etching and does not require the use of the
expensive CMP. SEM image in Figure 10, a proves the capability of RIE process to ensure quite vertical walls of binary
gratings formed on fused silica surface through Cr mask
20
. The structure was etched by Plasmalab 80 Plus RIE system
(Oxford Instruments).
Next stage after determining the sequence of technological steps is to define geometrical target parameters. To
reveal the advantages of the SCM application it is necessary to analyze the light diffraction on the linear grating formed
by means of OCMM.
Figure 10: (a) – profile of binary grating in fused silica fabricated by RIE process,
(b) – schematic profile shape formed at dry etching through SCM with linewidth D.
The diffractive grating fabrication was modeled as a process of direct laser writing on the photoresist by laser beam
scanned with interscan distance. The profile is represented as a convolution of ideal grating profile with Gaussian
intensity distribution in the beam16. The profile depth is proportional to the exposure dose distribution. It is quite fair
assumption for photoresists previously exposed by uniform illumination of UV light for operating on a linear portion of
its characteristic curve. The profile obtained by RIE etching through the SCM was simulated by replacement of a part of
the backward slope BWS along the boundaries of the diffractive zones by a ridge with a flat top and vertical walls and
having a width D and depth
H defined relative to the peaks of ideal grating profile with depth H and period T (Figure
10, b). The calculation of the diffraction efficiency was carried out in frame of scalar diffraction theory. The following
parameters were used in the simulation:
x=0.4µm, 1.65 µm writing-spot diameter (FWHM) or 1.4 µm at level e-2. The
same parameters were used for simulation and optimization of direct laser writing in papers16,
21
. It simplifies comparing
different methods.
Figure 11 shows the dependence of DE1 and 0th order diffraction efficiency (DE0) as functions of the SCM
normalized linewidth D/W for linear gratings with different normalized periods T/W. Optimum linewidth D1 for the DE1
maximum differs from optimum linewidth D0 for DE0 minimum. The choice between these two optima can be
determined from requirements to manufactured diffractive element. The dependence of normalized optimum values of
D1/W and D0/W from T/W can be approximated with quite good accuracy in range of T/W from 3 to 50 by following
expressions:
0.2024
1/ 0.3136 ln 0.5407,
0 / W 0.9053 .
T
DW W
T
DW
(1)
For T/W> 20 the linewidth of the SCM can be remained without change, since the extremes of the diffraction efficiency
curves are hardly noticeable (Figure 11, a, b) for larger periods.
Figure 11: Dependences of the DE1 (a) and DE0 (a) as function of normalized linewidth D/W (a, b). The curves were calculated for
T/W changed from 3 to 36.
The backward slopes BWS defining SCM linewidth depends on spot size diameter W but also photoresist and
developer types. Low-contrast development expands backward slopes. It should be also taken into account at modeling
and optimization. One of ways to make it is to define a generalized point-spread function (GPSF) of whole fabrication
process17,
22
. If the GPSF is quite close to Gaussian shape one can use the expressions (1) for defining D(T), otherwise it
is necessary to make the optimization of the linewidth for the special case.
Utmost error of the linewidth of chrome masks for
existing photolithographic technologies is not more than ±
0.2µm or about 0.12D/W for our simulation parameters.
According to Figure 11, a the error leads to a 0.5-1.5% loss of
the diffraction efficiency for T/W in range of 3-6. However,
when OCMM is applied to the process with a smaller GPSF,
the requirements become tougher. For example, while reducing
the writing-beam diameter to 0.6µm (FWHM) the backward
slope of the diffractive zones reduces to 1.3-1.5µm (nonlinear
reduction of the backward slope is associated with the
photoresist development behavior). In that case, the linewidth
of the contour mask should be about 1µm, and in accordance
with Figure 11, a DE1 drops by 2-3% at linewidth error of
0.2D/W.
It is interesting to compare OCMM with laser direct
writing methods based on exposure optimization 16,17,21 which
are simpler from technological point of view. Figure 12 allows
one to estimate considerable improvement in the diffraction
efficiency in 1st order for grating formed by OCMM (curve
CM1) in comparison with values for the linear gratings
simulated in papers16,17 by different methods of exposure
distribution optimization: Diff - differential algorithm16,17, SQP - sequential quadratic programming16 , ZBO6 - zone
boundary optimization with 6-steps stepped transfer function21. Curves M1-M3 depict calculated diffraction efficiency
Figure 12: The diffraction efficiency as function of the
normalized period T/(M*WE2). WE2 – spot diameter
defined at e-2 level.
for the convoluted profiles of the gratings working in 1st, 2nd, and 3rd orders16. Curves CM2 and CM3 demonstrates
application of OCMM to the same gratings working in 2nd and 3rd orders. If to take into account a fine tolerance for
profile depth error at operation with higher M16 one can conclude that OCMM at M=1 makes unreasonable the use of
higher reconstruction orders for enhancing the diffraction efficiency. The only reason for it can be achromatization of
diffractive optical element.
5. CONCLUSIONS
The present paper has reviewed some techniques and equipment for the fabrication of binary and continuous-
relief DOEs developed at IA&E SB RAS for some last years. We have designed and built several generations of high
precision polar coordinate laser writing system. Manufacturing of DOEs by circular scanning of focused laser beam with
mathematical description in polar system of coordinates appeared fruitful and revealed a number of important advantages
in comparison with traditional xy writers. Unlike our previous CLWSs, last system has two optical cannels for realization
of thermal and photosensitive fabrication techniques. The system allows us to manufacture high precision DOEs
generating conical wavefront, non-axially symmetric DOEs for cylindrical and freeform surface testing, multilevel and
continuous-relief DOEs with arbitrary structure. Accuracy of wavefront shape generation by fabricated DOEs reached
/20 at apertures of an order of f/0.5. It corresponds to the highest standards of classical optics. Commercial version
developed jointly with TDI SIE can write multi-level diffractive structures on spherical surfaces.
High-precision DOEs are mainly fabricated on CLWS-30IAE with a thermochemical method based on laser
heating of the chromium films. Testing of the conical needed DOE with extremely small period of 0.9 µm. Cylindrical
and freeform surfaces have been interferometrically tested with DOEs which had no axial symmetry. The problem of the
alignment have been solved by introduction of auxiliary lenses that focused light in predefined positions on the surface
under test.
The contour mask method combines the advantages of the analog and binary processes. It can dramatically
increase the 1st order diffraction efficiency and reduce 0th order efficiency. At usage of Gaussian writing spot the optimal
(for the maximization of 1st order diffraction efficiency) linewidth of the contour mask is about 0.7 of the backward slope
width. Level and center of the flat top of the ridge shaped by the contour mask should be at the peak of ideal grating
profile. For gray-scale methods which can be simulated by convolution with Gaussian-like generalized point-spread
function the application of OCMM method can increase the 1st order diffraction efficiency by 10-20% for normalized
grating period T/(M·WE2) in range of 4-14 in comparison to other published methods optimizing the exposure
distribution and grating profile shape. The application of the OCMM to existing laser writers requires availability of the
alignment subsystem with sub-micron accuracy and using the contour mask with AR-coating to reduce an influence of
the mask on autofocus subsystem and back scattering of the exposing laser beam.
Acknowledgements.
This work is funded in a part of DOE fabrication by SB RAS interdisciplinary projects No 43 and No 112. The
measurements of aspheric surface is funded by RFBR project No 12-02-01118а.
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