Keynote Paper
Developing the refractive light beam shapers
as lossless apodization systems suppressing
the side-lobes in Fourier transform optical systems
Alexander Laskina, Alexandre S. Shcherbakovb, Vladimir Molchanovc,
Vadim Laskin a, Oleg Makarovc
a
AdlOptica GmbH, Rudower Chaussee 29, 12489, Berlin, Germany
Phone: +49 (179) 789-8848; E-mail: alex@adloptica.com
b
National Institute for Astrophysics, Optics & Electronics, Puebla, 72000, Mexico
Phone: +52 (222) 266 3100, ext. 2205; E-mail: alex@inaoep.mx
c
MISIS, Acousto-Optical Research Center, Leninsky prospect 4, 119049 Moscow, Russia
Phone: +7 (495) 951-1265; E-mail: aocenter@misis.ru
ABSTRACT
The Fourier transform optical systems, creating an image and/or realizing its accurate spectral characterization, suffer
from appearing remarkable level of side-lobes in the image intensity distribution that reduce performances, in particular,
the dynamic range of these systems. Therefore, suppressing side-lobes in the image plane represents an actual practical
task being important for various scientific and technical applications such as, for example, direct imaging and spectral
characterization of Earth-like extra-solar planets or spectrum analysis of ultra-high frequency radio-wave signals with
exploiting an advanced acousto-optical technique. We suggest applying as apodization systems novel refractive optical
beam shapers of the field mapping type, which are able to convert the input (more or less) uniform intensity distribution,
peculiar to the majority of usually exploited sources of light, to arbitrary pre-scripted intensity distributions. In the case
of choosing, for instance, Gaussian, cosine on a pedestal, etc. distributions, these shapers make it possible to minimize
the total level of side-lobes significantly and to increase, in doing so, the dynamic range of optical data processing up to
40 dB or more. The operation principle of these beam shapers is based on inducing, in a control manner, spherical
aberration in order to provide the required intensity profile transformation and further compensation of that aberration.
As a result, the beam shapers operate as telescopes of special type; they produce a low divergence collimated beam with
a target intensity distribution and flat wave front. We describe the beam shaper design, implementation examples, and
results of practical applications to the acousto-optical technique of precise multi-channel spectrum analysis.
Keywords: Beam Shaping, Gaussian apodization, suppressing side-lobes, flattop, Gaussian
1. INTRODUCTION
The problem of appearing side-lobes in Point Spread Function (PSF) of imaging optical systems with uniform input
aperture is well-known and there are various scientific techniques whose performances can be essentially improved by
suppressing the side-lobes. For example, this task is important in astronomy1 by imaging and spectral analysis of Earthlike extra-solar planets, which should be observed in close proximity to a star with orders of magnitude higher brightness
than a planet to be investigated. As a result, when an imaging optical system with a pupil of uniform transmission
function applied, the intensity of high order diffraction rings in the star image is larger than intensity of the central zeroorder spot of a planet image, so the planet simply cannot be observed. To overcome this problem it is necessary to
22nd Congress of the International Commission for Optics: Light for the Development of the World,
edited by Ramón Rodríguez-Vera, Rufino Díaz-Uribe, Proc. of SPIE Vol. 8011, 80110L
2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.901944
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eliminate or, at least strongly reduce the intensity of first and higher order diffraction rings (or side-lobes) of the PSF
inherent in an imaging optical system, thus, enlarging its dynamic range. Rather usual and simple technique to do this in
astronomy is so-called apodization of the entrance pupil in an imaging system, i.e. the modification of the pupil
transmission function through applying a Gaussian profile amplitude mask with the transmission of about 100% in the
pupil center and its decreasing towards a periphery of the pupil. In so doing, the PSF in the focal plane is described by
Gaussian function with suppressed side-lobes and an optical system gets enlarged dynamic range. The essential
disadvantage of this apodization technique is connected with losses of light, theoretically up to 63%, that becomes
critical when observing low-brightness planets. The task of suppressing the PSF side-lobes is important also in spectrum
analysis of ultra-high frequency radio-wave signals with exploiting an advanced acousto-optics. The apodization of a
light beam passing through an acousto-optical cell lets it possible to increase the dynamic range and to provide accurate
multi-channel spectrum analysis in a parallel regime of operation. However, significant losses of light power are
undesirable in acousto-optic systems as well. To overcome the problem of high losses inherent in the above-noted
simplest apodization technique one can suggest to replace the amplitude mask with Gaussian transmission profile by a
beam shaping optical system converting the uniform intensity profile to the Gaussian profile. The opposite task, i.e.
converting the Gaussian profile to uniform (or flattop, top hat) one, is an important task in various laser techniques and
as solutions there are applied so called refractive beam shapers of field mapping, for example πShaper. Being installed in
reverse ray path these beam shapers will realize the apodization required and, hence, can be used as lossless apodization
systems. We will consider design features of the refractive field mapping beam shapers πShaper, there will be also
presented experimental results of applying πShaper products.
2. DESCRIPTION OF THE TECHNIQUE
The principles of designing the refractive beam shapers of field mapping type are well-known and described in
literature 2,3,4,5. These systems are widely used in industrial applications and various scientific techniques to convert
intensity distribution of laser beams. An idea of the refractive field mapper operation is illustrated in Fig. 1. A Gaussian (or
close to Gaussian) intensity distribution of a TEM00 or multimode laser beam is converted to a flat-top distribution that
stays invariable over long distance after the beam shaper, this type of conversion is most frequently asked.
I'
Fig. 1 Result of refractive field mapper operation.
Fig. 2 Example of optical layout of the refractive field mapper.
This transformation is realized through distortion of the beam wave front inside the optical system under the condition of
energy conservation, this effect is illustrated with a picture in Fig. 2. Mathematically this condition is formulated as follows
rin
Rout
xIin (r)⋅r⋅dr
=
xIout (R)⋅R⋅dR ,
(1)
0
0
where r is the input beam radius in polar coordinates, Iin (r) is the function of intensity distribution of the input laser
beam section, rin is the maximum radius of the input beam subjected to considered intensity distribution, typically it is
equal to radius of an input laser beam at 1/e2 intensity level, R is the output beam radius in polar coordinates, Iout (R) is
the function of intensity distribution of the output beam, Rout is the maximum radius of the output beam resulting after
the intensity redistribution. The intensity redistribution could be realized for various light beams, however most often in
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the practice it is necessary to convert TEM00 laser beams, which intensity distribution is described by Gaussian function,
to beams of uniform intensity (flattop or top-hat). Accordingly, the intensity distribution of the input beam could be
defined as
Iin (r) = Iin0 exp(-2r 2/ω 2 ) ,
(2)
where ω is the waist radius of the Gaussian laser beam, Iin0 is the constant. To present an output beam intensity
distribution it is convenient to apply, for example, Fermi-Dirac4,6 or Super Gaussian6 functions, it can be presented also
as
Iout (R) =
s
Iout0 for R
0 for R
OR
>R
out
(3)
out
where Iout0 is the constant. Another basic principle of a beam shaper is zero wave aberration; by this is meant that the
aberration introduced by first optical component is then compensated by the second one. The other details of refractive beam
shapers of field mapping type can be found in publications2-6, here we will emphasize on some features important in applying
these devices for the apodization task.
An essential optical design feature of the refractive field mapper is in consisting of two optical components and
controlled wave-front transformation in the space between them due to applying of special optical surfaces, as a
result, the necessary intensity redistribution is achieved. Another important feature of the optical design is zero or
negligible for practical applications residual wave aberration, this fact leads to equal path lengths for all rays of input
beam passing through the optical system. This condition is very important for practice since it guarantees flat output
wave-front, and moreover, it provides also low output divergence and keeping the result intensity profile over long
distance after the refractive field mapping beam shaper.
One of important optical design features of the beam shapers from the πShaper family over other approaches is in
their achromatic design that guarantees simultaneous fulfillment of conditions of intensity redistribution and zero or
negligible wave aberration for a certain spectral range, as result the achromatic optical systems provide the same
operation at each wavelength of this spectral range. This feature is realized through using materials with different
dispersion characteristics.
Summarizing, the most important features and basic principles of refractive field mappers are:
•
telescopic or collimating refractive optical systems
that transform Gaussian, or close to Gaussian
intensity distribution of source laser beam to a flattop
(or top-hat, or uniform) one;
•
The initial laser beam can be either a TEM00 or a
multimode one;
•
The uniform intensity is kept after the beam shaper
Fig. 3 Examples of refractive field mappers.
over a large distance;
•
The output beam is free of aberration and as result the phase profile is maintained flat and low beam
divergence is provided;
•
In achromatic beam shapers the intensity transformation is provided for a certain spectral range;
•
Galilean design, thus there is no internal focusing of a beam.
A few examples of refractive field mapping beam shapers capable to work with laser beams of various input size at
various wavelengths are shown in Fig. 3. Most of models are implemented as a telescope, thus requiring collimated
input beam and providing a collimated output.
Evidently, when used in condition of inverse ray path the refractive field mapping beam shapers πShaper will realize
just inverse intensity profile conversion – from a uniform distribution to a Gaussian one. In other words, they can be
used as apodization optical systems providing lossless transformation of intensity profile to Gaussian one that is
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optimum in imaging optical systems from the point of view of absence, or at least, suppressed side-lobes of the PSF.
Small residual aberrations, typically below λ/10, allows using these apodizing beam shapers in high resolution
optical systems. Being initially developed for operation with the axial beam the πShaper are capable to work in
certain angle field, so they can be used in such application like imaging in astronomy or acousto-optics.
3. EXPERIMENTAL RESULTS
3.1 Example of operation of the refractive beam shaper πShaper
Essential features of operation of the refractive field mapping beam shapers can be seen from the example of beam
intensity re-distribution realized according to the layout presented at Fig. 1. One can see on Fig. 4 profiles: TEM00 input
beam (a), Flattop output beam (b); here there are presented beam profiles measured with a camera based beam profiler,
as a beam shaper the πShaper 6_6_532/1064 in right orientation was applied, the laser wavelength is 532 nm.
(a)
Fig. 4 Intensity profiles: (a) input TEM00 beam; (b) output flattop beam after πShaper 6_6_532/1064.
(b)
In spite of deviation of intensity distribution of the input beam from the perfect Gaussian function the beam shaper
provides quite good quality of re-distribution. Due to operational principle a field mapping beam shaper cannot suppress
high frequency intensity modulation of original beam; that is why that modulation presents in resulting profile as well. In
general, very good converting of smooth Gaussian profile to Flattop one is provided, so when used in inverse ray path
the πShaper 6_6_532/1064 should realize the apodization function required.
3.2 Description of experimental setup
The basic layout of experimental setup to investigate operation of the refractive beam shaper πShaper as an apodizing
device is presented on Fig. 5.
5,
A
532cm
B
C
D
E
F
Beam-Expander
Iris Diaphragm
rShaper 6_6_532/1064
(reverse ray path)
Lens
Beam Profiler
LaserCam-HR
f' = I m
Fig. 5 Layout of experimental setup.
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In order to simulate a flattop input beam it was used a Laser A (TEM00, CW, P = 70 mW, λ = 532 nm) which beam was
expanded with using a Beam-expander B and then main part of the beam was stopped by a circular Iris diaphragm C in
such a way the only central portion of the beam is passing to further optical system.
Then a unit of πShaper 6_6_532/1064 D was
installed, its orientation was chosen in such a way
the Flattop input beam intensity profile is
converted to Gaussian output profile. A focusing
Lens E of 1 meter focal length was installed right
after the πShaper 6_6_532/1064, analysis of the
beam profile behaviour in area of focal plane of
the Lens E was performed by a CMOS camera
based beam profiler F installed at distance S’ that
was varied during experiments.
Fig. 6 Experimental setup
To attenuate the beam while measurements of PSF near the Lens focus neutral filters were applied. Outlook of the
experimental setup are presented in Fig. 6.
To compare features of the beam profile behaviour in various conditions of focusing, there were used also some
modifications of the layout presented at Fig. 5:
- without the πShaper 6_6_532/1064, so focusing of flattop beam realized,
- with an acousto-optical cell installed in space between the πShaper 6_6_532/1064 D and the Lens E;
the acousto-optical cell realized Bragg diffraction, 1 st order radiation was considered; this modification allows
to analyze operation of the πShaper as an apodizing optical system in combination with acousto-optics.
3.3 Measurements of beam profile near the focal plane of the Lens
Some characteristic intensity profiles corresponding to the case of using acousto-optics and showing behaviour of beam
in area close to focal plane of a Lens are presented in Fig. 7. The distances S’ from the Lens E to the Beam profiler F are
indicated on right side of tables. The set of profiles in left column in Fig. 7 corresponds to the case of focusing the beam
with the Lens E being installed after the Iris C. This is a typical behaviour of intensity variation for an optical system
with uniform pupil when both beam profile and its size are variable. The focal plane corresponds to S’ = 1100 mm.
after πShaper
The right column in Fig. 7 relates to the layout when
flattop input
a uniform beam after the Iris C gets intensity reS’, mm
distribution to Gaussian profile by the πShaper. One
can see the beam intensity profile stays stable over
whole zone near the focus, can be described by
1100
Gaussian function, there exists variation of beam size
that is similar to one for typical TEM00 laser beams.
The residual 1st order diffraction ring is very weak, so
O,.
kkIP
the side-lobes of PSF are strongly suppressed. When
the πShaper was applied, the intensity profiles in
zone of focal plane demonstrated stability with
1250
variation of beam size only and with about 500 mm
distance along the optical axis where the beam
diameter variation was less than 20%, so a quite long
depth of field was provided.
Fig. 7 Profiles near focal plane of the Lens with AO cell.
::,
_J
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::,
3. DISCUSSION
The experimental data show good correspondence to the theoretical predictions of principal possibility of using the
refractive beam shapers of field mapping type as apodization systems to convert uniform intensity profile of a light beam
to the Gaussian one. Being used in reverse ray path the πShaper 6_6_532/1064, that is a standard product for beam
shaping of laser beams, realizes the beam intensity re-distribution from flattop to close to Gaussian. Further focusing of
the output beam with an imaging system allows getting the PSF with strongly reduced intensity of 1 st and higher orders
diffraction rings. The beam profile behaviour becomes analogous to one of TEM00 laser beams in field of a beam waist
when the beam profile itself stays invariable but its diameter varies. This behaviour differs from one being typical in case
of focusing of a beam of uniform intensity – both intensity profile and beam size get instant variation while the beam
propagating along the optical axis in zone near the focus.
Another feature of a beam transformed with using the πShaper 6_6_532/1064 is extended depth of field, this might be
very important in various imaging applications.
The profiles corresponding beams with re-distributed intensity (right column) have certain residual side-lobes in PSF,
this means the transformation provided by the πShaper 6_6_532/1064 is not perfect and output intensity profile
somewhat differs from a perfect Gaussian distribution. The reason of this is in some design features of the
πShaper 6_6_532/1064 – the exact intensity re-distribution is provided for the central portion of the input Gaussian beam
covered by diameter at 1/e2 intensity, see the Fig. 2 and formula (1). This portion of input beam transfers about 84% of
beam energy, so essential part of a beam gets necessary transformation, the rest peripheral part of beam gets
transformation that is not completely controlled. This approach works good for most of practical applications with
homogenized laser beams, but when the beam shaper is used in reverse orientation the might appear unwished diffraction
effects that lead to not complete suppressing of side-lobes of PSF. This effect can be overcome by developing a
dedicated beam shaping optical system presuming re-distribution for larger portion of input beam. For example, when
exact intensity re-distribution is provided for central part of a beam covered by diameter 1.5 larger than 1/e2 intensity
diameter, more than 99% of beam energy is transformed in proper way and this corresponds to almost perfect beam
shaping and, hence, perfect apodization function for this system used in reverse ray path.
4. CONCLUSION
The approach of designing the refractive field mapping beam shapers can be successfully applied to developing of
lossless apodization optics intended to suppress side-lobes of the PSF of imaging systems. Example of a refractive beam
shaper πShaper confirms that even a ready beam shaper operating in reverse ray path realizes the necessary intensity
profile conversion from uniform to Gaussian distribution. This conversion can be essentially improved by developing a
dedicated beam shaping system with providing exact fulfilment of the conditions of intensity re-distribution for output
beam diameter larger than 1/e2 intensity diameter. As a result, a lossless apodization optical system providing imaging
with strongly suppressed side-lobes of the PSF and enlarged dynamic range can be created.
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