Light Robotics is a new field of research where ingredients from photonics, nanotechnology and
biotechnology are put together in new ways to realize light-driven robotics at the smallest scales to
solve major challenges primarily within the nanobio-domain but not limited hereto. Exploring the
full potential of this new ‘drone-like’ light-printed, light-driven, light-actuated micro- and nanorobotics
in challenging geometries requires a versatile and real-time reconfigurable light addressing
that can dynamically track a plurality of tiny tools in 3D to ensure real-time continuous light-delivery
on the fly. Our latest developments in this new and exciting research area will be reviewed.
Recently we proposed the concept of so-called Light Robotics including the new and disruptive 3D-fabricated micro-tools coined Wave-guided Optical Waveguides that can be real-time optically manipulated and remote-controlled with a joystick in a volume with six-degrees-of-freedom. Exploring the full potential of this new ‘drone-like’ light-driven micro-robotics in challenging microscopic geometries requires a versatile and real-time reconfigurable light addressing that can dynamically track a plurality of tiny micro-robots in 3D to ensure continuous optimal light coupling on the fly. Our latest developments in this new and exciting research area will be reviewed.
Early detection of diseases can save lives. Hence, there is emphasis in sorting rare disease-indicating cells within small dilute quantities such as in the confines of lab-on-a-chip devices. However, before diseased cells can be studied in isolation, it is necessary to identify them against normal healthy cells. With the richness of visual information, a lot of microscopy techniques have been developed and have been crucial in biological studies. To utilize their complementary advantages we adopt both fluorescence and brightfield imaging in our optical cell sorter. Brightfield imaging has the advantage of being non-invasive, thus maintaining cell viability. Fluorescence imaging, on the other hand, takes advantages of the chemical specificity of fluorescence markers and can validate machine vision results from brightfield images. Visually identified cells are sorted using optical manipulation techniques. Scattering forces from beams actuated via efficient phase-only efficient modulation has been adopted. This has lowered the required power for sorting cells to a tenth of our previous approach, and also makes the cell sorter safer for use in clinical settings. With the versatility of dynamically programmable phase spatial light modulators, a plurality of light shaping techniques, including hybrid approaches, can be utilized in cell sorting.
We show a simplified method of generating extended regions of destructive interference with near arbitrary shapes using the generalized phase contrast (GPC) method. For Gaussian input beams, GPC typically results in a 3× intensified user-defined input mask shape against a dark background. In this work, we investigate conditions wherein GPC’s synthetic reference wave destructively interferes with what is typically the foreground pattern. Using alternate conditions for the input phase mask, the locations of light and darkness are interchanged with respect to typical GPC output mappings. We show experimentally how “dark GPC” allows the dark regions to be easily reshaped using a binary-only phase mask encoded on a spatial light modulator. Similar to standard GPC, the method does not require complex calculations or the fabrication of complex gray-level phase elements. The simplified approach and flexibility in the output shapes make dark GPC attractive for applications such as optical trapping of low-index particles or superresolution microscopy like stimulated emission depletion.
As celebrated by the Nobel Prize 2014 in Chemistry light-based technologies can now overcome the diffraction barrier for imaging with nanoscopic resolution by so-called super-resolution microscopy1. However, interactive investigations coupled with advanced imaging modalities at these small scale domains gradually demand the development of a new generation of disruptive tools, not only for passively observing at nanoscopic scales, but also for actively reaching into and effectively handling constituents in this size domain. This intriguing mindset has recently led to the emergence of a novel research discipline that could potentially be able to offer the full packet needed for true "active nanoscopy" by use of so-called light-driven micro-robotics or Light Robotics in short.
Generalized Phase Contrast (GPC) is a light efficient method for generating speckle-free contiguous optical distributions using binary-only or analog phase levels. It has been used in applications such as optical trapping and manipulation, active microscopy, structured illumination, optical security, parallel laser marking and labelling and recently in contemporary biophotonics applications such as for adaptive and parallel two-photon optogenetics and neurophotonics. We will present our most recent GPC developments geared towards these applications. We first show a very compact static light shaper followed by the potential of GPC for biomedical and multispectral applications where we experimentally demonstrate the active light shaping of a supercontinuum laser over most of the visible wavelength range. Finally, we discuss how GPC can be advantageously applied for Quantitative Phase Imaging (QPI).
Early detection of diseases can save lives. Hence, there is emphasis in sorting rare disease-indicating cells within small
dilute quantities such as in the confines of lab-on-a-chip devices. In our work, we use optical forces to isolate red blood
cells detected by machine vision. This approach is gentler, less invasive and more economical compared to conventional
FACS systems. As cells are less responsive to plastic or glass beads commonly used in the optical manipulation
literature, and since laser safety would be an issue in clinical use, we develop efficient approaches in utilizing lasers and
light modulation devices. The Generalized Phase Contrast (GPC) method that can be used for efficiently illuminating
spatial light modulators or creating well-defined contiguous optical traps is supplemented by diffractive techniques
capable of integrating the available light and creating 2D or 3D beam distributions aimed at the positions of the detected
cells. Furthermore, the beam shaping freedom provided by GPC can allow optimizations in the beam’s propagation and
its interaction with the catapulted cells.
Material transport is an important mechanism in microfluidics and drug delivery. The methods and solutions found in
literature involve passively diffusing structures, microneedles and chemically fueled structures. In this work, we make
use of optically actuated microtools with embedded metal layer as heating element for controlled loading and release.
The new microtools take advantage of the photothermal-induced convection current to load and unload cargo. We also
discuss some challenges encountered in realizing a self-contained polymerized microtool. Microfluidic mixing, fluid
flow control and convection currents have been demonstrated both experimentally and numerically for static metal thin
films or passively floating nanoparticles. Here we show an integration of aforementioned functionalities in an optically fabricated
and actuated microtool. As proof of concept, we demonstrate loading and unloading of beads. This can be
extended to controlled transport and release of genetic material, bio-molecules, fluorescent dyes. We envisioned these
microtools to be an important addition to the portfolio of structure-mediated contemporary biophotonics.
Generalized Phase Contrast (GPC) is an efficient method for efficiently shaping light into speckle-free contiguous
optical distributions useful in diverse applications such as static beam shaping, optical manipulation and recently, for
excitation in two-photon optogenetics. GPC typically results in a 3x intensified user defined input mask shape against a
dark background. In this work, we emphasize GPC’s capability of optimal destructive interference, normally used to
create the dark background surrounding the shaped light. We also study input parameters wherein the locations of light
and darkness are interchanged with respect to typical GPC output, thus resulting to a well-defined structured darkness.
The conditions that give destructive interference for the output are then applied to near-arbitrary shapes. Preliminary
experimental results are presented using dynamic spatial light modulator to form scaled arbitrary darkness shapes.
Supporting demonstrations that reverse the light and dark regions of amplitude-modulated input are also presented as a
related case of structuring destructive interference. Our analysis and experimental demonstrations show a simplified
approach in the generation of extended regions of destructive interference within coherent beams.
We have previously demonstrated on-demand dynamic coupling to optically manipulated microtools coined as wave-guided optical waveguides using diffractive techniques on a “point and shoot” approach. These microtools are extended microstructures fabricated using two-photon photopolymerization and function as free-floating optically trapped waveguides. Dynamic coupling of focused light via these structures being moved in three-dimensional space is done holographically. However, calculating the necessary holograms is not straightforward when using counter-propagating trapping geometry. The generation of the coupling spots is done in real time following the position of each microtool with the aid of an object tracking routine. This approach allows continuous coupling of light through the microtools which can be useful in a variety of biophotonics applications. To complement the targeted-light delivery capability of the microtools, the applied spatial light modulator has been illuminated with a properly matched input beam cross section based on the generalized phase contrast method. Our results show a significant gain in the output at the tip of each microtool as measured from the fluorescence signal of the trapping medium. The ability to switch from on-demand to continuous addressing with efficient illumination leverages our microtools for potential applications in stimulation and near-field-based biophotonics on cellular scales.
We originally proposed and experimentally demonstrated the targeted-light delivery capability of so-called Wave-guided
Optical Waveguides (WOWs) three years ago. As these WOWs are maneuvered in 3D space, it is important to maintain
efficient light coupling through their integrated waveguide structures. In this work we demonstrate the use of real-time
diffractive techniques to create focal spots that can dynamically track and couple to the WOWs during operation in a
volume. This is done by using a phase-only spatial light modulator to encode the needed diffractive phase patterns to
generate a plurality of dynamic coupling spots. In addition, we include our proprietary GPC Light Shaper before the
diffractive setup to efficiently illuminate the rectangular shaped spatial light modulator by a Gaussian laser beam. The
method is initially tested for a single WOW and we have experimentally demonstrated dynamic tracking and coupling
for both lateral and axial displacements of the WOWs. The ability to switch from on-demand to continuous addressing
with efficient illumination leverages our WOWs for potential applications in near-field stimulation and nonlinear optics
at small scales.
We have previously proposed and demonstrated optimal beam shaping of contiguous light patterns using the Generalized Phase Contrast (GPC) method. The concept has been packaged into a compact add-on module, which we call the GPC light shaper (LS) that can be conveniently integrated to existing optical setups requiring optimal illumination of devices such as spatial light modulators (SLMs). In this work, we integrated the GPC LS into a holography setup to generate more intense focal spots and extended patterns. The output of the holography setup with the GPC LS is compared with a similar setup but using only hard-truncated beams. Our results show that, we get a ~3x gain in intensity of the generated patterns when using GPC LS.
We have previously demonstrated on-demand dynamic coupling of an optically manipulated wave-guided optical waveguide (WOW) using diffractive techniques on a “point and shoot” approach. In this work, the generation of the coupling focal spots is done in real-time following the position of the WOW. Object-tracking routine has been added in the trapping program to get the position of the WOW. This approach allows continuous coupling of light through the WOWs which may be useful in some application. In addition, we include a GPC light shaper module in the holography setup to efficiently illuminate the spatial light modulator (SLM). The ability to switch from on-demand to continuous addressing with efficient illumination leverages our WOWs for potential applications in stimulation and nonlinear optics.
We have previously proposed and demonstrated the targeted-light delivery capability of wave-guided optical waveguides (WOWs). The full strength of this structure-mediated paradigm can be harnessed by addressing multiple WOWs and manipulating them to work in tandem. We propose the use of diffractive techniques to create multiple focal spots that can be coupled into light manipulated WOWs. This is done by using a spatial light modulator to project the necessary phase to generate the multiple coupling light spots. We incorporate a diffractive setup in our Biophotonics Workstation (BWS) and demonstrate holographic shaping, tracking of light in 3D with the purpose of coupling light in the WOWs.
The science fiction inspired shrinking of macro-scale robotic manipulation and handling down to the micro- and nanoscale
regime opens new doors for exploiting the forces and torques of light for micro- and nanoscopic probing,
actuation and control. Advancing light-driven micro-robotics requires the optimization of optical forces and torques
that, in turn, requires optimization of the underlying light-matter interaction. This report is two-fold desribing the new
use of proprietary strongholds we currently are harnessing in the Programmable Phase Optics in Denmark on new
means of sculpting of both light and matter for robotically probing at the smallest biological length scales.
We demonstrate the use of microfabricated supporting structures for maneuvering and supporting polystyrene microspheres for use as magnifying lenses in imaging applications. The supporting structure isolates the trapping light from the magnifier, hence avoiding direct radiation to the sample being observed which could be damaging, especially for biological specimens. Using an optical trapping setup, we demonstrate the actuation of a microsphere not held by optical traps, and show the possibility of imaging through such microspheres.
We demonstrate the efficient generation of line patterns using matched-filtering Generalized Phase Contrast (mGPC). So far, the main emphasis of mGPC light addressing has been on the creation of rapidly reconfigurable focused spots. This has recently been extended to encoding extended line patterns for structured light applications and advanced microscopy.
We propose the use of consumer pico projectors as cost effective spatial light modulators in cell sorting applications. The
matched filtering Generalized Phase Contrast (mGPC) beam shaping method is used to produce high intensity optical
spots for trapping and catapulting cells. A pico projector’s liquid crystal on silicon (LCoS) chip was used as a binary
phase spatial light modulator (SLM) wherein correlation target patterns are addressed. Experiments using the binary
LCoS phase SLM with a fabricated Pyrex matched filter demonstrate the generation of intense optical spots that can
potentially be used for cell sorting. Numerical studies also show mGPC’s robustness to phase aberrations in the LCoS
device, and its ability to outperform a top hat beam with the same power.
We are presenting so-called Wave-guided Optical Waveguides (WOWs) fabricated by two-photon polymerization and capable of being optically manipulated into any arbitrary orientation. By integrating optical waveguides into the structures we have created freestanding waveguides which can be positioned anywhere in a sample at any orientation using real-time 3D optical micromanipulation with six degrees of freedom. One of the key aspects of our demonstrated WOWs is the change in direction of in-coupled light and the marked increase in numerical aperture of the out-coupled light. Hence, each light propelled WOW can tap from a relatively broad incident beam and generate a much more tightly confined light at its tip. The presentation contains both numerical simulations related to the propagation of light through a WOW and preliminary experimental demonstrations on our BioPhotonics Workstation. In a broader context, this research shows that optically trapped micro-fabricated structures can potentially help bridge the diffraction barrier. This structure-mediated paradigm may be carried forward to open new possibilities for exploiting
beams from far-field optics down to the sub-wavelength domain.
Robotics can use optics feedback in vision-based control of intelligent robotic guidance systems. With light’s miniscule momentum, shrinking robots down to the microscale regime creates opportunities for exploiting optical forces and torques in microrobotic actuation and control. Indeed, the literature on optical trapping and micromanipulation attests to the possibilities for optical microrobotics. This work presents an optical microrobotics perspective on the optical microfabrication and micromanipulation work that we performed. We designed different three-dimensional microstructures and fabricated them by two-photon polymerization. These microstructures were then handled using our biophotonics workstation (BWS) for proof-of-principle demonstrations of optical actuation, akin to 6DOF actuation of robotic micromanipulators. Furthermore, we also show an example of dynamic behavior of the trapped microstructure that can be achieved when using static traps in the BWS. This can be generalized, in the future, towards a structural shaping optimization strategy for optimally controlling microstructures to complement approaches based on lightshaping. We also show that light channeled to microfabricated, free-standing waveguides can be used not only to redirect light for targeted delivery of optical energy but can also for targeted delivery of optical force, which can serve to further extend the manipulation arms in optical robotics. Moreover, light deflection with waveguide also creates a recoil force on the waveguide, which can be exploited for controlling the optical force.
The synergy between photonics, nanotechnology and biotechnology is spawning the emerging fields of nano-biotechnology
and nano-biophotonics. Photonic innovations already hurdle the diffraction barrier for imaging with
nanoscopic resolutions. However, scientific hypothesis testing demands tools, not only for observing nanoscopic
phenomena, but also for reaching into and manipulating nanoscale constituents in this domain. This report is two-fold
desribing the new use of proprietary strongholds we currently are establishing at DTU Fotonik on new means of
sculpting of both light and matter for bio-probing at the smallest scales.
We develop an active cell sorter that utilizes machine vision for cell identification. Particles are identified based on
visual features such as shape, size and color using image processing. The sorter shares features from our previously
developed BioPhotonics Workstation. Hence, it benefits from the extended axial manipulation range provided by the
low numerical aperture geometry. Detected particles are catapulted axially by several hundred microns, allowing
them to be moved from one laminar flow region to another. As the sorting motion is transverse to the viewing plane,
multiple particles can be catapulted at the same time, therefore enabling parallel sorting. The sorter is developed with
a minimal footprint such that it can operate as a table top device, an advantage over flow cytometry or FACS
systems.
Conventional optical trapping or tweezing is often limited in the achievable trapping range because of high numerical
aperture and imaging requirements. To circumvent this, we are developing a next generation BioPhotonics Workstation
platform that supports extension modules through a long working distance geometry. This geometry provides three
dimensional and real time manipulation of a plurality of traps facilitating precise control and a rapid response in all sorts
of optical manipulation undertakings. We present ongoing research and development activities for constructing a
compact next generation BioPhotonics Workstation to be applied in three-dimensional studies on regulated microbial cell
growth including their underlying physiological mechanisms, in vivo characterization of cell constituents and
manufacturing of nanostructures and new materials.
In its standard version, our BioPhotonics Workstation (BWS) can generate multiple controllable counter-propagating
beams to create real-time user-programmable optical traps for stable three-dimensional control and manipulation of a
plurality of particles. The combination of the platform with microstructures fabricated by two-photon polymerization
(2PP) can lead to completely new methods to communicate with micro- and nano-sized objects in 3D and potentially
open enormous possibilities in nano-biophotonics applications. In this work, we demonstrate that the structures can be
used as microsensors on the BWS platform by functionalizing them with silica-based sol-gel materials inside which dyes
can be entrapped.
Optical trapping and manipulation have established a track record for cell handling in small volumes. However, this cell
handling capability is often not simultaneously utilized in experiments using other methods for measuring single cell
properties such as fluorescent labeling. Such methods often limit the trapping range because of high numerical aperture
and imaging requirements. To circumvent these issues, we are developing a BioPhotonics Workstation platform that
supports extension modules through a long working distance geometry. Furthermore, a long range axial manipulation
range is achieved by the use of counter-propagating beam traps coupled with the long working distance. This geometry
provides three dimensional and real time manipulation of a plurality of traps - currently 100 independently
reconfigurable - facilitating precise control and a rapid response in all sorts of optical manipulation undertakings. We
present ongoing research activities for constructing a compact next generation BioPhotonics Workstation.
An experimental characterization of the 3D forces, acting on a trapped polystyrene bead in a counter-propagating
beam geometry, is reported. Using a single optical trap with a large working distance (in the BioPhotonics
Workstation), we simultaneously measure the transverse and longitudinal trapping force constants. Two
different methods were used: The Drag force method and the Equipartition method. We show that the counterpropagating
beams traps are simple harmonic for small displacements. The force constants reveal a transverse
asymmetry as κ- = 9.7 pN/μm and κ+ = 11.3 pN/μm (at a total laser power of 2x35 mW) for displacements in opposite directions. The Equipartition method is limited by mechanical noise and is shown to be applicable
only when the total laser power in a single 10 μm counter-propagating trap is below 2x20 mW.
We present a versatile technique that enhances the axial stability and range in counter-propagating (CP) beam-geometry optical traps. It is based on computer vision to track objects in unison with software implementation of feedback to stabilize particles. In this
paper, we experimentally demonstrate the application of this technique by real-time rapid repositioning coupled with a strongly enhanced axial trapping for a plurality of particles of varying sizes. Also exhibited is an interesting feature of this approach in its ability to automatically adapt and trap objects of varying dimensions which simulates biosamples. By working on differences rather than absolute values, this feedback based technique makes CPtrapping nullify many of the commonly encountered pertubations such as fluctuations in the laser power, vibrations due to mechanical instabilities and other distortions emphasizing its experimental versatility.
The counter-propagating geometry opens an extra degree of freedom for shaping light while subsuming single-sided
illumination as a special case (i.e., one beam set turned off). In its conventional operation, our BioPhotonics Workstation
(BWS) uses symmetric, co-axial counter-propagating beams for stable three-dimensional manipulation of multiple
particles. In this work, we analyze counter-propagating shaped-beam traps that depart from this conventional geometry.
We show that projecting shaped beams with separation distances previously considered axially unstable can, in fact,
enhance the trap by improving axial and transverse trapping stiffness. We also show interesting results of trapping and
micromanipulation experiments that combine optical forces with fluidic forces. These results hint about the rich potential
of using patterned counter-propagating beams for optical trapping and manipulation, which still remains to be fully
tapped.
The effect of a 1070-nm continuous and pulsed wave ytterbium fiber laser on the growth of Saccharomyces cerevisiae single cells is investigated over a time span of 4 to 5 h. The cells are subjected to optical traps consisting of two counterpropagating plane wave beams with a uniform flux along the x, y axis. Even at the lowest continuous power investigated-i.e., 0.7 mW-the growth of S. cerevisiae cell clusters is markedly inhibited. The minimum power required to successfully trap single S. cerevisiae cells in three dimensions is estimated to be 3.5 mW. No threshold power for the photodamage, but instead a continuous response to the increased accumulated dose is found in the regime investigated from 0.7 to 2.6 mW. Furthermore, by keeping the delivered dose constant and varying the exposure time and power-i.e. pulsing-we find that the growth of S. cerevisiae cells is increasingly inhibited with increasing power. These results indicate that growth of S. cerevisiae is dependent on both the power as well as the accumulated dose at 1070 nm.
We describe a diffracting beam with orbital angular momentum (OAM) but with a helical profile in both phase and
amplitude components of the beam. This is different from Laguerre-Gaussian (LG) beams where only the phase
component has a helical profile. Such profile in LG beams introduces a phase singularity at the centre and produces a
dark region surrounded by a ring-shaped light pattern. For LG-beams, the ring radius is proportional to the degree of
helicity or topological charge of the beam. The beam we describe here is initially characterized with an apodized helical
phase front at the outskirts and linearly scaled towards no phase singularity at the centre of the beam. At the focal
volume, we show that our beam forms an intensity distribution that can be accurately described as an "optical twister" as
it propagates in the forward direction. Unlike LG beams, an optical twister can have minimal changes in radius but with
a scalable OAM. Furthermore, we characterize the OAM in terms of its capacity to introduce spiral motion on particles
trapped along its orbit. We also show that our "optical twister" maintains a high concentration of photons at the focus
even as the topological charge is increased. Such beams can be applied to fundamental studies of light and atoms such as
in quantum entanglement of the OAM, toroidal traps for cold atoms and for optical manipulation of microscopic
particles.
We adapt concepts from matched filtering to propose a method for generating
rapidly reconfigurable multiple beams. As a phase-only spatially filtering extension of the
Generalized Phase Contrast (GPC) technique, the proposed method coined mGPC can yield
dynamically reconfigurable optical beam arrays with high light efficiency for optical
manipulation, high-speed sorting and other parallel spatial light applications [1].
We demonstrate a system for constructing reconfigurable microstructures using multiple, real-time configurable
counterpropagating-beam traps. We optically assemble geometrically complementary microstructures with complex
three-dimensional (3D) topologies produced by two-photon polymerization. This demonstrates utilization of
controllable 3D optical traps for building hierarchical structures from microfabricated building blocks. Optical
microassembly with translational and tip-tilt control in 3D achieved by dynamic multiple CB traps can potentially
facilitate the construction of functional microdevices and may also lead to the future realization of optically actuated
micromachines. Fabricating morphologically complex microstructures and then optically manipulating these archetypal
building blocks can also be used to construct reconfigurable microenvironments that can aid in understanding cellular
development processes.
We have studied the effect of a 1070 nm continuous wave Ytterbium fiber laser on exponentially growing
Saccharomyces cerevisiae yeast cells over a span of 4 hours. The cells were immobilized onto Concanavalin A covered
microscope slides and the growth was measured using the area increase of the cells in 2D. Using a continuous dual beam
plane wave with a uniform spatial intensity distribution, we found that a continuous radiant flux through a single cell as
low as 0.5 mW in 1.5 hours significantly changed the growth and division rate of S. cerevisiae. With the dual beam setup
used we were able to successfully manipulate single S. cerevisiae cells in 3 dimensions with a minimum flux thorough
the cell of 3.5 mW. In the regime investigated from 0.7 mW to 2.6 mW we found no threshold for the photo damage, but
rather a continuous response to the increased accumulated dose.
The generation of optical landscapes may be regarded as a communication system: A user sends information to a
designated region in space where the information is represented using optical parameters like intensity. Information
capacity has been used for understanding superresolution in optical systems and we adapt this concept to gain useful
insights for characterizing techniques for generating optical landscapes. In particular, we investigate the information
capacity of the generalized phase contrast method and computer-generated holography. We also consider the invariance
of information capacity and discuss its implications for the generation of dynamic optical landscapes.
We outline the specifications of a portable Bio-photonics Workstation we have developed that utilizes just a single spatial light modulator to generate an array of up to 100 reconfigurable laser-traps with adjustable power ratios making 3D real-time optical manipulation possible with the click of a laptop mouse. We employ a simple patented optical mapping approach from a fast spatial light modulator to obtain reconfigurable intensity patterns corresponding to two independently addressable regions relayed to the sample volume where the optical manipulation of a plurality of nano-featured micro-objects takes place. The stand-alone Biophotonics Workstation is currently being tested by external partners with micro-biologic and chemistry expertise.
The generalized phase contrast method (GPC) can produce a rich variety of optical landscapes from an incident flattop
beam. Here we show that the GPC can generate various intensity distributions directly from an incident Gaussian
illumination. This is illustrated by using GPC-based implementation of phase-only apertures that efficiently redirect the
available photons from an initial bell-shaped intensity distribution into desired configurations. GPC can reshape a
Gaussian beam into patterns having sharp intensity transitions and a flat phase profile in the bright regions with superior
energy efficiency over amplitude masks. Eliminating the initial Gaussian-to-flattop beamshaping requirement can be
beneficial for various applications employing GPC-based patterns.
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