Imaging techniques with refractive beam shaping optics

Imaging techniques with refractive beam shaping optics

Alexander Laskin, Vadim Laskin

AdlOptica GmbH, Rudower Chaussee 29, 12489 Berlin, Germany

ABSTRACT

Applying of the refractive beam shapers in real research optical setups as well as in industrial installations requires very often manipulation of a final laser spot size. In many cases this task can be easily solved by using various imaging optical layouts presuming creating an image of a beam shaper output aperture. Due to the unique features of the refractive beam shapers of field mapping type, like flat wave front and low divergence of the collimated resulting beam with flattop or another intensity profile, there is a freedom in building of various imaging systems with using ordinary optical components, including off-the-shelf ones. There will be considered optical layouts providing high, up to 1/200 ^x , de-magnifying factors, combining of refractive beam shapers like  Shaper with scanning systems, building of relay imaging systems with extended depth of field. These optical layouts are widely used in such laser technologies like drilling holes in PCB, welding, various micromachining techniques with galvo-mirror scanning, interferometry and holography, various SLM-based applications. Examples of real implementations and experimental results will be presented as well.

Keywords: beam shaping, flattop, tophat, galvo mirror, micromachining, drilling, holography, interferometry.

1. INTRODUCTION

Refractive field mapping beam shapers find applications in plenty of industrial and scientific laser technologies which performance is improved through transformation of intensity distribution, for example from Gaussian to flattop. On the other hand variety of applications leads to variety of necessary laser spot sizes, therefore successful using of off-the- shelf beam shapers and building of an optimum beam shaping system for a particular application require flexibility in size of resulting laser spots. Obviously, imaging technique can be a powerful tool to meet these demands, and combination of refractive beam shapers like  Shaper with imaging optical systems allows getting resulting spots with necessary intensity profile and sizes spanning from tens of microns to meters. Implementation of an imaging optical system depends on a particular laser technology, for instance they should include scanning mirror systems and F-theta lenses in industrial micromachining installations, while telecentric optical systems conserving phase front are preferable in interferometry and holography.

The essential feature of the refractive beam shapers  Shaper is that the laser beam profile transformation is done in a

control manner by accurate introducing and further compensation of wave aberration, therefore the resulting collimated

output beam has low divergence and there is no deterioration of the beam consistency. This design feature provides

flexibility in building complex beam shaping systems on the base of  Shaper.

2. THEORETICAL CONSIDERATIONS

By building beam shaping optical systems it is necessary to take into account some features of light propagation in space. Behavior of laser beams, especially TEM ₀₀ lasers, is very good investigated and described in details in plenty of literature sources. However, that single mode laser beam with Gaussian intensity profile is just a special case of light beams and general description of light beams propagation is typically more complicated, it is based on the diffraction theory described, for instance, in books ^2,5 . Therefore, when beam shaping optics is applied and intensity distribution of a light beam is transformed to flattop or other profiles, it is necessary to analyze those transformed laser beams “from basics”, i.e. with using laws of the diffraction theory. Some important for practice features of laser beams transformed with using field mapping beam shapers are considered in this chapter.

2.1 Propagation of flattop beams

When a TEM 00 laser beam with Gaussian intensity distribution propagates in space its size varies due to inherent beam divergence but the intensity distribution stays stable, this is a famous feature of TEM 00 beams that is widely used in practice. But this brilliant feature is valid for Gaussian beams only! When light beams with non-Gaussian intensity distributions, for example flattop beams, propagate in space, they get simultaneously variation of both size and intensity profile. Since the case of flattop beam is of importance for practice, and most often just conversion of Gaussian to flattop laser beam is a task for beam shaping systems, it is suggested to consider behaviour of light beam with uniform intensity distribution.

Suppose a coherent light beam has uniform intensity profile and flat wave front, Fig. 1, this is a popular example considered in diffraction theory ² , this is also a typical beam created by field mapping refractive beam shapers converting Gaussian to flattop laser beam.

Fig. 1 Intensity profile variation by a flattop beam propagation.

Due to diffraction the beam propagating in space gets variation of intensity distribution, some typical profiles are shown in Fig. 1: at certain distance from initial plane with uniform intensity distribution (a) there appears a bright rim (b) that is then transformed to more complicated circular fringe pattern (c), finally in infinity (so called far field) the profile is featured with relatively bright central spot and weak diffraction rings (d) – this is the well-known

“Airy disk” distribution described mathematically by formula

I (  ) = I 0 [J 1 (2  )/(2  )] ² (1) where J 1 is the Bessel function of 1 ^st kind, 1 ^st order,  is polar radius, I 0 is a constant.

The “Airy disk” function is result of Fourier-Bessel transform for a circular beam of uniform initial intensity ² . Evidently, even a “pure” theoretical flattop beam is transformed to a beam with essentially non-uniform intensity profile. There exists, however, certain propagation length where the profile is relatively stable, this length is in reverse proportion to wavelength and in square proportion to beam size. For example, for visible light and flattop beam diameter about 6 mm the length where deviation from uniformity doesn’t exceed +10% is about 200-300 mm, for the 12 mm beam it is about 1 meter.

(a) (b) (c) (d)

2.2 Image formation

Imaging with using a lens is a proved way to overcome the above considered effect of intensity transformation due to diffraction and create a resulting spot of optimum size and profile. Basic imaging optical layout is shown in Fig. 2.

Fig. 2 Imaging with a lens.

Here the lens is just a singlet, but for high quality imaging more sophisticated optical systems should be applied, for example aplanats (with correction of spherical aberration and coma), microobjective lenses. Calculation of parameters of a particular imaging setup can be done with using well-known formulas of geometrical optics, described, for example in book ⁵ . Let us note several important for practice issues:

- approximation of geometrical optics presumes that each Image point is created by a beam of rays emitted by a corresponding Object point,

- Object and Image are located in optically conjugated planes featured with the equal optical path length for all rays of a particular beam,

- the real Image is always created after the lens focus,

- the transverse magnification  is defined as a ratio between distances from principal planes of the lens to, correspondingly, Image and Object:

 = - h’ / h = - s’ / s , (2) - the product of object size h and aperture angle u (exactly sinu) is constant all over the optical system:

h

u = h’

u’ = const , (3) it is presumed here that an optical system is free of aberrations, for example, is aplanatic.

2.3 Features of imaging with laser beams

It is well-known that laser beams are characterized by low divergence defined by physics of creating the laser radiation, for example the full divergence angle 2  of a single mode beam with  = 532 nm and waist diameter 2  = 6 mm is about 0.12 mrad, so about 24 arc seconds! This feature effects on intensity transformation by imaging. Fig. 3 demonstrates behavior of intensity profile of a low divergent laser beam in the above considered imaging optical system. It is assumed here that the Object plane is featured with uniform intensity profile and flat wave front, a beamlet from each point of the object plane has low divergence - near the same like divergence 2  of a laser beam of the similar size, i.e. 2u = 2  ; these conditions are typical for output beam of a refractive field mapping beam shaper like

 Shaper which details are described later. Let’s consider intensity profiles in various planes of optical layout.

According to the diffraction theory the intensity distribution in a certain plane is result of interference of light diffracted

from previous plane of observation. The result of interference in the considered imaging layout is that intensity

distribution in the Image plane, being optically conjugated with the Object plane, will be similar to one of the Object

plane. If the intensity distribution is uniform in the Object plane, it is uniform in the Image plane as well; these profiles

are shown on left and right sides of the Fig. 3. Sure, the Image size will be defined by the transverse magnification  of

the imaging optical system.

Fig. 3 Intensity profile transformation of flattop laser beam in imaging layout

The beam in Object space has low divergence, 2u = 2  , hence, as discussed in paragraph 2.1, the beam propagating from the Object to the lens gets transformation of intensity due to diffraction. As result before and immediately after the imaging lens, Fig. 3, the intensity distribution isn’t uniform, it depends on wavelength, beam size and distance from the Object to the lens.

A positive lens has a well-known ability to perform two-dimensional Fourier transform ² and create in its back focal plane intensity distribution proportional to one in far field. This means in the considered case that intensity distribution in focal plane, marked in Fig. 3 as F’, is just “Airy disk” described by formula (1), evidently essentially non-uniform.

Summarizing results of this example one can see that initial uniform intensity of the Object plane was transformed to non-uniform intensity in area around the imaging lens, then to essentially non-uniform “Airy disk” distribution in back focal plane of that lens, and finally is restored to uniform intensity profile in the Image plane as result of interference of diffracted beam. The evident conclusion for practice is that it doesn’t matter how the intensity profile is transformed along the beam path, since the intensity distribution in the Image plane repeats the Object plane distribution with taking into account transverse magnification. This conclusion is valid not only for flattop beams but also for any other intensity profile. For instance, the  Shaper allow realizing also such profiles like “inverse Gauss” or super-Gauss ¹¹ and these profiles can be successfully reproduced in the Image plane as well.

Since the Image is a result of interference of light beams being emitted by the Object and diffracted according to physics of light propagation, it is necessary to take care of full light energy transmitting through an optical system and avoid any beam clipping.

Another important feature of imaging of low divergent laser beams is extended depth of field; this effect is illustrated in Fig. 4.

Fig. 4 To evaluation of depth of field in imaging layout.

The Object at the exit of the  Shaper can be implemented as a physical aperture or iris diaphragm, then the Image will have very sharp edges and repeat the shape of that aperture. If no apertures applied and output collimated beam simply propagates towards the imaging lens the Object has no a definite plane and whole space after the  Shaper, where the intensity profile is flattop, will be mapped to a corresponding space on the Image side. As discussed in paragraph 2.1 that length  s of stable profile in the Object space depends on wavelength and beam size, it can achieve values of several hundreds of mm or several meters depending on applied laser and  Shaper. Hence, the beam profile is stable over relatively long length  s’ in the Image space as well, in other words the extended depth of field (DOF) is provided. The DOF length can be approximately evaluated with taking into account that longitudinal magnification of imaging system is equal to square of the transverse magnification ⁵ .

The Fig. 4 demonstrates also that Image size within the length  s’ is variable; evidently it depends on transverse magnification for particular planes in the Object space. This effect can be used in some applications for fine tuning of size of final spot by simple shift of working plane along the optical axis. When an application requires constant size of resulting spot one can apply a telecentric (or relay) imaging system composed from two positive objective lenses with coincidence of focal points. Such a system presents a Keplerian telescope and provide collimated output beam that guarantees constant Image size over whole length  s’ of flattop profiles, it is considered in paragraph 3.3.

2.4 Design of refractive field mapping beam shapers  Shaper

Refractive beam shapers of field mapping type  Shaper were already mentioned as optical systems converting Gaussian intensity distribution of laser beams to uniform one with simultaneous providing flat wave front. Design basics of field mapping beam shapers is well-known and described in literature 1,3,4,6,7,8

, their operational principle is shown in Fig. 5, and example of beam shaping is presented in Fig. 6.

Fig. 5 Principle of the  Shaper operation.

Summarizing, the main optical features of the

 Shaper systems:

- telescopic refractive optical systems to transform laser intensity distribution from Gaussian to flattop (tophat, uniform) one;

- the transformation is realized through the phase profile manipulation in a control manner, without deterioration of the beam consistency and increasing its divergence;

- the output phase profile is maintained flat, hence output beam has low divergence;

- optical systems of beam shapers consists of two refractive optical components, variation of the distance between them is used to adjust a  Shaper in a real optical setup;

- TEM ₀₀ or multimode beams applied;

- Output beam is collimated and resulting beam profile is kept stable over large distance;

- Galilean design, no internal focusing beam;

- achromatic optical design - the re-distribution is provided for a certain spectral band.

Fig. 6 Experimental and theoretical intensity profiles:

Left – Input TEM

beam, Right - after the  Shaper

(Courtesy of Laser-Laboratorium Göttingen e.V.)

Today the refractive beam shapers  Shaper are widely used in such industrial and scientific laser technologies like

drilling holes in PCB, welding, various micromachining techniques with galvo-mirror scanning, interferometry and

holography, various SLM-based applications and many others.

3. BEAM SHAPING OPTICAL LAYOUTS

Choosing of optimum combination of a beam shaper and imaging optical system depends on features of a particular laser application. We suggest considering de-magnifying and magnifying optical layouts that are used correspondingly in industrial laser micromachining equipment and in holography and interferometry installations.

3.1 Two lens imaging system

So far we considered imaging optics implemented as a single objective lens, but the imaging system can be also composed from two lenses, and all considerations of paragraph 2 would be valid for such a composed optics. The two lens approach is presented in Fig. 7, the Object is located in front focal plane of the lens 1, and thereby this lens works as a collimator producing a collimated beam from each point of the Object. The lens 2 focuses the beams and the Image is created in its back focal plane; this lens can be, for example, an F-theta lens of a scanning optical system. The transverse magnification in this layout can be calculated as a ratio of focal lengths of those lenses:

 = - h’ / h = - f 2 ’ / f 1 ’ , (4)

Please, pay attention, the common focus F’ 1+2 of the composed system is located between the lens 2 and its back focus F’ ₂ , so the Image is again located after the common focus of the combined system.

Fig. 7 Two lens imaging layout.

Since the beams from each Object point are collimated in space between the lenses 1 and 2 (marked by dashed line) the distance between those lenses isn’t critical and can be chosen from the point of view of design requirements of a particular laser installation. Here, for instance, a galvo-mirror scanning system can be located.

3.2 Combining beam shaping and scanning optics for micromachining

The imaging optical system composed from two lenses can be successfully applied with refractive beam shapers in laser installations of micromachining technologies to create de-magnified laser spots of required intensity profile, shape and size. A widely used approach in building the laser micromachining equipment is applying scanning heads with galvo mirrors and F-theta lenses providing fast scanning of the laser spot over the working field. Evidently, it would be very fruitful to use the F-theta lens as a part of the imaging optical system intended to create image of the output of a  Shaper. Then it would be possible to continue to use usual optical components responsible for functionality of laser micromachining equipment and combine them with beam shaping optics.

The lens 2 in the layout in Fig. 7 can be implemented just as an F-theta lens, therefore to realize imaging it is

necessary to put one more lens serving as a collimator, the lens 1 in fig. 7. Example of optical layout of combined

optical system including a laser, a beam expander, a beam shaper and imaging system composed from a Collimator,

galvo mirror scanning head and F-theta lens is presented in Fig. 8. Output of the  Shaper is imaged to the working

plane coinciding with back focal plane of the F-theta lens. The imaging beams from each Object point are parallel in

space between the Collimator and the F-theta lens, therefore the distance between them isn’t critical and any

scanning head with flat mirrors can be installed in that space. Another advantageous feature of this layout is that the

final image is created in back focal plane of the F-theta lens, i.e. in the same working plane like before using a beam shaper. That plane is optimum one from the point of view of the F-theta lens design (field flatness, aberration correction), therefore providing the same conditions of the F-theta lens operation is very important for its performance and conserving necessary functionality of whole scanning system.

Fig. 8 Combined beam shaping system including  Shaper, Collimator and Scanning Head with F-theta lens.

Most often the focal length of the F-theta lens is determined by requirements of a laser technology like working distance or working field, the transverse magnification is defined as a ratio of sizes of a final spot and output of a

 Shaper, hence the focal length of the Collimator can be easy calculated with using the formula (4).

For example, when focal length of the F-theta lens is 100 mm, the  Shaper 6_6 with output beam diameter 6 mm is applied and the final spot diameter to be 60 microns the transverse magnification of the imaging system to be 1/100 ^x , hence focal length of the collimator to be 10 meters. This means also, that it is necessary to provide in a system the distance between the  Shaper 6_6 and the Collimator 10 meters! No doubts, if the Collimator is implemented as an ordinary singlet like is shown in Fig. 8 the imaging layout is difficult to realize in practice, the installations to be either bulky or require using of many mirrors to bend the beam path. There are however simple ways to overcome this obstacle of realizing the imaging system.

The Collimator design can be implemented as a so called telephoto lens – combination of positive and negative lenses, this approach is demonstrated in Fig. 9, it allows in practice to shorten the collimator length up to 10 times.

Most often it is possible to realize this design of the Collimator with using the off-the-shelf lenses. To pass a laser beam through whole imaging optical system it might be also necessary to apply field lenses installed right after the

 Shaper.

Fig. 9 Beam shaping system with compact Collimator.

Another way is applying 2-step imaging when strong de-magnifying of the beam and creating an intermediate Image

is performed on 1 ^st step with using objective lens of short focal length, then on the 2 ^nd step the final Image is created

with using compact imaging system similar to one in Fig. 8. Again, most often this multi-component optical systems

can be assembled from off-the-shelf lenses. The real practice of building the compact imaging system shows that

their designs aren’t complex and assembly and adjustment are not difficult, but they are rather unusual in laser technics. Nevertheless, this imaging approach is a powerful tool in solving various technological tasks.

Please, pay attention, parameters of the imaging layout do not depend on the wavelength, therefore the same layout can be applied with different lasers, and sure the particular components should be optimized for operation with a chosen laser.

Let’s evaluate the achievable transverse magnification in imaging systems based on widely used industrial optical components. Assume the wavelength  = 532 nm and the imaging optical system is composed from a collimator and an F-theta lens, Fig. 8. Let the focal length of the F-theta lens be f 2 ’ = 100 mm and the entrance pupil diameter D = 10 mm, optical designs of modern F-theta lenses with such specifications allow to provide diffraction limited image quality over whole working angular field. Evidently, the maximum aperture angle u’ for that F-theta lens can be found as ratio of the pupil diameter and the focal length:

u’ = D / 2f 2 ’ (5)

On the other hand the double aperture angle 2u is defined by specifications of the beam shaping optical system providing beam profile in the Object space. In case of the refractive beam shaper  Shaper it is the same like natural divergence of a laser beam: 2u = 2  . The angle of divergence  of a TEM ₀₀ laser beam is defined by the formula ⁵

 =  HM ² /(  H  ) (6) where  is wavelength, M ² is laser beam quality factor,  is a waist radius of the Gaussian beam.

Transforming the formulas (3), (4), (5) and (6) and taking the  = h, that is valid for most popular refractive beam shapers like  Shaper 6_6, one can get a common expression for an achievable transverse magnification:

 = -2  HM ² Hf 2 ’/(  H  HD) (7)

By substituting values of the considered example:  = 532 nm,  = 3 mm (for  Shaper 6_6), M ² = 1, f 2 ’ = 100 mm, D = 10 mm the calculations give the magnification down to 1/1000 ^x ! In other words, theoretically with ordinary modern off-the-shelf industrial optical components and lasers it is possible to reduce drastically the output beam of a

 Shaper and provide resulting spot sizes of several tens of microns. In practice there are used compact imaging layouts with transverse magnification down to 1/200 ^x .

Since the imaging of the  Shaper output beam is a best way to create de-magnified laser spots with uniform intensity profile and high edge steepness it is typically recommended to be applied in techniques where the required flattop laser spots are of size below 1 mm diameter, for example in microwelding, patterning on polymer layers, welding of polymers, laser marking, in some solar cell microprocessing applications like drilling holes, scribing thin-film layers and others.

3.3 Combining beam shaping and relay imaging for holography and interferometry

The holographic and interferometric applications as well as other techniques based on spatial light modulators get

essential benefits from homogenizing a laser beam, therefore beam shaping optics becomes more and more popular

in that field. A principle requirement of these techniques is conserving the phase front of a laser beam, so they

require simultaneously flat wave front and flattop (uniform) intensity profile. This condition is exactly fulfilled in

the considered in paragraph 2.4 refractive field mapping beam shapers  Shaper. Most often these devices are

implemented as telescopic systems with two optical components, it is presumed the wave fronts at input and output

are flat, the transformation of intensity profile from Gaussian to uniform one is realized in a controlled manner by

accurate introducing of wave aberration by the first component and further its compensation by the second one ^7,9,11 .

Thus, the resulting collimated output beam has a uniform intensity and flat wave front, it is characterized by low

divergence – almost the same like one of the input beam. In other words, the  Shaper transforms the beam profile

without deterioration of the beam consistency and without increasing its divergence.

The holographic and interferometric applications often require expansion of a beam after a  Shaper, for example, to illuminate a SLM or a mask with a collimated laser beam of uniform intensity which sizes are larger than output beam diameter of a standard  Shaper. This is an actual option in techniques like mastering of security holograms, Denisyuk holography, field illumination in Confocal Microscopes, interferometric techniques of recording the Volume Bragg Gratings and periodic structuring, holographic data storage and many others.

Obviously this expansion can be realized with using a telescopic beam expander. Popular solutions are beam expanders of Galilean type built from negative and positive lenses that provides system compactness and avoidance of internal focusing, these beam expanders are widely used in industrial applications. However, the Galilean expanders do not overcome the problem of intensity distribution transformation described in paragraph 2.1 and do not create a real Image to restore the flattop intensity distribution like it is realized by imaging optical systems, paragraph 2.3.

Therefore, the more advisable solutions for holography and interferometry are beam expanders of Keplerian type built from two positive lenses. The unique feature of Keplerian telescopes is that on the one hand they have zero optical power, so the input and output beams are collimated, on the other hand they operate as imaging optics and create real Images, thus realizing so called telecentric or relay imaging optical systems ⁵ . Example of two lens imaging system composed as a Keplerian telescope is shown in Fig. 10, this layout can be considered as one of implementations of the optical system in Fig. 7.

Fig. 10 Telecentric layout (relay imaging).

When applying with a  Shaper the Object plane, front focal plane of the 1 ^st lens, should be output of the  Shaper;

the Image is created in back focal plane of the 2 ^nd lens where both the flattop intensity profile and flat phase front are restored and thus optimum conditions for a holographic or an interferometric effect are realized. Magnification of this telecentric system is a ratio between focal lengths of the lenses 2 and 1. In Fig. 10 it is shown a case of de- magnifying the beam size, but, no doubts, by choosing appropriate optical components the system can be implemented to magnify a beam.

There is one useful effect accompanying the magnifying of a homogenized beam – the extended DOF leads to

creation of flattop intensity profile not only in area of the Image but practically in whole Image space after the 2 ^nd

lens. As discussed in paragraph 2.3 the longitudinal magnification of an imaging system is proportional to square of

the transverse magnification. The transverse magnification of the considered telecentric system is constant and

doesn’t depend on position of an Object, hence the DOF in image space is proportional to square of transverse

magnification as well and can reach large values. Practically a resulting intensity profile (most often flattop) is

restored right after the second component of the telecentric system. An important conclusion for practice of using

the beam shaping optics is that when a Keplerian beam expander is applied the beam of uniform intensity and flat

wave front is created almost right after that expander, hence in a real holographic or interferometric installation a

work piece or other optical components can be installed close to the expander, this makes an installation more

compact and easier to use.

The telecentric optical system has also some capabilities for spatial filtering of a beam that is typically required in holographic and interferometric techniques. As a general rule it is recommended to realize spatial filtering before a

 Shaper and do not do this after it in order to conserve the conditions for interference of diffracted beams. But in some cases in holography it is strongly advisable to carry out spatial filtering after a  Shaper to eliminate high frequency modulation of beam intensity happening because of dust or other reasons, and here t is possible to use one trick. Majority of holographic and interferometric technologies apply TEM 00 lasers featured with low divergence, hence in the plane of common focuses, F’ 1 = F 2 in Fig. 10, the intensity distribution is described by just “Airy disk”

function (1) (paragraph 2.1, 2.3) and this plane can be used to put a pinhole for the spatial filtering. Using an ordinary pinhole transmitting only the central spot has no sense, since this would destroy the beam structure and lead to close to Gaussian intensity profile that is useless for the considered applications. It is possible, however, to apply a pinhole of larger diameter that transmits not only the central spot but several diffraction rings carrying all together majority of beam energy. For example, a pinhole, which diameter is 3.5 times larger than one of a typical pinhole for classical spatial filtering, transmits the central spot (84% of energy) and 3 outer rings (correspondingly 7%, 2.7%

and 1.6% of energy), totally more than 95% of energy. Evidently, when putting such a pinhole and further beam collimation with the 2 ^nd lens the flattop intensity profile would be approximately restored, at the same time that pinhole would filter the high frequency modulation components. Sure, the diameter of such a pinhole is a trade-off between the high frequency modulation to be removed and diffraction effects appearing due to beam clipping.

3.4 Creating of square laser spots

Till now we were discussing the round laser beam, but the technique of imaging of the flattop beam can be applied to creating resulting laser spots of other shapes, for example a square one that is very important in some laser applications like patterning of thin-film solar cells. The task of creating a square spot can be easily solved by putting after the  Shaper a square aperture serving as an Object for further the imaging system. Then in the Image plane there will be reproduced not only the intensity profile but also the shape of the laser spot. Example of creating a flattop square laser spot is shown in Fig. 11.

Fig. 11 Profiles in example of creating square spots with using  Shaper and imaging system according to Fig.8 or Fig. 9:

On left – input of  Shaper, Centre - output of  Shaper, On right – final square spot 50 x 50 m

. The TEM 00 laser beam at the entrance of the  Shaper 6_6 has circular shape and Gaussian intensity distribution, Fig. 11, on left; therefore the round collimated beam after the  Shaper 6_6 has uniform intensity profile, Fig. 11, centre. The square aperture to be installed at the  Shaper exit is shown in Fig. 11, centre by a dashed line. Imaging of that square aperture with using the Collimator and F-theta lens, see Fig. 8, gives a resulting 50 x 50 m ² spot of square shape and flattop intensity profile, Fig. 11, on right. Please, pay attention to high steepness of the spot edge.

The high frequency intensity modulation in final spot comes from the modulation of the laser source. Operational

principle of field mapping refractive beam shapers doesn’t presume suppressing of that high frequency modulation,

but when necessary it can be removed by using a spatial filtering before the  Shaper.

5. CONCLUSIONS

Imaging techniques are powerful tools to extend capabilities of beam shaping optics, combination of these systems allow realizing resulting laser spots with size, shape and intensity profile required by a particular laser technology.

This approach demonstrate essential improvements of such laser micromachining technologies like drilling holes in PCB, microwelding, thin-film patterning, various techniques based on galvo-mirror scanning. It is also fruitful in various holographic, interferometric and SLM-based applications like mastering of security holograms, Denisyuk holography, field illumination in Confocal Microscopes, techniques of recording the Volume Bragg Gratings and periodic structuring, holographic data storage and many others. Depending on the features of a particular application: spot size and shape, edge steepness, working distance, required intensity profile, etc., one can build a solution on the base of available types of refractive field mapping beam shapers and off-the-shelf optical components.

6. REFERENCES

[1] Dickey, F.M., Holswade, S.C., [Laser Beam Shaping: Theory and Techniques], Marcel Dekker, New York, (2000).

[2] Goodman, J.W. [Introduction to Fourier Optics], McGraw-Hill, New York, (1996).

[3] Hoffnagle, J. A., Jefferson, C. M., “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam” Appl. Opt., vol. 39, 5488-5499 (2000).

[4] Kreuzer, J., “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface” US Patent 3476463, (1969).

[5] Smith, W.J. [Modern Optical Engineering], McGraw-Hill, New York, (2000).

[6] Laskin, A. “Achromatic refractive beam shaping optics for broad spectrum laser applications” Proc. SPIE 7430, Paper 743003 (2009).

[7] Laskin, A., “Achromatic Optical System for Beam Shaping” US Patent 8023206, (2011).

[8] Laskin A., Laskin V. “Variable beam shaping with using the same field mapping refractive beam shaper” Proc.

SPIE 8236, Paper 82360D (2012).

6. ACKNOWLEDGEMENTS

The authors are grateful to users of  Shaper in Laser-Laboratorium Göttingen e.V., for their active and patient work

with optics discussed in this paper and kind permission to publish some results achieved during their experiments.