Thermal history due to laser heating of solid surfaces
Using the finite integral transformation along the spatial Cartesian coordinates, an analytical expression for calculating the temperature distribution T (x, y, z) due to laser pulses in a solid located in the half-space z<0 is obtained. The numerical calculations show that a uniform warming of t...
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Інститут хімії поверхні ім. О.О. Чуйка НАН України
2011
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irk-123456789-821692015-05-27T03:02:06Z Thermal history due to laser heating of solid surfaces Semchuk, O.Yu. Lerman, L.B. Willander, M. Nur, O. Теория химического строения и реакционной способности поверхности. Моделирование процессов на поверхности Using the finite integral transformation along the spatial Cartesian coordinates, an analytical expression for calculating the temperature distribution T (x, y, z) due to laser pulses in a solid located in the half-space z<0 is obtained. The numerical calculations show that a uniform warming of the body surface takes place only during a part of the pulse duration. Deep inside the solid, the maximum temperature value compared to the surface takes place with a time delay. This time delay depends on the heat wave propagation velocity. Along with heat penetration into the solid, a maximum temperature zone degradation process takes place. Cooling velocity in the upper layers appears to be higher than that in the deeper layers. However, the cooling period in deeper layers is less than that in upper layers. The results obtained are qualitatively consistent with published experimental data. За допомогою кінцевого інтегрального перетворення по декартових координатах в площині поверхні отримано аналітичний вираз для розподілу температури Т(x,y,z) в зразку, що займає напівпростір z<0. Проведені чисельні розрахунки показали, що в більш глибоких шарах значення температури досягається пізніше, ніж на поверхні, оскільки нижніх шарів теплова хвиля досягає пізніше. Швидкість охолодження нижніх шарів менша, ніж верхніх. Крім того, чисельні розрахунки показали, що максимальна температура на заданій глибині слабко залежить від форми розподілу інтенсивності в лазерному пучку. Отримані результати якісно співпадають з експериментальними даними. С помощью конечного интегрального преобразования по декартовым координатам в плоскости поверхности получено аналитическое выражение для распределения температуры Т(x,y,z) в образце, занимающем полупространство z<0. Проведенные численные расчеты показали, что в более глубоких слоях максимальное значение температуры достигается позже, чем на поверхности, поскольку в нижние слои тепловая волна доходит позже. Скорость охлаждения верхних слоев оказывается больше, чем нижних, однако время охлаждения нижних слоев меньше, чем верхних. Кроме того, численные расчеты показали, что максимальная температура на заданной глубине слабо зависит от формы распределения интенсивности в лазерном пучке. Полученные результаты качественно совпадают с экспериментальными данными. 2011 Article Thermal history due to laser heating of solid surfaces / O.Yu. Semchuk, L.B. Lerman, M. Willander, O. Nur // Поверхность. — 2011. — Вип. 3 (18). — С. 7-12. — Бібліогр.: 21 назв. — англ. XXXX-0106 http://dspace.nbuv.gov.ua/handle/123456789/82169 535:537:539:546 en Поверхность Інститут хімії поверхні ім. О.О. Чуйка НАН України |
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Теория химического строения и реакционной способности поверхности. Моделирование процессов на поверхности Теория химического строения и реакционной способности поверхности. Моделирование процессов на поверхности |
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Теория химического строения и реакционной способности поверхности. Моделирование процессов на поверхности Теория химического строения и реакционной способности поверхности. Моделирование процессов на поверхности Semchuk, O.Yu. Lerman, L.B. Willander, M. Nur, O. Thermal history due to laser heating of solid surfaces Поверхность |
| description |
Using the finite integral transformation along the spatial Cartesian coordinates, an analytical expression for calculating the temperature distribution T (x, y, z) due to laser pulses in a solid located in the half-space z<0 is obtained. The numerical calculations show that a uniform warming of the body surface takes place only during a part of the pulse duration. Deep inside the solid, the maximum temperature value compared to the surface takes place with a time delay. This time delay depends on the heat wave propagation velocity. Along with heat penetration into the solid, a maximum temperature zone degradation process takes place. Cooling velocity in the upper layers appears to be higher than that in the deeper layers. However, the cooling period in deeper layers is less than that in upper layers. The results obtained are qualitatively consistent with published experimental data. |
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Article |
| author |
Semchuk, O.Yu. Lerman, L.B. Willander, M. Nur, O. |
| author_facet |
Semchuk, O.Yu. Lerman, L.B. Willander, M. Nur, O. |
| author_sort |
Semchuk, O.Yu. |
| title |
Thermal history due to laser heating of solid surfaces |
| title_short |
Thermal history due to laser heating of solid surfaces |
| title_full |
Thermal history due to laser heating of solid surfaces |
| title_fullStr |
Thermal history due to laser heating of solid surfaces |
| title_full_unstemmed |
Thermal history due to laser heating of solid surfaces |
| title_sort |
thermal history due to laser heating of solid surfaces |
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Інститут хімії поверхні ім. О.О. Чуйка НАН України |
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2011 |
| topic_facet |
Теория химического строения и реакционной способности поверхности. Моделирование процессов на поверхности |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/82169 |
| citation_txt |
Thermal history due to laser heating of solid surfaces / O.Yu. Semchuk, L.B. Lerman, M. Willander, O. Nur // Поверхность. — 2011. — Вип. 3 (18). — С. 7-12. — Бібліогр.: 21 назв. — англ. |
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2025-07-06T08:28:58Z |
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Поверхность. 2011. Вып. 3(18). С. 7–12 7
ТЕОРИЯ ХИМИЧЕСКОГО СТРОЕНИЯ И РЕАКЦИОННОЙ
СПОСОБНОСТИ ПОВЕРХНОСТИ.
МОДЕЛИРОВАНИЕ ПРОЦЕССОВ НА ПОВЕРХНОСТИ
________________________________________________________________________________________________________________
УДК 535:537:539:546
THERMAL HISTORY DUE TO LASER HEATING
OF SOLID SURFACES
O.Yu. Semchuk1, L.B. Lerman1, M. Willander2, and O. Nur2
1Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine
17 General Naumov Str., Kyiv, 03164, Ukraine, aleksandr1950@meta.ua
2Department of Science and Technology, Campus Norrköping, Linköping University
SE 601 74 Norrköping, Sweden
Using the finite integral transformation along the spatial Cartesian coordinates, an analytical
expression for calculating the temperature distribution T (x, y, z) due to laser pulses in a solid located
in the half-space z<0 is obtained. The numerical calculations show that a uniform warming of the body
surface takes place only during a part of the pulse duration. Deep inside the solid, the maximum
temperature value compared to the surface takes place with a time delay. This time delay depends on
the heat wave propagation velocity. Along with heat penetration into the solid, a maximum temperature
zone degradation process takes place. Cooling velocity in the upper layers appears to be higher than
that in the deeper layers. However, the cooling period in deeper layers is less than that in upper layers.
The results obtained are qualitatively consistent with published experimental data.
Introduction
Recently, research for any sort of solid surface structures created by means of laser
radiation and/or laser beams interference pattern has essentially been of interest [1-10]. Heating
due to laser ablation can be additionally used for the formation of nanosized particles in solid
electrolytes [11]. Pulse laser ablation of solid targets in the gas phase has been widely used for
the preparation of various nanostructured materials such as nanoparticles, nanotubes and nano-
composites [12–14]. The study of laser-induced heating and melting are of great importance for
achieving high quality materials processing when using lasers [15–19]. However, until recently
there is a question on the features of the spatial and temporal distribution of temperature due to
laser heating of solid surfaces.
In this paper, the distribution of the temperature Т (x, y, z) on a solid surface occupying
a semi-space of z<0 is studied. A temperature on the surface of the solid is due to streams of
energy taken in from the surface due to heat conductivity. The numerical calculations showed
that in the deeper layers of the solid the maximum value of the temperature is reached with a
delay compared to the surface of the solid. This is due to the heat-wave delay. A rate of cooling
of the top layers of the solid appears to be faster than for the deeper layers. In addition,
numerical calculations showed that the maximal temperature at a certain depth depends slightly
on the form of intensity distribution of the laser beam used.
Statement of the problem
Let us consider the process of heating a solid surface by two-dimensional laser beam
interference pattern represented in Fig. 1. It is assumed that the laser beams are identical, fall
normally to the surface and the interaction between the beams is negligible. It is also assumed
that the thermo-physical characteristics of the medium are independent on the temperature or
8
spatial coordinates. In this case, the heat diffusion equation describing the distribution of
temperature T in the half-space 0 z< < ∞ can be written as:
( )
2 2 2
2 2 2 , , , ,
p
T T T T I x y z t
t cx y z
⎛ ⎞∂ ∂ ∂ ∂
= + + +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠
αχ
ρ
(1)
where t is the time, , ,x y z are the Cartesian coordinates, / pc=χ κ ρ is the thermal
diffusivity, κ is the heat conductivity, pc is the heat capacity, ρ is the density, α is the
absorption coefficient, and I is the power density of the laser beam.
Fig. 1. Two-dimensional periodic structure formed by laser beams.
We assume that a laser beam is represented by the Gaussian intensity distribution:
{ }2 2 2
0( , , , ) ( , ) (1 ) exp ( ) / ( )zI x y z t H x y I R e x y r f tα−= − − + , (2)
where 0I is the maximum intensity of laser beam, R is the reflection coefficient, r is the
radius of one laser beam, 1),( =yxH if 2 2 2x y r+ ≤ , and ( , ) 0H x y = otherwise, and ( )tf is a
function which describes the distribution of a laser impulse as time function.
The required distribution of temperatures is subjected to the following initial and
boundary conditions:
( ) 0
0
0
, , ,0 ,
0, 0, 0, lim ,
→∞=± ==±
=
∂ ∂ ∂
= = = =
∂ ∂ ∂ zx a zy b
T x y z T
T T T T T
x y z
(3)
where 2 ,2a b are the dimensions of a rectangular pulse period, 0T is the initial value of the
temperature.
The solution of the problem can be constructed using Green functions as it was done by
some authors [19, 20]. However, the problem of calculating infinite integrals is not a trivial
one, so in the present paper other approach is offered. It may be noticed that the linear equation
(1) contains a constant coefficient, and variables that can be divided in the function of the
source (2). Under such circumstances, for solving equation (1), infinite integral transformation
on coordinates ,x y and Fourier transformation on coordinate z can be used. Consecutive
performance of these transformations (independent of execution sequence) leads to system of
9
non-uniform differential equations of the first order over time. The solution of these equations
is then straightforward. Using reverse transformation, an analytical solution in the form of
converging series and integrals can be then obtained.
Analysis of the general solution and numerical results
Two-dimensional periodic structures are investigated with active sources within the
limits of a circle with radius r , and with Gaussian intensity distribution in space. The cases
analyzed when the time function ( )f t is represented by the Dirac function ( )tδ or Heaviside
function ( )H t . The square cell ( )b a= is assumed. Dimensionless time is used 2/t t a′= χ ( t′
is natural time), also dimensionless temperature * /T T= θ , where 2
0 /a Jθ = α χ , and
dimensionless space coordinates / , / , /x x a y y a z z a′ ′ ′= = = , where , ,x y z′ ′ ′ are the
linear ones.
Some numerical calculation results are shown in Figs. 2 and 3. The data make it
possible to get an idea about the temperature distribution in the layers when the time of the
laser activity is long enough (stationary solution) depending on the distance z of the layer
from the surface of the solid and on the beam radius r . Fig. 2 shows the distribution of a
stationary temperature in the location of a heating spot for different beam radii r and some z
value.
a b c
Fig. 2. The temperature ( *T ) in the middle section of a solid (y = 0) versus the layers distance
(z) from its surface and beam radius r for: a – z = 1; b – z = 5; c – z =10: 1 – r = 1.0;
2 – r = 0.8; 3 – r = 0.4; 4 – r = 0.4, 5 – r = 0.2.
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0 2 4 6 8 10 12 14 16 18 20
*T
z
Fig. 3. Stationary temperature *T versus the distance z from the solid surface.
10
The calculations were realized using a formula given by:
2
0
2( , , ) (1 ) α= − ×
π χstT x y z I R
ab
( )2 2
2 2 22 20 0
exp ( , )exp( ) ,
∞ ∞
= =
⎧ ⎫⎡ ⎤− λ +μ⎪ ⎪⎢ ⎥−α
× ε −⎨ ⎬⎢ ⎥α λ +μ −αλ +μ⎪ ⎪⎢ ⎥
⎣ ⎦⎩ ⎭
∑ ∑
n m
nm nm
nm
n m n mn m
z G K x yz (4)
where
22 2 2
2 2
0 0
4 cos cos ,
yxr r x
r rnm n mG e xdx e ydy
− −−
= λ μ∫ ∫ ( ) ( ) ( ), cos cos ,= λ μmn m nK x y x y
/ , /m nm a n bλ = π μ = π , , 0,1, ,= ∞…n m , 2a and 2b − the dimensions of an elementary
rectangular cell with periodical structure on the solid surface (Fig. 1), 1=nmε if 0, 0n m≠ ≠ ;
1/ 2nmε = if 0, or 0n m= = ; 1/ 4nmε = if 0, 0n m= = .
Every function ( ),mnK x y meets the boundary conditions (3). It is held down as much
as 49 members in the two-fold series. An attenuation coefficient in the Gaussian beam of about
0.15 1/m is accepted. All the calculations are realized in dimensionless coordinates.
As would be expected, it follows from the results presented that while retreating from
the solid surface the temperature in the layers decreases because of diminishing the beam
radiation intensity. Along with it, a temperature distribution with respect to the coordinates
retains its form (conformity). The temperature value depends substantially on the beam radius,
and this dependence is not a linear one. Herewith, for instance, at z = 1, that is near the surface,
the temperature *T in the beam centre changes from 0.371 to 0.0556 for the biggest ( 1 0= .r )
and the smallest ( 0 2= .r ) beam radii, respectively.
Graphic representation of a heat penetration in the solid is illustrated by curve of the
type shown in Fig. 3. It must be emphasized that the dependence differs from purely
exponential character in the beam. The results represented give evidence of high effectiveness
of the approach elaborated. With its help, the depth of heating can be evaluated in connection
to the laser radiation source parameters.
Conclusion
The results presented show a high effectiveness of the elaborated approach. With its
use, the depth of heating can be evaluated in connection to the laser radiation source The results
obtained are qualitatively consistent with the published experimental data, e.g. those in [21].
References
1. Aktag A., Michalski S., Yue L., Roger D.K., Liou Sy-H. Formation of an anisotropy
lattice in Co/Pt multilayers by direct laser interference patterning // J. Appl. Phys. –
2006. – V. 99, N 7. – P. 093901.
2. Semchuk O.Yu., Semioshko V.N., Grechko L.G., Willander M., Karlsteen M. Laser
ablation lithography on thermoelectric semiconductor // Appl. Surf. Sci. – 2006. –
V. 252. – P. 4759–4762.
3. John F.R. Industrial Applications of Lasers. – Academic Press, 1997. – 300 p.
4. Lasagni A., Mucklich F. Study of the multilayer metallic films topography modified by
laser interference irradiation // Appl. Surf. Sci. – 2005. – V. 240. – P. 214–221.
11
5. Daniel C., Balk T.J., Wubben T., Muklich F. Bio-mimetic scaling of mechanical
behavior of thin films, coatings, and surfaces by laser interference metallurgy // Adv.
Eng. Materials. – 2005. – V. 7, N 9. – P. 823–826.
6. Lasagni A., Holzapfed C., Muklich F. Periodic pattern formation of intermetallic phases
with long range order by laser interference metallurgy // Adv. Eng. Materials. – 2005. –
V.7, N 5. – P. 487–492.
7. Muklich F., Lasagni A., Daniel C. Laser interference metallurgy – periodic surface
pattering and formation of intermetalics // Intermetalics. – 2005. – V. 13. – P. 437–442.
8. Lasagni A., Holpzapfer C., Weirich T., Muklish F. Laser interference metallurgy: a new
method for periodic surface microstructure design on multilayered metallic thin films //
Appl. Surf. Sci. – 2007. – V. 253, N 19. – P. 8070–8074.
9. Wochnowski C., Cheng Y., Meteva K., Sugioka K., Midorikawa K., Metev S.
Femtosecond laser induced formation of grating structures in planar polymer substrates //
J. Opt. A: Pure Appl. Opt. – 2005. – V. 7, N 9. – P. 493–500.
10. Liy Y., Barther J., Zhong J.X. Interference pattern from an array of coherent laser
beams // J. Vac. Sci. Technol. – 2002. – V. B 20 , N 6. – P.2602 – 2605.
11. Mafune F., Kohno J., Takeda Y., Kondow T., Sawabe H. Structure and stability of silver
nanoparticles in aqueous solution produced by laser ablation // J. Phys. Chem. B. – 2000.
– V. 104. – P. 8333–8337.
12. Chem Y.H., Yet C.S. A new approach for the formation of alloy nanoparticles: laser
synthesis of gold-silver alloy from gold-silver colloidal mixtures // Chem. Commun. –
2001. – V 4, N 1. – P. 371–372.
13. Liang C.H., Shimizu Y., Sasak T., Koshizaki N. Photoluminescence of ZnO
nanoparticles prepared by laser ablation in different surfactant solutions // J. Phys. Chem
B. – 2005. – V. 109, N 1. – P. 120–124.
14. El-Adavi M.K., El-Shehawey E.F. Heating a slab induced by a time-dependent laser
irradiance. An exact solution // J. Appl. Phys. – 1986. – V. 60, N 7. – P. 2250–2255.
15. Hassan A.F., El-Nicklawy M.M., El-Adavi M.K. Heating effects induced by pulsed laser
in semi-infinite target in view of the theory of linear systems // Opt. Laser. Tech. –
1996. – V. 28, N 5. – P. 337–343.
16. Rantala T.T., Levoska J.A. A numerical simulation method for the laser-induced
temperature distribution // J. Appl. Phys. – 1989. – V. 65, N 12. – P. 4475–4479.
17. Amon E., Zving V., Soldan A. Metal drilling with CO2 laser beam // J. Appl. Phys. –
1989. – V. 65, N 12. – P. 4995–5002.
18. Rar A., Mazumber J. Two-dimensional model for material damage due to melting and
vaporization during laser irradiation // J. Appl. Phys. – 1990. – V. 68. – P. 3884–3891.
19. Conde J.C., Lusquinos F., Gonzalez P. Temperature distribution an a material heated by
laser radiation: modeling and application // Vacuum. – 2002. – V. 64. – P. 259–366.
20. Carslaw H.S., Jaeger J.C. Conduction of heat in solids. – Oxford: Clarendon Press, 1959.
– 750 p.
21. Kawasumi H. Metal surface hardening by CO2 laser // Technocrat. – 1978. – V. 11,
N 6. – P. 11–20.
12
ТЕПЛОВА ІСТОРІЯ ПРИ ЛАЗЕРНОМУ НАГРІВІ
ПОВЕРХНІ ТВЕРДОГО ТІЛА
О.Ю. Семчук1, Л.Б. Лерман1, М. Вілландер2, О. Нур2
1Інститут хімії поверхні ім. О.О. Чуйка Національної академії наук України
вул. Генерала Наумова, 17, Київ, 03164, Україна, aleksandr1950@meta.ua
2Відділення науки тa технології Лінчопинського університету
SE 601704, Норчопінг, Швеція
За допомогою кінцевого інтегрального перетворення по декартових координатах в
площині поверхні отримано аналітичний вираз для розподілу температури Т(x,y,z) в зразку, що
займає напівпростір z<0. Проведені чисельні розрахунки показали, що в більш глибоких шарах
значення температури досягається пізніше, ніж на поверхні, оскільки нижніх шарів теплова
хвиля досягає пізніше. Швидкість охолодження нижніх шарів менша, ніж верхніх. Крім того,
чисельні розрахунки показали, що максимальна температура на заданій глибині слабко
залежить від форми розподілу інтенсивності в лазерному пучку. Отримані результати якісно
співпадають з експериментальними даними.
ТЕПЛОВАЯ ИСТОРИЯ ПРИ ЛАЗЕРНОМ НАГРЕВЕ
ПОВЕРХНОСТИ ТВЕРДОГО ТЕЛА
А.Ю. Семчук1, Л.Б. Лерман1, М. Вилландер2, О. Нур2
1Институт химии поверхности им. А.А. Чуйко Национальной академии наук Украины
ул. Генерала Наумова, 17, Киев, 03164, Украина, aleksandr1950@meta.ua
2Отделение науки и технологии Линчопинского университета
SE 601704, Норчопинг, Швеция
С помощью конечного интегрального преобразования по декартовым координатам в
плоскости поверхности получено аналитическое выражение для распределения температуры
Т(x,y,z) в образце, занимающем полупространство z<0. Проведенные численные расчеты
показали, что в более глубоких слоях максимальное значение температуры достигается позже,
чем на поверхности, поскольку в нижние слои тепловая волна доходит позже. Скорость
охлаждения верхних слоев оказывается больше, чем нижних, однако время охлаждения нижних
слоев меньше, чем верхних. Кроме того, численные расчеты показали, что максимальная
температура на заданной глубине слабо зависит от формы распределения интенсивности в
лазерном пучке. Полученные результаты качественно совпадают с экспериментальными
данными.
<<
/ASCII85EncodePages false
/AllowTransparency false
/AutoPositionEPSFiles true
/AutoRotatePages /All
/Binding /Left
/CalGrayProfile (Dot Gain 20%)
/CalRGBProfile (sRGB IEC61966-2.1)
/CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2)
/sRGBProfile (sRGB IEC61966-2.1)
/CannotEmbedFontPolicy /Warning
/CompatibilityLevel 1.4
/CompressObjects /Tags
/CompressPages true
/ConvertImagesToIndexed true
/PassThroughJPEGImages true
/CreateJDFFile false
/CreateJobTicket false
/DefaultRenderingIntent /Default
/DetectBlends true
/DetectCurves 0.0000
/ColorConversionStrategy /LeaveColorUnchanged
/DoThumbnails false
/EmbedAllFonts true
/EmbedOpenType false
/ParseICCProfilesInComments true
/EmbedJobOptions true
/DSCReportingLevel 0
/EmitDSCWarnings false
/EndPage -1
/ImageMemory 1048576
/LockDistillerParams false
/MaxSubsetPct 100
/Optimize true
/OPM 1
/ParseDSCComments true
/ParseDSCCommentsForDocInfo true
/PreserveCopyPage true
/PreserveDICMYKValues true
/PreserveEPSInfo true
/PreserveFlatness true
/PreserveHalftoneInfo false
/PreserveOPIComments false
/PreserveOverprintSettings true
/StartPage 1
/SubsetFonts true
/TransferFunctionInfo /Apply
/UCRandBGInfo /Preserve
/UsePrologue false
/ColorSettingsFile ()
/AlwaysEmbed [ true
]
/NeverEmbed [ true
]
/AntiAliasColorImages false
/CropColorImages true
/ColorImageMinResolution 300
/ColorImageMinResolutionPolicy /OK
/DownsampleColorImages true
/ColorImageDownsampleType /Bicubic
/ColorImageResolution 300
/ColorImageDepth -1
/ColorImageMinDownsampleDepth 1
/ColorImageDownsampleThreshold 1.50000
/EncodeColorImages true
/ColorImageFilter /DCTEncode
/AutoFilterColorImages true
/ColorImageAutoFilterStrategy /JPEG
/ColorACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/ColorImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000ColorACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000ColorImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasGrayImages false
/CropGrayImages true
/GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK
/DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic
/GrayImageResolution 300
/GrayImageDepth -1
/GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000
/EncodeGrayImages true
/GrayImageFilter /DCTEncode
/AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG
/GrayACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/GrayImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000GrayACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000GrayImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasMonoImages false
/CropMonoImages true
/MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK
/DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic
/MonoImageResolution 1200
/MonoImageDepth -1
/MonoImageDownsampleThreshold 1.50000
/EncodeMonoImages true
/MonoImageFilter /CCITTFaxEncode
/MonoImageDict <<
/K -1
>>
/AllowPSXObjects false
/CheckCompliance [
/None
]
/PDFX1aCheck false
/PDFX3Check false
/PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true
/PDFXTrimBoxToMediaBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXOutputIntentProfile ()
/PDFXOutputConditionIdentifier ()
/PDFXOutputCondition ()
/PDFXRegistryName ()
/PDFXTrapped /False
/Description <<
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/DEU <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>
/ESP <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>
/FRA <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>
/ITA <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>
/JPN <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>
/KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020b370c2a4d06cd0d10020d504b9b0d1300020bc0f0020ad50c815ae30c5d0c11c0020ace0d488c9c8b85c0020c778c1c4d560002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken voor kwaliteitsafdrukken op desktopprinters en proofers. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
/NOR <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>
/PTB <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>
/SUO <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>
/SVE <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>
/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /NoConversion
/DestinationProfileName ()
/DestinationProfileSelector /NA
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure true
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles true
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /NA
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|