Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods
The diffraction losses of laser mirrors were determined by using specially designed spectrometer of spatial frequencies. Reflection surface (70 mm diameter) was made by diamond microgrinding, but instead of an ideal plane, the circular phase grating was formed. The Fourier-optics was applied to m...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2009
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| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Цитувати: | Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods / V.S. Staschuk, G.L. Kononchuk, L.V. Poperenko, V.V. Stukalenko, Y.V. Filipov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 280-283. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1188752017-06-01T03:02:49Z Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods Staschuk, V.S. Kononchuk, G.L. Poperenko, L.V. Stukalenko, V.V. Filipov, Y.V. The diffraction losses of laser mirrors were determined by using specially designed spectrometer of spatial frequencies. Reflection surface (70 mm diameter) was made by diamond microgrinding, but instead of an ideal plane, the circular phase grating was formed. The Fourier-optics was applied to measure a real shape of flat laser metal mirrors. We analysed the diffraction pattern of light reflected from metal mirror in the Fraunhofer zone and determined periodic deviation of a surface from an ideal plane and its parameter – spatial frequency. 2009 Article Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods / V.S. Staschuk, G.L. Kononchuk, L.V. Poperenko, V.V. Stukalenko, Y.V. Filipov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 280-283. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 42.15.F, 42.25.F http://dspace.nbuv.gov.ua/handle/123456789/118875 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
The diffraction losses of laser mirrors were determined by using specially
designed spectrometer of spatial frequencies. Reflection surface (70 mm diameter) was
made by diamond microgrinding, but instead of an ideal plane, the circular phase grating
was formed. The Fourier-optics was applied to measure a real shape of flat laser metal
mirrors. We analysed the diffraction pattern of light reflected from metal mirror in the
Fraunhofer zone and determined periodic deviation of a surface from an ideal plane and
its parameter – spatial frequency. |
| format |
Article |
| author |
Staschuk, V.S. Kononchuk, G.L. Poperenko, L.V. Stukalenko, V.V. Filipov, Y.V. |
| spellingShingle |
Staschuk, V.S. Kononchuk, G.L. Poperenko, L.V. Stukalenko, V.V. Filipov, Y.V. Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Staschuk, V.S. Kononchuk, G.L. Poperenko, L.V. Stukalenko, V.V. Filipov, Y.V. |
| author_sort |
Staschuk, V.S. |
| title |
Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods |
| title_short |
Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods |
| title_full |
Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods |
| title_fullStr |
Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods |
| title_full_unstemmed |
Energy loss researches of diamond microgrinded laser mirrors by Fourier optics methods |
| title_sort |
energy loss researches of diamond microgrinded laser mirrors by fourier optics methods |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118875 |
| citation_txt |
Energy loss researches of diamond microgrinded laser mirrors
by Fourier optics methods / V.S. Staschuk, G.L. Kononchuk, L.V. Poperenko, V.V. Stukalenko, Y.V. Filipov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 3. — С. 280-283. — Бібліогр.: 10 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T14:49:15Z |
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2025-07-08T14:49:15Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 280-283.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
280
PACS 42.15.F, 42.25.F
Energy loss researches of diamond microgrinded laser mirrors
by Fourier optics methods
V.S. Staschuk, G.L. Kononchuk, L.V. Poperenko, V.V. Stukalenko, Y.V. Filipov
Taras Shevchenko Kyiv National University, Department of Physics,
6, prospect Glushkova, 03127 Kyiv, Ukraine;
E-mail: stu@univ.kiev.ua; filipov@univ.kiev.ua
Abstract. The diffraction losses of laser mirrors were determined by using specially
designed spectrometer of spatial frequencies. Reflection surface (70 mm diameter) was
made by diamond microgrinding, but instead of an ideal plane, the circular phase grating
was formed. The Fourier-optics was applied to measure a real shape of flat laser metal
mirrors. We analysed the diffraction pattern of light reflected from metal mirror in the
Fraunhofer zone and determined periodic deviation of a surface from an ideal plane and
its parameter – spatial frequency.
Keywords: metal mirror for laser, energy losses, Fourier-optics method, circular phase
grating, spatial frequency.
Manuscript received 11.11.08; revised manuscript received: 28.04.09; accepted for
publication 14.05.09; published online 29.05.09.
Development of a new technology to produce high
quality metal mirrors with the reflection coefficient
value higher than R 0.99 is a serious problem in a
powerful laser design [1, 2]. Even small diffraction
losses have the same negative influence as transmission
losses for a laser resonator with these mirrors. The
energy losses can be caused by deformation of the
reflection surface structure during metal shaping. That
deformation influences both on power and spatial
characteristics of radiation [3, 4]. The most important
characteristic of high quality laser mirrors is the
minimum of energy losses in reflection, including the
diffraction ones, too.
For diagnostics of a metal mirror surfaces, a few
optical methods can be used. One of them is the shadow
method. It can be specified by simplicity of acquired
visual data about mirror surface. But quantitative data
about surface shape cannot be acquired from shadow
method results. Another one is the Hartmann method
that after appropriate handling of initial results allows us
to acquire visionary as well as quantitative data.
Unfortunately, one of the main disadvantages is a low
dimensional resolution capability for both of these
methods. Therefore, for detection and describing a
small-scale deformation of a laser mirrors surface, the
interferometric method was chosen. Fourier-optics
methods [5-7] find a wide application as a solution
method for different scientific and applied tasks. The
principle of this method is to get some certain function
spectrum and then to reproduce that unknown function
by spectrum handling. Fourier-optics methods are very
sensible to the surface shape. Thus, they can be used for
research of surface quality, in particular case, for
surfaces of laser metal mirrors.
There a few main methods to make a reflection
surface – polishing, grinding, turning, etc. Better purity
of surface is obtained by the diamond microgrinding of a
metal specimen. But a grinding process modifies shape
from an ideal plane by cutter track. Moreover, surface of
a mirror retains phase modulation even after deposition
of a coating with reflection up to 100 %. Hence, almost
always there are diffraction losses in light reflected from
laser metal mirrors made by method of a diamond
microgrinding. The light diffraction pattern in the
Fraunhofer area explicitly depends on spatial parameters
of the grating on which light diffracts. Thus, control and
analysis of a diffraction influence on reflection allow
making a proposal for further decreasing the small-scale
deformations of surface made by diamond micro-
grinding.
The objects of research are flat round copper and
aluminium mirrors with 70 mm diameter. Reflection
surfaces are made by a diamond microgrinding of a
metal specimen. Metal surface of investigated specimens
are made by galvanic or vacuum deposition of a metal
layer with 250-300 m thickness on a ceramic. Vacuum
deposition was carried out with controlled variation of a
high-energy electron beam at the surface of evaporated
metal. Galvanic deposition was carried out in special
tank with a sulphuric electrolyte that contained salt of
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 280-283.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
281
1 32 4
5
Fig. 1. The principal scheme of the experimental device:
1 – laser mirror; 2 – beam splitter; 3 – lens; 4 – detector;
5 – light source.
required metal. Several modes for deposition were used
– variation of the current intensity, mixing of electrolyte
in the ultrasonic tank and others. Selected specimens
were annealed at high temperature after galvanic
deposition. Finally, the reflecting surface was shaped by
diamond microgrinding with fixed cutting depth of 5 m
and speeds of cutter serve of 5 and 10 m. Diamond
microgrinding is the method to produce high quality
metal mirror surfaces, it allows on-line handling of
required geometry of metal mirror surface. Moreover,
the surfaces with the parameters of roughness
Rmax 0.01 m and deviation from predefined form less
than 0.1 m can be produced while increasing the
productivity by 10-50 times [8].
In theory, such surface would be absolutely flat
because of orthogonality of rotation axis and motion
direction of cutter. However, the mirror surface is not
absolutely flat as a result of mutual vibrations between
instrument and specimen during the grinding process. The
surface has defects: concentric rings, cavities and humps.
In our particular case, this circular structure has regular
character (mutual vibrations of detail and instrument of
grinding machine in the automatic mode are stable during
processing), and a circular phase diffraction grating
appears on surface. The period of circular structure gives
information about the frequency and source of mutual
vibrations. The amplitude of circular structure (deviation
from an ideal plane) is proportional to the amplitude of
mutual vibrations of specimen and cutter during a
grinding. This value contains information about quality of
the technological process.
Thus, a flat laser metal mirror with a circular
structure can be considered as a planar reflective phase
grating with concentric grooves. Hence, it is possible to
find relations between diffraction patterns of light in a
far area and the spatial characteristic of this grating.
Let’s consider a phase modulation of a plane wave
reflected from a mirror:
rpieEE sin
0
0 , (1)
where E0 is the value of electric field of initial wave,
0
0
2
2
x
is the amplitude of wave phase
modulation, x0 is the maximal deviation of mirror
surface from an average plane position, is the
wavelength of light,
T
p
2
is the spatial frequency, and
T is the modulation period along the radius of mirror.
Fourier transformation of the function (1) with
assumption of system axial symmetry:
0
0
0
0
sin
0
2
)()(
r
rpi
Fi
rdrrJeE
Fi
e
G . (2)
Here, F is the focal distance of a lens, 2r0 is the
beam (or mirror) diameter,
F
2 is the spatial
frequency, is a radial coordinate in the screen plane,
J0(r) is the zero order Bessel function, and G() is a
distribution of explored field density in the lens focal
plane. This equation (2) determines a spectrum position
in the Fraunhofer range in the case of symmetric object.
The formula consists of two parts: first (before the
integral sign) is the ordinary term describing the wave
amplitude and phase in the lens focal plane, second term
(integral) – describing a field distribution in a lens focal
plane as dependent on the object character – distribution
of the intensity along the radius. The spectrum of our
object can be found applying the Fourier-Bessel
transformation, because our objects have axial
symmetry [9].
However, in our case of weak modulation (0 << 1)
an influence of phase modulation is similar to that of
amplitude modulation [10]. It means that the energy of
an incident wave forms three characteristic beams after
diffraction on the grating. The first beam propagates
without a change of initial direction and has the energy
2
1
2
0
0W . (3)
Two other beams propagate as diffraction peaks
with a vertex of cone
T
2arcsin2 , and each of
them has the energy 4/2
00 W . However, these beams
absolutely coincide in space because of symmetry of the
system.
The principal scheme of the experimental device is
shown in Fig. 1. As a light source, we used 1 mW
helium-neon laser LGN-208 with 632.8 nm wavelength;
the light detector is a photomultiplier FEU-68; beam
splitter is a plane-parallel glass plate with multilayer
coating; beam shaping system is a telescopic system
based on objective OF-41 with a beam diameter 85 mm
and a focal length 400 mm. This telescopic system,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 280-283.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
282
a b
Fig. 2. Photos of examples of the diffraction patterns for the laser metal mirror. Axes of symmetry of the mirror and lens (see
Fig. 1) coincide (a) or are slightly shifted (b).
Table
The number
of a mirror Spatial frequency, cm–1
Diffraction losses,
102
1 50 150 200 300 – – – – 1.43
2 50 200 300 400 600 – – – 1.14
3 50 150 280 310 – – – – 0.62
4 50 120 330 370 – – – – 0.29
5 50 100 320 380 650 700 880 900 0.62
6 80 200 280 300 450 550 600 – 0.83
7 80 150 300 380 1005 2150 – – 0.64
8 100 150 300 450 780 – – – 0.43
9 80 140 300 400 650 730 830 1002 0.40
10 60 140 250 300 730 900 1002 1100 0.37
which increases beam size to 40 mm, forms the plane
wave front 5. There is an optical detector FEU-68 with a
small aperture in the screen plane. Shown in Fig. 2 are
photos of examples of the diffraction pattern on
specified metal mirrors, and in Fig. 3 there is an example
of the photo-electric registration. To register the high-
frequency components of a spatial frequency spectrum
for the beam reflected from the mirror, an axis
misalignment is required. To be exact, beams don’t
match in lens 3 after reflection from the mirror 1 within
this coaxial scheme. Therefore, the lens 3 should be
shifted from the axis of the mirror 1, and symmetry of
the picture in the focal plane disappears.
As can be seen from the figures, in light reflected
from a mirror one can observe a central diffraction
maximum and a few other (lateral) peaks from diffracted
waves. In our approximation (0 << 1), there is only one
first order maximum. Therefore, we can suppose that
these few lateral maxima are caused by a few sinusoidal
diffraction gratings with different spatial periods Т.
100
510–9
510–8
510–7
510–6
510–5
i, A
p, cm–1–100 0
Fig. 3. The diffraction spectrum registered by PMU. X-axis is
the spatial frequencies, Y-axis is an output signal of detector.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 3. P. 280-283.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
283
The total dispersion energy in i-ring is obtained by
integrating:
0
0
2 22
r
i
i d
F
GW , (4)
where i means the number of a diffraction ring (i =
1, 2, 3...), and
F
G 22 is the radial distribution of
the light intensity in a ring. That distribution can be
acquired from an experimental data. The coefficient of
diffraction losses is obtained in the following way:
01 i
i
i
i WW , (5)
where Wi is the light intensity in the i-th order of
diffraction.
The diffraction losses of light reflected from
mirrors with phase modulation of surface and the spatial
frequency values of the laser metal mirrors made by
diamond microgrinding are given in Table. The
proposed method of interferometric analysis allows to
find mechanical vibration frequencies and quantitatively
describe defects of mirror surface. After appropriate
handling the obtained data, it is possible to define and
eliminate sources of vibrations.
As a result, application of the Fourier
transformation to the diffraction pattern from metal
mirrors allowed:
a) to determine the deviation level of a mirror
surface from an ideal plane and parameters of periodic
components – amplitude and spatial frequencies;
b) to experimentally determine the diffraction
losses of laser metal mirrors by the specially designed
spectrometer of spatial frequencies.
The results of such researches have an applied
importance, as they make a basis for numerous
applications of lasers in science and industry.
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