Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object
Classification of surfaces as roughness is carried out. The roughness can have the determined, stochastic
 or chaotic character, depending on a method of their forming. In the work the problem of finding
 of normal vector to a surface and coordinates of a point of lighting by a laser...
Збережено в:
| Опубліковано в: : | Физическая инженерия поверхности |
|---|---|
| Дата: | 2013 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Науковий фізико-технологічний центр МОН та НАН України
2013
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/100308 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object / M.I. Dzubenko, S.N. Kolpakov, I.V. Popov, A.A. Pryyomko // Физическая инженерия поверхности. — 2013. — Т. 11, № 3. — С. 254–259. — Бібліогр.: 10 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860269890989981696 |
|---|---|
| author | Dzubenko, M.I. Kolpakov, S.N. Popov, I.V. Pryyomko, A.A. |
| author_facet | Dzubenko, M.I. Kolpakov, S.N. Popov, I.V. Pryyomko, A.A. |
| citation_txt | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object / M.I. Dzubenko, S.N. Kolpakov, I.V. Popov, A.A. Pryyomko // Физическая инженерия поверхности. — 2013. — Т. 11, № 3. — С. 254–259. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Физическая инженерия поверхности |
| description | Classification of surfaces as roughness is carried out. The roughness can have the determined, stochastic
or chaotic character, depending on a method of their forming. In the work the problem of finding
of normal vector to a surface and coordinates of a point of lighting by a laser beam for the case
of approximation of a roughness by a flat reflective diffraction grating is solved.
Keywords: surface, roughness, diffraction grating, coherent radiation.
Проведена класифікація поверхонь за типом шорсткостей. Шорсткість залежно від методу виникнення може мати детермінований, стохастичний або хаотичний характер. У роботі вирішено завдання знаходження вектора нормалі до поверхні і координати точки освітлення променем
лазера для випадку апроксимації шорсткості плоскими відбивними дифракційними гратками.
Проведена классификация поверхностей по типу шероховатостей. Шероховатость в зависимости
от метода возникновения может иметь детерминированный, стохастический или хаотический
характер. В работе решена задача нахождения вектора нормали к поверхности и координаты
точки освещения лучом лазера для случая аппроксимации шероховатости плоской отражательной дифракционной решёткой.
|
| first_indexed | 2025-12-07T19:05:31Z |
| format | Article |
| fulltext |
254
Surface of objects can have various character of
a roughness (fig. 1). The roughness, as a rule, is for-
med as a result of external mechanical (or another)
impacts on object, for example, polishing. The sur-
face with the determined roughness turns out by im-
pact on object of the determined process. For
example, diffraction gratings possess such surface.
The surface with a stochastic roughness is formed
at action on object of several processes some of
which are determined, and others are casual. The
surface with a chaotic roughness turns out at impact
on object of chaotic process, for example, a polis-
hing by a sand stream. In many cases it is possible
to present a roughness of surfaces of the first two
types as a combination of several diffraction gratings
with various options of their relative positioning
(fig. 2).
The simplest case – one diffraction grating use.
At approximation by several gratings there are
options of their relative positions, there is need to
enter concept of conjugation of gratings. Conjugation
defines mechanical ways of their imposing at each
UDC 53.06
USE OF THE DETERMINED PROPERTIES OF A ROUGHNESS OF A SURFACE
IN MEASUREMENT OF A GEOMETRICAL FORM OF OBJECT
M.I. Dzubenko, S.N. Kolpakov, I.V. Popov, A.A. Pryyomko
Usikov institute of radiophysics and electronics NAS of Ukraine (Kharkiv)
Ukraine
Received 01.07.2013
Classification of surfaces as roughness is carried out. The roughness can have the determined, sto-
chastic or chaotic character, depending on a method of their forming. In the work the problem of fin-
ding of normal vector to a surface and coordinates of a point of lighting by a laser beam for the case
of approximation of a roughness by a flat reflective diffraction grating is solved.
Keywords: surface, roughness, diffraction grating, coherent radiation.
ИСПОЛЬЗОВАНИЕ ДЕТЕРМИНИРОВАННЫХ СВОЙСТВ ШЕРОХОВАТОСТИ
ПОВЕРХНОСТИ В ИЗМЕРЕНИИ ГЕОМЕТРИЧЕСКОЙ ФОРМЫ ОБЪЕКТА
М.И. Дзюбенко, С.Н. Колпаков, И.В. Попов, А.А. Приёмко
Проведена классификация поверхностей по типу шероховатостей. Шероховатость в зависимости
от метода возникновения может иметь детерминированный, стохастический или хаотический
характер. В работе решена задача нахождения вектора нормали к поверхности и координаты
точки освещения лучом лазера для случая аппроксимации шероховатости плоской отража-
тельной дифракционной решёткой.
Ключевые слова: поверхность, шероховатость, дифракционная решетка, когерентное
излучение.
ВИКОРИСТАННЯ ДЕТЕРМІНОВАНИХ ВЛАСТИВОСТЕЙ ШОРСТКОСТІ
ПОВЕРХНІ У ВИМІРІ ГЕОМЕТРИЧНОЇ ФОРМИ ОБ’ЄКТУ
М.І. Дзюбенко, С.Н. Колпаков, І.В. Попов, А.А. Приемко
Проведена класифікація поверхонь за типом шорсткостей. Шорсткість залежно від методу ви-
никнення може мати детермінований, стохастичний або хаотичний характер. У роботі виріше-
но завдання знаходження вектора нормалі до поверхні і координати точки освітлення променем
лазера для випадку апроксимації шорсткості плоскими відбивними дифракційними гратками.
Ключові слова: поверхня, шорсткість, дифракційні грати, когерентне випромінювання.
Fig. 1. Object surfaces classification.
Fig. 2. The approximation of the roughness of polished
surfaces by gratings.
Dzubenko M.I., Kolpakov S.N., Popov I.V., Pryyomko A.A., 2013
255ФІП ФИП PSE, 2013, т. 11, № 3, vol. 11, No. 3
other. So, the diffraction pattern, received at in-
teraction of coherent radiation with similar surfaces,
represents quite determined structure (fig. 3) [1].
Diffraction maxima from each of gratings form a
diffraction curve. The quantity of diffraction curves
in a diffraction pattern corresponds to the quantity
of the diffraction gratings which have taken part in
formation of a roughness of this surface. The
considered model of roughness gives the grounds
to apply the diffraction methods based on approach
of Fresnel-Kirchhoff [2, 3]. For the solution of a
number of tasks, as well, the geometrical theory of
diffraction is used [4].
The result of diffraction depends on a ratio of
the spatial sizes of a beam and object. When a
diameter of a beam is much smaller then the spatial
extent of object, the result of section of a beam and
a surface represents the tangent plane to this surface.
In this case the object surface unambiguously is
defined by a set of the tangent planes in each point
of a surface. For this case the primary measuring
information in the analysis of a geometrical form are
parameters of a normal to a surface in a point of
lighting and coordinate of this point.
In this work the theoretical and experimental
research of the diffraction picture, received as a result
of interaction of coherent radiation with a surface,
was made for the purpose of measurement of
parameters of a normal and coordinates of a point
of lighting.
Two options of the achievement of objective point
are possible. The first: the diffraction picture in the
aperture plane of the receiver is analyzed. In this
case the contradiction between the sizes of the
receiver and the picture demands permission. The
second option assumes formation of a diffraction
picture on the coordinate screen. In this work the
second case, as more interesting from the practical
point of view, is considered.
Let’s consider diffraction of coherent radiation
on one-dimensional reflecting grating for inclined
falling of a beam. Thus, the beam is focused arbitrarily
in relation to strokes of a grating (fig. 4). The flat
wave, which direction of distribution is defined by
corners θ and ϕ , falls on a grating. The angular
spectrum of diffracted light is described by the
following expression [5]:
( ) 2
1, ( , ,0)exp[ ( )]
(2 )x y x yF k k u x y i k x k y dxdy
∞
−∞
= − +
π ∫ ∫ .
(1)
There u(x, y, 0) – an intensity of electric field in
a point (x, y, 0);
kx = k⋅cosθ, ky = k⋅cosϕ , k = 2⋅π/λ;
λ − wave length of the used radiation.
The angular range of a falling flat wave looks like:
F1(kx, ky) = δ(kx)⋅δ(kx). (2)
The angular spectrum of a field after diffraction
on a grating is equal to convolution of an angular
spectrum of a falling wave F1 and function of
reflection amplitude coefficient of a grating Φ(x) [5]:
( ) ( )1( , ) , ,x y x yF k k F k k d d
∞
−∞
= ξ η Φ − ξ − η ξ η∫ ∫ .
(3)
For infinite uniform periodic structure the range
of coefficient of reflection is:
( ) ( ) 2,
n
x y n y x
n
nk k a k k
d
=∞
=−∞
π⋅ Φ = δ δ −
∑ , (4)
where n – a number of a diffraction order; d – a
a)
b)
Fig. 3. Diffraction patterns received from surfaces after
mechanical machining. a) – one polishing direction,
b) – polishing was made in two directions.
M.I. DZUBENKO, S.N. KOLPAKOV, I.V. POPOV, A.A. PRYYOMKO
256
grating period; аn – coefficient of Fourier num-
ber of amplitude coefficient of reflection of a grating:
( )
2
2
1 2exp
d
n
d
n xa R x i dx
d d−
π⋅ ⋅ = −
∫ .
R(x) – is defined by concrete model of diffraction
structure of a surface and the direction of beam falling
on it. Substituting (2) and (4) in (3) and carrying out
integration, we will receive an angular spectrum of a
field after diffraction on a grating [6]:
( ) ( )2, cos cos cosx y n y x
n
nF k k a k k k k
d
∞
=−∞
π⋅ � �= δ − ϕ− − θ � �
� �
∑ .
From the last expression we define directing
cosines of diffraction orders:
cosθn = cosθ, cosϕ n = cosϕ − nλ/d,
2
2cos sin cosn
n
d
λ η = θ − ϕ −
. (5)
Apparently from (5), next ratio is true for any
orders: there kn – a single vector of n − order of
diffraction in the direction of distribution, i(1, 0, 0)
– ort in the direction of the OX axis (fig. 4).
Thus, at normal falling of a beam on a surface the
diffraction maxima lie on a straight line. In this case
formation of diffraction orders is described by
classical laws of diffraction of a beam on a grating
[7, 8]. At diffraction of randomly focused beam all
diffraction orders lie on a surface of the circular angle,
which axis coincides with the OX axis, and the
corner at top is equal 2⋅β (fig. 5). It was confirmed
completely by experimental check [9].
Section of a similar surface by the plane of the
screen leads to that diffraction orders on the plane
of the receiver form diffraction maxima as the curve
of the second order (fig. 6).
The third formula in (5) defines the quantity of
diffraction orders at a beam assumed position
concerning grating strokes. Recognizing that a
radicand shouldn’t be negative, the maximum number
of diffraction orders is defined by the following
expression:
( )sinθ cosdN = +
λ
ϕ .
The system of coordinates, in which it is necessary
to define the position of a normal to a surface and
coordinates of a point of lighting, is formed by the
plane of the screen, on which the diffraction pattern
is formed, and a perpendicular to it. The position of
a beam in this system of coordinates is described
by the straight line equation:
Fig. 4. Diffraction on a grating. Fig. 5. Surface, formed by diffraction orders.
Fig. 6. Diffraction maxima at arbitrary falling of a beam on
a grating.
USE OF THE DETERMINED PROPERTIES OF A ROUGHNESS OF A SURFACE IN MEASUREMENT OF A GEOMETRICAL FORM OF OBJECT
ФІП ФИП PSE, 2013, т. 11, № 3, vol. 11, No. 3
257ФІП ФИП PSE, 2013, т. 11, № 3, vol. 11, No. 3
b b b
xb yb zb
x x y y z z
u u u
− − −= = ,
there xb, yb, zb – coordinates of a point of the falling
of a beam on the screen; uxb, uyb, uzb – directing
cosines of the straight line, containing a beam.
The perpendicular to the screen forms an axis X,
the beginning of coordinate lies on the screen.
Therefore xb = 0. Directing cosines of diffraction
orders (5) are found in the system of coordinates
formed by a diffraction grating. The analysis of a
diffraction pattern is kept in system of coordinates
formed by the screen. The equations of the plane,
that is tangent to a surface, also are in this coordinate
system. Therefore for the processing of a diffraction
pattern it is necessary to find coordinates of directing
vectors of diffraction orders in screen system of
coordinates.
The solution of this task assumes the definition
of a matrix of transition from one system of co-
ordinates to another. Thus, some properties of the
diffraction curves should be noted, allowing connect
coordinates of diffraction maxima on the screen with
coordinates of a point of lighting and parameters of
the tangent plane to a surface. As it was already
noted, diffraction orders form a circular conic surface
in space. As a result of a section of this surface by a
flat screen diffraction curves represent second order
curves. In this task the spatial position of a beam
was set so that diffraction curves have ellipse forms.
Cases of a parabola, hyperbole and straight line are
almost unrealizable. The parabolic form turns out in
case of a screen arrangement strictly parallel to a
forming conic surface, hyperbolic – strictly parallel
to a cone axis, the straight line turns out only when
the projection of an incident beam to a grating is
parallel to its strokes.
For transformation of coordinates of directing
vectors of diffraction orders the oblique-angled
system of coordinates formed by the screen and a
beam of the laser was interpolated. At first coor-
dinates were transformed from the system of coor-
dinates connected with a grating in system of coor-
dinates, connected with a beam, and then from this
system of coordinates to system of coordinates for-
med by the screen. Such two-level approaching
allowed us considerably reduce time of computing
procedures.
The matrix of transition Tb0 from the oblique-
angled system of coordinates, formed by a beam
and the screen, in rectangular system, formed by
the screen and a perpendicular to it, is:
0
cos cos cos
0 1 0
0 0 1
x y z
bT
δ δ δ
=
.
There δx, δy, δz − the angles between a falling
beam and axes of rectangular system of coordinates.
The following step is calculation of a matrix of
transition T from system of coordinates of a grating
in system of coordinates of a beam. For this purpose
it is necessary to find the equation of the straight line
containing diameter of an ellipse on the screen. The
ellipse, as a second order curve, unambiguously is
defined by coordinates of five points. The beam is
generator of conic surface. Therefore its point of
intersection with the screen lies on a considered
ellipse. Thus, for a complete definition of an ellipse
it is necessary to measure coordinates of four maxima
on a diffraction curve. The equation of the ellipse
passing through five points with coordinates (y1, z1),
(y2, z2), (y3, z3), (y4, z4), (y5, z5) looks like [10]:
2 2
2 2
1 1 1 1 1 1
2 2
2 2 2 2 2 2
2 2
3 3 3 3 3 3
2 2
4 4 4 4 4 4
2 2
5 5 5 5 5 5
1
1
1 01
1
1
y yz z y z
y y z z y z
y y z z y z
y y z z y z
y y z z y z
y y z z y z
=
Calculation of determinant of this matrix gives
the ellipse equation.
There A, B, C, D, E – equation coefficients.
Passing simple, but quite bulky mathematical calcu-
lations, we will write down a matrix of transition T
from rectangular system of coordinates of a grating
to the oblique-angled system of coordinates formed
by a beam and the plane of the screen, consisting of
directing cosines of the axes, that form system of
coordinates, connected with a grating, in the system
of coordinates, connected with a beam:
xx xy xz
gb yx yy yz
zx zy zz
u u u
T u u u
u u u
=
.
To find coordinates of directing vectors of
diffraction orders in the system of coordinates,
formed by the plane of the screen and a
perpendicular to it, the following equation must be
solved
1
0
t
b gb gX T Т X− = ⋅ . (6)
There X(ux, uy, uz) – a required directing vector;
M.I. DZUBENKO, S.N. KOLPAKOV, I.V. POPOV, A.A. PRYYOMKO
258
Хр(uxg, uyg, uzg) – a directing vector of diffraction
orders in system of grating coordinates, it is defined
by expressions (5).
Angles θ and ϕ , which define the position of a
normal to a surface in a lighting point, are in the
equation (6). Knowing coordinates (yn, zn) of n-th
diffraction maximum on the screen, it is possible to
write down the equation of n-th diffraction order
( ) ( ) ( ), , , , , ,
n n
x y y
y y z zx
u n u n u n
− −= =
ϕ θ ϕ θ ϕ θ . (7)
The point of illumination of a surface with coor-
dinates (xb, yb, zb) belongs to a straight line (7),
therefore the following equalities have to be carried
out
( ) ( ) ( ), , , , , ,
b b n b n
x y y
x y y z z
u n u n u n
− −= =
ϕ θ ϕ θ ϕ θ . (8)
From expression (8) it follows that coordinates
of three diffraction maxima completely define the
equation of the plane tangent to a surface in a lighting
point, and coordinates of this point. I.e. the system
decision
there n, m, h – the numbers of diffraction maxima,
allows to calculate (xb, yb, zb) and ϕ , θ – angles.
Substituting the found values of θ and ϕ angles
in the equation (6) we find coordinates (uxk, uyk, uzk)
of directing vector of a normal to the tangent plane.
The required equation of the tangent plane is.
Thus, the measured coordinates of three diffrac-
tion maxima in a diffraction pattern allow calculate
the coordinates of laser lighting point on a surface
and directing cosines of a vector of a normal to a
surface in a lighting point.
The roughness of a surface is approximated by a
reflective diffraction grating. As model the reflective
diffraction grating with the period of 5 microns was
used. Ne-Ne LG-208 laser forms a beam with a
diameter of 1.5 mm and divergence 1.2 mrad. Wave
length of the laser radiation is 0.6328 microns. The
screen represents diffusely reflecting plane, with the
coordinate grid put on it. In the experiment the graph
paper pasted on glass was used. The screen size is
350 to 280 mm.
The laser beam incidence was normal to the
screen. It allowed create in space three-dimensional
system of coordinates in which all measurements
have been carried out. The point of a beam inciden-
ce on the screen corresponded to the origin of co-
ordinates (fig. 7).
The diffraction grating was located on a small
rotary table perpendicular to the XOY plane. The
angle г was fixed by means of indication of a small
rotary table. It allowed install a grating with exact
knowledge of its spatial parameters. At this relative
positioning of a beam and the screen the attitude of
a point of lighting is defined completely by distance
l from the origin of coordinates to it. Thus, the point
of lighting has coordinates (l, 0, 0).
The true attitude of the grating plane is defined
by the equation.
True coordinates of a point of illumination on a
grating surface B(141.5, 0, 0).
As a result of diffraction the diffraction curve is
formed on the screen. The measured coordinates
of diffraction maxima are specified in tab. 1.
On the basis of these points coordinates and a
point of intersection of a beam with the screen the
equation of the ellipse approximating a diffraction
curve (fig.8) was received
−0.444y2+ 0.018yz−0.623z2+ 93.32y−2.236z = 0.
The algorithm of restoration of the equation of
the plane is based on theoretical conclusions pro-
duced above.
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
,
, , , ,
,
, , , ,
,
, , , ,
,
, , , ,
,
, , , ,
b b n
x y
b b n
x z
b b m
x y
b m b m
y z
b h b h
y z
x y y
u n u n
x z z
u n u n
x y y
u m u m
y y z z
u m u m
y y z z
u h u h
−=
ϕ θ ϕ θ
−
=
ϕ θ ϕ θ
− = ϕ θ ϕ θ
− −
=
ϕ θ ϕ θ
− − =
ϕ θ ϕ θ
Fig. 7. Scheme of experiment.
Table 1
Y, mm 144.5 203.7 210 142.5
Z, mm 82.5 31.5 0 –82.5
USE OF THE DETERMINED PROPERTIES OF A ROUGHNESS OF A SURFACE IN MEASUREMENT OF A GEOMETRICAL FORM OF OBJECT
ФІП ФИП PSE, 2013, т. 11, № 3, vol. 11, No. 3
259ФІП ФИП PSE, 2013, т. 11, № 3, vol. 11, No. 3
As a result the following equation of the plane of
a grating (fig. 9) has turned out. The values of the
measured coordinates of a point of lighting are
(139.2, 0, 0). So, the relative error of measurement
of coordinates was 1,6%. For the estimation of an
error of the restored plane position next corners
were calculated:
− between the true position of the plane and
measured one − 0.36, 0;
− between the restored plane and the plane of
coordinates XOY (the true plane is perpendicular
to XOY plane) – 90.29, 0.
The made experiments on restoration of the
equation of the plane in space completely confirmed
theoretical conclusions. Distinctions in spatial
positions of the true and restored planes are caused
by the following factors:
− inaccuracy of measurement of coordinates of
diffraction maxima on the screen because of their
ellipticity;
− divergence of laser radiation wasn’t considered
in calculations;
− intensity distribution in diffraction maxima
wasn’t considered in calculations;
− inaccuracy of measurement of true position of
a grating.
Fig. 8. Diffraction curve.
CONCLUSION
Approximation of roughness of a surface by in-
tegration of reflective diffraction gratings allowed to
measure normal parameters in a point of lighting by
a beam of the laser and coordinate of this point.
Measurements were made on the basis of the ana-
lysis of the diffraction field, received as a result of
interaction of coherent radiation with a surface. These
data from all surface of object allow measure its
geometrical form unambiguously.
The material presented in article can be of interest
for developers of monitoring systems of a geometrical
form of products of mechanical engineering, for
example shovels of gas-turbine engines.
REFERENCES
1. Dzubenko M.I., Kolpakov S.N., Popov I.V.,
Pryyomko A.A. Diffraction of coherent radiation
on surfaces having non Gaussian statistics of
roughness//Radiophysics and electronics. −
Vol.17, № 4. − P. 92-97.
2. Nasarov V.N., Lin‘kov A.E. Diffraction methods
of control of geometric parameters and spatial
positioning of objects//Optical magazine. − 2002.
− Vol. 69, № 2. − P. 76-81.
3. Born M., Vol‘f E. Basis of optics. − M.: Science,
1970.
4. Borovikov V.A., Kinber B.E. Geometric theory
of diffraction. − M.: Communication, 1978. −
247 p.
5. Vinogradova M.B., Rudenko O.V., Suhoru-
kov A.P. Theory of waves. – M.: Science, 1979.
– 384 p.
6. Volkov V.V. et al. Measuring of dimensions of
integrated circuits taking into account real profile
of etching by diffraction pattern//Microelectro-
nics. – 1984. – Vol.13, ed.1. – P. 64-72.
7. Shestopalov V.P., Kirilenko A.A., Masalov S.A.,
Sirenko Yu.K. Resonant scattering of waves.
V. 1. Diffraction gratins. − K.: Scientific mind,
1986. – 232 p.
8. Andrenko S.D., Evdokimov A.P., Sidorenko
Yu.B., Shestopalov V.P. Features of scattering
of waves from skew grating. − Kharkiv: AS
USSR Preprint №244, 1984. – 40 p.
9. Lahno V.I., Priyomko A.A. Speckle method of
measuring of configuration of industrial products
//Col. Of Sci. Articles KhStTURE. – 1999. –
Vol. 1. – P. 105-108.
10. Korn G., Korn T. Reference book on mathema-
tics. – M.: Science, 1984. – 831 p.
Fig. 9. Restored plane.
M.I. DZUBENKO, S.N. KOLPAKOV, I.V. POPOV, A.A. PRYYOMKO
|
| id | nasplib_isofts_kiev_ua-123456789-100308 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1999-8074 |
| language | English |
| last_indexed | 2025-12-07T19:05:31Z |
| publishDate | 2013 |
| publisher | Науковий фізико-технологічний центр МОН та НАН України |
| record_format | dspace |
| spelling | Dzubenko, M.I. Kolpakov, S.N. Popov, I.V. Pryyomko, A.A. 2016-05-19T15:34:00Z 2016-05-19T15:34:00Z 2013 Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object / M.I. Dzubenko, S.N. Kolpakov, I.V. Popov, A.A. Pryyomko // Физическая инженерия поверхности. — 2013. — Т. 11, № 3. — С. 254–259. — Бібліогр.: 10 назв. — англ. 1999-8074 https://nasplib.isofts.kiev.ua/handle/123456789/100308 53.06 Classification of surfaces as roughness is carried out. The roughness can have the determined, stochastic
 or chaotic character, depending on a method of their forming. In the work the problem of finding
 of normal vector to a surface and coordinates of a point of lighting by a laser beam for the case
 of approximation of a roughness by a flat reflective diffraction grating is solved.
 Keywords: surface, roughness, diffraction grating, coherent radiation. Проведена класифікація поверхонь за типом шорсткостей. Шорсткість залежно від методу виникнення може мати детермінований, стохастичний або хаотичний характер. У роботі вирішено завдання знаходження вектора нормалі до поверхні і координати точки освітлення променем
 лазера для випадку апроксимації шорсткості плоскими відбивними дифракційними гратками. Проведена классификация поверхностей по типу шероховатостей. Шероховатость в зависимости
 от метода возникновения может иметь детерминированный, стохастический или хаотический
 характер. В работе решена задача нахождения вектора нормали к поверхности и координаты
 точки освещения лучом лазера для случая аппроксимации шероховатости плоской отражательной дифракционной решёткой. en Науковий фізико-технологічний центр МОН та НАН України Физическая инженерия поверхности Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object Використання детермінованих властивостей шорсткості поверхні у вимірі геометричної форми об’єкту Использование детерминированных свойств шероховатости поверхности в измерении геометрической формы объекта Article published earlier |
| spellingShingle | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object Dzubenko, M.I. Kolpakov, S.N. Popov, I.V. Pryyomko, A.A. |
| title | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object |
| title_alt | Використання детермінованих властивостей шорсткості поверхні у вимірі геометричної форми об’єкту Использование детерминированных свойств шероховатости поверхности в измерении геометрической формы объекта |
| title_full | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object |
| title_fullStr | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object |
| title_full_unstemmed | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object |
| title_short | Use of the determined properties of a roughness of a surface in measurement of a geometrical form of object |
| title_sort | use of the determined properties of a roughness of a surface in measurement of a geometrical form of object |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/100308 |
| work_keys_str_mv | AT dzubenkomi useofthedeterminedpropertiesofaroughnessofasurfaceinmeasurementofageometricalformofobject AT kolpakovsn useofthedeterminedpropertiesofaroughnessofasurfaceinmeasurementofageometricalformofobject AT popoviv useofthedeterminedpropertiesofaroughnessofasurfaceinmeasurementofageometricalformofobject AT pryyomkoaa useofthedeterminedpropertiesofaroughnessofasurfaceinmeasurementofageometricalformofobject AT dzubenkomi vikoristannâdetermínovanihvlastivosteišorstkostípoverhníuvimírígeometričnoíformiobêktu AT kolpakovsn vikoristannâdetermínovanihvlastivosteišorstkostípoverhníuvimírígeometričnoíformiobêktu AT popoviv vikoristannâdetermínovanihvlastivosteišorstkostípoverhníuvimírígeometričnoíformiobêktu AT pryyomkoaa vikoristannâdetermínovanihvlastivosteišorstkostípoverhníuvimírígeometričnoíformiobêktu AT dzubenkomi ispolʹzovaniedeterminirovannyhsvoistvšerohovatostipoverhnostivizmereniigeometričeskoiformyobʺekta AT kolpakovsn ispolʹzovaniedeterminirovannyhsvoistvšerohovatostipoverhnostivizmereniigeometričeskoiformyobʺekta AT popoviv ispolʹzovaniedeterminirovannyhsvoistvšerohovatostipoverhnostivizmereniigeometričeskoiformyobʺekta AT pryyomkoaa ispolʹzovaniedeterminirovannyhsvoistvšerohovatostipoverhnostivizmereniigeometričeskoiformyobʺekta |