Computer supported interferogam evaluation
Paper presents a method of phase shift calculation and interpretation of complicated interferograms taken in the cylindrically symmetrical medium. Method is applicable for any finite–width interferogram, incl. those with individual closed interference fringes causes by abrupt changes of the refracti...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Цитувати: | Computer supported interferogam evaluation / J. Olejnicwek, J. Pichal, J. Blazek, P. Spatenka // Вопросы атомной науки и техники. — 2005. — № 2. — С. 235-237. — Бібліогр.: 4 назв. — англ. |
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Olejnicwek, J. Pichal, J. Blazek, J. Spatenka, P. 2015-04-04T20:38:19Z 2015-04-04T20:38:19Z 2005 Computer supported interferogam evaluation / J. Olejnicwek, J. Pichal, J. Blazek, P. Spatenka // Вопросы атомной науки и техники. — 2005. — № 2. — С. 235-237. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 42.40.Kw https://nasplib.isofts.kiev.ua/handle/123456789/79820 Paper presents a method of phase shift calculation and interpretation of complicated interferograms taken in the cylindrically symmetrical medium. Method is applicable for any finite–width interferogram, incl. those with individual closed interference fringes causes by abrupt changes of the refractive index. Phase shift calculation were performed in the MATLAB computing environment. Представлено метод обчислення й інтерпретації фазового зсуву складних інтерферограм, взятих в вісесиметричному проміжку. Метод може бути застосовано для будь-яких інтерферограм, включаючи ті, що мають особливості інтерференційних смуг, викликані раптовими змінами коефіцієнта переломлення. Обчислення фазового зсуву здійснювалося в комп'ютерному середовищі MATLAB. Представлен метод вычисления и интерпретации фазового сдвига сложных интерферограмм, взятых в осесимметричном промежутке. Метод применим для любых интерферограмм, включая те, что имеют особенности интерференционных полос, вызванные внезапными изменениями коэффициента преломления. Вычисление фазового сдвига осуществлялось в компьютерной среде MATLAB. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma diagnostics Computer supported interferogam evaluation Комп'ютерна обробка інтерферограм Компьютерная обработка интерферограмм Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Computer supported interferogam evaluation |
| spellingShingle |
Computer supported interferogam evaluation Olejnicwek, J. Pichal, J. Blazek, J. Spatenka, P. Plasma diagnostics |
| title_short |
Computer supported interferogam evaluation |
| title_full |
Computer supported interferogam evaluation |
| title_fullStr |
Computer supported interferogam evaluation |
| title_full_unstemmed |
Computer supported interferogam evaluation |
| title_sort |
computer supported interferogam evaluation |
| author |
Olejnicwek, J. Pichal, J. Blazek, J. Spatenka, P. |
| author_facet |
Olejnicwek, J. Pichal, J. Blazek, J. Spatenka, P. |
| topic |
Plasma diagnostics |
| topic_facet |
Plasma diagnostics |
| publishDate |
2005 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Комп'ютерна обробка інтерферограм Компьютерная обработка интерферограмм |
| description |
Paper presents a method of phase shift calculation and interpretation of complicated interferograms taken in the cylindrically symmetrical medium. Method is applicable for any finite–width interferogram, incl. those with individual closed interference fringes causes by abrupt changes of the refractive index. Phase shift calculation were performed in the MATLAB computing environment.
Представлено метод обчислення й інтерпретації фазового зсуву складних інтерферограм, взятих в вісесиметричному проміжку. Метод може бути застосовано для будь-яких інтерферограм, включаючи ті, що мають особливості інтерференційних смуг, викликані раптовими змінами коефіцієнта переломлення. Обчислення фазового зсуву здійснювалося в комп'ютерному середовищі MATLAB.
Представлен метод вычисления и интерпретации фазового сдвига сложных интерферограмм, взятых в осесимметричном промежутке. Метод применим для любых интерферограмм, включая те, что имеют особенности интерференционных полос, вызванные внезапными изменениями коэффициента преломления. Вычисление фазового сдвига осуществлялось в компьютерной среде MATLAB.
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| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/79820 |
| citation_txt |
Computer supported interferogam evaluation / J. Olejnicwek, J. Pichal, J. Blazek, P. Spatenka // Вопросы атомной науки и техники. — 2005. — № 2. — С. 235-237. — Бібліогр.: 4 назв. — англ. |
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2025-11-26T22:39:59Z |
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| fulltext |
COMPUTER SUPPORTED INTERFEROGRAM EVALUATION
J. Olejnicwek 1, J. Pichal 2, J. Blazek 3, P. Spatenka 3
1Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic;
2Czech Technical University, Faculty of Electrical Engineering, Department of Physics,
Prague, Czech Republic;
3University of South Bohemia, Pedagogical Faculty, Department of Physics,
Ceske Budejovice, Czech Republic
Paper presents a method of phase shift calculation and interpretation of complicated interferograms taken in the
cylindrically symmetrical medium. Method is applicable for any finite–width interferogram, incl. those with individual
closed interference fringes causes by abrupt changes of the refractive index. Phase shift calculation were performed in
the MATLAB computing environment.
PACS: 42.40.Kw
1. INTRODUCTION
Study of plasma characteristics by means of optical
interferometry makes possible to exclude the problem of
plasma interaction with the phase object. The
characteristics under study may be quantities related with
or influencing the index of plasma refraction at least to
such a degree that the shift related with the plasma
refraction changes can be registered in an interferogram.
Interferogram is usually created by a distorted system of
originally parallel interference fringes. Knowing the
fringe shift and assuming the phase object rotational
symmetry the distribution of characteristics under
investigation can be calculated. In case of high-ionised
plasma the total refractive index change mostly depends
on electron concentration and in comparison with electron
concentration both the temperature and pressure of neutral
particles and ions effects may be neglected.
2. PHASE SHIFT CALCULATION
Phase shift subtraction from the interferogram seems to
be a rather difficult process moreover complicated by
further factors – taken interferograms may be unfocused
due to apparatus vibration or non-stationarity of studied
phenomena during the measurement. Fringes may join in
points of large phase shifts and, sometimes-new fringes
can originate in some regions.
For better interference pattern evaluation a new
algorithm has been developed. It is simple and easy to be
used also for evaluation of patterns containing complex
distorted or closed interference fringes.
For model processing a complex interference pattern
(Fig. 1) taken in the Z 150 equipment of Institute of
plasma physics and laser microfusion (IPPLM), Warsaw,
Poland was used [1].
Before the phase shift subtraction and subsequent
evaluation the original interferogram had to be digitally
modified. This modification can be described as:
•Limitation of investigated area in such a way that
resultant area-rectangle contains maximum of complete
interference fringes and therefore the most
comprehensive information about the phase setting.
Then the matrix of these data was standardized.
• Indistinct lines of the processed image were joined by
hand, some parasitic pixels were removed. Resultant
interferogram was transferred back into degrees of shade
and modified with Gaussian filter of size 3x3. Finally
the modified interferogram was reduced into 600x600
pixels. This reduction does not influence final results, it
is important for the interference fringe approximation
used algorithm only.
Fig. 1. Interference pattern used for model processing
Fig.2. Part of modified interferogram used for
calculation
Phase shift calculation had been performed in the
MATLAB computing environment.
Evaluation algorithm is as follows: coordinates of a
point and relevant phase shift value expressed in multiple
of π are entered into the programme. Multiple of π being
even means that interfering rays are shifted just a whole
wavelength multiple farther in this point and the
programme finds all points of maximum intensity along
the fringe. For multiple of π being odd the programme
searches for points of minimum intensity. Searching
algorithm works in two regimes. Be a fringe slope smaller
than 45°, the programme shifts in location by one pixel to
Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 235-237 235
the left, eventually to the right and checks surrounding
pixels placed up and under the current pixel and a new
position is relocated into the point of maximum (or
minimum) intensity. The algorithm repeats itself until the
boundary of the interferogram is reached. For fringesґ or
parts of fringesґ slopes greater than 45°, the algorithm
moves up, eventually down and locates pixels
characterized with extreme intensity value in the left or in
the right environs of the current point. During every step
the programme saves a predefined value of the phase shift
into the matrix on position corresponding to the actual
location of the ascertained pixel. The result of the whole
process is represented with a sparse matrix. This matrix
contains information about the phase shift of lines created
by points whose coordinates approximately correspond to
the centres of individual interference fringes.
To obtain as much as possible precise and “smooth”
information about the phase shift distribution the data are
triangulated so that the final phase shift forms dense
continuously defined matrix. Points lying outside the area
under interpolation, i.e. outside the 1st and the last
interference line contain no data. The matrix represents
phase shift with introduced space frequency caused by
slight decline of interfering rays.
The interference pattern structure in case of the finite
width interferogram can be expressed as
g(x, y) = a(x, y) + b(x, y) · cos[2πf0(x, y) + φ(x, y)], (1)
a(x, y) and b(x, y) are invariables, φ(x, y) wanted phase
shift and f0(x, y) introduced undesirable space frequency.
To get information about the real phase shift, the
subtraction of this space frequency is fundamental.
Before the subtraction it is essential to find a shiftless
region within the investigated area. For evaluation
reasons these regions were declared as those with the
linear phase shift and interpolated with the method of
least squares. Knowing the linear phase in these regions
the original undisturbed interferogram and original phase
shift distribution were restored.
Fig. 3. Resultant phase shift values
Resultant phase shift δφ values (see eq. 1) for individual
points of the interferogram (Fig. 2) are displayed in
Fig. 3.
3. CALCULATION OF REFRACTIVE INDEX
AND ELECTRON DENSITY
Obtained phase shift distribution must be converted into
the refractive index distribution. To get from a two-
dimensional interferogram the three-dimensional image of
the refractive index distribution, the studied phenomena
must show the cylindrical symmetry. Discharge related
with studied interference pattern fully satisfied this
condition. For calculation of refractive index distribution
the discrete Abel transformation was used.
Outside the evaluated region under study the difference
between refractive index values and one are very small
(of 10-7 order) and measurable refractive index changes
are of order 10-5. The electron density can be immediately
calculated from refractive index changes values.
4. RESULTS
Obtained electron density distribution is presented in
Fig. 4. It shows evident increase of electron density
Fig. 4. Distribution of electron density in the discharge
channel
values in y–axis direction. Free electron densities values
are about (1017 ч 1018) cm-3. The calculation of electron
density values has been limited into the area with borders
determined by zero phase shift values. The accuracy of
the calculation decreased with the growth of phase shift
values near evaluated region borders (i.e. in the shock
wave region).
SUMMARY
Paper presents an algorithm for interference patterns
digitalization and phase shift calculation from finite–
width interferograms. The algorithm is very simple and
easy also to be used for evaluation of interferograms
containing complex distorted or closed interference
patterns. The algorithm was tested by determination of
electron density distribution in the pinch discharge
channel at the moment of maximum compression. Final
results seem to be in a good agreement with expected
values. All calculations were performed in the MATLAB
computing environment.
REFERENCES
1. IPPLM, Warsaw, Poland.
2. National Science and Technology Research Center for
Computation and Visualization of Geometric Structures
(The Geometry Center), University of Minnesota 1993.
3. Y. I. Ostrovskii, G.B. Ostrovskaya, M.M. Butusov //
Holographitcheskaya interferometria. Moscow:
“Nauka“, 1977 (in Russian).
236
4. E. Klier // Optika. Praha: SPN, 1986 (in Czech).
КОМПЬЮТЕРНАЯ ОБРАБОТКА ИНТЕРФЕРОГРАММ
Я. Олейнишек, Я. Пихал, Я. Блазек, П. Спатенка
Представлен метод вычисления и интерпретации фазового сдвига сложных интерферограмм, взятых в
осесимметричном промежутке. Метод применим для любых интерферограмм, включая те, что имеют
особенности интерференционных полос, вызванные внезапными изменениями коэффициента преломления.
Вычисление фазового сдвига осуществлялось в компьютерной среде MATLAB.
КОМП'ЮТЕРНА ОБРОБКА ІНТЕРФЕРОГРАМ
Я. Олєйнішек, Я. Піхал, Я. Блазєк, П. Спатєнка
Представлено метод обчислення й інтерпретації фазового зсуву складних інтерферограм, взятих в
вісесиметричному проміжку. Метод може бути застосовано для будь-яких інтерферограм, включаючи ті, що
мають особливості інтерференційних смуг, викликані раптовими змінами коефіцієнта переломлення.
Обчислення фазового зсуву здійснювалося в комп'ютерному середовищі MATLAB.
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