16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Some Aspects of a Schlieren Technique Sensitivity Increasing
Alexandre Pavlov, Alexei Pavlov, Maxim Golubev*
Dept. of Optical Methods of Gas Flow Diagnostics,
Khristianovich Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia
* correspondent author: emaxya@yandex.ru
Abstract In the present work a variation of schlieren technique increasing its sensitivity and usability is
described. New self-adjustable adaptive transparencies (cutoffs) based on bleaching effect are suggested. The
transparencies are thin layers made of translucent substance which are placed in the focal plane of the
receiving lens of a shlieren system. To implement the technique laser light sources have to be used. It was
shown the transparencies have low response time (10-20 µs) allowing significantly reduce liability of the
system to vibrations. Such adaptive visualizing transparencies (AVT) increases the sensitivity and usability
and enable quantitative data obtaining.
1. Background
Shadow methods are most widespread of the optical methods used in aerophysical
experiment. However, their application at real installations frequently faces a number of difficulties.
The restrictions connected with insufficient sensitivity, in particular, concern them. For the most
widespread schemes with Foucault's knife the sensitivity usually associates with the minimum
registrable angle Δθmin in of a deflection of the probing radiation which has passed through
investigated heterogeneity. Similar deflections lead to a displacement of the light source image in a
focal plane of a reception objective where Foucault's knife is located, per δ = F2Δθ (here F2 –
reception objective focal length). As a result, the portion of passed radiation is changed, and in a
corresponding point of the image there will be more or less bright areas depending on a sign and
size of δ value. The relative change of the image intensity for slit-shaped a light source is
F Δθ F Δθ
ΔI
δ
=
= 2 = 1
I0 d F
dF
d
(1)
where ΔI = IΔθ – I0, IΔθ − intensity of the image in the presence of heterogeneity, I0 – the maximum
possible intensity realized at completely open image of a light source, F1 − focal length of a
collimator lens, d – width of a slit, dF = F2d / F1 − width of the slit image in a focal plane of a
reception lens.
The relation (1) allows one to estimate the minimum registrable angle of deflection Δθmin
which depends not only on parameters of the optical scheme, but also on a quality of a used
photodetector (television camera). One of defining parameters thus is the effective quantity of
registered gray gradations N which, taking into account a noise, can be essential less than passport
values of a photodetector. N parameter defines the minimum changes of intensity of images giving
in to reliable registration ΔImin, and ΔImin / I0 ≈ N−1. Usually, for stationary devices F1 = F2 = F. As a
result, taking into account (1), we have
Δθmin ≈
-1-
d
F⋅N
(2)
16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
From the relation (2) it follows that sensitivity increases with increase in focal length F of
objectives, number of gray gradations N, and also with reduction of the size of a light source d.
With some approximation the relation (2) is valid for light source of a different shape also. In this
case the d parameter gets sense of some characteristic dimension. Usually sensitivity change is
possible only by means of variation of d value, as far as F and N values are invariable for the
concrete device. However in practice we can't make the characteristic dimension of a light source
infinitesimal for the following reasons.
(1) Not-laser light sources of the small sizes don't provide a necessary power of radiation for
registration of images. And their size, as a rule, gets out not less than 0.1 mm.
(2) The relation (2) is received in approach of geometrical optics, and d acts in the capacity of the
real geometrical size of a used light source. However, at d values comparable with a wave
length λ of probing radiation, as the characteristic dimension it is necessary to take not the
geometrical sizes, but the size of the light source image at the focal plane of a reception lens,
subject to the diffraction effects. For the single-mode laser light source which is coming most
nearer to ideal (point) source, diffraction diameter dF the focused spot in a focal plane of a
reception objective is defined by a relation dF ≈ λF / D, where D – diameter of an objective
entrance pupil.
As a result, taking into account a relation (2), for the minimum registrable angle in a diffraction
limit, we have
Δθmin .d ≈
λ
D⋅N
(3)
The important result appearing from (3), is the fact that Δθmin.d, so and the method sensitivity
doesn't depend on a focal length F of objectives used.
Let's substitute the characteristic values of D = 150 mm, F = 1500 mm, N = 1000, d = 0.1 mm,
λ = 0.5 µm in relations (2) and (3). As a result we will receive Δθmin ≈ 7·10−8, Δθmin.d ≈ 3·10−9 that
theoretically allows one to register to (visualize) a change of gas density of perturbation with the
characteristic sizes of 20 mm at level of Δρ / ρ0 ≈ 2·10−3 and Δρ / ρ0 ≈ 10−4. Such a density variation
are realized, for example, in subsonic gas flows with characteristic changes of speed at level about
of 20 m / s и 3 m / s accordingly. (The estimation is carried out with use of gas dynamic functions
ε = ρ / ρ0.)
With some approximations the relations (2) and (3) are valid and for schemes with different
visualizing transparencies. Thus the theoretical sensitivity can be high enough. However, as a rule,
it is not possible to reach a theoretical value at real wind tunnels. One of the reasons is rather poor
quality of optical elements of the installation itself (optical windows, folding mirrors, etc.) and
directly of the shadow device. For example, in the fig. 1, a the image of a focal spot of a laser light
source of IAB - 451 device in comparison with a diffraction spot of a high-quality objective
(fig. 1,b) is resulted. It is visible that the size of a
focal spot of a high-quality objective practically
coincides with theoretical value (dF ≈ 1 µm).
Use of a similar objective has allowed to raise the
sensitivity of a method by an order in comparison
with IAB - 451device that agree well with the
Fig. 1. The focal spot images.
resulted estimations.
Other factor limiting possibilities of increase of sensitivity is narrowing of an operating range
of the device. The operating range in this case is understood as a one-to-one registrable range Δθ of
deflection angles. The maximum one-to-one registrable angle is limited by an angle which is not
leading to full darkening or brightening of the light source image, at its displacement relative to a
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
knife edge. For schemes with slit-like source and a symmetric arrangement of its image relative to a
knife edge the module of the maximum single-valued registrable angle is |Δθmax| ≈ d / 2F. Thus, the
sensitivity increase, leads to proportional reduction of an operating range. It limits the efficiency of
a method at research of the flows characterized by the presence of weak perturbations against the
background of stronger ones or characterized by simultaneous presence of areas with weak and
strong perturbations in the flow. It is especially characteristic for supersonic flows in which along
with registration of strong perturbations (compression shock, flow separation regions, etc.) it is
necessary to register a weak perturbations (transitions at boundary layers, sound perturbations, etc.).
Along with reduction of operating range, the sensitivity increase leads to increase of criticality
of the device adjustment to vibrations accompanying the functioning of many wind tunnels. As
illustration to it can serve, light source images in a focal plane of a reception lens of the shadow
device realized at supersonic wind tunnel Т-325 ITAM Siberian Branch of the Russian Academy of
Science (fig. 1, b, c). The image in the fig. 1, b is received at not operating wind tunnel. In the
fig. 1, c four similar images registered at the flow presence by imposing on one shot are resulted.
An exposure time is 1 µs, frequency of frame registration is 10 Hz. Racks of shadow device
objectives of the given installation are located directly on a floor of an operational hall and don't
provide a vibration resistance of optical elements. It leads to random chaotic displacement of the
light source image relative to Foucault's knife edge, and doesn't allow to register reliable a flow
visualization picture.
The following problem at sensitivity increase is relative growth of intensity of parasitic
artifacts, which are not connected with the features investigated flows. Such artifacts may be caused
by poor quality of optical elements of installation, by parasitic flares which become especially
apparent at use of coherent light sources. Level of similar noise can be lowered essentially by
optimization of the optical scheme and by using of high-quality optical elements, including with
bloomed surfaces. It is difficult enough to achieve it at real installations. It is connected with
difficulties of maintenance of ideal quality of optical elements. While in service dust particles
inevitably settle on open surfaces, at optical windows of wind tunnels micro-cracks and cleavages,
etc. appear. Therefore in spite of the fact that formally similar noise can be completely excluded,
they, to some extent, always are presented at the images received in real experiments. Relative level
of similar noise, in case of its stationarity, in certain cases can be lowered essentially. Simple
enough image processing algorithms were used: based on subtraction of a base shot (received
before flow initiation) from working images, or based on division of the working or intermediate
image (received with use of the first algorithm) by a base shot. In the present paper this question
isn't considered in detail, however we will notice that images in the fig. 3 b,c are received with use
of similar processing.
More important problem arising at increase of sensitivity is a possibility of occurrence
essentially not removable artifacts. Their presence is connected with the physical features of a
method expressed in nonlocality of transformation of a wave of probing radiation at the visualizing
transparency in coordinates across the field of the image. We will consider this question in more
details.
Complex amplitude of a monochromatic wave of probing radiation behind investigated
heterogeneity it is possible to present in the form of A1(x, y) = a0eiφ(x, y), where φ(x, y) − phase
incursion characterizing the investigated heterogeneity. We will assume that A1(x, y) corresponds to
distribution of complex amplitude in a forward focal plane of a reception lens. In its back focal
plane it is possible to present amplitude in the form of A2(ξ, η) = F[A1(x, y)], where F – Fourier
conversion operator. (Incursion of phases, defined by the distance between focal planes, hereinafter
isn't considered). We will assume that the back focal plane of a reception lens coincides with a
forward focal plane of a lens forming the image. Without scale factors and restriction of the angular
aperture on lenses, using the theorem of Fourier transform of product of two functions (the
convolution theorem), in a registration plane we will receive
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
A3(x', y') = F[T(ξ, η) A2(ξ, η)] = F{T(ξ, η) F[A1(x, y)]} = A1(−x, −y) ⊗ F[T(ξ, η)]
(4)
Here T(ξ, η) – amplitude transmission of a visualizing transparency (generally complex-value), ⊗ −
a symbol designating operation of convolution.
With no of visualizing transparency T(ξ, η) = const, the given transformation is local
(biunique), i.e. the change of complex amplitude at some point of the image registration plane
depends only on the change of complex amplitude at a corresponding point at the exit of
investigated object. However, use of any transparency with non-uniform amplitude transmission in
spatial coordinates leads to nonlocality of the transformation described by operator of convolution
in the ratio (4). It conducts to occurrence of the artifacts at registered images which are not
connected with the change of refractive index of investigated heterogeneity. Especially these effects
are notable at research of weak heterogeneities.
a
b
c
d
e
Fig. 2. Demonstration of nonlocality of transformation. a, c - visualization of a flow of a sphere
(diameter 40 mm, Re ~104); b,d,e − numerical emulation.
Position of the knife edge: a, b – vertical; c, d– horizontal; e – at angle of 30 ° to a vertical.
In the fig. 2 the images illustrating nonlocality of transformation at use of Foucault's knife are
presented. Results of visualization of freely falling sphere with vertical and horizontal position of
knife edge are shown. Artifacts in the form of a wide bar passing through the sphere image
orthogonally to a knife edge are distinctly observed. In spite of the presence of similar artifacts, it is
possible to receive the information of flow structure at visualization of horizontal density gradients
(fig. 2, а). Absolutely other situation presented in the fig. 2, c. In this case vertical gradients of
density are visualized which are essentially weaker then horizontal ones for given type of flow.
Thus, the parasitic change of brightness is located in the field of significant changes of a flow
density, and, as consequence, almost completely damps a useful signal.
Nevertheless, it is possible to use the transparencies which allows one essentially to reduce the level
of such artifacts. These are transparencies with amplitude transmission type of
T (ξ, η) = C1 + C2δ(ξ, η) ,
(5)
where С1 and С2 are the constants, generally the complex values. The second summand in the ratio
(5) is equivalent to addition of a flat wave to initial wave in a registration plane. As a result, the
interference of two waves is observed. Images are similar to infinite width fringe interferogram.
Thus the problem of decrease in a operating range disappears. Amplitudes of subject and basic
waves in the plane of registration are set by ratios
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Aob(x', y') = C1a0eiφ(x, y) = aobeiφ(x, y),
Aref(x', y') = arefeiΨ,
The intensity of radiation:
I(x', y') = |Aob(x', y') + Aref(x', y')2| = Iob + Iref + 2(IobIref)1/2cos[Ψ − φ(x, y)].
In spite of the fact that the amplitude of Aref and a phase ψ depend in an integrated way on a
phase of a subject wave across the whole image field, it doesn't lead to emergence of undesirable
artifacts. The change of intensity leads only to change of contrast of interferential fringes, and phase
change, to their phase shift constant across the whole field.
It is impossible to make physically a transparency with the transmission identical to a relation
(5) because of appearing of delta function in it. Besides, the use of a similar transparency is
senseless because of the zero energy passing through a mathematical point. However the approach
essence won't change, if transmission is kind of T(ξ, η) = C1 + C2circ(r). Similar transparencies are
widely known. It, not that other, as a version of filter Zernike-type used in a method of phase
contrast Zernike (1935). Value of argument r of a circular function is chosen equal to a radius of the
light source image.
In spite of high efficiency, a method of phase contrast is rather uncommon in aerophysical
experiments. As well as in usual shadow methods, at the small sizes of a light source the careful
adjustment of the device is necessary. Random displacement and vibrations, complicate, and
sometimes does impossible use of this method. Somewhat this problem managed to be solved by
means of use of real-time self-induced Zernike-type filters in Pavlov et al (2008), Golubev et al
(2010), Gastillo et al (2001), Bubis (2010). As such filters the layers of phototropic substance
changing the optical properties (colour, transmitting efficiency and/or refraction ratio) under the
influence of radiation are used. For objects with small changes of density the main part of radiation
energy is localized at zero spatial frequency range. It allows one to achieve a significant change of
optical properties of a layer only within this range (zero spatial frequency) by means of adjustment
of a light source power. As a result, the real-time self-induced amplitude and/or phase filter of
spatial frequencies is formed.
In papers Pavlov et al (2008), Golubev et al (2010) as darkened filter the layers of phototropic
silicate glass were used. In Bubis (2010) Zernike-type filter is executed as cuvette with the liquid
medium, operating because of thermal nonlinearity. In work Gastillo et al (2001) as real-time selfinduced Zernike-type filter the film of a bacteriorhodopsin of 50 µm thickness was used. Similar
real-time self-induced filters allow one essentially to increase the sensitivity and to simplify the
adjustment process and operation of the shadow device. However, the general for these devices
shortcoming is rather long-time inducing and a relaxation (about several seconds) of the filter. In
the presence of vibrations it leads to increase in the effective size of a visualizing spot to sizes
comparable with amplitude of vibration shifts of the light source, and, as a result, to reduction of
method sensitivity. Quite a big thickness of a working layer (more than 1 mm) brings in works
Pavlov et al (2008), Golubev et al (2010), and Bubis (2010) to increase in the sizes of a spot,
essentially exceeding the focal waist sizes as well as spreading of a thermal lens (Bubis (2010)).
2. New bleaching effect Zernike-type filters
The specified lacks managed to be eliminated almost completely in new, real-time selfdirected Zernike-type filters with relaxation time τ ~ 10−8 ÷ 10−4 s developed in ITAM SB RAS.
The filter is executed in the form of a layer with the thickness not exceeding the length of focal
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
waist of a reception objective and is made of the solid or liquid absorbing substance possessing of
bleaching property (bleaching effect, absorption saturation), that is reduction of absorption factor, at
increase in intensity of incident radiation.
Several mechanisms of bleaching effect of a material are known. Most widespread of them is
caused by absorption saturation, and is explained by equalization of population of two levels of
quantum energy system under the influence of resonant radiation. At increase of intensity of falling
radiation the rate of induced quantum transitions from the bottom to top level (absorption) grows.
Rate of decay of the excited level is defined by radiationless relaxation processes and by the
stimulated radiation. The probability of radiationless transitions is defined by properties of
substance and doesn't depend on intensity of incident radiation. The probability of the stimulated
transitions is proportional to intensity of falling radiation. As a result, with increase in intensity of
radiation the part of energy absorbed in the material decreases — transition is being saturated, and
saturation level is defined by a ratio of the stimulated transition rate and relaxation transition rate. In
a stationary mode the factor of absorption α is defined by a ratio
α=
α0
,
1+ I IH
where α0 − initial factor of absorption (in the weak field), I − intensity of incident radiation,
IН = Nhν / 2τα0 − intensity of saturation, N − full density of active atoms (molecules), ν − frequency
of incident radiation, τ − relaxation time in homogeneously broadened system. At bleaching of a
material the change of the refractive index is also observed. It is connected with reduction of the
additive caused by absorption.
The bleaching effect is to some extent observed for any transparent substances which have a
region of resonant absorption at wave length of incident radiation. The intensity of saturation value
IН is defined by transition type, its homogeneous width and time of a relaxation and can have values
from parts of W/cm2 up to hundreds of kW/cm2 and more (Zernike (1935)). Other mechanisms
leading to bleaching effect are possible also: such as a level depopulation near upper edge of a
valence band and filling of levels near a bottom edge of conduction band (inner photoeffect), Stark
frequency shift of quantum transition in the field of electromagnetic wave and others
During works on creation of real-time self-induced filters based on bleaching effect, the
visualization of test objects (a candle flame, microscopic cover glass) with use of various firm and
liquid substances has been carried out. In particular the painted glasses and polymeric films,
polarizer films, water, glyceric and ethanol solutions of dyes and other substances were tested
(brilliant green, rhodamine 6G, methyl violet, Lugol’s solution, ink for jet printers, etc.). In all cases
it was possible to carry out an effective visualization. Characteristic power of incident laser
radiation, depending on used substance and scene encumbering had a value of 5-20 mW. (The
power of laser source itself was approximately three times higher). By adjustment of a thickness of
the filter and power of radiation the variation of coefficient C2 in the ratio (5) for maintenance of an
optimum operating mode of the device is possible.
Manufacturing of filters for any wave length of visible radiation is possible. By analogy to the
term accepted in papers Pavlov et al (2008), Golubev et al (2010), similar filters are named by us
SA AVT (adaptive visualizing transparencies on effect of saturation of absorption). It should be
noted that the effect of filter inducing was observed by us as well for semitransparent layers of
metals (Cr, Сu), possessing an inner photoeffect in a visible range, and also practically for all
mentioned substances in a reflected light, including for thick, obviously non-transparent layers. In
the latter case, inducing of the filter is caused by change of reflection factor.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
As it was noted above, for real-time
self-induced
filters
the
important
parameters are: turnon time ton (inducing)
and turnoff time toff. (relaxation).
Measurements of these parameters with
use of the semiconductor laser with wave
length λ ≈ 0.65 µm, for some substances
having absorption lines in this spectral
range were carried out. The scheme of
Fig. 3. Scheme of shadow installation.
installation is presented in the fig. 3 and
essentially differs nothing from the usual
shadow scheme. Radiation from the laser
(1) is formed by lens (2) in a planeparallel beam of probing radiation.
Radiation passed through the investigated
heterogeneity (3) is focused by a lens (4)
in its focal plane where the visualizing
transparency (5) is located. The objective
(6) forms the image of studied object in
the plane of registration (7) (a television
camera matrix). We used objectives (2),
a
b
(4) with the relation of entrance pupil
diameter to a focal length of D / F ≈ 0.1.
Thus the waist length l of the focused
radiation in the focal plane of the
reception lens (4), defining the most c
admissible thickness of operating layer of
Fig. 4. The images of test object modulated by
SA AVT, made of 100 µm.
For ton detection the laser radiation
interferential fringes at td1 = 10, 50, 100, 300 µs.
was turned on at some moment of time
P ≈ 17 mW.
(fig. 4, а). The power of laser radiation P was regulated by changing of control impulse U
amplitude. After a period of time td1 the television camera lock for xposition period te was turned
on. Images of test object (microscopic cover glass 18х18 mm of thickness of 0.17 mm), modulated
by interferential fringes were registered. With increase of delay time, the contrast K(td1)
asymptoticly tended to the maximum value Kmax(P) depending on power of laser radiation. As
turnon time ton time td1 which is necessary for achievement of interference fringes contrast of
K(td1 ≈ ton) ≈ 0.8 was get.
For detection of turnoff time toff two
Substance
ton [ µs ] toff [ µs ]
laser impulses (fig. 4, b) were generated.
Duration of the first impulse was set
Polarizing optical filter
equal to turnon time ton. The second
100
1000
d = 100 µm
impulse of radiation with duration of te
necessary for image registration was
Ethanol. 1,25% solution of
20
≈ 100
generated with a delay of td2. At increase
brilliant green, d ≈ 50 µm
in td2, contrast of interference fringes
decreased. As turnoff time toff time td2
Ink Epson E0010 MLCS
10
≈ 100
which is necessary for achievement of
(Light Cyan), d ≈ 50 µm
interference
fringes
contrast
of
K(td2 ≈ toff) < 0.2was get.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
In the fig. 4, c the characteristic
images of test object modulated by
interference fringes, received while
detection of ton for a polarizing optical
filter are presented. Similar images, but
with inverse time-relation were registered
while toff. detecting. In the fig. 5 plots of
dependence of interference fringes
contrast on td1 and td2 times for SA AVT
are presented (on the basis of ethanol
solution of brilliant green and of jet ink
Epson E0010 MLCS printers (Light
Cyan)). Apparently from the given results,
the full cycle of turning on and turning off
of the filter for some substances can make
about 100 µs. It allows one almost
Fig. 5. Dependence of contrast on delay time.
completely to exclude the influence of
vibrations on quality of registered images.
In the table the received ton and toff values for these substances and for a polarizing optical filter are
given (power of the incident radiation falling at SA AVT was P ≈ 20 mW). With reduction of
power of radiation, the maximum achievable contrast goes down, and the filter inducing time ton
increases, that is quite explainable for physical reasons. In a configuration of the scheme used by us
the minimum radiation power made nearby 5 mW for all substances. It allowed to register
interferograms with contrast not less K ≈ 0.7 that in certain cases it is quite enough for reception of
the necessary information. The increase in power of radiation leads to increase of contrast and
reduction of filter induce time. SA AVT allow to work both with continuous, and with pulse (pulseperiodic) lasers. Their working capacity with use of the pulse laser (YAG Nd laser, with the
modulated Q-factor, with frequency doubling, λ = 0.53 µm, duration of an impulse of 10 ns) and
with continuous lasers (Nd DPSS laser, λ = 0.53 µm and laser diode, λ = 0.65 µm) was shown.
3. SA AVT application results
As test experiments have showed, the most effective in aero physical experiment in most
cases are SA AVT on the basis of solutions of dyes, with semi-conductor lasers controlled on power
and duration of an impulse. It is connected with rather small times of inducing and relaxation of
filters on their basis. Besides, intensity of radiation necessary for inducing of the filter is rather
high, and as a result of absorption effect the formation of a thermal lens can occur. As it was noted
above, this effect reduces the sensitivity of a method and increases turnoff time of the filter, this is
undesirable at research of weak heterogeneities and doesn't allow one to use a method effectively on
installations with high level of vibrations. Usage of pulse lasers allows to lower radiation dose of
active layer and probability of its degradation, and also excludes formation of a thermal lens.
Radiation impulse is turned on in time ton (it is time necessary for a filter bleaching) prior to the
beginning of an exposition of the registering device (television camera) and is turned off after
ending of exposition time.
In the fig. 6 the images of the candle flame which has been partially blocked by a cover glass
for some substances, received with pulse illumination are presented. In all images legible contrast
interference patterns are registered. Use of the wedge-shaped objects similar to a cover glass, allows
one to register interference fringes of finite width in the allocated area. In certain cases it can be
useful when obtaining quantitative information on a fringe shift, especially with the unknown or
changing across the image field direction of a gradient of an optical way. In the fig. 6, d for
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
comparison the image of the candle flame received earlier with use of AVT on the basis of
phototropic silicate glass is provided. Visualization is essentially worse, interference fringes
practically aren't visible.
a
b
c
d
Fig. 6. The flame of the candle partially blocked by cover glass. λ = 0.65 µm, P ≈ 5 mW.
a) polarizer film. d = 100 µm, ton = 400 µs.
b) 0.125 % ethanol solution of brilliant green. d ≈ 50 µm, ton = 20 µs.
с) Ink Epson E0010 MCS (CYAN). d ≈ 50 µm, ton = 30 µs.
Fig. 7. Visualization of subsonic gas flows.
Continuous laser P ≈ 5 mW, λ = 0.53 µm.
a – flow of a falling sphere. V = 4.2 m / s.
b –flow of a transverse cylinder. V = 10 m / s.
a
b
Fig. 7, а illustrates the SA AVT possibilities of subsonic flows visualization. The image
received at visualization of a flow of freely falling sphere in diameter of 38 mm is provided. Speed
of falling at the moment of registration was V = 4.2 m / s. SA AVT on the basis of ethanol solution
of the Rhodamine 6G, thickness about 50 microns was used. For comparison, in the fig. 7, b the
image received in subsonic wind tunnel T-324 of ITPM SB RAS with use of AVT on the basis of
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Fig. 8. Flow of a triangular plate М = 2, Re1 = 107 м−1.
silicate glass at visualization of a flow of the transverse cylinder (length of 1 m, diameter of 80 mm)
is provided.
In the fig. 8 it is given an example visualization of the supersonic flow which is realizing at a
flow of a flat triangular plate with blunted edges in supersonic wind tunnel T-325 (ITAM SB RAS).
This wind tunnel (as it was noted above) is characteristic that collimators of its regular equipment
shadow device undergo rather strong vibrations. This fact didn't allow to register reliably and stably
the image of shadow visualization, even when using of rather big (d ≈ 0.5 mm) light sources.
Application of fast SA AVT, along with use of collimators of diffraction quality, allowed to remove
completely a problem of vibrations and to increase the sensitivity of a method with preservation of
a wide operating range. In images it is visible that perturbations in the form of inclined waves
extend from strips of a thin film in the thickness of 0.1 mm and width of 15 mm. Film strips are
pasted on the top wall of a working part of wind tunnel and on a plate surface across to a direction
of the basic flow. The bottom image shows the flow area near a film on a plate surface. Flow
separations at film edges, interference fringes in boundary layer and weak perturbations at periphery
of a boundary layer are distinctly visualized. Chaotic, changing in time (moving downstream)
perturbations, most likely, are connected with turbulent perturbations in boundary layers on vertical
walls of a working chamber. Use of standard schemes with Foucault's knife didn't allow one to
visualize such perturbations at all.
The method was used at research of the outflowing of a jet flow from a convergent shaped
nozzle with the polished internal surface with exit radius Ra = 15 mm, and geometrical Mach
number M = 1.0 at various values of parameter Npr = p0/pc, (p0 and pc – pressure in the settling
chamber and in Eiffel's chamber). In the fig. 9, a images of a cold jet flow for several Npr. numbers
are given. In all modes the jet structure is distinctly registered. On border there is a tangential
current rip arises. In connection with its instability the whirlwinds moving streamwise and
crosswise of a flow are formed.
For Npr = 3 mode (fig. 9, b,) comparison of experimentally received interference fringe shifts
(markers) for cross-section at a nozzle cut (X = 0) and on a flow axis for cross-sections at X = 5, 10,
15 and 20 mm with their values received from calculated profiles of density (continuous lines) was
carried out. The commercial Fluent program package was used. The stationary axisymmetric
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Navier-Stokes equations with application of k-ω SST model of turbulence were solved. Flow
parameters for numerical calculation were close to experimental values: p0 = 0.3 MPa,
a
b
Fig. 9. Typical interferogram of underexpanded jet (a) and interference fringe shift (b). Npr = 3.
pс = 0.1 MPa, total temperature corresponding to stagnation temperature in a settling chamber
T0= 282 K, temperature of ambient space Tc = 288 K, Mach number at a cut of a nozzle М = 1.0.
Level of initial turbulence in a jet was defined by a fixing of pulsations intensity of a flow speed in
nozzle equal to 1 %, and the relation of turbulent viscosity to laminar, equal 10. The rectangular
regular grid with the size of each cell of 0.25×0.25 mm was applied.
Comparison of experimental and numerical data on fringe shift allowed to exclude the need of
solving of inverse poorly conditioned problem of definition of a field of density. Owing to one-tooneness of forward and backward Abelian transformation and other transformations which are
using for the solving of similar problems, this comparison is quite correct. Apparently from the
received results, at a nozzle cut where the stationary current is realized, a good coincidence of
experimental and numerical data is observed. Downstream the variation of data caused by a
nonstationarity of a flow and by difficulties of irregular fringes detection is observed. Nevertheless,
in certain cases the considered approach gives the chance to verify results of calculations, especially
for mixture layers at the jet periphery.
4. Conclusion
Thus, the new real-time self-induces Zernike-type filter based on bleaching effect (SA AVT),
possessing a number of advantages in comparison with the earlier known filters is developed. SA
AVT allow one to receive images similar to interferograms in an infinite width fringe, almost
completely to exclude the influence of vibrations of optical elements, to increase the sensitivity
without reduction of operating range of a method.
The work is supported by the Russian Fund of Basic Research (project No. 10-01-00418) and
the Interdisciplinary integration project of the Siberian Branch of the Russian Academy of Science
No. 113.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
5. Referenses
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laser beams on a weakly absorbing extended medium. LAT 2010: International Conference on
Lasers, Applications, and Technologies. V. 7994, pp. 79941I-79941I-6
• Gastillo MDI., Sanchez-de-la-liave D, Garsia RR et al (2001) Real-time self-induced nonlinear
optical Zernike-type filter in a bacteriorhodopsin film Opt. Eng., v.40, № 11, p. 2367-2368.
• Gibbs H. (1985) Optical Bistability: Controlling Lightwith Light, Academic, Orlando, Fla.
• Golubev MP, Pavlov AA (2010). Development of Schlieren Technique. 14 International
Symposium on Flow Visualization ISFV-14. [ISFV14-7B-4].
• Pavlov AA, Pavlov AlA, Golubev MP (2008) Use of AVT for gas flow visualization. XIV Int.
Conference on the Methods of Aerophysical Research ICMAR-2008.
• Zernike F (1935). Das Phasenkontrastverfahren bei der mikroscopischen Beobachtung. Zs.
Techn. Phys. 16, 454; Phys. Zs. 36, 848.
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