Particle and Particle Systems Characterization – To appear August 99
Droplet Sizing by Mie Scattering Interferometry
in S.I engine.
Christine Mounaïm-Rousselle, Olivier Pajot

Ass. Prof. Christine Mounaïm-Rousselle and PhD Stud. Olivier Pajot
Laboratoire de Mécanique et d’Energétique
Université d’Orléans
45072 Orléans cédex 2 (France)
Particle and Particle Systems Characterization – To appear August 99
Abstract
In this paper, we explain theoretically a technique based on Mie scattering interferometry
(M.S.I.), obtained by a defocusing of the collecting optics, to size droplets. The originality of
this study is the development of a droplet sizing method by planar laser light scattering for the
case of a scattering angle range close to 90°. The feasibility of this method and its limitations
are fully described. The dependence on intensity levels and refractive index variations can be
neglected. After discussion of some practical details about particle size, imaging and camera
constraints, the results obtained in the combustion chamber of a Spark Ignition engine, near
the spark plug, prior to ignition and for different injection timings are described and
discussed.
It can be concluded that the implementation of the M.S.I. method in our experimental setup has been realised successfully to provide droplet distributions in an S.I. engine. To enable
easier use of the technique, image processing software is going to be developed in the Matlab
environment.
Particle and Particle Systems Characterization – To appear August 99
1. Introduction
To reduce fuel consumption and pollutants emissions in Spark Ignition engine, one
working mode can be the lean burn one. Unfortunately, this mode is prone to misfires. To
reduce this problem, the air-fuel mixture must be correctly prepared around the spark plug.
For a better understanding of mixture preparation effects, experimental data are needed. One
way is to determine the influence of the presence of fuel droplets inside the combustion
chamber before the ignition. Indeed, it has been shown by Ballal and Lefebvre [1], and, Singh
and Polymeropoulos [2], that the ignition of vapour fuel is affected by the presence of fuel
droplets. They have studied the ignition phenomena for different droplet diameters and
different liquid/vapor fuel ratios. Moreover, spark ignition affects strongly the initiation of the
flame kernel, its propagation and finally formation of pollutants. Therefore the knowledge of
the droplet life time near the spark plug and prior to ignition in engines is relevant.
As in most experimental devices, the use of optical diagnostics is limited by optical
accesses. The final purpose is to estimate fuel droplets diameter distribution in a “transparent”
Internal Combustion engine, where the light scattering angle is orthogonal. This collection
angle is commonly used and available in the majority of experimental set-ups, designed for
planar imaging techniques. To record experimental data in engine environments is relatively
difficult and one needs to choose the most appropriate technique. The advantage of optical
diagnostics is evident due to their non-intrusivity and because they can provide the spatial
evolution of droplet diameter distributions. In S.I. engines, information on the spatial
distribution of droplets near the spark plug is sparse.
Droplet sizing techniques can be divided in two classes :
 Local measurement techniques, provide temporal local histories of particle size for
particles passing trough a spatial measurement volume, but spatial distribution can only be
obtained by mapping out the whole flow field. For example, Kadota et al. [3] have
Particle and Particle Systems Characterization – To appear August 99
successfully shown the feasibility of local fuel droplet diameter measurements in engine by
using laser Mie scattering. One HeNe laser beam was focused inside the chamber and the
scattered light due to the interaction between the ray and the droplet was collected via a
photomultiplier placed at 90°. The limitation was related to the quantitative sizing of droplets
: a calibration was required or a complex Mie theory simulation. The best developed
diagnostics is the Phase Doppler Anemometer. Vannobel et al. [4] and Posylkin et al. [5]
have done preliminary studies on optical engines with PDA. It seems to be attractive due to
simultaneous droplet size and velocity measurements. Unfortunately, this technique needs a
collection optics located in the scattering plane at scattering angles from 25 to 75 degrees and
provides temporal data but spatial data have to be mapped out with multiple measurements.
Another technique to size droplets developed by Massoli et al. [6] is based on the polarization
properties of light. The quality of the light detectors is important because it needs to compare
measured polarized intensities ratios with those computed by Mie theory simulation.
 Two dimensional planar configurations provide instantaneous spatial resolution.
Nowadays, due to the extensive development of CCD cameras, image grabbers and processing
systems, these techniques have become very attractive. Peters [7] has estimated droplets size
distribution during intake and compression strokes with a basic imaging technique based on
Mie light scattering. The difficulties were that to estimate droplet diameter, it was necessary to
assume a predetermined droplet density and size range. Moreover, the analysis was not easy
due to out-of-focus droplets. Hofeldt et al. [8] have followed the same idea and developed
successfully their imaging configuration, providing spatially resolved measurements of
particle size for hundreds of droplets in essentially real time ; but with the same difficulties
discussed above : necessity to calculate particle scattering intensities with Lorenz-Mie theory,
and to perform accurate intensity measurements with intensified CCD cameras. Recently,
Skippon et al. [9] have applied another imaging technique in an optical accesses engine :
Particle and Particle Systems Characterization – To appear August 99
interferometry based on Mie scattering. Glover et al. [10] initiated this method based on the
interference between light reflected from and refracted through individual droplets in the
wide-angle forward-scatter region. The advantage is the independence on the absolute
scattering intensities : out-of-focus images of laser scattering droplets from the 45° direction
consist of a set of lighted spots with fringes. They showed that due to geometrical analysis, the
diameter can be easily determined from the number of fringes. They first applied this
technique in sparse calibrated sprays and showed a good agreement between their results and
those measured with a Malvern sizer.
To perform droplet sizing and distribution data in an S.I. engine, Mie Scattering
Interferometry (M.S.I.) has been selected in this study, but in our configuration a unique
scattering collection angle of 90° was chosen. In this case, not only the scattered intensity is
very low but the geometrical analysis must be performed carefully. Ragucci et al. [11] have
tested the Mie Scattering Interferometry method in this particular case, but their analysis has
been done with only one drop although their conclusion was very promising, indicating the
possibility to develop the planar configuration. The emphasis of this paper is on the
development of this diagnostic technique. Firstly we will remind its theoretical basis to
express clearly the relation between number of fringes and droplet diameter by using a
geometrical hypothesis. The experimental setup will be described and advice about
experimental constraints will be given. The final section presents and discusses results of
preliminary experiments performed near the spark plug in an engine working under different
conditions during the compression stroke, prior to ignition.
2. Theoretical bases of the M.S.I.
In this part, the basic phenomena and hypothesis will be clearly described in order to get
the simple relation between the number of fringes and the droplet diameter.
Particle and Particle Systems Characterization – To appear August 99
One of the most important results of Lorenz-Mie theory is that the light scattered by a
spherical particle is inhomogeneously distributed in space, depending on droplet diameter,
refractive index and incident light characteristics. By using the Generalised Lorenz-Mie theory
as in Gouesbet et al. [12], it can be shown that the scattered light intensity is an oscillating
function of the angle in the range of 0<.
These oscillations, due to interference between diffracted, refracted and reflected rays
emanating from the particles, are the bases of the Mie Scattering Interferometry. Van de Hulst
[13] has demonstrated that for large size parameter x where x = d/, with d, the droplet
diameter and  the incident light wavelength, the scattering of light by a spherical particle
illuminated by planar wave fronts can be described by geometrical optics rules, simpler than
the complex Mie theory. In our case droplet diameters lie within the range from a few
micrometers up to 100 µm. So for a 532 nm wavelength, x ranges from 5.9 up to 590. Ungut
et al. [14] have shown that this approximation is valid for droplets as small as 1 µm for
forward scattering angle (0-20°).
In Fig.1, we compare the scattered light in the plane perpendicular to the incident
polarisation, estimated by Mie theory and geometrical analysis for two droplet diameters : 50
µm and 10 µm, with a real refraction index of 1.39 (iso-octane droplet). One can see that a
very good agreement occurs when the scattering angle range is 30°<<70°.
Figure 1….
Therefore it is possible to use a geometrical analysis to apply M.S.I.. However, if we
make a similar comparison for a scattering angle range centred around 90° as in Fig.2, one can
note that the intensity value and shape are not in good agreement. But, the number of
oscillations, for instance for an angle range of 10° are nearly similar. The geometrical analysis
can be inappropriate therefore in our application but it does provide a simple relation to
estimate droplet size.
Particle and Particle Systems Characterization – To appear August 99
Figure 2….
2.1 Geometrical analysis
All droplets are considered perfectly spherical and homogeneous. The interaction between
a light ray (i.e. here a laser beam) and a droplet is shown schematically in Fig. 3. The total
scattering light intensity is due to the sum of reflection and successive refractions. For the
interferometric Mie scattering method, only the reflection and first refraction rays are
considered. The reflection ray is not attenuated by absorption but the first refracted one is :
the difference of both optical paths, which form dark and bright fringes, is a function of the
droplet diameter. The advantage is that this sizing method is totally independent of the
intensity of the illuminating light source. The droplet itself acts as an interferometer.
Figure 3…
o and 1 are the incidence angles of reflected and refracted beams respectively and ’1 the
refraction angle. By the Snell’s law, the relation between ’1 and 1 can be expressed as below,
with m the real part of the refractive index:
cos 1 
1
cos 1
m
(1)
The scattering angle from the incident ray is, for pure reflection, o=2o and for one refraction,
1=2( 1 -1). There exist only two rays for which these scattering angles are the same. Table
[1] shows that for a scattering angle of 90° and for droplets with a range of refractive indices
m, the value of 1 is very low. So only very few rays can be reflected once and leave the
droplet with a 90° scattering angle.
Table 1…
The phase difference between both rays can be easily expressed via the phase term
determined by simple geometry (Mounaïm-Rousselle and Pajot [15], Golombok et al.(16])
Particle and Particle Systems Characterization – To appear August 99
2d
2d
sin 0 
(sin 1  m sin 1' )


2d



(sin  m 2  1  2m cos )

2
2
 0  1 
(2)
As Ungut et al.[14] have shown, the phase difference is taken account in total scattered
light intensity expression via a cosine. Therefore, an infinitesimal variation of the scattering
angle induces a maximum or minimum light intensity variation and occurs when an
infinitesimal phase difference is equal to 2. These considerations allow one to write :
m sin
d

(0  1 ) 
(cos 

2

2

m 2  1  2m cos
2
)  2
(3)
So as Van de Hulst [14] and Roth et al. [17] indicated, the angular inter-fringe spacing
is linked to the droplet diameter by : 
 
2
d
1
cos


2

m sin
2
m 2  1  2m cos
(4)

2
Glover et al. [10] have used a simplified formula (Eq. 5), based on the assumption that the
angle of incidence of the refracted ray on the droplet is close to zero. In fact, it is not
appropriate for a scattering angle of 45° (in their application) but can be used for a scattering
angle of 90°, as shown Golombok et al. [16].
 
2 1
d 1 1
m
(5)
2.2 Comparison between Mie theory and geometrical analysis
In Fig. 4, the angular inter-fringe spacing, obtained by Mie theory, general geometrical
analysis (via Eq.4) and the approximation (via Eq.5) is plotted versus (iso-octane) droplet
diameter, for a 90° scattering angle.
Particle and Particle Systems Characterization – To appear August 99
Figure 4 …
The trends are globally the same but an overestimate of approximately 14% appears with
the geometrical analysis, for droplets smaller than 10 µm. In fact, we will see below that
experimentally, by counting integer numbers of fringes, the droplet size is not an absolute
value but is classified with a size class as probability function.
2.3 Influence of refractive index variations.
As all techniques based on Mie scattering, the refraction index changes play an important
role on droplet sizing. From Eq.5, it is possible to estimate this effect. As it can be seen below
in Fig.5, for iso-octane droplets the refraction index ranges between1.3 and 1.5, due to the
temperature field, we can evaluate that this 6% variation around the standard value of 1.39
only induces an angular inter-fringe frequency variation of 0.07 % ! It is clear that one of the
advantages of this technique is that the refractive index variation does not sharply affect
droplet sizing.
Figure 5…
3. Experimental considerations
The Planar Mie Scattering Interferometry set-up is simple as can be seen in Fig. 6 : a
laser sheet illuminates the droplets and a light collection lens images the droplets onto a CCD
or photographic camera. However, to visualise the fringes inside the droplet the camera needs
to be positioned out of the focal plane. At the focal plane, the fringes are superimposed and
droplet images uniformly lighted are obtained. For a scattering plane at 90°, the main
drawback is the low scattered intensity; however with modern CCD cameras, intensifiers are
not necessary.
Figure 6….
Particle and Particle Systems Characterization – To appear August 99
One important experimental parameter is the collection angle  : it must allow to get a
number of fringes sufficiently high to distinguish them.  is equal to the number of fringes N
multiplied by the angular fringe spacing . This angle can be also approximated as function
of the magnification ratio G, defined as the ratio between the image size and the object size,
and the numerical aperture N.A. :
  2 arcsin(
G
1
.
)
G  1 2 N.A.
(6)
Finally, from Eq.5 and Eq.6, the droplet diameter can be expressed as :
d
N
1
G
1
1
arcsin(
.
) 1
G  1 2 N.A.
m
(7)
3.1 Influence of the collection angle
The importance of the collection angle is shown in Fig. 7 where the number of fringes in
the image is plotted against the droplet diameter for different collection angles. It is evident
that for a given diameter, the number of fringes inside the droplet image increases with
increasing value of this angle. Therefore, for example a collecting angle of 20° allows a good
estimate of droplet diameters range of 5-20 µm, which generates a number of fringes from 3
to 11. A bad knowledge of the collecting angle can add also other errors.
Figure 7….
In general experimental geometric constraints may limit the collection angle. So there is a
compromise between the possible choice of this angle, linked to the magnification ratio and
the lens-object distance, and the more appropriate angle to determine a given droplet diameter
range. On the other hand, in most applications, as in engine environment, it is easier to use a
CCD camera than photographic one, to follow cycle-by-cycle a phenomena but the current
CCD size is not more than 100 mm2. This implies that the image area will be sharply
restricted, involving a low magnification ratio. So the useful parameter becomes the number
Particle and Particle Systems Characterization – To appear August 99
of aperture : in conclusion, with CCD camera, a good collecting system is an objective which
enables a large aperture with a large lens diameter.
3.2 Imaging constraints
The droplet image with out-of focus technique is a disk with fringes superimposed. The
centre of the disk corresponds to the droplet position in the planar laser sheet. So, with M.S.I.
images as in Fig. 8, it is possible to measure simultaneously the droplet spatial distribution
and droplet size.
Figure 8…
We have underlined that to image fringes on the CCD pixels, the camera must be
defocused. In fact, this defocusing distance must not be too large in order to allow a sufficient
visualisation area. It is evident also that the measurable maximum droplet size is limited by
the minimum distinguishable angular inter-fringe spacing. This problem can be seen in Fig. 8 :
the biggest droplet, i.e. the brightest image, can not be sized due to the too large number of
fringes. So the fringes contrast does not allow an easy count. On the other hand, droplets with
one fringe are also difficult to evaluate : it is not possible to know if there is only one fringe or
if the droplet is not totally in the laser sheet.
As it can also be seen on this image, two interference images can overlap, due to droplets
very near to each other and after defocusing they overlap. It is clear that in the case of a fixed
out-of focus distance, dense sprays can not be sized. The unique solution would be to increase
the magnification but then the image area becomes smaller generating less droplet images. An
example of M.S.I. image, taken in an alcohol dense spray (Bissonnier [18]), but with a Nikkon
F4S camera, is shown in Fig.9. In this case, the magnification ratio is unity, so the image area
is 24 x 36 mm. The focal length is 136 mm with a out-of-focus of 5 mm, so the defocus
distance is around 4 %. When the film plane is normal to the lens axis, the size of the droplet
image varies with position across the film, so with the defocus distance. When the
Particle and Particle Systems Characterization – To appear August 99
Scheimpflug condition is satisfied, the size of individual out-of-focus images from different
droplets is the same. Experimentally, it is verified only when the defocusing is sufficiently at
least of 4% of the focal length. This characteristic becomes very relevant to develop an
automatic image analysis software.
Figure 9…
We have shown theoretically that the maximum drop size is determined by the angular
inter-fringe spacing but experimentally, also by the imaging area, the magnification ratio and
the objective lens characteristics.
We have previously verified the accuracy obtained by this technique with a 90° scattering
angle in sparse sprays of water (Mounaïm-Rousselle and Pajot [15]). For example, a spray of
droplets of mean classical Sauter diameter of 10 µm, measured by a Malvern sizer was used.
To get the size distribution by M.S.I., 100 images have been taken, and 500 droplets were
counted. The mean Sauter diameter estimated by MSI was 12.91 µm at a scattering angle of
45° and 12.97 µm at 90°. Agreement between the two techniques was reasonable, mainly due
to the non evaluation of small droplets (below than 4 µm for the experimental set-up used in
this case) with the M.S.I., and also due to the inherent differences in spatial and temporal
sampling. Moreover, the results obtained with both scattering angles are very close.
4 Experimental set-up
Optical engine. A schematic of the engine and optical system is shown in Fig.10. This
optical accessed spark-ignition engine is derived from a standard 4 cylinder-2 litre engine. A
single cylinder head is mounted on top of an elongated crankcase. This raised cylinder houses
a piston with a transparent quartz crown, allowing optical access to the 4 valve pentroof
combustion chamber. Two quartz windows enable access through the cylinder head.
Figure 10…
Particle and Particle Systems Characterization – To appear August 99
An optical shaft encoder with 3600 pulses per revolution provides the crank angle
position to a timer card, which generates pulses for injection, ignition, laser triggering and
video capture. The engine was driven at 2000 revolutions per minute by an electrical motor.
Iso-octane was the fuel. The mean admission pressure is fixed at 500 mbar and the injection
duration at 5 ms. The global equivalence ratio of air/fuel mixture was maintained, for all
cases, at stoichiometric level. Three modes of injection were studied : mode 1 corresponding
to an injection at the beginning of the intake valves opening ; mode 2, just after the intake
valves closing and ; mode 3, at the middle of the intake valves opening.
Planar Mie Scattering Interferometry set-up. To implement this technique, a frequency
doubled YAG laser beam (532 nm, 200 mJ) passes through a set of cylindrical and spherical
lenses to form a sheet with a minimum thickness of 0.5 mm (the sheet thickness must be
larger than maximum droplet diameter). This 40 mm width vertical sheet enters in the
combustion chamber via the transparent piston head as it can be seen on Fig.10. The location
for visualisation of droplets location inside the combustion chamber is just below the spark
plug. A laser pulse was triggered once per engine cycle, the light scattered by the fuel droplets
was collected at 90° and imaged into a KPM2 Hitachi CCD camera. The CCD resolution is
768 by 568 pixels and its size 6.47mm by 4.83 mm. However, due to the asynchronous
trigger, only 768 by 284 pixels were used. The camera was aligned to have the maximum
pixel number in the direction of the fringes. The resolution seems to be too low as discussed
by Glover et al. [10]. They used a photographic film to get a better resolution. But high
resolution is not essential to provide quantitative results which depend on the diameter
resolution and the diameter range required : the camera objective is also one of the most
important component to select the appropriate droplet diameter range. In our case, several
camera objectives have been tested to optimise the collection angle. The best choice in our
configuration was the Nikkor AF80-200f/2.8 ; it allows large aperture collection with its non
standard lens diameter of 77 mm. For this study, the visualisation area in the focal plane is 10
Particle and Particle Systems Characterization – To appear August 99
x 13 mm which gives a magnification ratio of 1:2 and the distance between the laser sheet and
the objective lens is 150 mm at 80 mm macro position. To achieve an approximate sufficient
number of distinguishable fringes, the out-of-focus distance used was 11 mm, corresponding
to 7% of the objective-object distance. In this case, the size of the area visualised becomes 9 x
12 mm. With this set-up, a droplet with a diameter of 3.5 µm gives one fringe image. For this
study, we were particularly interested on a droplet diameter range between 10 µm to 50 µm.
5 Results and discussion
Firstly we studied the injection mode, i.e. the injection is made at the beginning of the
intake valve opening, to analyse the presence of droplets and their diameter distribution. Some
of the images do not allow fringe detection due to too small droplet size and also droplets out
of the field of view. So some images were not considered; on average, about 75 images from
100 images taken were validated. The images in Fig.11 have been taken at different crank
angles relative of the ignition timing (which is 45° before T.D.C.) but not during the same
cycle. It is not easy to draw a conclusion concerning the droplet field. It can be noted first that
15° before start of ignition droplets are more at the top of the image, i.e. nearer the spark plug
location. Indeed, during this compression stroke, droplets are pushed to the cylinder head, by
the piston itself. We can see, also that 5° after the ignition, droplets are still present in this
area
Figure 11…
. To analyse the droplet diameter is difficult, as it can be seen on Fig. 12 where droplet
diameter distributions are plotted. It seems that just after the start of ignition, droplets still
exist, certainly also due to the piston rise. It can be concluded that larger number of droplets
occurs far from ignition due to piston rise and also to the liquid deposits on the piston head.
During the rise, with pressure and temperature effects, these droplets due to the deposit
vaporise and fewer droplets are found just prior to ignition. After ignition, certainly droplets at
Particle and Particle Systems Characterization – To appear August 99
spark plug location have been pushed away by the flame kernel and they appear on the image
area. The mean Sauter diameter is about 20 µm in this imaging area and for this injection case.
Figure 12 …
To emphasise the feasibility of the Planar Mie Scattering Interferometry technique for
engine applications, we have visualised droplets for the two other injection modes, 5° prior to
ignition. Mode 2 corresponds to an injection when the valves are closed at the beginning of
the compression stroke so the liquid droplets stay in the intake pipe for 540° crankrotation. In
mode 3, the injection is done 120° after the beginning of intake valves opening.
The droplets size distribution for the modes 1 and 3 are plotted on Fig.13. In fact, in mode
2, usually called closed valve injection mode, only two images contain one discernible
droplet. This result can be explained by the vaporisation process occurring in the intake pipe
itself.
Figure 13…
For mode 3, the average number of droplets per image is higher than for mode 1 : 2.26
and 1.72 respectively and also the mean Sauter diameter, 23 µm. In fact, for mode 1, the
intake flow velocity is lower at the beginning of the intake. Then it can be expected that
deposits on the intake wall are more important, introducing less droplets in the combustion
chamber. Moreover, the injection is done during the back flow of exhaust gases, where an
increase of temperature may induce earlier droplet vaporisation.
6 Conclusion and perspectives
The Planar Mie Scattering Interferometry has been applied in an engine environment
where optical access is limited but allowing a collecting plane perpendicular to the laser sheet.
The theoretical bases of this technique were clearly exposed to illustrate fundamental concepts
and assumptions. The experimental arrangement for P.M.S.I. was described and the technical
Particle and Particle Systems Characterization – To appear August 99
problems for implementing it was discussed in detail. This technique was used successfully to
investigate the distribution of iso-octane droplets as function of engine crank angle during the
compression stroke around the spark ignition and just below the spark plug. Three injection
modes were also studied to achieve an idea of the droplets life in this area. These results will
be used to study the earliest flame kernel in Spark Ignition engine.
It can be concluded from this work that the Planar Mie Scattering Interferometry
technique is an easy and simple optical diagnostic. It can provide good resolved spatial
information about droplet location and size. The simple geometrical analysis is sufficient to
establish the relation between optical characteristics of the collecting system, number of
fringes detected and droplet diameter. Compromise must be found in terms of droplets size
range, maximum distinguishable number of fringes, image area and also the required diameter
precision. To avoid the manual fringe count, we are developing an automated image
processing software in Matlab environment. Finally, it would be interesting to develop this
technique in parallel with Particles Imaging Velocimetry to perform simultaneously, planar
measurements of droplet distribution, size and velocity.
Acknowledgements
The authors wish to thank G. Grehan, CORIA Rouen, for his theoretical help and C.
Preterre, Renault S.A., for providing access to a transparent engine during this work.
Particle and Particle Systems Characterization – To appear August 99
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[16] Golombok M., Morin V. and Mounaïm-Rousselle C. : Droplet diameter and the
interference fringes between reflected and refracted light., J. Phys. D: Applied Physics, vol 31,
n°18, (1998), pL59-pL62.
[17] Roth N., Anders K. and Frohn A. : Refractive-Index Measurements for Correction of
Particle Sizing Methods, Applied optics, Vol 30 n°33, (1991), pp. 4960-4965.
[18] Bissonnier A. : Etude expérimentale du TétraChloroBenzene-Applications à
l’incinération, PhD Thesis, University of Orléans, Nov. 1998.
Particle and Particle Systems Characterization – To appear August 99
Symbols and Abbreviations
x : size parameter
d : droplet diameter
m : real part of the refractive index
G : magnification ratio
M.S.I. : Mie Scattering Interferometry
N : number of fringes
N.A. : numerical aperture
P.M.S.I : Planar Mie Scattering Interferometry
T.D.C. : Top Dead Center
incident light wavelength
scattering angle
 : incidence angle
’: refraction angle
 angular inter-fringe spacing
: phase term
collection angle
subscript
0 : relative to reflected ray
1 : relative to refracted ray
Particle and Particle Systems Characterization – To appear August 99
Legends of Illustrations
Figure 1. Comparison of the scattered intensity, Ip, in the plane perpendicular to the incident
polarisation, estimated by Mie theory and geometrical approximations for droplet diameters of
50 µm and 10 µm (real refractive index of 1.33).
Figure 2. Comparison of Ip estimated by Mie theory and geometrical approximations around a
scattering angle  = 90°, for a droplet of 50 µm (real refractive index of 1.33).
Figure 3. Light ray patterns through a droplet.
Figure 4. Angular inter-fringe spacing obtained via Mie and geometrical analysis, at 90°
scattering angle versus droplet diameter. (m = 1.39,  = 532 nm).
Figure 5. Effect of the refractive index on the angular inter-fringes spacing for two droplet
diameters : 20µm and 60 µm. (m = 1.39, = 90°,  = 532 nm).
Figure 6. The Planar Mie Scattering Interferometry experimental set-up.
Figure 7. Effect of the collecting angle on droplet diameter. (m = 1.39,  = 90°,  = 532 nm).
Figure 8. Defocussed CCD image for a sparse droplet distribution.
Figure 9. P.M.S.I. image obtained in dense spray with photographic camera. (Courtesy of
Buissonnier [18]).
Figure 10. Schematic view of the experimental set-up around the optical accesses engine.
Figure 11. Instantaneous P.M.S.I. images at different crank angles for injection mode 1.
Figure 12. Droplets diameter distribution for injection mode 1 at different crank angles
Figure 13. Droplets diameter distribution for three injection modes, 15° prior ignition.
Particle and Particle Systems Characterization – To appear August 99
Tables
m
1 (°)
’1 (°)
Real refractive
index
Incidence angle
Refraction angle
1,2
2,53
33,64
1,3
2,16
39,76
1,33
2,07
41,29
1,39
1,94
44,03
1,45
1,83
46,42
1,5
1,76
48,21
Table 1. Refracted incidence and refraction angles values for different refractive index
with a scattering angle of 90°.
Particle and Particle Systems Characterization – To appear August 99
1000000
Mie theory, d = 10 µm
Geometrical analysis
Mie theory, d = 50 µm
Geometrical analysis
Scattering light intensity (a.u.)
d = 50 µm
100000
10000
1000
100
d = 10 µm
10
1
30
35
40
45
50
55
Scattering angle (°)
Figure 1
60
65
70
Particle and Particle Systems Characterization – To appear August 99
Scattered light intensity (a.u.)
1,E+04
1,E+03
1,E+02
Mie theory
1,E+01
Geometrical
analysis
1,E+00
80
82
84
86
88
90
92
Scattering angle (°)
Figure 2
94
96
98
100
Particle and Particle Systems Characterization – To appear August 99
’

’
Spherical
droplet

on
racti
f
al re
Figure 3
n
inter
n
lectio
al ref
n
Exter
Incident wave
 

One


Particle and Particle Systems Characterization – To appear August 99
Angular inter-fringe spacing (°)
4
3,5
Mie theory
3
Simplified geometrical analysis
2,5
Geometrical analysis
2
1,5
1
0,5
0
5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105
Droplet diameter (µm)
Figure 4
Particle and Particle Systems Characterization – To appear August 99
Angular inter-fringes spacing (°)
1,9
1,6
d = 60 µm
d = 20 µm
1,3
1
0,7
0,4
1,15
1,25
1,35
Mean refractive index m
Figure 5
1,45
1,55
Particle and Particle Systems Characterization – To appear August 99
Figure 6
Particle and Particle Systems Characterization – To appear August 99
Influence of the collecting angle
Number of fringes
24
alpha = 5°
alpha = 10°
alpha = 15°
alpha = 20°
20
16
12
8
4
0
0
10
20
30
40
50
Droplet diameter (µm)
Figure 7
60
70
80
Particle and Particle Systems Characterization – To appear August 99
Figure 8
Particle and Particle System Characterisation – To appear August 99
90
75° before S.I. Ds = 18 µm
55° before S.I., Ds = 19 µm
35° before S.I., Ds = 21 µm
15° before S.I., Ds = 20 µm
5° before S.I., Ds = 20 µm
5° after S.I., Ds = 23 µm
80
Number of droplets
70
60
50
40
30
20
10
0
7
11
14
18
21
25
28
32
Droplet diameter class (µm)
35
Particle and Particle System Characterisation – To appear August 99
Figure 12
Particle and Particle System Characterisation – To appear August 99
Mean number of droplets
0,31
Mode 1
Mode 3
0,21
0,10
0,00
7,00
10,51 14,01 17,51 21,01 24,52 28,02 31,52 35,02 38,52
Droplet diameter (µm)
Particle and Particle System Characterisation – To appear August 99
Figure 13