Note: Descriptions are shown in the official language in which they were submitted.
B 15569 PV 1
METHOD FOR THE CONTACTLESS MEASUREMENT OF THREE-
DIMENSIONAL OBJECTS WITH TWO LAYERS BY SINGLE-VIEW
BACKLIT SHADOWGRAPHY
DESCRIPTION
Technical field
The present invention concerns a method for the
contactless measurement, or characterisation, of three-
dimensional objects with two layers by single-view
backlit shadowgraphy.
This method applies in particular to:
- the contactless measurement of the deformation
or roughness of the internal surface of a transparent
hollow object with two layers,
- the measurement of the refractive indices of an
isotropic transparent hollow object with two layers,
- the measurement of the thickness of the internal
layer of a transparent hollow object with two layers,
- putting the internal layer of such an object in
conformity, by controlling recovery, and
- calculation of the roughness of such an object,
on the basis of a three-dimensional reconstruction by
spherical harmonic analysis methods.
The contactless dimensional measurement of a
hollow three-dimensional object with two layers, which
is transparent or at least, translucent vis-a-vis
visible light, presents many difficulties.
To overcome these difficulties, it is known to use
a technique of measurement by backlit shadowgraphy.
This technique applies to the characterisation of
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objects that can be observed at a single viewing angle,
in particular objects to which it is difficult to gain
access.
In the present invention, the
objects
characterised are essentially hollow spheres.
This invention makes it possible to approximate
spatially an area of the internal surface of an
observed object, from a shadowgraphic exposure of this
object, and to determine the state of the internal
surface of a translucent hollow object with two layers,
by means of shadowgraphic and interferometric
observations.
Prior art
Two techniques are known for measuring the
thickness and diameter of hollow spheres, namely
interferometry and X-radiography. The latter cannot be
used if the object is placed in a complex
infrastructure and cannot be manipulated from the
outside.
Certainly there exist methods of three-dimensional
reconstruction of objects using a single image, but
their implementation assumes that these objects have a
large number of symmetries. In addition, the
reconstruction is global.
Interferometry for its part is a precise method
that can be used in a complex infrastructure, but its
implementation is fairly tricky.
Two methods are also known for measuring three-
dimensional objects by backlit shadowgraphy, through
,
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the following documents, to which reference will be
made:
[1] International Application WO 2004/083772 A
published on 30 September 2004, "Method of measuring
three-dimensional objects by single-view optical '
shadowgraphy"
[2] International Application WO 2006/030149 A
published on 23 March 2006, "Method of measuring
dimensional objects by single-view
optical
shadowgraphy, using light propagation optical laws".
The technique that is disclosed by document [1]
requires the systematic creation of a data table from
simulations made by means of optical software, this
table covering the whole range of dimension of the
objects to be observed. The data in the table make it
possible to go back, by interpolation, to a dimensional
measurement of the object. The greater the range of
dimensions introduced into the data table, the longer
it takes to create this table if it is wished to
maintain a certain degree of precision.
The technique disclosed by document [2] is based
on the Snell-Descartes optogeometric laws and
constitutes only a summary approximation of the state
of the internal surface of the hollow object that it is
wished to characterise. In this technique, the curve
observed is directly used as being the internal wall of
the internal layer of this object. In addition, the
observation zone is limited to the equatorial plane of
the object, which is generally spherical. No spatial
reconstruction of the internal surface of a hollow
object has been made using this technique. In addition,
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no spatial reconstruction method is mentioned in
document [2].
Disclosure of the invention
The aim of the present invention is tO remedy the
aforementioned drawbacks.
It concerns mainly the three-dimensional
reconstruction of the internal wall of a two-layer
object over an area close to the equator of this
object, from a shadowgraphic image of the object.
In addition to this contactless optical method,
another means of characterisation on several points is
used. Thus a global three-dimensional reconstruction of
the internal wall of a two-layer object, which is
translucent or transparent to light rays, is carried
out.
This three-dimension reconstruction is global
since the entire internal wall is reconstructed. To do
this, special functions are used that parameterise a
deformed sphere.
The shadowgraphic method makes it possible to
observe an area that is close to the equator of the
object. The image observed using this method must be
analysed. The information is situated in the main light
ring that the image comprises and is the intersection
of the plane of observation with a caustic.
A linear relationship exists between the
deformation of the main light ring and the disturbances
present on the internal wall of the two-layer object.
This relationship establishes a correspondence between
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bidimensional information obtained from the image and
three-dimensional information.
Spatial reconstruction from
bidimensional
information is the most important element of the
present invention. Up to the present time, nobody had
sought to establish a link between a deformed caustic
and a disturbance of the internal wall of a hollow
object.
In the invention, the interferometric method is
used to directly measure the thickness of the internal
layer of the object and therefore the deformation of
this internal layer. However, this method makes it
possible to make observations only over a limited area
of the two-layer object since the latter is generally
placed in a complex environment that greatly limits
movements.
This is why the spatial reconstruction of the
internal surface of the two-layer object is based on
the merging of the shadowgraphic and interferometric
data. The data merging is therefore another important
element of the present invention, after the spatial
reconstruction from an image obtained by backlit
shadowgraphy.
In precise terms, the present invention concerns a
method for the contactless measurement of a hollow
three-dimensional object, thus having an internal wall,
this object comprising an external layer and an
internal layer, this object being translucent or
transparent vis-à-vis a visible light, this method
being characterised in that:
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- an image of the object is acquired by single-
view backlit shadowgraphy, along a first viewing axis,
by observing this object with visible light, this image
comprising at least one luminous line (ring or band),
- an equaiion is established that connects at
least one optogeometric parameter of the object to at
least one geometric parameter of the luminous line,
- this geometric parameter is determined, and
- the optogeometric parameter is determined by
means of the equation and geometric parameter thus
determined.
According to a preferred embodiment of the method
that is the object of the invention:
- a three-dimensional reconstruction is made of
the internal wall of the three-dimensional object over
an area that is close to the equator of this object,
from the image of the object and the equation, this
reconstruction supplying a first set of data,
- the thickness of the internal layer of the
object is determined,
- a second set of data relating to the deformation
of this internal layer is determined from the thickness
thus determined, and
- a reconstruction of the entire internal wall of
the object is carried out by means of the first and
second sets of data.
Preferably a linear relationship is established
between a deformation of the luminous line and
disturbances that are present on the internal wall of
the object, in order to determine the second set of
data.
,
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According to a first particular embodiment of the
method that is the object of the invention, the
thickness of the internal layer of the three-
dimensional object is determined by an interferometric
technique.
According to a second particular embodiment, the
thickness of the internal layer of the three-
dimensional object is determined by a shadowgraphic
measurement made along a second viewing axis that is
not parallel to the first viewing axis.
According to a third particular embodiment, the
thickness of the internal object of the three-
dimensional objection is determined by a shadowgraphic
measurement made along the first viewing axis after
having made a rotation of the object.
Preferably the reconstruction of the entire
internal wall of the three-dimensional object is
carried out by combining the first and second sets of
data by means of the method of least squares.
According to a particular embodiment of the method
that is the object of the invention, two optogeometric
parameters are determined, consisting respectively of
the refractive index of the internal layer and the
refractive index of the external layer of the three-
dimensional object, from two geometric parameters,
respectively consisting of the thickness of the
internal layer and the thickness of the external layer.
Brief description of the drawings
The present invention will be better understood
from a reading of the description of example
,
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embodiments given below, purely by way of indication
and in no way limitatively, referring to the
accompanying drawings, in which:
- figure 1 is a schematic view of a backlit
shadowgraphic device that can be used in the present
invention,
- figure 2 shows the radial profile of a backlit
shadowgraphic image that is obtained during the
implementation of a method according to the invention,
- figure 3 is the image of the internal surface of
a hollow object that is reconstructed by a method
according to the invention,
- figure 4 shows transverse sections of this
surface,
- figure 5 is a schematic view of another backlit
shadowgraphic device that can be used in the present
invention,
- figure 6 is a schematic view of an
interferometry device that can be used in the
invention, and
- figures 7 and 8 illustrate schematically the
backlit shadowgraphic devices that are used for
characterising respectively a hollow cylinder and a
hollow ellipsoid in accordance with the invention.
Detailed disclosure of particular embodiments
The present invention is characterised by
(a) a three-dimensional reconstruction over a
small vicinity close to the equator of the transparent
object that it is wished to characterise, and
(b) a merging of data.
,
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These data are obtained both by a single-view
backlit shadowgraphic device in visible light and an
interferometric device.
The observation of the transparent object by
visible light shadowgraphy is associated with an
optical light propagation model that takes account of
the interactions of this propagation at the various
interfaces of the object. This measurement principle
makes it possible to connect the direct measurement on
the image, which is obtained by shadowgraphy, to the
deformations of the internal surface of the object
studied and the dimensional quantities of this object.
Backlit shadowgraphy is a simple measurement
method for studying flat objects but, for objects in
three dimensions, the image obtained by this method
does not provide enough information. This is because
the image observed of a cross section of an object is
not solely the image of the cross section through the
objective lens of the shadowgraphic device: it is the
image of the cross section through this lens and the
object itself.
Observation of the object by interferometry makes
it possible to connect the direct measurement with the
dimensional characteristics of the object.
The combination of the shadowgraphic measurements
with the interferometric measurements by means of an
algorithm based on the method of least squares gives a
spatial estimation of the internal surface of the
object observed.
Complementarity between backlit shadowgraphy and
interferometry is more simple to implement in a complex
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structure, where there is only a single viewing axis,
unlike tomography, which is normally used in this case
(three dimensions) but makes it necessary to observe
the object at several angles of incidence, which is not
possible in the present case.
A study has been carried out on two-layer hollow
spheres (spherical objects), all the characteristics of
which are known, in particular the optical index and
the thickness of each layer, except possibly the
optical index of the internal layer.
Shadowgraphy reveals luminous rings. Each of these
is characterised by a concentration of light rays,
referred to as a "caustic". An analysis of this caustic
establishes a link between the corresponding luminous
ring observed and the internal surface of the object.
This makes it possible to use the direct measurement on
the image.
A measurement method according to the invention is
mainly based on this analysis and on the combination of
measurements by the method of least squares.
An example of implementation of the method that is
the object of the invention is given below, for a
hollow spherical object, more simply referred to as a
"hollow sphere", which comprises two layers and is
transparent to visible light.
In this example, the first layer is a hollow
polymer sphere, the outside diameter and thickness of
which are equal respectively to 2430 pm and 175 pm and
the optical index of which is equal to 1.54 at the main
wavelength of the visible light source; and the second
,
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layer has a thickness of 100 pm and an optical index of
1.16 at this wavelength.
Figure 1 is a schematic view of a backlit
shadowgraphic device that can be used in this example
and comprises a collimated visible light source 2, an
objective 4 and a screen 6. The object studied 8 is
placed between the source 2 and the objective 4; its
external layer has the reference 10 while its internal
layer has the reference 12. A light ray 14 can also be
seen which goes from the source to the screen, passing
through the object and then the lens.
Let us consider first of all the characterisation
of the main luminous ring, that is to say the luminous
ring that is most visible on a real image, obtained by
single-view backlit shadowgraphy.
From such an image, on which the main luminous
ring is therefore visible, it is possible to form a
radial profile of this image, on which this luminous
ring is marked by an intensity peak.
Such a profile is shown in figure 2. The numbers
of the pixels (pxl) are entered on the X axis and the
amplitudes (grey levels) on the Y axis (I). The main
luminous ring is marked by the peak P and the arrow B
designates the external edge of the object. The centre
of the object corresponds to the Y axis.
The luminous ring is due to a concentration of
rays that have followed the same type of optical path
in terms of reflections and transmissions. In the
present case, the optical path that is the cause of
this luminous ring corresponds to the path followed by
the light ray 14 in figure 1.
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The concentration of light rays is also referred
to as "caustic" and constitutes the three-dimensional
envelope of these light rays. The main luminous ring is
the intersection of this caustic with the sensor of the
observation system that is in practice disposed in
place of the screen 6 in figure 1.
It should be noted that the sensor of the
observation system can make small movements along the
observation axis, around its initial position. A small
movement of this type is denoted u. The observation
axis is the optical axis 16 of the lens 4 in figure 1.
In an ideal case, the internal surface 18 (figure
1) of the object observed is a perfect sphere and the
luminous ring observed is then a circle.
The application p--->Ri:(9) is considered, which, with
a light ray issuing from the source 2 and situated at a
distance p from the optical axis 16, associates this
distance to the intersection of this ray with the
sensor of the observation system, after this ray has
passed through the entire optical system formed by the
object 8 and the lens 4. The following can then be
written:
R(p)= hi(p)+ uh2(p)
where h1(p) and h2(9) are smooth applications, that
is to say indefinitely differentiatable on R, which
depend solely on the optical system. They are given
by :
hjp)= ____________________________________________ P
cos 2v
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\ 1
h2(p)= ¨hi(p)+tan2v
with
( (
next P next P nextP next
P
v = arcsin ¨ ¨ arcsin + arcsin arcsin + arcsin
/ n r
Si 2 j n r
S2 2/2.5273
where nexonsi,ns, are respective optical indices of
the environment external to the object, of the first
sphere (layer 12 in figure 1) and of the second sphere
(layer 10 in figure 1); rl, r2, r3 are the respective
radii of the three interfaces that are defined by the
two-layer object, r1 being the external radius of the
external layer 12, r2 the internal radius of this layer
12 (and therefore the external radius of the layer 10)
and r3 the internal radius of the layer 10; and f
represents the focal distance of the lens 4.
The intersection of the caustic with the plane of
the sensor has the equation:
aR:(P) =0,
ap
For a fixed position of the sensor, the parameter
p* is a solution of the previous equation. Thus the
radius R, of the ideal main luminous ring (that is to
say without deformation of the internal surface 18) is
such that: Rc=hjp*).
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The acquisition of the measurements is considered
below.
Interferometric measurements made on the two-layer
object, at the optical axis of the object and close to
th'e poles of this object, by means of an interferential
device, directly supply the measurement of the
thickness of each layer.
The shadowgraphic images contain, as has been
seen, a luminous ring that is extracted by a
conventional subpixel contour detection method. The
shadowgraphic measurements are obtained by calculating
the distance between the centre of the external surface
of the two-layer object and the contour detection
points.
The backlit shadowgraphy analysis is now
considered.
The internal wall of the two-layer object can have
surface deformations. These are modelled by
- a disturbance sl on the radius of this sphere
that describes the internal wall of the object,
- a disturbance E2 on the normal to the sphere, in
the plane (P) that is determined by the point of
reflection of the light ray on the internal wall of the
object and by the optical axis 16 of the objective lens
4 of figure 1, the centre 0 of the object being on this
axis, and
- a disturbance c3 on the normal, in the plane (Q)
that is perpendicular to the plane (P).
An expression of order i with respect to the
disturbances Elf 2, 3 and their first derivatives is
designated hl.
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Let peR and L9E[0,27zi be the polar coordinates of
the light ray emerging from the collimated light source
in a plane perpendicular to the optical axis.
Let RER and ae[0,27-c[ be the polar coordinates of
the light ray that intersects the sensor of the
observation system in the particular plane of this
sensor.
Let Op) be the radius of the luminous ring in the
ideal case, that is to say without any disturbance of
the internal surface of the two-layer object.
It is assumed that the disturbances El, E2, E3 are
small 01 values, which means that they are of class 01
on R2 and that these disturbances as well as their
first derivatives are small.
Because of the axial symmetry of the optical
system and the continuity of the disturbances, the
polar coordinates (R, a) of the light ray intersecting
the plane of the sensor of the observation system can
be written as follows:
R(0,,9)= R* (P)+ a1(P)E1(P,t9)+ a2 (p)e2 (909)+ 772
ict(p,i9)----,9+a3(p)s3(p,,9)+772
where a1,a2,a3 are real functions that depend solely
on the properties of the optical system and are smooth,
that is to say indefinitely differentiable on R.
The equation of the caustic is always calculated
from the following equation:
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aR(o)
=0 .
ap
It is therefore possible to write:
9(P, a) = a cl3(9)E3 (P,a)+ 712 =
Thus the equation of any light ray emerging from
the optical system and intersecting the observation
plane (the plane of the sensor) is defined as follows:
- the equation of R in the system of coordinates
(p,a) is:
14p* , i9) = R* (p* + ajp* )ejp* , + ajpiejp*, 9) +
- and the equation of the caustic is always given
by: aR(p)=0 in this system of coordinates.
ap
It should be noted that the disturbance c3 has no
influence on the radius luminous ring at first-order
level. As a result the equation of the deformed
luminous ring (disturbed caustic) in the system of
coordinates (p,a) is written to the first order:
R0 (a) =R* (ID* ) +al (Pt ) g (ID*, a) +az (pt ) E2 (p*, a)
The above equation is very important since it is
from this that the use of the measurements on the
backlit shadowgraphy image is carried out. This
equation makes it possible to collect all the
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information concerning the deformations ejp%a) and
ejp*,a)of the ideal sphere.
There also exists a relationship between the
disturbances e1(o,19) and s3(p,0) that is as follows:
1 agi(P*,19)+ 772
3 (p* , 19) =
r COS2cO* ao
where p* is the angle between the point of
reflection of the internal surface 18 of the layer 10
and the optical axis, in the plane (1').
It is therefore possible to reconstruct 0(p*,a) to
the first order, according to the angle a, which is the
angle observed. However, for the following application,
this correction is not taken into account since it has
no significant influence on the final result.
The spatial estimation of the internal surface of
the two-layer object is now considered.
The data supplied by the backlit shadowgraphic
method and the interferometry method give information
on the surface state of the internal wall of the two-
layer object. It is therefore necessary to reconcile
the measurements in order to estimate the deformation
affecting the internal surface of this object.
For the remainder of the method according to the
invention, it is necessary to consider the angle 0 as
before and to associate with it another angle p in
order to form a system of coordinates of the Euler
coordinates type, whose origin is the centre 0 of the
object.
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The deformations of a sphere are generally
modelled by spherical harmonics ei(9,co), with iEN. In
this regard reference can be made to the following
document:
[3] H Groemer, Geometric Applications of Fourier
Series and Spherical Harmonics, Cambridge University
Press, 1996.
It is therefore natural to consider the topography
(or deformation) ep,o of the internal surface as being
a linear combination of spherical harmonics:
s(8, )= ite.(8 co)
"
where n is a natural (finite) integer.
Thus linear relationships are obtained between the
measurements and the disturbance of the internal
surface state, these linear relationships having the
amplitudes Ai as unknowns, with i=1, n.
It should be noted that, in the above, the
disturbances Elr2,E3 are independent. However, in the
example of the invention considered, the deformation
48,0 corresponds to the disturbance EIG9,0, and the
other two disturbances E2 and c3 are linked to the first
one ci. This amounts to stating that 48,0 entirely
determines the disturbances cl, c2, c3.
As explained previously, backlit shadowgraphy puts
in relationship the direct measurements on the image
and the deformation that is present on the internal
wall of the object. In addition, it is considered that
the ray issuing from the collimated light source, which
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is responsible for the formation of the luminous ring,
does not emerge from the initial osculatory plane. The
deformation considered is then:
This equality gives rise to a system of linear
equations, the variables of which are the Xi values,
with i=1, n. The number of equations in this
system is the number of angles a that are taken into
consideration, and the values of the radius of the
luminous ring come from the detection of contours that
was mentioned above.
Using the method of least squares, the deformation
on the normal and the variation in thickness on the
internal wall of the two-layer object are evaluated.
The interferometry directly connects the variation
in thickness in the zone observed to the linear
combination of spherical harmonics, since the
interferometry measurement is a simple reading of the
deformation of the internal wall.
Thus, by recombining the measurements obtained by
the interferometry and backlit shadowgraphy methods, by
means of an algorithm based on the method of least
squares, a global estimation of the surface state of
the internal wall of the two-layer object is obtained.
Figures 3 and 4 illustrate an. example of spatial
reconstruction of the internal wall of a two-layer
object performed in accordance with the invention.
Figure 3 is an image of the reconstructed surface and
figure 4 shows transverse sections I and 11 of this
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surface. The figures show the deformations accentuated
since they are not visible to the naked eye. It has
been checked that the estimation obtained is
superimposed on the real surface.
It has therefore been seen, in the present
invention, that the analysis carried out on the backlit
shadowgraphy method makes it possible to link the
deformation of the luminous ring (deformation in two
dimensions) to the deformation present on the internal
surface of the translucent or transparent, hollow
object, with two layers
(three-dimensional
information). It should also be noted that the known
methods do not translate bidimensional information into
three-dimensional information by means of a single
view.
The association of a method of measuring by
backlit shadowgraphy with an interferometry method
makes it possible to evaluate the roughness of the
internal surface of a translucent or transparent two-
layer hollow object. By means of these two methods,
which are implemented at different points, dimensional
information is merged.
In the invention, it is possible to replace the
interferometry measurement by a second shadowgraphy
measurement, made along a viewing axis that is not
parallel to the one along which the first shadowgraphy
measurement was made. In addition, if the observation
made along the second viewing axis is not complete but
is made through slits, the interpretation of the
shadowgraphy measurements will remain identical.
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It is also possible to replace the interferometry
measurement by a second backlit shadowgraphy
measurement, made along the viewing axis used for the
first backlit shadowgraphy measurement, provided that
this second measurement is made after the object has
been made to turn on itself.
Thus the rotation of the object on itself and the
use of a single shadowgraphy viewing axis also allow
the use of the method previously described, namely the
analysis of the image of the caustic making it possible
to go back to the three-dimensional information, and
then the reconciliation of the data in order to
reconstitute a complete three-dimensional estimation of
the internal surface state.
A shadowgraphic device and an interferometric
device for implementing the method that is the object
of the invention are described below.
The shadowgraphy device is shown schematically in
figure 5 and comprises a visible light source 19,
adjustable means 20 for collimating this source and
image acquisition means, comprising a lens 22 provided
with means 24 of varying the numerical aperture of this
lens (or which has the appropriate numerical aperture). .
The latter is followed by a CCD sensor 26 (charge
transfer device) provided with image processing means
28, with which a display device 30 is associated.
A double-layer hollow sphere 32 that it is wished
to study is placed between the source 19 and the lens
22 so that the centre of the sphere is substantially
placed on the optical axis 34 of the lens 22. This axis
34 constitutes the viewing axis along which the image
,
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of the object is acquired. The lens 22 makes it
possible to form the image of a cutting plane of the
hollow sphere 32 on the CCD sensor 26.
Figure 6 is a schematic view of the interferometry
_
device. It is more precisely an interferential
spectroscopy device for measuring thicknesses without
contact.
This device comprises a source of white light 35,
a set of shaping lenses 36, a telescope 38, a signal
transmission optical fibre 40, a spectrometer 42 and a
computer 44.
The light source 35 is used for illuminating the
object to be characterised 46. The illumination beam
supplied by this source is transmitted by an optical
fibre 48 and shaped by the set of lenses 36 so as to
adapt the profile of this beam to the geometry of the
object to be studied.
The telescope 38, for example of the type sold by
the company Questar und the reference QM100, is used
for illuminating the object to be analysed and
collecting the reflected light. The QM100 telescope
allows a working distance D ranging from 15 cm to 38
cm.
At the exit from the telescope, the light signal
reflected is injected into the optical fibre 40 and
routed as far as the spectrometer 42 in order to make
the acquisition of a channeled spectrum. An injector 50
is provided for injecting the light issuing from the
fibre 40 into the spectrometer.
The channeled spectrum is transmitted as far as
the computer 44 in order to be analysed. This computer
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is provided with means 52 of displaying the results
obtained.
Let us return to essential aspects of the present
invention. The latter relates essentially to a method
which is used for determining the deformation of the
internal surface of a two-layer object and the
essential elements of which are:
- an analysis of the physical phenomenon referred
to as "caustic", containing the information on the
deformation of the internal surface, this caustic being
defined by the inner edge of the luminous ring that the
image of the object has, obtained by backlit
shadowgraphy,
- determination of the information observed by the
backlit shadowgraphy chain, the bidimensional
disturbance of the luminous ring giving three-
dimensional information on the deformation of the
internal surface of the object, and
- elaboration of the principle of merging the
incomplete physical measurements (use of the method of
least squares and appropriate modelling of the
deformations of the internal wall of the object).
Other applications of the invention are described
below.
A method according to the invention, of the type
previously described for the characterisation of the
deformation of hollow spheres with two layers, can be
implemented for characterising the deformation of
hollow cylinders with two layers.
The same light source and the same image
acquisition chain can be used, as shown schematically
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B 15569 PV 24
by figure 7, where the cylinder has the reference 54.
Two white bands, relating to the internal surface of
the two-layer cylinder, then appear on the
shadowgraphic image. It is then necessary to reconsider
a modelling of the disturbances.
The same method can also be used for
characterising the deformation of hollow two-layer
ellipsoids.
The same light source and the same image
acquisition chain can also be used as shown
schematically in figure 8, where the ellipsoid has the
reference 56. There then appears, on the shadowgraphic
image, a white band that is related to the internal
surface of the two-layer ellipsoid. It is then also
necessary to reconsider a modelling of the
disturbances.
The same method can also be used for
characterising the deformation of hollow two-layer
spheroids.
The same light source and the same image
acquisition chain can also be used. There then appears,
on the shadowgraphic image, a white band that is
related to the internal surface of the two-layer
spheroid. It is then also necessary to reconsider a
modelling of the disturbances.
The present invention also applies to the
characterisation of the refractive indices of two-layer
objects: using the equation given above that defines
the radius of the luminous ring, it is possible to
determine the optical refractive index of each of the
1
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B 15569 PV 25
two layers, the dimensions of which will be determined
in advance by means of another measuring system.
It is also possible to determine the optical index
of each of the layers using another luminous ring of
the image obtained by backlit shadowgraphy.
Thus, from a single shadowgraphic picture, the
optical indices of an ideal two-layer object, that is
to say without small deformations, are characterised.
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