Device for the excitation of waves and especially ultrasonic waves including a cell

The device comprises a lens and a source for emitting a beam of parallel light rays or ultrasonic rays at right angles to a flat dioptric element. The lens surface which is located opposite to the radiation-emitting source is flat and the lens surface located opposite to the dioptric element is such that the refracted rays are incident upon the dioptric element at a constant angle. The wave which is incident upon the dioptric element and corresponds to the beam refracted from the lens and the wave refracted from the dioptric element and corresponding to the incident wave are in phase along a predetermined path on the surface of the dioptric element.

This invention relates to a wave-excitation device comprising a lens 
wherein rays and especially light or ultrasonic rays emitted by a source 
in the form of plane waves are refracted from said lens so as to produce a 
beam of waves which propagates in a couplant medium placed between the 
lens and a flat dioptric element. The surface of said lens is such that 
the wave which is incident upon said flat dioptric element and the wave 
refracted from the dioptric element are in phase along the paths which are 
constituted in particular by concurrent straight-line segments or circles, 
said paths being contained within the plane P of the flat dioptric 
element. 
As is already known, it often proves necessary to excite waves in phase in 
given directions within a medium limited by a flat face, especially in 
order to observe any possible flaws in the flat face or plate when 
ultrasonic waves are employed. The flaws in metallic plate are more 
clearly observed when the waves which are intended to be reflected from 
such flaws propagate at right angles to these latter within the plate. In 
point of fact, the direction of these flaws is not usually known 
beforehand. It is therefore necessary to send into the medium constituting 
the plate waves which propagate at a number of different angles in order 
to ensure efficient detection of these flaws. 
This is the case in particular when it is desired to observe flaws by 
producing Lamb waves in flat plates for testing the soundness of the 
plates or more particularly of welded zones. 
Since it is thus necessary in accordance with known practice at the time of 
ultrasonic inspection and testing of plates to sweep the surface with 
ultrasonic waves which propagate in at least two or even four directions 
in order to detect any possible flaws in almost any orientation, the 
devices of the prior art usually comprise carriages adapted to carry four 
transducers having perpendicular planes of incidence. This type of device 
entails the need for rather cumbersome electronic circuitry for detecting 
signals which are received after reflection from the flaws. 
The aim of the present invention is to solve the problem which consists in 
finding a method of associating a lens with a single transducer so as to 
ensure that the waves excited in a medium have varied directions or, 
better still, so as to ensure that the directions of propagation of the 
waves within said medium sweep an angle of 2.pi. radians when it proves 
possible to do so. As a result, in the case of application to the 
detection of flaws, at least one wave impinges upon the flaw at right 
angles to this latter. 
This invention makes it possible to provide a device which solves the 
problem under consideration, which is easy to construct and is limited in 
capital outlay. 
The device for excitation of waves in accordance with the invention 
comprises a source for emitting a beam F of rays which are parallel to 
each other (light rays or ultrasonic rays) and a lens. The rays of the 
beam F are perpendicular to a flat dioptric element P. Said flat dioptric 
element limits the top surface of the body in which it is desired to 
induce or excite waves. That surface of the lens of the device in 
accordance with the invention which is located opposite to the transducer 
is flat. The second lens surface located opposite to the flat dioptric 
element is such that the rays of the beam refracted from said second 
surface after passing through the lens having an index of refraction n 
arrive at the flat dioptric element P at a constant angle of incidence i; 
furthermore, the second lens surface is such that the wave which is 
incident on said dioptric element and corresponds to said ray of the beam 
refracted from the lens, and the wave refracted from said dioptric element 
corresponding to said incident wave are in phase along given paths. By way 
of example, said paths are constituted by concurrent straight-line 
segments or concentric circles. 
In one embodiment of the invention, it is desired to excite waves in phase 
along straight-line segments which are concurrent in a point. With this 
objective, it is possible to employ a flat transducer and, in accordance 
with the invention, a lens whose second surface is a conical surface 
having a semivertical angle of .pi./2-.alpha. or .pi./2+.alpha., depending 
on whether it is desired to excite divergent waves or convergent waves, 
.alpha. being such that tangent 
##EQU1## 
or in fact tan 
##EQU2## 
if the relative index of refraction of the medium constituting the lens 
with respect to a medium placed between the flat dioptric element and the 
second surface of said lens is smaller than 1 and tan 
##EQU3## 
if n is greater than 1. 
In another embodiment of the invention, the lens which is intended to 
ensure phase equalization of the incident and refracted waves permits said 
phase equalization along a closed curve marked on the surface of the flat 
dioptric element P. Said surface can be defined by its normal m at any 
point of said surface which: 
is contained in a plane .pi. at right angles to the flat dioptric element P 
and tangent to said closed curve, 
makes an angle .alpha. with the axis Oz at right angles to the plane P, the 
angle .alpha. being defined by the relation 
##EQU4## 
In order to excite waves of substantial amplitude within the medium limited 
by the flat dioptric element P in the case of closed curves, it is an 
advantage to adjust the frequency of vibrations of said ultrasonic wave in 
order to ensure that the wavelength associated with the refracted waves in 
the medium concerned and divided by the sine of the angle of refraction r 
is a submultiple of the length of said closed curve. The perimeter of the 
closed curve must in fact be a multiple of the distance between two 
consecutive equal-phase surfaces which are measured, not along a refracted 
radius but along the closed curve. In the case of Lamb waves, 
r=90.degree., sin r=1 and the perimeter of the closed curve is a multiple 
of the wavelength .lambda.. Thus, at the end of travel along said curve, 
the waves are added in phase by cyclic resonance effect. 
Further properties and advantages of the invention will become more readily 
apparent from the following description of exemplified embodiments which 
are given by way of explanation and not in any limiting sense, reference 
being made to the accompanying drawings, wherein:

There is shown in FIG. 1 a device in accordance with the invention for 
phase equalization of the incident waves refracted from the flat dioptric 
element P along any given curve C.sub.0 which may be polygonal. The device 
comprises a source S for emitting a beam F of parallel rays such as those 
designated by the references R.sub.1 and R'.sub.1. The lens L has a first 
flat face 2 located opposite to the wave source S and a second surface 4 
for converting the beam F comprising the rays R.sub.1 and R'.sub.1 among 
others into a beam of rays refracted from said second surface 4 and 
comprising the rays such as those designated by the references R.sub.2 and 
R'.sub.2. These rays impinge upon the medium 6 which is limited by the 
flat dioptric element P at A and A', thus exciting waves within said 
medium 6. The rays refracted from the flat dioptric element P and 
corresponding to excitation of the waves within said medium 6 are 
represented schematically by the rays R.sub.3 and R'.sub.3. The surface 4 
of the lens L is such that the angle of incidence i of the rays R.sub.2 
and R'.sub.2 on the flat dioptric element P is constant. Furthermore, the 
incident waves refracted from the dioptric element P are in phase. The 
second surface 4 of the lens L is defined by the orientation of the normal 
m at the point M (the point M corresponds to the incidence of the ray 
R.sub.2 at the point A of the curve C.sub.0 which is marked on the flat 
dioptric element P) and by a second condition of equality of length of the 
optical paths as will be defined hereinafter. 
The plane .pi. which passes through A and contains the tangent T to the 
curve C.sub.0 contained within the flat dioptric element P is associated 
with each point A of said curve C.sub.0. Said plane .pi. contains the ray 
R.sub.2, the normal at A to the plane P which is parallel to Oz as well as 
the ray R.sub.1 which passes through the point M. In accordance with the 
first law of Descartes, the normal m to the surface 4 of the lens L is 
also contained within said plane .pi. since the incident ray R.sub.1 and 
refracted ray R.sub.2 are contained within said plane. The normal m to the 
point M of the surface 4 makes an angle .alpha. with the vertical 
direction, namely the axis Oz. The refractive index n is the relative 
index between the medium which constitutes the lens L and the couplant 
medium which is located between the flat dioptric element P and the 
surface 4; the second law of Descartes makes it possible to write if n&lt;1: 
EQU n sin .alpha.=sin .beta.=sin (.alpha.-i), 
where .beta. is the angle of refraction in the couplant medium and, if n&gt;1: 
EQU n sin .alpha.=sin .beta.=sin (.alpha.+i). 
The solution of this equation in .alpha. is such that the angle which 
defines the normal m obtained by solution of the previous equation is: 
##EQU5## 
The mode of operation which permits of geometrical construction of the lens 
4 is as follows. The value of the angle i is fixed (for example in order 
to excite Lamb waves in the flat dioptric element P), thus determining the 
angle .alpha. by means of the relation given above and determining point 
by point the direction of the normal m to the surface 4. 
It can readily be demonstrated that the refracted wave and the incident 
wave along the curve C.sub.0 are in phase. In fact, in the case of any 
given curve C.sub.0, the segment AA' will be adopted as elementary path, 
namely that portion of curve which coincides with the direction of the 
tangent T to the curve C.sub.0 at the point A. The difference between the 
optical paths in the case of the rays R.sub.2 and R'.sub.2 in the couplant 
medium is equal to A'A.sub.1 and, in the case of the radii R.sub.3 and 
R'.sub.3 in the medium limited by the flat dioptric element P, is equal to 
AA'.sub.1. If r is the angle of refraction in the medium limited by the 
flat dioptric element P, the second law of Descartes sin i=n' sin r is 
such that the optical paths n'AA'.sub.1 =n'AA' sin r and A'A.sub.1 =AA' 
sin i are equal and that the waves are thus in phase over the entire path 
AA' along C.sub.0, n' is the relative index of the medium limited by the 
flat dioptric element P and of the couplant medium. 
There is shown in FIG. 2 a sectional view of the lens L, taken along a 
plane which is normal to the flat dioptric element P and passes through 
the segment AA'. The normals at M and M' are as defined earlier and the 
position of the point M' is such that n.sub.1 (MN)+n.sub.2 (MA)+n.sub.3 
(AB)=n.sub.1 (M'N')+n.sub.2 (M'A'). From a knowledge of the curve C and 
the refractive indices n.sub.1, n.sub.2 and n.sub.3, it is possible to 
construct the surface 4 of the lens L point by point by means of the 
equality which has just been mentioned and defines the positions of the 
points of the surface of the lens L and the orientation of the normals to 
the surface of said lens. 
In FIG. 3, there is shown a particular embodiment of the invention for 
exciting in the medium limited by the flat dioptric element P waves which 
are equalized in phase along segments which are concurrent in a point O 
such as the segments along the straight lines 10, 12, 14. The device has 
symmetry of revolution with respect to the axis Oz, thus making it 
possible to study only what takes place in a plane .pi. which passes 
through said axis. The radiation source S emits a beam F of rays R.sub.1 
and R'.sub.1 refracted from the second surface 4 of the lens L which has 
the shape of a cone frustum and a semivertical angle .gamma. 
.pi./2-.alpha.. The rays R.sub.2 and R'.sub.2 which are refracted from 
said second surface 4 impinge upon the surface constituted by the flat 
dioptric element P at a constant angle of incidence i, thus resulting in 
an angle of refraction r which is also constant. Compared with FIG. 1, the 
curve C.sub.0 in this embodiment is a straight line which passes through 
O. It can readily be established that the incident and refracted waves are 
in phase along straight lines such as the lines 10, 12, 14 which are 
marked on the plane P. In this embodiment, the normal m to the second 
surface 4 of the lens L also makes an angle .alpha. with the axis Oz, said 
angle .alpha. being also defined by the relation 
##EQU6## 
Since the entire device has symmetry of revolution about the axis Oz as 
already mentioned, it is apparent that the waves excited in the medium 
which is limited by the dioptric element P are in phase along an infinity 
of straight lines (consisting in practice of straight-line segments) which 
are concurrent in a point O. 
In this embodiment, the waves excited in the medium which is limited by the 
flat dioptric element P are waves which diverge from the point O. 
In FIG. 4, there is shown another embodiment of the device in accordance 
with the invention for exciting waves which propagate within the medium 
limited by the dioptric element P in convergent waves. The references 
which are adopted in FIG. 4 and are the same as those adopted in FIGS. 1 
and 2 designate identical elements. In this case, the lens L is 
constituted by a flat surface 2 and a conical surface 4. The conical 
surface has a semivertical angle .pi./2+.alpha.. The rays R.sub.2 and 
R'.sub.2 contained within the plane .pi. which passes through the axis Oz 
meet the straight line 10 at a constant angle of incidence i and are in 
phase with refracted waves corresponding to the rays R.sub.3 and R'.sub.3 
along said straight line 10. The line 10 is defined by the intersection 
between the plane .pi. and the flat upper surface of the element P. 
In FIG. 5, there is shown an embodiment of the device according to the 
invention for exciting waves in phase at the constant angle of incidence 
on a closed curve such as a circle C having a radius R which is marked on 
a flat dioptric element P. The surface 4 of the lens L is represented by 
the following equation in semipolar coordinates: 
EQU .rho..sup.2 =(z cotg .alpha.+R .theta.).sup.2 +R.sup.2 
wherein the axes Oxyz are as shown in FIG. 4. The structure L' corresponds 
to a bottom view of the lens L of FIG. 5. 
The rays such as R.sub.1 emitted by the source S gives rise to rays such as 
R.sub.2 which impinge upon the flat dioptric element P at points of 
incidence which are distributed along the circle C. These rays such as the 
ray R.sub.2 arrive at the same angle of incidence i and the waves which 
are incident on and refracted from the flat dioptric element P are in 
phase along the circle C, which is the particular case of the curve 
C.sub.0 of FIG. 1. In this example of construction, the lens L is limited 
by two coaxial cylinders 30 and 32 having an axis Oz. In addition and as a 
result of the shadow, the surface 4 is limited to a single pitch 
(.theta..sub.0 &lt;.theta.&lt;.theta..sub.0 +2.pi.). 
In FIG. 6, there is shown the structure of incident waves refracted from 
the flat dioptric element P in the case in which the medium limited by 
said flat dioptric element P is a flat plate, the angle of incidence i 
being chosen in known manner so as to excite Lamb waves within the 
material which constitutes said plate. The structure shown in FIG. 6 
corresponds to a lens L as illustrated in FIG. 1. The Lamb waves which are 
excited at the point A propagate along the tangent T to the circle C. 
Similarly, the waves excited at A' travel along the tangent T' and the 
waves excited at A" travel along the tangent T". 
The Lamb waves derived from each of the points AA'A" are rapidly destroyed 
by interference as soon as the distance from the circle C increases in the 
outward direction. On the other hand, the amplitude of said waves is added 
along the circle C since there is a maintenance of phase between incident 
wave and refracted wave along this path, namely a circle in this instance. 
As is the case with all vibrational phenomena, it is only necessary to 
ensure that this phase equalization is achieved to within an approximation 
of one-quarter of a wavelength in order to ensure efficacious phase 
equalization along the path, in which case phase equalization is achieved 
along a ring located outside the circle C and corresponds to this 
phase-displacement. 
As has been mentioned in the foregoing, if the wavelength .lambda. (in the 
case of Lamb waves it is not necessary to divide .lambda. by sin r since 
r=90.degree.) of the excited waves within the medium limited by the flat 
dioptric element P is a submultiple of the perimeter 2.pi.R of the circle 
C, the waves which propagate along said perimeter arrive at A with the 
same phase as the waves which are excited by a new vibration and propagate 
along the ray R.sub.2 and with addition of amplitudes, thus permitting of 
resonant excitation along said circle or along closed curves. This results 
in intense effects which are favorable to the reception of echos produced 
by flaws having small dimensions. 
The description of FIG. 6 applies to Lamb waves but can be extended more 
generally to any other type of waves in which the angle r is other than 
90.degree.. 
The device as herein described can also be employed as a resonator for 
waves induced in the flat dioptric element. 
The device in accordance with the invention is particularly applicable to 
the detection of flaws in plates by exciting Lamb waves in said plates 
which are limited by a flat dioptric element P. In this case, the 
radiation source is an ultrasonic transducer which operates as an 
emitter-receiver in order to collect the echos which are reflected from 
the flaws and circulate along paths which are opposite to the excitation 
paths. It is readily apparent that, in order to inspect the state of a 
plate, the transducer-lens unit is displaced along two coordinate axes xy 
which are parallel to the flat dioptric element P. The device is also 
applicable to the excitation of mechanical waves other than Lamb waves. 
Approximate calculations enable anyone versed in the art to apply this 
technique to other surfaces for limiting a medium in which it is desired 
to induce waves in phase, such as cylinders, spheres, tori and the like. 
The use of the device according to the invention which mainly comprises 
the lens L can be extended to electromagnetic waves and particle waves. It 
would be particularly useful in the event that the radiation source S is a 
laser beam, in which case the structure of the lens L can be employed for 
the purpose of producing a pencil of refracted light rays corresponding to 
the characteristics set forth in the foregoing. 
It would also be possible within the scope of the present invention to cut 
the surface of an emitter so as to form a surface at right angles to the 
rays R.sub.2 in order to obtain the same result. In this case, the normal 
to the surface m makes an angle i with Oz (it is only necessary to adopt 
n=1 and .alpha.=i in the equations given earlier). However, this design 
appears to be more costly since the construction gives rise to greater 
practical difficulty. 
One example in which the invention can be carried into effect consists in 
inspecting a stainless steel plate P having a thickness of 1 mm by means 
of an ultrasonic transducer in which a frequency of 4 Mc/s is adopted. The 
excitation of Lamb waves in the A.sub.1 mode results in an angle of 
incidence i=16.9.degree.. In the case of an Araldite lens and coupling in 
water (n=0.57), the application of the relation 
##EQU7## 
gives a value of the angle .alpha.=36.9.degree.. 
These Lamb waves propagate in steel at a velocity of 5150 m/s, namely a 
wavelength .lambda.=1.288 mm. If 2.pi.R=10 .lambda. is adopted in order to 
have resonant excitation, R=2.05 mm is obtained (the use of an emitter 
having a variable frequency makes it possible to adjust the frequency in 
order to obtain the desired resonance). 
In FIG. 4, there is shown the lens L corresponding to these values of 
.alpha. and of R. 
Another definition of this surface which limits the bottom face of the lens 
L consists in stating that it is a surface generated by a segment in which 
the line of extension remains tangent to a circular helix having a radius 
R in which a pitch p=2.pi.R tg.alpha.=9.67 mm is described.