Optimization method and device for direct measurement of an optical component

A method and device for measurement of the geometrical or optical structure of an optical component such as a lens or a mold for making lens are provided. The method comprises the steps of illuminating the optical component to be measured with incident light having a known wavefront, measuring, in a given plane, the maps of the wavefront slopes of the light, after reflection at or transmission by the optical component, and deducing the surface topography or refraction index map of the optical component to be measured from the measurements of the slope maps by the application of at least one calculating procedure. The calculating procedure comprises a step in which a result surface is initialized using a simple starting surface SD' and at least one optimization step; each optimization step involves calculation of the value of a merit function representative of the departure between the result surface and the surface to be measured of the optical component and, minimization of said value varying said result surface, said variation being expressed in the form of at least one intermediate surface S.sub.i.

BACKGROUND OF THE INVENTION 
The present invention relates to a method for absolute measurement of the 
geometrical or optical structure of an optical component and to a device 
implementing it. 
The method according to the invention makes it possible to provide absolute 
measurement of a polished surface or the distribution of the refractive 
index of an optical component. 
Measurement of polished surfaces and/or refractive index distribution finds 
many practical applications in industry. It is particularly useful in the 
ophthalmic field for checking and measuring ophthalmic lenses. It can also 
be used for checking or measuring molds, for example those used in 
manufacturing ophthalmic lenses. 
In the checking of optical components, the use of the so-called Ronchi test 
employing phase detection has already been proposed. 
As is known, the Ronchi test consists of inserting a grating of alternately 
opaque and transparent parallel lines at the point of convergence of the 
light waves originating from an optical component to be checked, and then 
analysing the component of the fringes which are then observable 
downstream thereof. 
If we limit ourselves to the laws of geometrical optics, without taking 
account of diffraction phenomena, these fringes represent the direction of 
the light rays that constitute the waves concerned and are characteristic 
of the aberrations thereof. Their slope reflects the difference between 
the corresponding wave surface and a spherical wave surface, the center of 
curvature of which is situated in the plane of the grating. It is 
consequently sufficient to measure this slope at all points on the optical 
component to be checked, this being achieved in practice using phase 
detection, and then to carry out integration in order to find defects in 
the surface of said component. 
An optical device enabling such a method to be implemented is notably 
described in the article "Fringe Scanning Ronchi test for aspherical 
surfaces" published in "Applied optics", volume 23, number 20 of Oct. 15, 
1984, as well as in the article "Phase measuring Ronchi test" in this same 
periodical, volume 27, number 3 of Feb. 1, 1988. Generally, this optical 
device comprises, arranged along an optical axis, light emitting means 
suitable for constituting a coherent point light source, a control station 
designed to carry the optical component being checked, a Ronchi grating, 
receiving means adapted to receive the observable image downstream of said 
Ronchi grating, and computing means designed to exploit this image, using 
phase detection. 
Other optical component checking devices have been proposed. Thus, the use 
of two associated, substantially parallel Ronchi gratings has been 
proposed, the moire fringes obtained on a screen by coherent light 
transmission or reflection on the surface under study then being observed. 
Just like the Ronchi test, the moire patterns obtained give an indication, 
in terms of slope, of the differences between a plane theoretical wave 
surface and the wave surface obtained by transmission or reflection at the 
surface under study. 
An optical device employing this principle is for example described in 
"Moire Deflectometry--Ray Tracing Interferometry" by I. Glatt and O. 
Kafri, published in "Optics and Lasers in Engineering" 8 (1988), pages 277 
to 320. Such a device typically comprises a collimated light source which 
is transmitted or reflected by the surface to be analysed, to a pair of 
Ronchi gratings, the image being projected onto a mat screen. Qualitative 
analysis of the moire patterns obtained, when compared to the expected 
patterns, enables aberrations to be located. Varying the distance between 
the gratings allows quantitative measurements to be made together with 
calculation of the variations in measured wave surface compared to the 
plane theoretical wave surface. 
Finally, in the device described in French patents 2 647 912 and 2 647 913, 
a map of the slopes of the actual surface to be measured is obtained by 
deflectometry using phase detection and, after subtracting the map of the 
nominal theoretical surface from the map of the the actual surface slope 
obtained, it is simple to obtain a map of the slopes of the defects, thus 
enabling the actual surface to be reconstructed, using integration. This 
known device, even if it enables a known ophthalmic lens to be checked 
with a high degree of accuracy or, more generally any known surface, does 
nevertheless suffer from the disadvantage of being limited to measurement 
of variations between a real surface and a theoretical surface. In other 
words, it implements a relative method involving prior knowledge of the 
theoretical shape of the surface to be measured. 
SUMMARY OF THE INVENTION 
The present invention sets out to provide a method for measuring the 
geometrical or optical structure of an optical component, which provides 
an absolute or direct measurement as it requires no prior knowledge of the 
theoretical shape of the surface, or the theoretical distribution of 
refractive index. The method makes it possible to determine the 
geometrical shape of a surface, or how refractive index varies within an 
optical component. 
The present invention also provides a device enabling this method for 
measuring the geometrical or optical structure to be implemented with a 
high degree of accuracy. 
The invention provides absolute or direct measurement of the geometrical 
structure of the surface either using transmitted or reflected light for 
convex or concave surfaces. It enables the actual shape of the surface to 
be measured accurately. 
The invention also makes it possible to provide absolute measurement of the 
distribution of refractive index in a graded index optical component, in 
other words a component constituted by a material having a refractive 
index that varies within a range comprised between two known dioptric 
values. 
The invention accordingly provides a method for absolute measurement of the 
geometrical or optical structure of an optical component comprising the 
steps consisting of: 
illuminating said optical component with incident light having a known 
wavefront, 
measuring, in a given plane, the maps of the wavefront slopes of said 
light, after reflection at said optical component or transmission by said 
optical component, 
and deducing the geometrical or optical structure of said optical component 
from said measurements of the slope maps by the application of at least 
one calculating procedure. 
Two ways of carrying out the said calculating procedure are offered by the 
invention. 
In order to measure the slope maps of the wavefront of said light after 
reflection at said optical component or transmission by said optical 
component, the method of the invention preferably includes the step of 
determining, using a deflectometric method, the paths of the plurality of 
rays of said light in an image space of the optical component being 
measured. 
By deflectometric method, any method that gives access to the lines of 
slope of a light beam is meant. 
These methods fall into three categories: 
"geometrical" methods, obtained by inserting a mask on the path of the beam 
(Foucault, Ronchi, Hartman, etc . . . ); 
moire methods (Moire deflectometry, Talbot interferometry, etc . . . ); 
differential interferometric methods (lateral, radial, etc . . .). 
Such methods are described in "Optical Shop Testing" by D. Malacra, 
published by Wiley. 
Advantageously, the rays are transposed into the space of the optical 
component to be measured, using optical calculation. 
In a first embodiment of the method, the invention makes it possible to 
measure absolutely the geometrical or optical structure of the component 
to be measured. 
Firstly, the geometrical structure of a surface of the optical component to 
be measured can be determined by a calculating procedure comprising: 
a step in which a result surface is initialized using a simple starting 
surface S.sub.D, 
at least one optimization step involving: 
calculation of the value of a merit function representative of the 
variations induced by replacement of the surface of the optical component 
to be measured by said result surface and, 
minimization of said value by varying said result surface, said variation 
being expressed in the form of at least one intermediate surface S.sub.I. 
Advantageously, the result surface, the simple surface S.sub.D and the one 
or several intermediate surfaces S.sub.I are represented by a linear 
combination of a family of orthogonal functions. 
This absolute surface measurement then allows, among other things, the main 
characteristics of this surface to be calculated at each point, for 
example altitude, slope, principal local curvatures, etc. 
Secondly, the invention makes it possible to absolutely determine the 
optical structure of the optical component to be measured, i.e. 
measurement of the refractive index distribution within a graded index 
optical component, in other words a component constituted by a variable 
index material delimited by two known dioptric values. The calculation 
step then comprises: 
an initialization step for a result refractive index distribution, using a 
simple starting refractive index distribution N.sub.D, 
at least one optimization step comprising: 
calculation of the value of a merit function representative of the 
variations induced by replacement of the refractive index distribution of 
the optical component to be measured by said result refractive index 
distribution, and 
minimization of said value by varying said result refractive index 
distribution, said variation being expressed in the form of at least one 
intermediate refractive index distribution N.sub.I. 
Advantageously, said result refractive index distribution, said simple 
starting refractive index distribution N.sub.D and the one or several 
intermediate refractive index distributions N.sub.I are represented by a 
linear combination of a family of orthogonal functions. 
In this first embodiment of the method, the calculation procedure includes 
a plurality of optimization steps. 
The orthogonal functions can be polynomials and in this case, the maximum 
degree of the polynomials of said linear combination in an optimization 
step is higher than or equal to the maximum degree of the polynomials of 
said combination in the preceding optimization step. 
Minimization of the value of said merit function can be carried out using 
the least squares method. 
Calculation of the value of the merit function can be carried out: 
by calculating, for each ray of a plurality of rays of said light, after 
reflection at said optical component or transmission by said optical 
component: 
the incident luminous ray which, upon arriving at said result surface or 
said result refractive index distribution calculated in said optimization 
process, would be reflected or transmitted in the direction of the 
measured ray, 
the distance, in the plane of the source of the incident light or in a 
plane conjugate with said plane, between the point of impact of said 
incident ray in said plane and the center of said quasi-point source, 
by adding, for said plurality of rays, the squares of the distance thus 
calculated for each one of said rays. 
According to a second embodiment, the invention makes it possible to 
determine the characteristics of a surface of the optical component to be 
analyzed in the form of maps of its principal curvatures. The calculating 
procedure then comprises: 
a step in which derivatives are calculated, in several directions, of the 
maps of the slopes of the wavefront of said light after reflection at said 
optical component or transmission by said optical component, 
a calculation step starting from said derivatives, for the curvatures of 
the wavefront of the light after reflection at said optical component or 
transmission by said optical component, 
a step for computing a map of the principal curvatures of the surface of 
the optical component to be measured, starting from the curvatures thus 
calculated, and knowing the wavefront of the light incident on the optical 
component. 
The invention also provides a device for carrying out the method for 
absolute measurement of a surface or the distribution of refractive index, 
comprising: 
means for illuminating the optical component to be measured with light 
having a known wavefront, 
means for supporting the optical component to be measured, 
means for measuring the slopes of the wavefront of said light after 
reflection at said optical component or transmission by said optical 
component, and 
calculating means adapted to receive the results from said measuring means. 
In one embodiment of the device, the measuring means comprise a Ronchi 
grating, a mat screen and a charge-coupled-device camera; in another 
embodiment they comprise a Ronchi grating and a charge-coupled-device 
camera. 
The means for illuminating the surface to be measured preferably comprise a 
quasi-point source and a system for imaging said source. 
The calculating means comprise a ray tracing program. 
The device can also employ a laser beam to materialize the optical axis of 
said device. 
Finally, the support means are adapted to be displaceable along the optical 
axis of the device or in a plane orthogonal thereto. 
The features and advantages of the invention will become more clear from 
the description that follows of various embodiments of the invention 
provided by way of example, and with reference to the attached drawings.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
The description that follows considers the case of absolute measurement of 
the geometrical structure of a polished surface. It applies, mutatis 
mutandis, to a method for measuring the refractive index distribution of a 
graded index optical component, in other words a component constituted of 
a variable index material, comprised within two known dioptric values. For 
this, it is sufficient to replace the unknown "surface" S defined by 
z(x,y) by the unknown "refractive index distribution" n(x,y). 
The measurement process can then be carried out only using transmitted 
light, for example using a device of the type described below in relation 
with FIGS. 1 and 3; a knowledge of the geometrical shape of dioptric 
powers and the thickness of said optical component enables its refractive 
index distribution n(x,y) to be measured. 
The initialization step is carried out with a simple starting index 
distribution N.sub.D, of constant refractive index. 
FIG. 1 shows a simplified diagram of a device according to the invention 
for measuring a polished surface using transmitted light. The term 
"measurement" should be taken to mean determination of the geometrical 
characteristics of the polished surface, such as its geometrical shape or 
the provision of a map of its principal curvatures. The expression 
"polished surface" should be taken to mean an unknown face of an optical 
component, such as, for example, a progressive lens. For such a lens, for 
which the shape of one face and the refractive index is known, it is 
useful to be able to analyse the characteristics of the other face, in an 
absolute manner. The expression "measurement using transmitted light" 
should taken to mean measurement of the polished surface through 
measurement of the light transmitted through the optical component, and in 
particular through the polished surface to be measured. 
FIG. 1 shows the setup of a device according to the invention which 
comprises, disposed along optical axis A, illuminating means 1, supporting 
means which are not shown and measuring means 2. The device additionally 
comprises calculating means 3. The supporting means, which are not shown, 
should be able to receive an optical component the surface of which is to 
be analysed and which, in the example shown in FIG. 1, is a progressive 
lens 4. The shape and position within the setup of one face 5 of this lens 
4 are known, and it is desired to determine the characteristics of the 
second face 6 of the lens 4, in an absolute manner. It will be supposed 
that the refractive index of progressive lens 4, together with its 
thickness at a given point, are known. 
The illuminating means 1 deliver light having a wavefront of known shape, 
to the lens 4. This light passes through the lens 4, and is transmitted to 
the measuring means 2. The measuring means 2 are linked to the calculating 
means 3, and enable maps of the wavefront slopes of the light to be 
determined, after transmission thereof by the polished surface 6 to be 
measured. Determination is done in an image plane of the optical component 
being measured. 
As the shape of the incident wavefront on surface 5 of lens 4 is known, and 
as the shape of said face 5 together with the refractive index of lens 4 
are also known, it is possible to determine, using the calculating means 
3, the shape of the wavefront of the incident light hitting the polished 
surface 6 to be measured. According to the invention, the light 
transmitted through polished surface 6 is subsequently received by the 
measuring means 2 which, in combination with the calculating means 3, 
determine the maps giving the slopes of the wavefront of the light after 
transmission through the polished surface 6. 
The calculating means 3 enable the absolute characteristics of the surface 
6 to be obtained from these slopes, as will be explained with reference to 
FIGS. 6 and 7. 
The basic setup shown in FIG. 1 is also suitable for measuring refractive 
index distribution in an optical component. 
FIG. 2 shows the essentials of a device according to the invention for 
measuring a polished surface, using reflected light. By this we mean 
measuring the characteristics of polished surface 6 by measuring the light 
reflected by said surface. The device in FIG. 2 comprises, arranged along 
optical axis A, illuminating means 1, splitting means 12, supporting 
means, which are not shown, designed to receive the optical component 4 
having the surface 6 which is to be measured. The light supplied by 
illuminating means 1 is transmitted by the splitting means 12 to the 
surface 6 at which it is reflected and sent to the measuring means 2 via 
the splitting means 12. The measuring means, like in the case of the 
device shown in FIG. 1, determine maps of the wavefront slope of the light 
in the image plane, and, following this, by the use of calculating means 
3, maps of the wavefront slopes of the light after reflection at polished 
surface 6. 
From these slope maps, the computing means 3 enable the absolute 
characteristics of the surface 6 to be obtained, as will be explained with 
reference to FIGS. 6 and 7. 
FIG. 3 is a more detailed diagram showing one embodiment of a device for 
measuring an optical component using transmitted light, of the type shown 
in FIG. 1. In the example in FIG. 3, the optical component consists of a 
progressive lens 4 having a surface that is to be measured. The device in 
FIG. 3 comprises, disposed along optical axis A, illuminating means 
consisting of a quasi-point source 20, an optical system 21 able to be 
moved along axis A, and a focusing optical system 22. The movable optical 
system 21 is set to a position along axis A as a function of the power 
addition factor of the lens to be measured. The focusing optical system 22 
has a positive or negative focal point making it possible to analyse 
lenses of positive or negative optical power. Thus, when measuring 
progressive lenses, focusing optical system 22 will be positive or 
negative depending on the sign of progressive lens power in the far vision 
portion of said lens. The device in FIG. 3 further comprises, arranged 
along axis A, means for supporting the optical component 4 supported by 
three translation stages and two rotation elements shown as 100 (see also 
FIGS. 4, 5, 5a). The measuring means, which are disposed next along 
optical axis A comprise an optical system 23 for forming the image of 
component 4 on a mat screen 24. This optical system 23 is followed by a 
Ronchi grating 25 of a known type, fixed to the former. The image formed 
through the Ronchi grating on the mat screen 24 is picked up by a camera 
26 of the mosaic pattern type. This camera is for example a charge coupled 
device (CCD) camera able to measure light intensity at a plurality of 
points on the mat screen. Camera 26 is thus able to supply the computing 
means 3 with information on light intensity at every point on the mat 
screen. It can furthermore supply the operator with a picture of the mat 
screen on a video monitor, for following the measurement operations. In 
another embodiment of the invention, the image of component 4 formed by 
the optical system 23 is directly filmed by camera 26, without the 
intermediary of a mat screen. 
The various stages in the measurement of the geometrical structure of the 
polished surface in the device in FIG. 3 are described in more detail with 
reference to FIG. 6. 
FIG. 4 shows a more detailed diagram of one embodiment of a device using 
measurement by reflected light, for obtaining the geometrical 
characteristics of an optical component 4, this device being of the type 
shown in FIG. 2. The device in FIG. 4 is adapted to measurement of convex 
surfaces. The device in FIG. 4 comprises a quasi-point source 30 located 
at the focal point of a focusing optical system 31 which generates a 
collimated beam. This collimated beam passes through a splitter 32 and an 
adaptor 33 the power of which depends on the power of the polished surface 
6 of the optical component 4 being measured. Adaptor 33 illuminates the 
surface 6 of the component 4 located at point S using light having a known 
wavefront. Point I in FIG. 4 is the optical conjugate of point source 30. 
The power of adaptor 33 is selected as a function of the power of the 
surface 6 being measured. More precisely, point I is situated between the 
image of the source provided by the highest power region of surface 6 and 
that provided by the lowest power region thereof. If we consider the case 
of a convex progressive lens, point I will be located between the image of 
the source provided by the near vision region of surface 6 and the image 
provided by the far vision region thereof. 
The light reflected by the surface to be measured passes through the 
adaptor 33 and then through the splitter 32 to an objective 34, which 
forms, approximately, an image of the surface to be measured on a mat 
screen 35 via the Ronchi grating 36. The intersection of the Ronchi 
grating and the optical axis is the optical conjugate of point I which, in 
its turn, is the conjugate of point source 30. A camera 37 of the mosaic 
pattern type picks up the image formed on the mat screen in the same way 
as was described with reference to FIG. 3. 
In the device in FIG. 4, all the portion downstream of splitter 32, in 
other words objective 34, grating 36, mat screen 35 and camera 37 can be 
employed for measurement of all convex surfaces and, in the same way, the 
illuminating portion, in other words source 30 and focusing optical system 
31 can be used for all measurements. It is only necessary to change 
adaptor 33, if needed, as a function of the power of the surface 6 of the 
lens. 
FIG. 5 shows a device similar to the one in FIG. 4, but for the measurement 
of concave surfaces. Identical elements bear the same reference numerals. 
This device comprises, like the device in FIG. 4, a light source 30, a 
focusing optical system 31 and a splitter 32. The device next comprises an 
adaptor 40 similar to the adaptor 33 in the setup in FIG. 4. Adaptor 40 
sends light of a known wavefront towards the concave surface to be 
studied, situated at point S. Point I is the optical conjugate of point 
source 30, this being obtained by the optical systems 31, 32 and 40. The 
relative positions of points S and I, just like the case of the setup in 
FIG. 4, depends on the minimum and maximum powers of the surface to be 
measured. The light reflected by the concave surface passes through 
adaptor 40, splitter 32 towards two objective lenses 41 and 42 which, just 
like in the device in FIG. 4, form an approximate image of the surface to 
be measured on the mat screen 35, conjugating point I onto a Ronchi 
grating 36. The image of element 4 on the mat screen 35 is picked up by 
mosaic camera 37. 
Just like in the case of the device for measuring convex surfaces, the 
imaging portion, consisting of objective lenses 41 and 42, grating 36, mat 
screen 35 and camera 37 can be employed for measuring all concave 
surfaces. The "illuminating" portion consisting of light source 30, 
focusing optical system 31 and splitter 32 can be common to the device in 
FIG. 4 and the one in FIG. 5. 
FIG. 5a shows a more detailed diagram of one embodiment of a device of the 
type shown in FIG. 5, but for the measurement of convex surfaces using 
reflected light. It is identical to the one shown in FIG. 5, except for 
the fact that objective 42 has been replaced by an objective 33' of 
different focal lens, without modifying its position in the device. In 
this way, the setup in FIG. 5 can easily be transferred to the one in FIG. 
5a for measuring convex surfaces instead of concave surfaces. Obviously, 
the reverse modification is also possible. It is thus possible to measure, 
using one single device, all types of surface simply by replacing one 
objective lens with another. 
The devices described with reference to FIGS. 3, 4, 5 and 5a are designed 
to illuminate the surface to be measured with light having a 
quasi-spherical wavefront. However, this is only a particular embodiment 
and the method according to the invention being able to be applied to any 
form of incident wavefront. 
The operation of the device according to the invention will now be 
described with reference to FIG. 6. In order to simplify the description, 
only the operation of the device in FIG. 5 will be described, it being 
understood that the devices in FIGS. 3, 4 and 5a operate in a similar way. 
FIG. 6 shows a flow chart of the steps in the complete measurement of the 
geometrical characteristics of a polished surface; the first step 50 
consists in mounting the optical component having the surface to be 
measured in the support means. It is fixed therein in such a way that the 
surface to be measured is approximately centered on optical axis A, the 
normal to the surface at the point of intersection with optical axis A 
substantially coinciding with said axis A. 
Once the optical component has been fixed in place, the support means are 
shifted, at step 51, in order to bring the surface substantially into 
proximity with the focal point of adaptor 40. In the device in FIG. 5, the 
support means bring the surface to be measured close to the point I. 
Depending on the characteristics of the surface to be measured, a suitable 
choice is made of the power of adaptor 40. In practice, it is sufficient 
to have a rough idea of the average power of the surface to be measured 
(in the case of measurement using reflection) or of the optical component 
(in the case where transmitted light is used), this being able to be 
determined by any known means. For example, in the case of a progressive 
lens, the basic value is, a priori, a known value, which makes it possible 
to chose the power of adaptor 40. A set of four adaptors makes it possible 
to cover the ordinary range of powers between 0.50 and 10 diopters. 
At step 52, the tilt of the element is finally adjusted to ensure it is 
correctly aligned. By alignment we mean determination of the path of a 
given ray leaving source 30 right up to the mat screen 35, or, what 
amounts to the same thing, determination of the normal to the surface to 
be measured, at the point of intersection with the optical axis. Such 
alignment makes it possible to fix an origin in the plane of the grating. 
According to the invention, such alignment can be done in a simple and 
accurate manner using a laser beam 43 sent along the optical axis A of the 
device. For this, when constructing the device, the intersection of the 
optical axis with the mat screen 35 is materialized using, for example, a 
mirror situated at point I in the support means, arranged perpendicularly 
to the optical axis. The intersection of the optical axis with the mat 
screen 35 can subsequently be materialized on the actual image supplied by 
the camera 37, for example by means of a software-generated grating. 
To facilitate successive computations, the invention proposes to correct, 
on the support means, the orientation of the surface to be measured so as 
to bring the intersection of the laser beam inside the grating in the 
image from camera 37. In this way, the line normal to the surface to be 
measured at the point of intersection with optical axis A coincides with 
said optical axis. 
Obviously, it will also be possible, in order to achieve such alignment, to 
leave the orientation of the surface to be measured unchanged and to 
acquire, on the image from camera 37, the position of the reflected laser 
beam. 
At step 53, the surface to be measured is accurately positioned at the 
focal point of adaptor 40. 
At step 54, the measuring means move along optical axis A, in order to 
bring the surface to be measured to the measurement position. As explained 
with reference to FIG. 4, the measurement position is a position for which 
point I, which is a virtual source, is situated between rays that have 
passed through the area of highest power of the surface to be measured and 
the rays that have passed through the region of lowest power. In practice, 
the measurement position is determined by approximate prior knowledge of 
the base value and power addition factor of the surface to be measured. 
At step 55, a first series of measurements is made in a direction 
perpendicular to the optical axis and, for example, in the direction X 
perpendicular to said optical axis, and lying in the plane of FIG. 5. As 
described in the literature, these measurements consist in recording light 
strength information at different points of camera 37, for varying 
positions of the Ronchi grating. Stated in other terms, recordings are 
made of the images corresponding to the fringes due to the grating, the 
grating being moved on each occasion in its plane, perpendicularly to the 
direction of the lines on the grating. 
At step 56, the grating is turned through 90.degree., and a new series of 
measurement is commenced similar to those obtained for step 55. 
At step 57, the results obtained in steps 55 and 56 are supplied to the 
computing means in order to be processed, as explained more in detail with 
reference to FIG. 7. In this way, the characteristics of the surface to be 
measured are determined. 
At step 58, the characteristics of the surface to be measured are known; 
nevertheless, these characteristics are known in a reference frame linked 
to the device and not to the actual surface to be measured. Stated in 
other terms, the characteristics determined according to the invention are 
known with respect to the means used to support the surface to be 
measured. It is hence important, in order to be able to use these results, 
to carry out a change of reference frame in order to know the 
characteristics of the surface in its own reference frame. In the case of 
an optical lens, this reference frame is generally constituted by 
engravings on the surface, for example two engraved micro-circles. 
According to the invention, the change of reference frame can be done by 
employing the support means for the element to be measured, said support 
means being designed to move not only along the optical axis but also in a 
plane orthogonal thereto. For example, the support means are mounted on 
two motor-driven slides which move parallel to the rows and columns of 
camera 37. Change of reference frame can then be achieved using the laser 
beam which puts into material form the optical axis of the device, and 
which has already been mentioned in the description of step 52. 
In order to change reference frame, the initial step consists in bringing 
back the surface to be measured to the focal point of adaptor 40. This is 
achieved, like in step 51, by moving the support means along the optical 
axis. After this, the element to be measured is moved in a plane 
perpendicular to the optical axis, and optionally along the optical axis 
in order to bring an engraving into coincidence with the focal point of 
adaptor 40. The image of the engraving provided by adaptor 40 is received 
by the camera 44 on which the intersection of the optical axis with the 
plane of the CCD (charge-coupled device) of the camera is viewed with the 
aid of cross-hairs. 
When the image (of the engraving) supplied by the camera 44 is centered on 
the cross-hairs, the displacements made in the plane perpendicular to the 
optical axis are noted. Following this, a similar procedure is adopted for 
the other engravings. 
In this way, the position of the engravings is known in a reference frame 
linked to the measurement device. Thanks to the alignment procedure, the 
line normal to the surface to be measured at its intersection with optical 
axis is known. These elements make it possible to carry out a simple 
change of reference frame, in order to supply, as an output signal, the 
characteristics of a surface to be measured in a reference frame linked to 
the engravings thereon. 
Following step 58, the characteristics of the surface to be measured are 
available in a reference frame linked to said surface. It is then possible 
to go on to measurement of another surface. 
Description of the operation of the device, which has been done with 
reference to FIG. 5 extents, mutatis mutandis, to the devices in FIGS. 3 
and 4. 
FIG. 7 shows a flow chart of the measurement and computing steps in one 
embodiment of the method according to the invention. In the remainder of 
the description, we have employed, to facilitate explanation, an 
ortho-normed reference frame the z axis of which lies along the optical 
axis of the system. In such a reference frame, the surface to be measured 
can be represented by a function z=f(x,y). 
At step 60, the images obtained at step 55 and 56 make it possible to 
calculate, by phase detection, the position of intersection of each light 
beam in the plane of the grating. 
As the transverse magnifications of camera 37 are known, it is possible to 
deduce therefrom the position of the intersection of each light beam with 
the plane of the mat screen; knowing perfectly the distance between the 
grating and the mat screen, it is possible to deduce the equation for each 
light beam therefrom. 
Following this, using optical calculation, transposition of the light beams 
from the space where they were measured to the space of the optical item 
being measured is achieved. Such transposition of the rays makes it 
possible to simplify, and accelerate, the computing step of the method 
according to the invention. This will become more clear below, when the 
merit function employed in the calculation step according to the invention 
is described. 
In a first embodiment of the invention, the computing steps 61 to 64 make 
it possible to determine the geometrical characteristics of the optical 
component to be measured, in the form of a three-dimensional 
representation of the surface to be measured. 
At step 61, a final result surface is initialized by making use of a simple 
starting surface S.sub.D, in other words an initial surface shape is 
provided. 
At step 62, calculation is done for this final result surface, and, 
consequently for the first time for said simple starting surface S.sub.D, 
of the value of a merit function, said merit function representing 
variations introduced into the measurement system when the surface to be 
measured is replaced by the result surface. 
Stated in other terms, a comparison is made between the real situation in 
the measurement system and the situation that the result surface would 
have created if it had been placed in the measurement system as a 
replacement for the surface to be measured. It is possible to calculate 
the effects of the result surface as, a priori, all the characteristics of 
the measurement are known, only the surface to be measured being unknown. 
It is thus possible to simulate the presence of the result surface in the 
measurement system. 
The merit function is chosen so as to have a zero minimum value when the 
result surface is exactly equal to the measurement surface. One example of 
a merit function is described in more detail below. 
At step 63, the value of the merit function thus calculated is compared 
with a first predetermined threshold value. If the value found is higher 
than said threshold value, control passes to step 64; otherwise, it is 
considered that the result surface thus obtained is a good approximation 
of the surface to be measured. This calculation makes it possible to avoid 
pursuing calculation if the result surface has made it possible to rapidly 
obtain a representation of the surface to be measured with sufficient 
accuracy. 
At step 64, optimization of the result surface is carried out. In effect, 
the merit function is a function of a result surface. Because of this, it 
is possible to optimize the result surface using a optimization method 
such as, for example optimization using the least squares method. This 
makes it possible to obtain a fresh result surface in the form of an 
intermediate surface S.sub.I. This surface S.sub.I represents an 
approximation of the surface to be measured which can be sufficient at 
least in certain embodiments of the invention. According to the invention, 
it is also possible to proceed with a plurality of optimization steps. In 
this case, following steps 64, return to step 62 occurs, with the surface 
S.sub.I obtained. 
Then fresh calculation of the merit function is made for the result surface 
or current intermediate surface; at step 63 it is possible not only to 
compare the value of the merit function with the first predetermined 
threshold value, but also to compare it with the value obtained at the 
preceding step. If the difference between the values obtained between two 
successive steps is only very small, in other words if it is less than a 
second predetermined threshold value, it is considered that surface 
S.sub.I is a sufficiently accurate representation of the surface to be 
measured. This in fact means that there is only a small variation between 
the calculated result surfaces in two successive steps. 
We shall now describe, by way of example, a merit function that can be used 
in the method according to the invention. This merit function is obtained 
by considering a plurality of light beams which are reflected or 
transmitted by the surface to be measured. For each light beam, 
calculation is made, using a ray tracing program, of the theoretical light 
beam, which, upon arriving at the result surface, i.e. at the simple 
starting surface S.sub.D or at an intermediate surface S.sub.I, would be 
reflected or transmitted in the same way. In other words, a light beam 
downstream of a surface to be measured is considered and, using the ray 
tracing program, the path that this light beam would have travelled if the 
surface to be measured had been replaced by the simple starting surface 
S.sub.D or an intermediate surface S.sub.I is traced backwards. Knowledge 
of the various parts of the measurement device makes it possible to 
calculate the path of the light beam S.sub.D up to the plane of the 
source. 
As has been mentioned above, it is advantageous to have transposed, using 
optical calculation, the light beams from the space they were measured at 
to the space of the measured item. Because of this, when calculating the 
merit function, the path of the light beam is traced back not from the 
space where it was measured at, but from the space immediately following 
the surface to be measured. 
In the case where a point source is used in the measurement device, it is 
possible to trace the light beam back right up to the plane of the source. 
The distance between the light beam and the center of the point source is 
calculated in this plane. 
In order to obtain the merit function, the squares of the distances thus 
calculated are added for the plurality of the rays. This merit function is 
thus representative of the local deviations between the surface to be 
measured and the result surface (simple starting surface S.sub.D or 
intermediate surface S.sub.I) at the points of reflection or transmission 
of each light ray of the plurality of rays. 
Obviously, any other type of merit function can be employed and, in 
particular, the deviations between the rays can be calculated in a plane 
other than the plane of the source. 
In order to represent the result surface, the simple starting surface or 
the intermediate surfaces, it is advantageous to employ a function which 
is a linear combination of a family of orthogonal functions. In this case, 
the merit function is a function of the various coefficients of the linear 
combination. Optimization can then be carried out by varying the various 
coefficients, for example using a least-squares type method. 
The use of a family of orthogonal functions is particularly advantageous if 
the method according to the invention includes a plurality of optimisation 
steps. Because of this, if in an optimization step, functions are added to 
the linear combination, it can be supposed that because of the 
orthogonality of the various functions, the coefficients of the 
previously-calculated linear function will only vary slightly, if at all. 
Thus, Zernike polynomials, which are orthogonal on a disc can be employed 
to represent the result surface. The simple starting surface can then be 
initialized using a parabola, represented by a second degree Zernike 
polynomial. At the initialization step, the surface to be measured is a 
parabola and is thus represented by the zero, first and second degree 
Zernike polynomials: optimization is performed on three coefficients. A 
plurality of optimization steps are carried out repeatedly using a 
function represented by the zero, first and second degree polynomials as 
long as, at each step, the variation in the value of the merit function is 
above a third predetermined threshold value. When the value of the merit 
function starts to only vary by an amount less than the third threshold 
value, the function representing the intermediate surface is completed by 
the third, fourth and fifth degree Zernike polynomials. The merit function 
is calculated once again (step 62), and then at step 63, it is determined 
if the approximation obtained is sufficient, by comparing the value of the 
merit function with the first threshold value mentioned above. In the case 
of a relatively regular surface, one can thus already obtain a 
satisfactory representation. 
One then continues in the same way, progressively increasing the maximum 
degree of the Zernike polynomial to 10, 15 and 20. 
The use of a plurality of increasing degree optimization steps, according 
to the invention, offers, on the one hand, the advantage that it is 
possible to stop the calculations at any time if the value of the merit 
function falls below the first predetermined threshold value as explained 
above. This, secondly, gives the advantage of speeding up the calculations 
which are much faster for the lower degrees. It also makes it possible to 
converge to a solution in which the degree of noise is reduced. 
The description above can be readily extended to the measurement of the 
optical structure of an optical component, and, for example, to 
measurement of the refractive index distribution of a graded index optical 
component, in other words a component consisting of a variable refractive 
index material bordered by two known dioptric values. 
In a second embodiment of the invention, the computing step makes it 
possible to determine the characteristics of the surface under analysis in 
the form of maps giving the principal curvatures of said surface. 
At step 65, one starts out by calculating, at a plurality of points, the 
derivatives of the information obtained in the optical system's space, 
during the measurement phase. 
At step 66, the curvatures of the wavefront after reflection at the surface 
to be measured, or transmission at said surface, are determined on the 
basis of said derivatives. 
At step 67, knowing the shape of the incident wave, the principal 
curvatures of the surface to be measured are determined. 
The present invention is obviously not limited to the embodiments that have 
been described and illustrated, but may undergo numerous variations 
available to those skilled in the art without this however leading to a 
departure from the invention as claimed.