CERTIFICATE OF TRANSLATION
`
`|, John Dawson, located at 615 Dickson Street, Saint Louis, Missouri, am fluent in the French and English
`languages. | have been translating documentsfor 33 years and am competentto translate documents
`from French into English. | hereby certify that the documentidentified below, translated from French
`into English, is true and accurate, to the best of my knowledge and belief.
`
`FR2707018B1
`
`| declare under penalty of perjury under the laws of the United States of America that the foregoingis
`true and correct.
`| hereby declare that all statements made herein of my own knowledgeare true and
`that all statements made on information and belief are believed to be true; and further that these
`statements were made with the knowledgethat willful false statements and the like so made are
`punishable by fine or imprisonment, or both, under Section 1001 ofTitle 18 of the United States Code.
`
`John Dawson
`
`Name
`
`28 April 2018
`
`Date
`
`abwunason
`
`Signature
`
`3SHAPE EXHIBIT 1003
`3SHAPE EXHIBIT 1003
`3Shape v. Align
`3Shape v. Align
`IPR2019-00150
`IPR2019-00150
`
`-1-
`
`

`

`19. FRENCH REPUBLIC
`______
`
`
` NATIONAL INSTITUTE OF
`
`INDUSTRIAL PROPERTY
`______
`PARIS
`
`
`
`
`
`11. Publication No.:
`(to be used only for
`ordering copies)
`
`21. National Registration No.:
`
`51. Int Cl5: G 02 B 27/22
`
`12.
`
`PATENT
`
`2 707 018
`
`93 07534
`
`
`B1
`
`
`
`
`
`
`FR 2 707 018 – B1
`
`
`
`54. DEVICE FOR ACQUISITION OF THREE-DIMENSIONAL IMAGES.
`
`
`
`
`22. Date of filing: 06/22/1993.
`
`30. Priority:
`
`
`
`
`
`
`
`
`
`43. Date application made available to the
`public: 12/30/1994 Bulletin 94/52.
`
`
`60. References to other related national
`documents:
`
`
`
`
`71. Applicant(s): COMMISSARIAT À
`L’ÉNERGIE ATOMIQUE, a Scientific,
`Technical and Industrial Establishment —
`FR.
`
`
`
`
`
`72. Inventor(s): PICARD BERNARD
`
`
`
`
`
`
`
`73. Holder(s):
`
`
`
`74. Attorney(s): BREVATOME
`
`
`
`45. Date patent made available to the
`public: 07/21/1995 Bulletin 95/29.
`
`
`
`56. List of documents cited in the search
`report:
`
`
`
`
`
`
`
`
`
`
`See end of this specification
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`2707018
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`1
`
`
`DEVICE FOR ACQUISITION OF THREE-DIMENSIONAL IMAGES
`
`DESCRIPTION
`The present invention concerns a device for acquisition of three-dimensional
`
`images.
`
`In preferred embodiments, the present invention enables acquisition of images at a
`
`rate on the order of 10 images per second or more, and in particular, acquisition of
`images “in real time,” i.e., at the video rate (25 images per second).
`
`The field of three-dimensional imagery (i.e., acquisition of three-dimensional
`
`images) is a fast-growing one and involves more and more areas in industry as well as
`biomedicine.
`
`
`
`
`
`The main fields concerned by three-dimensional imagery are:
`
`- dimensional control,
`- quality control,
`robot guidance,
`-
`- biomedical imaging.
`
`Numerous techniques are used in three-dimensional imaging.
`
`5
`
`10
`
`15
`
`On this subject, reference will be made to document (1), which, like the other
`
`documents cited hereinafter, is mentioned at the end of the present description.
`
`20
`
`
`
`Among these techniques, the following in particular can be cited:
`
`triangulation by laser (using a lighted spot or line produced by laser),
`-
`confocal imaging,
`-
`scanning tunneling microscopy,
`-
`interferometry,
`-
`- moiré fringes,
`
`
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`25
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`-3-
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`2707018
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`2
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`
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`- phase shifting technique,
`- photogrammetry,
`- measurement by radar,
`flight time measurement,
`-
`- voludensitometry,
`- mechanical profilometry.
`
`5
`
`One of the principal limitations of three-dimensional image acquisition systems is
`
`that they often work at acquisition rates far lower than the video rate (25 images per
`second).
`
`10
`
`The few systems working at the video rate are often complex and costly (see
`
`documents (2) and (3)).
`
`As will be seen further on, in a preferred embodiment, the three-dimensional
`
`imaging device according to the present invention is capable of working at the video rate
`while being far simpler than the known devices capable of working at that rate.
`
`15
`
`
`
`The present invention utilizes the technique of confocal imaging.
`
`This technique has been the object of numerous articles, particularly in the field of
`
`microscopy (see document (4)), where it is nearly exclusively used.
`
`
`
`The diagram of figure 1 illustrates the principle of confocal imaging.
`
`According to this principle, an object to be observed is lighted by means of a
`
`point source and the light reflected by that object is detected by means of a point detector.
`
`20
`
`
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`
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`More specifically, the light emitted by a source S is focused by a lens 1 onto
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`-4-
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`2707018
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`3
`
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`a diaphragm 2 in order to obtain a point source Ao.
`
`The source S can be a conventional source such as arc, filament or laser.
`
`An objective lens 3 allows the light transmitted by the diaphragm or filter 2 to be
`
`focused onto a spot located at the point A1o.
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`5
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`A semi-transparent lamina 4 allows the light collected by the objective lens 3 to
`
`be reflected onto a photodetector 5.
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`10
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`15
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`20
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`A diaphragm 6, placed at the point A2o, combined with the point A1o by the
`
`objective lens 3, allows the light reflected by the semi-transparent lamina 4 to be filtered,
`the photodetector 5 receiving only the light energy transmitted through the opening of the
`diaphragm 6.
`
`A two-dimensional image is obtained by scanning the lighted spot on the object to
`
`be observed.
`
`A confocal imaging device is therefore a particular form of scanning optical
`imaging devices.
`
`When the point of the object to be observed is located in the focal plane P of the
`objective lens 3, i.e., at A1o, the image thereof through the objective lens 3 is the point
`A2o located at the center of the opening of the diaphragm 6.
`
`In this configuration, the width of the lighted point at the diaphragm or filter 6 is
`minimal and the amount of light received by the photodetector 5 is maximal.
`
`When the point of the object to be observed is moved away from the focal plane
`of the objective lens 3 and is located for example at A1, the image thereof through the
`objective lens 3 is then the point A2 and the width of the lighted point at the filter 6
`increases while
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`2707018
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`4
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`the amount of light received by the photodetector 5 decreases.
`
`5
`
`10
`
`This property of confocal imaging systems to produce images for which the light
`intensity is a decreasing function of the distance from the object to the focal plane of the
`objective lens is designated by the term “axial selectivity.”
`
`When there is a slight lack of focus, the axial transmission T(z) of the confocal
`filter, which is the ratio of the light intensity transmitted by the filter 6 to the incident
`light intensity on said filter, is given by the following formula (1):
`T(z) = sin2(u/2)/(u/2)2
`
`with:
`
`where:
`
`
`
`
`λ
`z
`
`u = (2π/λ) ∙ z ∙ sin2α
`represents the wavelength of the observation light
`is the distance from the object to the focal plane, calculated parallel
`to the axis Z of the objective lens 3
`sin α is the numerical aperture of the objective lens.
`
`15
`
`In confocal imaging, the two-dimensional image of the object to be observed is
`obtained by scanning of the light spot.
`
`This scanning is achieved by moving the object or the light spot, or by moving the
`object in a direction and movement of the light spot in a direction perpendicular to the
`previous one.
`
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`-6-
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`2707018
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`5
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`
`The great majority of confocal imaging systems and scanning optical systems use
`the light from a laser beam because of the extremely high focusing power thereof, power
`that makes it possible to obtain high light intensities in spots of very small dimensions.
`
`5
`
`These systems operate at acquisition rates that are lower than the video rate,
`because the scanning device is generally mechanical and works at frequencies that are not
`very high.
`
`Nevertheless, some systems operate at the video rate, due to the use of a
`polygonal mirror turning at very high speed (see document (2)).
`
`However, these systems are complex and costly.
`
`10
`
`Other systems operating at the video rate use a device for the acousto-optical
`deflection of the laser beam (see document (5)).
`
`A scanning technique by Nipkow disk also makes it possible to work at the video
`rate (see documents (4), (6) and (7)).
`
`This scanning technique has the advantage of being able to be used with
`conventional light sources such as the arc lamp, and is easy to implement.
`
`15
`
`A confocal imaging device utilizing a Nipkow disk is schematically represented
`in figure 2.
`
`A Nipkow disk is a metal disk, for example a chrome mask, which is drilled with
`tens of thousands of holes a few micrometers in diameter and arranged in spirals (see
`document (7)).
`
`20
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`-7-
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`2707018
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`6
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`The device schematically represented in figure 2 comprises an arc lamp 7 that
`illuminates a Nipkow disk 8 through a focusing lens 9.
`
`An objective lens 10, the axis of which bears the reference Z, projects the image
`from this disk 8 onto an object to be observed O.
`
`5
`
`The light reflected by this object O passes back through the disk 8.
`
`A separator cube 11 enables the light transmitted by the disk to be reflected
`towards the focusing lens 12, and this lens forms the image from the disk on the
`photosensitive surface of a CCD video camera 13.
`
`10
`
`15
`
`When the disk 8 is driven in rotation by appropriate means 14, this disk behaves
`like a set of point light sources and confocal filters, according to the basic diagram in
`figure 1, which synchronously scan the object to be observed O.
`
`The rotation of the disk makes it possible to generate a two-dimensional image at
`the camera 13.
`
`The arrangement of the holes in spiral form on the disk 8 causes an apparent
`radial movement of these holes, which avoids the formation of lines on the image
`obtained.
`
`In confocal imaging, the intensity of the image is maximal when the points of the
`object to be observed are located in the focal plane P of the objective lens 10.
`
`This property can be utilized
`document (4)).
`
`20
`
`to obtain
`
`three-dimensional
`
`images (see
`
`To do this using a confocal imaging device, a series
`
`
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`-8-
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`2707018
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`7
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`of acquisitions of N images (optical cuts) In(x,y), at different heights zn (the object is
`moved vertically to do this), where zn is equal to the height zo of the focal plane P
`increased by a quantity n∙Dz (n varying between 1 and N).
`
`5
`
`A search for the maximum from the series of light intensities at each point of
`coordinates (x,y) in a plane perpendicular to the axis Z makes it possible to determine the
`position of the point in question along the axis Z.
`
`That axial position corresponds at each point to the position z where the light
`intensity obtained is maximal.
`
`In other words, for each point (x,y), there are N images along the axis Z, and the
`position z corresponding to the intersection of the object and an axis parallel to the axis Z
`corresponds to the maximum light intensity.
`
`If a confocal imaging device working at the video rate is used to achieve the
`acquisitions, the rate of acquisition of the three-dimensional images is divided by the
`number N, which represents the number of images necessary to cover the topography of
`the object to be observed.
`
`The present invention makes it possible to obtain the three-dimensional image of
`the object in a single acquisition.
`
`Considering that the number of acquisitions N can currently reach one hundred, or
`even one thousand in certain applications, the benefit the present invention can represent
`is obvious.
`
`Known from document (8), to which reference will be made, is a scanning
`confocal light-optical microscopic and in-depth examination of an extended field.
`
`10
`
`15
`
`20
`
`This known device utilizes:
`
`
`
`
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`-9-
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`

`2707018
`
`8
`
`
`a polychromatic light source, i.e., one having at least two different wavelengths,
`a confocal imaging system,
`an objective lens having longitudinal chromatism or axial chromatism, and
`a spectral analysis of the light.
`
`-
`-
`-
`-
`
`5
`
`These four elements make it possible to obtain a three-dimensional image of the
`observed object, in a single acquisition.
`
`The longitudinal dynamic of the known device is equal to the number of
`secondary light beams.
`
`10
`
`This known device only makes it possible to measure longitudinally, parallel to
`the axis of the objective lens, a limited number of points corresponding to the number of
`secondary light beams.
`
`In order for the production of this known device to not be too complex, the
`polychromatic light source used is an argon laser whose light contains no more than
`seven sufficiently intense wavelengths in the visible spectrum.
`
`15
`
`Such a device, therefore, only allows images to be acquired in seven planes.
`
`This device is sufficient for use in microscopy, for observation of microelectronic
`objects such as integrated circuits, but is unusable for applications requiring a significant
`longitudinal dynamic.
`
`The purpose of the present invention is to remedy this disadvantage by proposing
`a device having a high longitudinal dynamic.
`
`20
`
`More precisely, an object of the present invention is a device for acquisition of
`three-dimensional images of an object, characterized in that it comprises:
`
`-10-
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`

`

`2707018
`
`9
`
`
`
`a source of broad-spectrum light,
`-
`- means of forming point light sources from the light produced by the source of
`broad-spectrum light,
`- means of focusing the light from each point source onto the object, said focusing
`means having an axial chromatism varying monotonically (preferably linearly) as
`a function of the wavelength of the light from the source,
`- beam separation means, intended to reflect the light reflected by each point of the
`object,
`filtering means comprising at least two chromatic filters whose respective spectral
`responses are different from each other and vary monotonically (preferably
`linearly), as a function of the wavelength of the light from the source, and which
`are intended to receive the light reflected by the beam separation means,
`- photodetection means comprising at least two photodetectors respectively
`associated with filters and intended to receive the light respectively filtered by
`said filters, said two photodetectors simultaneously receiving light information
`relative to the same point of the object, and
`electronic means of processing signals furnished by the photodetectors, said
`electronic processing means being intended to form the relation of one of said
`signals to the other and to determine the position of each point of the object
`parallel to the axis of the focusing means, by means of said relation and
`information that is
`
`-
`
`-
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`
`
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`5
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`10
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`15
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`20
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`-11-
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`

`

`10
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`stored in memory in said electronic processing means and which is the result of a
`prior calibration of the device.
`
`2707018
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`5
`
`10
`
`The device according to the present invention has a much greater longitudinal
`
`dynamic, greater simplicity and therefore lower cost than the known device disclosed by
`the document (8), which requires as many detection or modulation devices as there are
`secondary light beams (while two photodetectors are sufficient to the present invention).
`
`According to a particular embodiment of the device according to the invention,
`the photodetection means comprise two CCD or tube-type video cameras, arranged in
`such a way that the photosensitive pixels of one of said cameras are respectively
`associated with the photosensitive pixels of the other camera, and that each point of the
`object is observed by two associated pixels.
`
`According to another particular embodiment, the device according to the
`invention comprises a color video camera that constitutes both the filtering means and the
`photodetection means.
`
`15
`
`In a first particular embodiment of the invention, the means of forming point light
`sources comprise:
`
`a Nipkow disk, and
`-
`- means of rotating said disk around the axis thereof.
`
`In a case in which the two aforementioned video cameras are used, the means of
`forming point light sources can comprise a fixed mask having openings,
`
`20
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`-12-
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`2707018
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`11
`
`
`each of said openings corresponding to one photosensitive pixel from each of the two
`cameras.
`
`In a case in which the aforementioned color video camera is used, the means of
`forming point light sources can comprise a fixed mask having openings, each of said
`openings corresponding to one photosensitive pixel of the color video camera.
`
`5
`
`In another particular embodiment of the invention, the means of forming point
`light sources comprise:
`
`a mask at an opening, forming a confocal filter, and
`-
`- means of relative movement of the object with respect to the light beam produced
`by the source of broad-spectrum light.
`
`The device according to the invention can further comprise an ordered fiber-optic
`
`bundle, placed between the means of forming point light sources and the focusing means.
`
`The present invention will be better understood from the following description of
`embodiments provided below, purely by way of example and in no way limiting, with
`reference to the appended drawings in which:
`
`-
`
`-
`
`-
`
`figure 1, already described, schematically illustrates the principle of confocal
`imaging,
`figure 2, already described, is a schematic view of a known confocal imaging
`device utilizing a Nipkow disk,
`figure 3 is a schematic view of a particular embodiment of the device according to
`the invention,
`
`10
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`15
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`20
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`-13-
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`2707018
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`12
`
`
`figure 4 is a schematic view of an objective lens that has an axial chromatism and
`is used in the device of figure 3,
`figure 5 is a schematic and partial view of another device according to the
`invention utilizing a color video camera,
`figure 6 is a schematic and partial view of another device according to the
`invention utilizing an opening playing the role of confocal filter, two point
`detectors and means of scanning the object to be studied,
`figure 7 is a schematic view of a mask usable in the present invention, and
`figure 8 is a schematic and partial view of another device according to the
`invention utilizing an ordered fiber-optic bundle.
`
`-
`
`-
`
`-
`
`-
`-
`
`The device according to the invention, which is schematically represented in
`
`figure 3, enables an acquisition of images at the video rate and comprises, like the device
`represented in figure 2:
`
`-
`-
`-
`-
`-
`
`the broad-spectrum light source 7, for example a xenon arc lamp,
`the Nipkow disk 8 provided with means of rotation 14,
`the lens 9 for focusing the light emitted by the source 7 onto the disk 8,
`the separator cube 11, and
`the focusing lens 12.
`
`The device of figure 3 also comprises an objective lens 15 having an axial
`chromatism, instead of the objective lens 10, the axis of the objective 15 being referenced
`Z, the axis of rotation of the disk 8 being parallel to said axis Z in the example of
`figure 3.
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`
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`
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`5
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`10
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`15
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`20
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`-14-
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`2707018
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`13
`
`
`The width of the spectrum of the source 7 is adapted to the desired longitudinal
`dynamic (the greater the desired dynamic, the broader the spectrum that should be
`chosen).
`
`5
`
`As before, the separator cube 11 is between the lens 9 and the disk 8, and the light
`produced by the source 7 passes through said separator cube 11, is focused by the lens 9
`and reflects the light from the axial chromatism objective lens 15 towards the lens 12 that
`focuses said reflected light.
`
`The effect of the axial chromatism, or longitudinal chromatism, of the objective
`lens 15 is schematically illustrated in figure 4.
`
`10
`
`The focal distance of said objective 15 depends on the wavelength of the light.
`
`Such an objective has as many different focal planes as there are wavelengths
`present in the incident light beam.
`
`Thus, a light source placed at a point A has as many images given by said
`objective as there are wavelengths present in the light beam.
`
`15
`
`These images are aligned along a light segment A1b, A1r, where A1b and A1r are
`respectively the blue and red images of the point A.
`
`Also represented is an intermediate image A1λ between A1b and A1r where λ is a
`wavelength between the blue wavelength and the red wavelength.
`
`Another point B can be seen in figure 4 for which the images B1b, B1λ and B1r
`correspond respectively to the images A1b, A1λ and A1r of the point A.
`
`20
`
`
`
`
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`-15-
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`2707018
`
`14
`
`
`The effect of the longitudinal chromatism of an objective, in confocal imaging, is
`described in the documents (5) and (7).
`
`It was seen previously that, in confocal imaging, the transmission of the confocal
`filter is a decreasing function of the distance, calculated along the axis Z of the objective,
`from the points of the object in the objective’s focal plane in accordance with the
`formula (1).
`
`Thus, if the objective lens has a longitudinal chromatism, at a given point of the
`object, the Nipkow disk transmits each wavelength differently depending on the distance,
`calculated along the axis Z of the objective, separating said point from the respective
`focal plane.
`
`The wavelength, for which the respective focal plane coincides with the point of
`the object, is transmitted with maximum light intensity and the other wavelengths are
`transmitted with decreasing intensities as the distance separating the object from the
`corresponding focal planes increases.
`
`In the device schematically represented in figure 3, if the spectra of the light
`source 7 and of the object are perfectly white, a colored image is obtained from the
`object O (which is placed in the focusing area of the objective 15) that is perfectly
`focused and for which the spectral composition of each point depends only on the axial
`position of said point relative to the objective lens 15.
`
`5
`
`10
`
`15
`
`20
`
`Thus, the device of figure 3 comprises an “encoding module” comprising a
`confocal device provided with an objective having a longitudinal
`
`
`
`
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`-16-
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`

`2707018
`
`15
`
`
`chromatism, for performing a chromatic encoding of the axial position of the points of
`the object O.
`
`Reciprocally, a point-by-point chromatic analysis of the colored image makes it
`possible to determine the axial position of the points of the object O.
`
`5
`
`This chromatic analysis is performed in a “decoding module” that also comprises
`the device of figure 3.
`
`Said decoding module D comprises another separator cube 16 (enabling two
`identical images to be obtained from the image formed by the lens 12), a first CCD or
`tube-type video camera, referenced C1 and associated with a first chromatic filter F1, as
`well as a second CCD or tube-type video camera, referenced C2 and associated with a
`second chromatic filter F2.
`
`The colored image, which is reflected by the separator cube 11, is then sent by the
`separator cube 16 onto the photosensitive pixels of the cameras C1 and C2 by means of
`the filters F1 and F2.
`
`More specifically, the cameras C1 and C2 are arranged so that the photosensitive
`pixels of said two cameras see the same points of the object O, i.e., each pixel of one of
`the cameras is associated with a pixel of the other camera, two associated pixels seeing a
`same point of the object O.
`
`The decoding module D also comprises:
`
`-
`
`-
`
`two electronic cards for acquisition and digitization of the video images
`respectively provided by the cameras C1 and C2, and respectively bearing the
`references MA1 and MA2,
`an electronic processing module MT intended to perform the division of one of
`the images digitized by the other, pixel by pixel, as well as the calculation of the
`position along the axis Z of the points of the object
`
`
`
`10
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`15
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`20
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`2707018
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`16
`
`
`O, and to control the operation of the device of figure 3 as a whole, and
`
`- display means 18, a video screen for example, intended to display the results of
`the calculations.
`
`In particular, a device for analyzing color by means of two photodiodes having
`
`different spectral sensitivities is described in the document (9).
`
`5
`
`The mathematical modeling of the operation of the device of figure 3 will now be
`
`described.
`
`
`
`
`
`In the following:
`
`- L(λ) designates the spectral composition of the light source 7
`
`10
`
`- r(x,y,θ,φ) designates the reflection factor of the object O at the point of
`
`coordinates (x,y), in the direction of the axis Z of the objective lens 15, which is oriented
`according to the angles θ and φ relative to the line perpendicular to the object at that point
`(the coordinates x and y being defined in a plane perpendicular to the axis Z)
`
`- R(λ) designates the spectral reflectivity of the object, which is assumed to be
`
`uniform over the entire object
`
`15
`
`- T(z) designates the axial transmission of the confocal filter as a function of z
`
`(see formula (1))
`
`- z designates the axial position of the points of the object (calculated along the
`
`axis Z)
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`20
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`- z(λ) designates the chromatism “curve” of the objective lens, i.e., the position
`
`(referenced on the axis Z) of the focal plane for a given wavelength λ (for the position of
`the Nipkow disk for which the objective lens 15 is calculated in such a way as to have
`good resolution and the desired chromatism)
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`- T1(λ) designates the spectral transmission of the filter F1
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`- T2(λ) designates the spectral transmission of the filter F2
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`- S1(λ) designates the spectral sensitivity of the camera C1
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`- S2(λ) designates the spectral sensitivity of the camera C2.
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`5
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`For the wavelength λ, the axial transmission of the Nipkow disk 8 is equal to
`
`T(z–z(λ)).
`
`The spectral composition of the image of the point of the object, of coordinates
`
`(x,y,z), which is received by the camera C1, is given by the equation (2):
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`10
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`
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`
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`Φ1(x,y,z,λ) = L(λ) ∙ r(x,y,θ,φ) ∙ R(λ) ∙ T(z–z(λ)) ∙ T1(λ) ∙
`
`
`
`The signal produced by the camera C1 is given by the equation (3):
`s1(x,y,z) = ∫ Φ1(x,y,z,λ) ∙ S1(λ) ∙ dλ
`
`This results in the equation (4):
`s1(x,y,z) = ∫ r(x,y,θ,φ) ∙ L(λ) ∙ R(λ) ∙ T(z–z(λ)) ∙ T1(λ) ∙ S1(λ) ∙ dλ
`
`15
`
`To be specific, all these integrals and the ones following are taken on the
`
`spectrum of the light source.
`
`If the objective lens 15 does not have lateral chromatism, the coordinates x and y
`
`of the points of the object targeted by each camera are independent of the wavelength λ.
`
`
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`
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`-19-
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`18
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`
`In this case, the term r(x,y,θ,φ) can be taken out of the integral and the
`
`equation (4) can then be rewritten as the equation (5):
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`s1(x,y,z) = r(x,y,θ,φ) ∙ F1(z)
`
`where F1(z) designates the integral
`∫ L(λ) ∙ R(λ) ∙ T(z–z(λ)) ∙ T1(λ) ∙ S1(λ) ∙ dλ
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`5
`
`This integral depends only on the axial position z of the point of coordinates (x,y)
`
`of the object.
`
`
`
`Similarly, the signal delivered by the camera C2 is given by the equation (6):
`
`s2(x,y,z) = r(x,y,θ,φ) ∙ F2(z)
`
`10
`
`where F2(z) designates the integral
`∫ L(λ) ∙ R(λ) ∙ T(z–z(λ)) ∙ T2(λ) ∙ S2(λ) ∙ dλ
`
`
`
`By calculating the ratio s1(x,y,z)/s2(x,y,z), the term r(x,y,θ,φ) is eliminated.
`
`The quantity s(z) is then obtained, which no longer depends on z, per the
`
`equation (7):
`
`15
`
`s(z) = F1(z)/F2(z)
`
`During calibration of the device, the variations of the equation ρ=s(z) are
`
`determined experimentally as a function of z, and these variations are stored in memory
`in the electronic processing module MT.
`
`
`
`
`
`-20-
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`

`19
`
`
`Thus, the calculation of the parameter ρ of the image of a point of the object, of
`
`coordinates (x,y), makes it possible to determine the axial position z of that point,
`according to the equation (8):
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`z = s-1(ρ)
`
`5
`
`In practice, two identical cameras C1 and C2 are used and the sensitivities S1(λ)
`
`and S2(λ) are therefore theoretically identical.
`
`
`
`If the filters F1 and F2 were not used, the result would be:
`F1(z) = F2(z) = ∫ L(λ) ∙ R(λ) ∙ T(z–z(λ)) ∙ S1(λ) ∙ dλ
`
`The parameter ρ would be equal to 1 and would not allow the axial position of the
`
`points of the object to be measured.
`
`10
`
`The use of the filters F1 and F2, for which the spectral sensitivities, or responses,
`
`are different from each other, makes it possible to obtain a ratio F1(z)/F2(z) evolving in
`particular as a function of the axial position of the points of the object.
`
`The case will now be considered in which the axial chromatism of the objective
`
`15 is high considering the axial selectivity of the confocal device.
`
`15
`
`For example, we shall consider a confocal device having the following
`
`characteristics:
`
`-
`-
`-
`
`axial selectivity Δz = 20 μm
`spectral width of the light source Δλ = 0.4 – 0.8 μm
`chromatism of the objective = 1 mm in the 0.4 – 0.8 μm band.
`
`
`
`20
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`-21-
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`20
`
`
`In this case, the width at mid-height of the function T(z–z(λ)) is equal to 20/1000,
`
`or 1/50th of the spectral width Δλ of the light source 7.
`
`The quantities L(λ), R(λ), T1(λ) and S1(λ) varying slowly as a function of λ, T(z–
`
`z(λ)) can be similar to a Dirac “peak” δ(λ–λz) where λz represents the wavelength
`corresponding to the focal plane of which the axial position is equal to z.
`
`5
`
`
`
`
`
`In this case, the following can be written:
`F1(z) = ∫ L(λ) ∙ R(λ) ∙ δ(λ–λz) ∙ T1(λ) ∙ S1(λ) ∙ dλ
`
`F1(z) = L(λz) ∙ R(λz) ∙ T1(λz) ∙ S1(λz)
`
`The equation (7) then becomes the equation (9):
`
`s(z) = (T1(λz) ∙ S1(λz))/T2(λz) ∙ S2(λz)).
`
`In a case in which the axial chromatism of the objective 15 is high relative to the
`
`axial selectivity of the confocal device, it is unnecessary to assume that the spectral
`reflectivity of the object is uniform.
`
`Indeed, the spectral reflectivity of the object at the point of coordinates (x,y) is
`
`denoted r(x,y,θ,φ,λ), in the direction of the axis Z of the objective lens, which is oriented
`according to the angles θ and φ with respect to the line perpendicular to the object at that
`point.
`
`Insofar as r(x,y,θ,φ,λ) varies slowly as a function of λ, the equation (4) is
`
`transformed into the following equation (10):
`s1(x,y,z) = ∫ r(x,y,θ,φ,λ) ∙ L(λ) ∙ δ(λ – λz) ∙ T1(λ) ∙ S1(λ) ∙ dλ
`
`
`
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`10
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`15
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`20
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`-22-
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`2707018
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`21
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`This results in the following equation (11):
`
`
`
`s1(x,y,z) = r(x,y,θ,φ,λz) ∙ L(λz) ∙ T1(λz) ∙ S1(λz)
`
`The ratio s1(x,y,z)/s2(x,y,z) makes it possible to eliminate the terms r(x,y,θ,φ,λz)
`
`and L(λz) and this ratio is expressed again by the equation (9).
`
`5
`
`Similarly, in this case where the axial chromatism of the objective 15 is high
`
`relative to the axial selectivity of the confocal device, it is unnecessary for the objective
`lens 15 to be corrected for lateral chromatism.
`
`Indeed, if the objective has lateral chromatism, this means that the coordinates x
`
`and y of the points of the object targeted by each camera depend on the wavelength λ,
`i.e., x=x(λ) and y=y(λ).
`
`10
`
`In this case, the term r(x,y,θ,φ) is written r(x(λ),y(λ),θ,φ) and the equation (11)
`
`becomes the following equation (12):
`
`s1(x,y,z) = r(x(λz),y(λz), θ,φ,λz) ∙ L(λz) ∙ T1(λz) ∙ S1(λz)
`
`The term r(x(λz),y(λz), θ,φ,λz) is also eliminated by calculating the ratio
`
`s1(x,y,z)/s2(x,y,z).
`
`15
`
`It is beneficial to the longitudinal chromatism of the objective lens 15 to be
`
`calculated in such a way that said longitudinal chromatism varies monotonically as a
`function of the wavelength of the light produced by the source, the ideal being a linear
`variation that gives a very simple variation between the different wavelengths and the
`associated focal planes.
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`20
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`2707018
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`22
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`
`Depending on the working conditions, this objective lens 15 can be corrected for
`
`lateral chromatism.
`
`Moreover, the objective lens 15 is calculated in such a way that it is corrected for
`
`geometric aberrations for all of the wavelengths used.
`
`5
`
`Furthermore, the two chromatic filters F1 and F2 should be chosen so that the
`
`amplitude of the signal s(z) in the formula (7) varies monotonically with the axial
`position z of the points of the object O, said variation preferably being linear.
`
`Figure 5 is a schematic and partial view of another particular embodiment of the
`
`device according to the invention.
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`10
`
`In the decoding module D represented in this figure 5, the two cameras C1 and C2
`
`and the two chromatic filters F1 and F2 of figure 3 are replaced by a color video
`camera C3.
`
`Said camera C3 is disposed in such a way that each photosensitive pixel thereof is
`
`associated with one point of the object O to be examined.
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`15
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`Such a color video camera compr

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