Method for correcting measurements of an optical element

Abstract

The invention relates to a method (100) for correcting distortion for a measurement of the apparent position of an interface, the method (100) being implemented by a measurement system (1) comprising interferometric measurement means and a low-coherence light source, configured to produce an interference signal resulting from interference between a beam referred to as a measurement beam reflected by an object to be measured and a beam referred to as a reference beam, the method comprising the following steps: - providing (102) at least one interface position correction function, for the reference beam and / or the measurement beam, configured to connect an apparent position to an actual position, the or each correction function being configured to correct optical distortions affecting the measurement beam and / or the reference beam; - measuring (106) a position of the interface in order to obtain a raw measured position of the interface from an interference signal; and - applying (108) the or each position correction function to the raw measured position in order to obtain an actual measured position of the interface.

Description

[0001] Method for correcting measurements of an optical element

[0002] technical field

[0003] The present invention relates to a method for correcting distortions in position measurements of interfaces of an optical element.

[0004] The field of the invention is, without limitation, that of optical control and measurement systems, in particular for the manufacture of optical elements or components.

[0005] State of the art

[0006] Imaging objectives generally consist of one or more lenses and possibly other components, such as slides or filters, designed to shape optical beams. These optical elements, or lenses, can be assembled in a stack along an axis within a support such as a barrel.

[0007] During the manufacture of optical elements, such as lenses or objectives with multiple lenses, it may be necessary to control or measure the shapes of the interfaces, or surfaces, of the optical elements.

[0008] Optical elements, such as optical assemblies or imaging lenses, generally consist of one or more lenses and possibly other components designed to shape optical beams. These components, or lenses, can be assembled in a stack within a support such as a barrel.

[0009] The optical performance of such an optical element, for example an imaging lens, depends essentially on the manufacturing precision of the optical components (such as lenses) that compose it, and on the precision with which they are positioned in the assembly, both in relation to their optical axes and their respective distances, if applicable.

[0010] It is therefore necessary to control the components and their assemblies. However, measurements of the position or thickness of a component, such as a blade, obtained by low-coherence interferometry, can generate different results depending on the relative position of the component with respect to a measurement beam, and in particular with respect to the focal point of the beam.

[0011] As an example, on such an interferometric system, over a displacement stroke of 2.5 mm of the optical objective relative to a measured flat plate of 3.9 mm thickness, the authors noted a difference in measured thickness of up to 0.5 pm.

[0012] Description of the invention

[0013] One aim of the invention is to provide a distortion correction method for an apparent position measurement of an interface, enabling the absolute accuracy of position and distance measurements of interfaces of objects such as optical elements to be improved.

[0014] Another aim of the invention is to provide a distortion correction method to improve the absolute accuracy of optical and physical thickness measurements.

[0015] At least one of these goals is achieved with a distortion correction method for an apparent position measurement of an interface, the method being implemented by a measurement system comprising interferometric measuring means and a low-coherence light source, configured to produce an interference signal resulting from interference between a so-called measurement beam reflected by an object to be measured and a so-called reference beam, the method comprising the following steps:

[0016] - providing at least one interface position correction function, for the reference beam and / or the measurement beam, configured to relate an apparent position to a real position, the correction function(s) being configured to correct for optical distortions experienced by the measurement beam and / or the reference beam; - measuring an interface position to obtain a raw measured interface position from an interference signal; and

[0017] - application of the position correction function(s) to the raw measured position to obtain an actual measured position of the interface.

[0018] In the method according to the invention, the interface comprises at least one of: at least one interface of the object to be measured, a moving element of an optical delay line forming part of the measurement system.

[0019] Thus, the distortion correction implemented by the method according to the invention can be applied to the correction of a position measurement, called a measurement of one or more interfaces of an object to be measured, to provide a so-called real measurement of the position of the interfaces of the object.

[0020] The object could be, for example, an optical element.

[0021] The optical element to be measured can be an optical assembly with a plurality of lenses, such as a lens. The lens can be an imaging lens, notably for a camera module in a smartphone, computer or tablet, or for a camera module used in the context of driving an automobile, or even for an endoscopic camera for a medical application, or more generally for any type of lens enabling the collection of light in an optical system.

[0022] The object to be measured can also be a stack of layers, such as layers of a semiconductor substrate, having on the surface layers or structures of different kinds, making up electronic elements or optical functions, for example, whose respective thicknesses we wish to know.

[0023] The object to be measured can be any object whose position or thickness is to be measured using an optical interferometry method. The distortion correction implemented by the method according to the invention can also be applied to correct an optical delay, referred to as a reference delay, provided by an optical delay line that is part of the measurement system and generates an optical delay. This optical delay can be introduced, for example, into a so-called reference beam.

[0024] In this case, the interface whose position is corrected can be, for example, a moving mirror of the delay line.

[0025] The distortion correction implemented by the method according to the invention can be applied jointly with the correction of a so-called reference optical delay and with the correction of the measurement of the so-called measurement position, to provide a so-called real measurement of the position of one or more interfaces of an object to be measured.

[0026] Thus, a distortion correction is applied to the correction of the measurement of the position of one or more interfaces of an object to be measured, and / or a distortion correction is applied to the correction of an optical delay provided by an optical delay line.

[0027] Thanks to the method according to the invention, the absolute accuracy of optical and physical thickness measurements is improved. Indeed, the method makes it possible to obtain an expression for the distance between the vertices or apexes of the measured interfaces, and not between points inside or outside the curvatures of the interfaces according to the relative differences between the local curvature of the wavefront of the measurement beam and the curvature of the interface on which it is reflected.

[0028] According to one embodiment, the step of providing the correction function can be carried out by the following steps:

[0029] - measurement of a position of at least two interfaces of a calibration optical element, the interfaces of the calibration optical element each having a known shape, and the calibration optical element having a stable thickness;

[0030] - generation of a correction function from the measured positions and the shapes of the calibration interfaces.

[0031] The number of position measurements of each of the at least two interfaces of the optical calibration element depends on the type of correction function and the extent of the measurement considered.

[0032] The correction function can be represented, for example, by a polynomial of a certain degree. It may be necessary to increase the degree of the polynomial as the range of the measure increases. For example, this degree could be 5.

[0033] The extent of the measurement can correspond, for example, to the extent of the displacement of the moving mirror of the delay line, or to the extent of the positions of the interfaces of an optical element to be measured along its axis.

[0034] The position measurement can be repeated for a plurality of positions of the calibration optical element relative to the interferometric measurement means, for each interface.

[0035] According to one embodiment, the method according to the invention may further include a step of calculating distances between actual measured positions of the interfaces. These distances are actual measured distances.

[0036] The optical calibration element may include, for example, a flat plate and / or a lens with curved interfaces.

[0037] The optical calibration element has a thickness that can remain stable during its movement.

[0038] Alternatively, the optical calibration element has a thickness that can vary during its movement, provided that said thickness can be determined by an auxiliary means. The thickness determined by an auxiliary means can also be produced between a face that is moved and a face that remains fixed. In one embodiment, the step of providing the correction function can be carried out by calculating a correction function from the optical properties of the measuring system.

[0039] The optical properties of the measurement system can be, for example:

[0040] - the optical properties of the optical elements of the lens, or the position of the optical center of the lens and its focal length, its numerical aperture, and any optical aberrations of this lens;

[0041] - in the case where the measurement system includes an optical fiber followed by a lens to refocus the beam from the fiber, the distance between the optical fiber from which the measurement beam originates and the refocusing lens, in addition to the properties of said lens.

[0042] Knowledge of these optical properties can be used to calculate the geometric shape of the measurement beam.

[0043] Alternatively, the step of providing the correction function can be carried out by calculating a correction function from the geometric characteristics of the measurement beam.

[0044] It is possible to evaluate the shape of the measurement beam and the position of its point of convergence, in order to model the behavior of the beam passing through the optical element to be measured and the resulting distortions of measured distances.

[0045] For example, when the measurement beam is a Gaussian beam, it is necessary to know only a limited number of parameters to be able to know its profile for any position along the propagation axis, that is to say, for a known wavelength, the minimum size of the beam and the position of the minimum size, allowing to know the amplitude and phase of the beam for other positions on the propagation axis.

[0046] The method according to the invention may further include a step of determining a corrected geometric position, also called the corrected physical position, from the corrected optical position. The corrected geometric position corresponds to the distance as it could be physically measured between the optical elements, for example by comparison with a graduated ruler, or by means of a caliper if such an object were compatible with such a measurement.

[0047] The step of applying the correction function may include modeling the propagation of the measurement beam through the object.

[0048] The modeling process may include the following steps:

[0049] - identification of an interference signal corresponding to an interface position for each interface measured;

[0050] - assigning a refractive index variation to each identified interference signal.

[0051] According to one embodiment, the correction function can be a function of the curvature of the measured interface.

[0052] The correction function may include one of the following:

[0053] - at least one table of values,

[0054] - at least one mathematical function.

[0055] Description of the figures and methods of realization

[0056] Other advantages and features will become apparent upon examination of the detailed description of examples, which are by no means exhaustive, and the accompanying drawings on which:

[0057] - Figure 1 is a schematic representation of an example of a measuring device that can be implemented within the framework of the present invention;

[0058] - Figure 2 is a schematic representation of an example of a low coherence interferometer in the time domain, usable within the framework of the present invention; - Figure 3 is a schematic representation of a non-limiting example of an embodiment of a correction method according to the invention;

[0059] - Figure 4 shows a schematic illustration of an example of the propagation of a measurement beam through interfaces of optical elements to be measured; and

[0060] - Figure 5 shows an example of calibration functions for different interface positions.

[0061] It is understood that the embodiments described below are by no means exhaustive. In particular, variants of the invention may be conceived comprising only a selection of the features described below, isolated from the other features described, if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one preferably functional feature without structural details, or with only a portion of the structural details if this portion alone is sufficient to confer a technical advantage or to differentiate the invention from the prior art.

[0062] In particular, all the variants and embodiments described can be combined with each other if there are no technical obstacles to this combination.

[0063] In the figures, elements common to several figures can retain the same reference.

[0064] Figure 1 is a schematic representation of an example of a measuring device that can be implemented within the scope of the present invention. In particular, the device can be used to implement the distortion correction method for an apparent position measurement of an interface according to the invention.

[0065] The device 1, shown in Figure 1, is arranged to perform interface position measurements, or thickness measurements, along an optical axis, on an object 5 of type optical element 5, such as an optical assembly with a plurality of lenses.

[0066] In the measuring device 1, a measurement beam 11 from a distance optical sensor 2 is brought, for example by a single-mode optical fiber 21, to a collimator 20. The collimator 20 forms a substantially collimated beam which is directed towards an object to be measured 5 by a beam splitter 17, preferably dichroic, or a beam splitter cube. The measurement beam 11 is focused onto the object by a distal objective 3.

[0067] The collimator 20 and the distal objective 3 constitute an imaging system which images the core of the fiber 21 from which the measurement beam 11 originates in or near the object 5.

[0068] When the measurement beam 11 is incident on a surface or interface of the object 5 to be measured in a direction substantially perpendicular to this surface or interface, within tolerance limits depending in particular on the angular opening at the level of the distal objective 3, the reflections which occur on this surface or interface are recoupled in the optical fiber 21 and processed in the optical sensor 2.

[0069] The optical distance sensor 2 may include a low-coherence interferometer.

[0070] Figure 2 illustrates an example of a low-coherence time-domain interferometer usable within the framework of the present invention.

[0071] In low-coherence interferometry, only reflections of the measurement beam 11 that have taken place in a measurement area or extent encompassing the interfaces of the object 5 (or at least at an optical distance equivalent to the optical distance between the collimator 20 and the object 5 along the beam 11) can cause exploitable interference.

[0072] The interferometer 2, as illustrated in Figure 2, comprises a double Michelson interferometer based on single-mode optical fibers. It is illuminated by a fiber light source 42. The light source 42 can be a superluminescent diode (SLD). The light from the source 42 is directed through a coupler 40 and the fiber 21 to the collimator 20, to form the measurement beam 11. A portion of the beam is reflected back into the fiber 21 at the collimator 20, for example at the silica-air or glass-air interface forming the end of the optical fiber, to constitute the reference wave.

[0073] The retroreflections from object 5 are coupled in fiber 21 and directed with the reference wave towards a decoding interferometer built around a fiber coupler 41. This decoding interferometer has an optical correlator function whose two arms are, respectively, a fixed reference 44 and a time delay line 45. The signals reflected at the reference 44 and the time delay line 45 are combined, via the coupler 41, on a detector 43. The function of the time delay line 45 is to introduce an optical delay between the incident and reflected waves, which varies over time in a known manner, obtained, for example, by moving a mirror.

[0074] The length of the arms 44 and 45 of the decoding interferometer is adjusted so as to allow the delay line 45 to reproduce the optical path differences between the reference wave reflected at the collimator 20 and the retro-reflections from the object 5, in which case an interference peak is obtained at the detector 43 whose shape and width depend on the spectral characteristics of the source 42. Thus, the measurement range is determined by the optical length difference between the arms 44 and 45 of the decoding interferometer 2, and by the maximum travel of the delay line 45.

[0075] The measurement of each interface position corresponds to the identification of the central positions of each detected interferogram, for example by detecting the maximum of the envelope of the modulated signal.

[0076] With reference to Figure 1, the device may optionally also include a camera 6, equipped with a CCD (“Charge Coupled Device”) or CMOS (“Complementary Metal Oxide Semiconductor”) matrix sensor 7, as well as optical imaging means capable of forming an image of the object 5, or at least of its entrance face, on the sensor 7 of the camera 6, according to a field of view on the object 5, the field of view being substantially proportional to the magnification of the optical imaging means and to the dimension of the sensor 7.

[0077] In the implementation example in Figure 1, the optical imaging means include a distal objective 3 disposed on the object side 5 and an optical relay 13.

[0078] A light source 8 emits a beam of light 9 that illuminates the object 5 in such a way as to allow imaging by reflection. For clarity, the beam of light 9 is not shown in Figure 1 after the slide

[0079] 10 which allows the light from the light source 8 to be directed towards the object 5 and the reflected light 12 towards the camera 6.

[0080] Device 1 may also include, in addition to or instead of light source 8, a light source 8a to illuminate object 5 in transmission.

[0081] The measurement beam 11 is inserted into the optical imaging means by coupling means 7 in such a way that it is incident on the object 5 according to a measurement area included in the field of view of the camera 6.

[0082] The setup in Figure 1 therefore allows the insertion of a measurement beam

[0083] 11. Interferometric in the field of view of an imaging system, consisting of the camera 6, the distal objective 3, and the relay 13 in the example shown. Thanks to this configuration, the position of the measurement beam 11 can be known or indexed, or at least fixed, relative to the images produced by the imaging system.

[0084] The collimator 20 can also optionally include displacement means 15 which allow the position of the measurement beam 11, and therefore the position of the measurement point, to be moved in a known manner on the object 5 relative to the field of view covered by the imaging means.

[0085] The device 1, according to the embodiment shown in Figure 1, further comprises a sample holder 30 for receiving the objects to be measured 5, as well as movement means 14, such as translation and / or rotation tables, for moving the holder 30 in a plane perpendicular to the optical axis of the imaging means. According to an example also shown in Figure 1, particularly for inspecting objects 5 in the form of optical elements 5 such as volumetric camera lenses, the sample holder 30 comprises a plurality of receptacles 31 for receiving a plurality of objects 5 to be measured.

[0086] As an example, these objects 5 can be lenses assembled in a barrel, and the receptacles are through openings of a diameter corresponding to that of the barrels, with a shoulder at the base on which the barrel rests.

[0087] Preferably, the sample support 30 is arranged so that the objects 5 to be measured are positioned with their respective optical axes parallel to the optical axis of the imaging system and especially parallel to the optical axis of the measurement beam 11. Thus, the alignment of the measurement beam 11 on the optical axis of the objects 5 can be achieved with the means of movement in the plane 14 only, and therefore at a high rate.

[0088] Device 1 according to the invention further comprises a processing module 50, or calculation module, configured to process distance and / or thickness measurements and to implement the correction method according to the invention. This calculation module comprises at least one computer, a central processing unit, a microprocessor (preferably dedicated), and / or suitable software.

[0089] Device 1 according to the embodiment shown in Figure 1 can be used to implement the steps of the process according to the invention which will be described below.

[0090] Figure 3 is a schematic representation of a non-limiting example embodiment of a measurement method according to the invention.

[0091] The method 100, shown in Figure 3, includes a calibration phase 102. During this calibration phase 102, a position correction function is obtained. The position correction function relates a position measured by the measuring device to an actual position of a measured interface of an optical element. It receives as input a measured position of an interface to be measured (and optionally the curvature of the interface), and it provides as output a distortion correction to be applied to the measured position. The correction function corrects optical distortions experienced by the measurement beam along its path. These optical distortions are induced, in particular, by the shape of the measurement beam and the shape of the interface, and must be applied to all measured interfaces.

[0092] Indeed, depending on the configuration of the measuring device and the optical settings, the measurement beam arriving at the interface can be convergent, parallel, or divergent. This determines the position of the focal point of the measurement beam in space along the beam axis, before or after the interface in question, or even at an infinite distance if it is parallel.

[0093] Depending on the case, the correction function may have one or two input parameters, namely the position of the interface or the position and curvature, or shape, of the interface.

[0094] In the first case, the correction function, named Call, takes as input the measured interface position and outputs the measured position error. This error can then be subtracted from the position measurement to obtain the corrected measurement of that position, that is, the actual position.

[0095] The Call correction function can be obtained from a set of measurements, including distance measurements on an optical calibration element, or calibration or reference object, such as a blade.

[0096] According to the embodiment shown in Figure 3, the calibration phase 102 includes a measurement step 103 of a reference object, or optical calibration element. The reference object has two interfaces of a defined shape, for example, a plane in the case of a blade. The calibration object is measured at at least two different positions. The movement between the two positions is performed along the axis of the measurement beam. The positions of the reference interfaces can be referenced with respect to an element of the device 1, for example, the distal objective 3. The optical positions z0ii of the interference peak of the first reference interface and the optical positions z12i of the interference peak of the second reference interface are obtained, the index i indicating the number of positions of the calibration object.

[0097] The displacement distance can be obtained from the measurement itself. Alternatively, the displacement distance can be obtained from the means of displacement implemented to move the calibration object, such as a translation table.

[0098] Thus, we obtain a variation in the apparent distance dOi-2(zFri) between the two interfaces of the reference object, as a function of a reference position. The reference position can be, for example, the position of the first interface to be measured (zFri) of the optical element.

[0099] The position measurement of the reference interfaces can be repeated for a plurality of positions of the calibration optical element. This iteration makes it possible to obtain a position-dependent correction curve.

[0100] Alternatively, it is possible to implement the calibration phase of the process according to the invention with an interferometric thickness measurement system using a measurement in the frequency domain.

[0101] The thickness to be measured is then expressed as a frequency. For example, systems exist that use a broadband source (white light). Beams reflected from both faces of a transparent plate interfere with a portion of the incident beam. The interferogram is analyzed by a spectrum analyzer. The Fourier transform of the spectrum can provide the distance between the two faces, and therefore the thickness of the plate, as well as the distance of the plate from a reference point.

[0102] By determining the distance to the blade, for example by a means other than the interferometer, or directly from its measurements, and the thickness from the interference processing, we obtain the list of measurements used for the calibration phase. Calibration phase 102 also includes a step 104 for extracting a correction function from the position measurements taken in step 103 for measuring the calibration object.

[0103] An example of the implementation of step 104 of process 100 is described using Figure 4.

[0104] Figure 4 is a schematic illustration of the propagation of a measurement beam from an optical fiber 21 and focused by a measurement lens LM through four interfaces, designated by k = 1...4. The horizontal axis corresponds to the z-axis.

[0105] The interfaces to be measured are designated by the index k, k = l...n. We consider k = 1 if the measurement beam is reflected at the first interface. The refractive index of the air before the first interface can thus be denoted n0, ni between interfaces 1 and 2, and so on. The last optical medium traversed is therefore identified by the index nki.

[0106] In Figure 4, point a corresponds to the free focal point of the measurement system, i.e., if there were no interfaces k. For convenience and as mentioned above, we can reference the zFrk positions of the interfaces with respect to this point a, i.e. give them a zero value at a.

[0107] Given the k-1 interfaces encountered before interface k, the measurement beam converges at a point b, generally different from point a. This focal point at b is reflected by mirroring as if it originated from a point c, by interface k, here k = 4 in Figure 4. From this point c, the beam is then reflected back towards the LM lens. After reflection, the extension of the rays entering the LM lens gives the impression that the rays originate, in free space, from point d. The z-coordinate of point d provides the value zFrk = FVr(zOk).

[0108] The position zFrk is the position parameter to be provided as input to the calibration function Call defined below. We denote zOk the optical position measurement of the interface k as measured by the measuring device (round trip distance of the measuring beam divided by 2), that is to say the so-called raw measurement of the device.

[0109] Thus, the position from which the beam reflected by interface k appears to originate can be written:

[0110] The expression zFRk represents the shift of the focal point in the optical detection means of the measuring device, this shift being due to the optical media traversed and the curvatures G of the interfaces i encountered.

[0111] The offset zFrk is injected as the input point of the correction function Cal2, which provides as output the offset of each interference peak, SzFr.

[0112] In particular, the relation 8zFrk = Cal2(zFrk_caicuié, Rc_eq) = Call(zFrk_effectif_) represents half the offset of the round-trip path of the measurement beam, which would correspond to the equivalent return beam in free space. The quantity SzFk must therefore be subtracted from the measured distance, the round-trip path being divided by 2 to correspond to the forward distance as measured. Rc_eq is the radius of curvature of the equivalent interface in free space. With zFrk_effe«if = zFrk.caicuié + Rc_eq, the radius of curvature must thus be transformed into the equivalent radius of the interface that would be seen without passing through the previous k-1 interfaces.

[0113] In order to use the method, it is therefore necessary to evaluate the position of point d, which provides the zFrk value to be used in the Call or Cal2 function. This can be done using the previously measured positions of interfaces k = l to k-1, as well as the position of point a, and by calculating the intermediate points b, c, and finally point d. The position of point a does not depend on the interfaces encountered and can be determined by any means that allows the convergence point of a light beam to be identified. For example, a maximum intensity of a reflected signal can be detected when a mirror is located at position a of the beam, thus locating this point a. In the case of planar interfaces, the z-coordinate of successive points a, b, c, d can be calculated by successively applying Snell's law to the different interfaces.

[0114] If the interfaces are curved, it is also possible, using a geometric optics approximation, to calculate the successive points.

[0115] Similarly, a curvature of an interface can be calculated as an equivalent curvature through an interface, which allows, step by step, the calculation of the equivalent curvature Rck_eq of the k-th interface with respect to the curvature that would be perceived by observing it from the optical beam between the measurement objective and before the sample to be measured.

[0116] One can also use optical propagation software, for example to avoid having to explicitly perform calculations in geometric optics, or to take into account more complex interface shapes.

[0117] An optical beam measurement can also be used for greater accuracy. The minimum beam size and its position can be measured using instruments such as beam profilers, for example, those offered by Thorlabs. Such an instrument allows the beam divergence angle to be measured, and from this, the information necessary to describe the incident light beam can be deduced.

[0118] The optical beam can also be approximated by a Gaussian shape. Once the characteristics of the incident Gaussian light beam and the position of the focal point are known, it is possible to construct an error correction curve taking into account the phase of the Gaussian beam and its power density profile, for displacement positions, for example, relative to that of the focal point along the direction of propagation.

[0119] Next, the SzFrk offset must be converted into an equivalent offset of the measured optical position, to take into account the local optical index.

[0120] For this purpose, we note the IFVr() function which can be conceived as the inverse of FVr(), locally.

[0121] We can also write

[0122] 8zOk = IFVr( nk-i, k, SzFrk ) = SzFrk * nk-i, where 8zFrk is from the Cal2() or Cal 1() function as previously written, and 8zOk corresponds to the correction of the equivalent optical distance for this interface k.

[0123] Finally, we denote zOck as the corrected optical position of the k interface:

[0124] Based on the previously established notation, we will then explain how the Cal 1() function is related to this notation. A method for calculating the Cal 1() function from a set of measurements obtained from the displacement of the calibration optical element with a stable thickness will be described.

[0125] Thus, from the measurements of the optical positions zOii of the interference peak of the first reference interface and the optical positions zÛ2i of the interference peak of the second reference interface, the corrected optical positions can be written: where no and ni are the refractive indices encountered by the measurement beam before the interface under consideration (no being the index of the air before the plate and ni the index of the plate), and i denotes the number of measurements (i = l...n). We denote zFru and zFr2i the positions from which the beam reflected by the two reference interfaces would appear to originate, respectively, in free space.

[0126] By subtracting the corrected optical positions, we obtain:

[0127] We therefore keep the TIs as output variables and the free space conversions zFri and zFr2 of the positions zOii and zÛ2i returned by the measuring device as input variables.

[0128] To explicitly define the Call relationship, several methods are possible.

[0129] One such method involves finding the coefficients of a polynomial, representing the Call function, using the least squares method. Representing this function with a polynomial P allows for analytical calculations to extract the correction function from a set of several position measurements zn, zzi of the calibration object.

[0130] The function Call(z) is therefore replaced by a polynomial expression P(z).

[0131] The term zO C2i - zO cliIn equation (1), corresponds to the thickness A of the calibration object and is therefore a constant. With ni the refractive index of the calibration object, we obtain zO c2 - zO cl = A n^.

[0132] The polynomial P(z) of degree 8 can be written as follows:

[0133] P(z) = Zp2i a p z p .

[0134] To find the set of coefficients a P of the polynomial P by the least squares method, we consider as output the TI and as input the (zF^J and (zFr 2i '). The aim is to find the coefficients a P and the Ko that minimize the sum of squared differences between the d and (P(zFr2i)-P(zFrii) + Ko):

[0135] El = P(zFr 2i ) * n1— PÇzFr^') * n0— KO.

[0136] We calculate E 2 = E;=fEi which is an expression in terms of the variables (Ko, ai, a2, ... a8).

[0137] By deriving E 2With respect to the 8+1 variables and setting the 8+1 partial derivatives to zero, we obtain a matrix system which, when inverted, yields the set (K0, ai, a2, ... a8) that makes the derivative of E equal to zero. 2 and minimizing the value of E 2 .

[0138] For this matrix system to be invertible, the number of positions n of displacement of the calibration blade must be at least equal to 8+1.

[0139] The Ko solution is related to the thickness of the calibration blade. The other coefficients a P provide a correction curve. It is important to know this correction curve relatively, not absolutely, that is, up to an additive constant. The constant corresponds to a shift of the set of positions, without affecting their difference. Thus, it is possible, for example, to arbitrarily set the correction curve to pass through 0 for z = 0, or any other value, of course.

[0140] This gives us the function Call(z) = P(z). The function Call(z) is a position correction function.

[0141] Optionally, it is also possible to choose zFr a equal to 0, in the case where the interface is located at the focal point of the beam.

[0142] Of course, other representations besides polynomials are possible. Other implementations can, for example, use linear combinations of other functions such as tangent arcs, hyperbolic tangents, or rational functions.

[0143] Other shapes are also possible for the optical calibration element. It can be, for example, a lens with two curved surfaces, the curvatures of which are taken into account when determining the calibration curve. In this case, the measurement beam can be positioned approximately in the middle of this lens.

[0144] Each interface of an optical element to be measured can be characterized by its position relative to the measuring device and its radius of curvature R.

[0145] Using the Call function, it is possible to configure a position and radius correction function, Cal2(z, R), to account for non-planar interfaces. The Cal2(z, R) function allows you to relate a position and radius of curvature measured by the measuring device to an actual position and radius of curvature, respectively.

[0146] For example, we can write: Cal2(z, R) = Call (z + R).

[0147] Figure 5 shows an example of Cal2 calibration functions for different radii of curvature R of interfaces, that is, for different interface positions. The x-axis represents z, that is, the position z to be entered into the CallQ function, named zFr, corresponding to the position of point d when several interfaces are encountered before the one whose position is being measured. The y-axis represents the correction to be applied to the physical position of this interface, which is then converted into an optical position.

[0148] Curve 50 passing through z = 0 represents a correction function for a planar interface. Curves 51 and 52 represent correction functions for interfaces with radii of curvature of R and 2R, respectively.

[0149] We deduce from Figure 5 that the position correction curves are derived by a translation in abscissa of each other, at least for the part in the vicinity of z = 0 of the curves.

[0150] It is therefore possible to know, without recalibration, all the curves associated with curved mirrors by simple translation of less their radius of curvature R.

[0151] The sign of R is chosen so that R < 0 if the center of curvature of the interface is located before this interface.

[0152] To account for the shape of the measured interface, the correction function Cal2 therefore has two input parameters: the position and the curvature of the interface. As a first approximation, that is, with a measurement beam having a curved wavefront, the curvature Rc_eq is equivalent to shifting the point zFrk, from which the beam appears to originate from a seemingly planar interface, by this distance Rc_eq. This relationship is directly applicable to the first interface traversed by the measurement beam (since Rc_eql = Rcl), but still requires calculating an apparent deformation of the interface k as soon as k is greater than or equal to 2, through the 1 to k-1 preceding interfaces.Thus, the curvature parameter to be entered as an argument for the Cal2() calibration function, or added to zFrk for the Cal1() function, is the equivalent curvature at interface k, that is, its apparent curvature as seen directly from the LM measuring lens, through the k-1 interfaces encountered before this interface k. The second parameter, "shape or curvature of the interface," can be expressed as the radius of curvature when considering a beam with a wavefront shape quite close to a classical spherical shape, as well as spherical interface shapes.

[0153] If we consider other beam shapes or interface shapes more complex than a spherical curvature (for example, with two different radii of curvature along two axes), it may be necessary to supplement the calibration measurements with more measurements of several types of interfaces.

[0154] It is possible to simplify the input variable "radius of curvature", by considering a determined radius of curvature, for example infinite.

[0155] It is worth noting that placing a plane mirror at the focal point of the beam is optically equivalent to placing a mirror with a radius of curvature -R at a distance R from the focal point. In both cases, the reflected beam has a similar shape. It follows that the nonlinearity correction is zero at this location for the mirror with radius of curvature -R, just as it is for the plane mirror at the focal point.

[0156] It is also possible to use the focal point of the measurement beam as a reference position and express the correction function with an input interface position relative to this reference position. However, when the focal point is at infinity or very far away, using this reference position is numerically undesirable because its numerical value is too high.

[0157] Once the correction function is obtained using the reference object, it is extrapolated to, or calculated for, other curvatures of the surface to be measured than the one used during calibration. The shape and focal point of the measurement beam are directly related to the optical convergence power of the lens(es) or objective(s) of the measurement system. A modification of this configuration requires a new calibration phase to account for these changes.

[0158] It is also possible to obtain a correction function for cases where the apices of the different interfaces are offset from the optical axis. These offsets can be taken into account, for example, by calibrating the measuring device with offsets of the refocusing point on the return path, relative to the optical axis on the forward path. This can be achieved, for example, by tilting the reference plane plate relative to the optical axis and relating the resulting offsets of the polynomials P(x) or curves such as those shown in Figure 5 to the offsets of the apices relative to the optical axis.

[0159] Thanks to the measurements in phase 102 of the calibration, all focusing elements between the optical fiber and the interface to be measured are taken into account, without requiring knowledge of the precise characteristics of these elements, provided they remain stable between phase 102 of the calibration and the use of the calibration for measuring an interface (see below). This differs from calibration by calculation, for which the characteristics of the focusing elements must be known.

[0160] The process 100, shown in Figure 3, also includes a measurement step 106. In step 106, a position of an interface to be measured is measured, for example by means of a measuring device such as that shown in Figure 1. The measurement step 106 thus makes it possible to obtain a measured position zOi of the interface i from an interference signal.

[0161] To perform measurement step 106, an interference signal must be identified, that is, an interference peak for each interface being measured. Peaks corresponding to indirect feedback from the interfaces are eliminated; that is, light reflected from one interface being measured and reflected off one of the previous interfaces can form other reflected peaks, shifted in position relative to the main peaks.

[0162] Once the measured interference peaks have been identified, a list of refractive index variations is assigned to these interference peaks.

[0163] With reference to the devices that can be implemented in the present invention, the delay line 45 may include a collimator (not shown) that focuses a measurement beam onto a movable mirror, the displacement of which produces a variable delay. This variable delay represents the so-called reference delay against which the interferometer performs the comparison with the so-called measurement optical delay, generated by the optical return from one of the interfaces whose position is to be measured. Knowing the value of the delay line then provides the measured value zOi of the position of interface i. Thus, the displacement of the mirror can be evaluated by a measuring means to provide the so-called reference optical delay value, which is used to measure the positions of the elements to be measured 5 under the objective 3.

[0164] However, the position of the moving mirror of the delay line may not correspond exactly to the value of the optical delay obtained, because the optical beam may not be reflected exactly at the location on the physical surface of the mirror, just as the measurement beam from the lens 3 is not reflected exactly at the position of the interface encountered by the optical element 5. Therefore, this optical assembly may exhibit distortions between the distance the mirror travels and the apparent optical delay obtained, in the same way that the lens 3 of the measurement section on the optical element 5 introduces its own distortions on the optical delay of the so-called measurement beam relative to the actual position of the interfaces of the optical element 5. In order to overcome this drawback, these distortions can be determined or estimated according to the method of the invention, so as to take into account the distortion between the position of the mirror and the generated optical delay.

[0165] Thanks to the method according to the invention, it is then possible to record the distortion curve, or function, between the apparent position of the mirror and its real position, called Call_LR(). The value of the Call_LR(zLR) curve at a particular (so-called real) position zLR of the mirror is subtracted from zLR to provide a position of the mirror that reflects a measure of the delay actually generated optically by the moving mirror, thus performing an evaluation of its apparent (optical) position which is the one to be taken into account to measure the position of the interfaces of the element to be measured, for the useful value of the mirror position.

[0166] To record this Call_LR() curve, the distal objective 3 of the so-called measurement section of the optical element of the interferometer 1, as well as the element 5 to be measured, are used. For this purpose, the distal objective 3 is preferably set for an infinite focusing distance, and a so-called reference plate with preferably flat faces is moved in place of the element to be measured 5, to generate a distortion-free image.

[0167] Other configurations of the distal objective 3 and / or the use of a blade with faces of a different shape are possible, having previously estimated, using the method, the distortion of the measurement channel thus configured, in order to be able to take into account its own distortions in the evaluation of the Call_LR() function.

[0168] We can then move the reference blade to obtain a calibration curve of the Call_LR() function relative to the delay line, according to the procedure.

[0169] Then, as described below, the Call_LR() function can be used to correct the distortions between the optical delay expected from a known position of the delay line mirror and the optical delay actually obtained, in the same way as correcting the actual position of the interfaces of the optical element being measured, that is, by subtracting (or adding, depending on the sign convention chosen during the measurement) it from the current position zOi. This can be written, for two positions zOii and zCi, by denoting n a the optical index of the air in the delay line:

[0170] In step 108 of process 100, the correction function obtained during calibration phase 102 is applied to the measured position for each interface measured in the preceding step 106. This correction step 108 corrects the position of the identified interference peaks, thus yielding a true optical position for each measured interface. For each interface k of the measured optical element, the position zFrk in free space, i.e., air, is calculated from the measured position Zk.

[0171] Next, the correction 8zFk = Call(zFrk) is calculated using the correction function Call as determined during phase 102 of calibration.

[0172] The actual optical position zOck of the interface k is obtained as follows. The apparent distance difference of the measurement position is calculated:

[0173] 8zOk = IFVr(nk-i, k, SzFk), where IFVr = nk-i . SzFk.

[0174] By deducing the optically measured difference in position SzOk, we obtain the real optical position: zOck = zOk - SzOk.

[0175] If the Call_LR() function has been determined previously to be used, this expression is written: zOck = zOk - SzOk - Call_LR(zOk).

[0176] Also, if only the Call_LR() function is used, the expression is written: zOck = zOk - Call_LR(zOk).

[0177] These operations are then performed for the next interface, and so on.

[0178] During a step 110 of process 100 according to the embodiment shown in Figure 3, the distances of the interfaces and in particular the thicknesses of the optical components formed by the interfaces are calculated from the actual optical positions.

[0179] The optically corrected thickness is written as:

[0180] EpOk = zOck+i - zOck = zOk+i - zOk - 8zOk+i + SzOk.

[0181] The physical thickness can then be obtained as follows: Epk = EpOk / rik-i, where rik-i is the refractive index of the component considered.

[0182] Of course, the invention is not limited to the examples just described and many modifications can be made to these examples without departing from the scope of the invention.

Claims

DEMANDS 1. A distortion correction method (100) for an apparent position measurement of an interface, the method (100) being implemented by a measurement system (1) comprising interferometric measurement means and a low-coherence light source, configured to produce an interference signal resulting from interference between a measurement beam reflected by an object to be measured and a reference beam, the method comprising the following steps: - provision (102) of at least one interface position correction function, for the reference beam and / or the measurement beam, configured to link an apparent position to a real position, the correction function or functions being configured to correct optical distortions suffered by the measurement beam and / or the reference beam; - measurement (106) of an interface position to obtain a raw measured interface position from an interference signal; and - application (108) of the position correction function or functions to the raw measured position to obtain an actual measured position of the interface.

2. A method (100) according to claim 1, characterized in that the interface comprises at least one of the following: - at least one interface of the object to be measured, - a moving element of an optical delay line forming part of the measuring system (1).

3. Method (100) according to claim 1 or 2, characterized in that step (102) of providing the correction function is carried out by the following steps: - measurement (103) of a position of at least two interfaces of a calibration optical element, the interfaces of the calibration optical element each having a known shape, and the calibration optical element having a stable and / or known thickness; - generation (104) of a correction function from the measured positions and the shapes of the calibration interfaces.

4. Method (100) according to the preceding claim, characterized in that the position measurement (103) is repeated for a plurality of positions of the calibration optical element relative to the interferometric measurement means, for each interface.

5. Method (100) according to any one of the preceding claims, characterized in that the calibration optical element comprises a flat plate and / or a lens with curved interfaces, the calibration optical element having a stable and / or known thickness.

6. Method (100) according to claim 1, characterized in that the step (102) of supplying the correction function is carried out by calculating a correction function from optical properties of the measuring system.

7. Method (100) according to any one of the preceding claims, characterized in that the step (102) of supplying the correction function is carried out by calculating a correction function from the geometric characteristics of the measurement beam.

8. Method (100) according to any one of the preceding claims, characterized in that it further comprises a step (110) of determining a corrected geometric position from the corrected optical position.

9. Method (100) according to any one of the preceding claims, characterized in that the step (108) of applying the correction function includes modeling the propagation of the measurement beam through the object.

10. Method (100) according to the preceding claim, characterized in that the modeling comprises the following steps: - identification of an interference signal corresponding to an interface position for each interface measured; - assigning a refractive index variation to each identified interference signal.

11. A method (100) according to any one of the preceding claims, characterized in that the correction function is a function of the curvature of the measured interface.

12. A method (100) according to any one of the preceding claims, characterized in that the correction function comprises one of the following: - at least one table of values, - at least one mathematical function.

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