Improved deflectometry method and associated system

Abstract

The invention relates to a deflectometry method for analysing a reflective surface (S) with a system comprising a display (Disp) and an imaging optical unit (IO), the method comprising the steps of: - A sequentially displaying n light images Ili on the display (Disp), a light image Ili having a binarised light intensity obtained by rasterising the pattern M(x-xi), - B detecting, on the matrix detector (Det), the n images Idi obtained by reflecting the n light images Ili onto the reflective surface (S), - C determining a function referred to as the object absolute phase function (fapS) on the basis of the n detected images Idi, the function g further satisfying the equation: g(k.M) = g(M) with any real k, - D comparing the object absolute phase function (fapS) with an absolute phase function (fapMref) referred to as the reference absolute phase function and deducing information therefrom on the shape of the surface.

Description

DESCRIPTION TITLE: Improved deflectometry method and associated system FIELD OF THE INVENTION

[0001] The present invention relates to the field of deflectometry for analyzing the shape of a surface. STATE OF THE ART

[0002] The principle of phase shift deflectometry or PSD is known for analyzing a surface S of an object Obj. A typical assembly of a PSD 5 device is illustrated in Figure 1. It comprises a display DispO configured to successively display 4 images l / 0i(x,y), i index varying from 1 to 4, the 4 images being a sinusoidal pattern in intensity MS(x) along an X axis respectively shifted by 0, t / 2, 7i, 3TI / 2. Figure 2 illustrates in A the sinusoidal pattern MS(x) and in B the four intensity profiles along x of the images / patterns MSi(x) with MS1 (x) corresponding to a phase of 0, MS2(x) corresponding to a phase of t / 2, MS3(x) corresponding to a phase of n and MS4(x) corresponding to a phase of 3TT / 2. In the example of figure 2 the amplitude of 1 of the sinusoid is coded in B between 0 and 255 (8 bits). We define the reference (X,Y) in the plane of the displayed image.

[0003] Considering that IZ0i(x,y) represents the intensity between 0 and 1 (amplitude) of an image and (x,y) the horizontal and vertical positions in pixels on the screen, we can say that for example MSi(x) = l / 0i(x,0) because the pattern is variable only according to x.

[0004] Thus, for all y, MSi(x) = l / 0i(x,y) = 0.5.[COS((2TT / A).X + <pi) +1 ]

[0005] where A is the spatial period in pixels on the screen of the sine (or cosine) and cpi is the phase of the ith image and takes for value for example 0, n / 2, n, 3% / 2.

[0006] The display DispO is arranged so that the displayed light images l / Oi are reflected on the surface S to be characterized (presenting locally a normal N) of the object Obj. We are interested here in the specular reflection and the reflection on the surface is oblique. The device also comprises an imaging optic (not shown) and a matrix detector DetO, the imaging optic being configured to image the surface S on the detector DetO. The imaging optic and detector assembly is for example a camera, which sequentially takes 4 images IdOi corresponding to the part of the sinusoidal pattern MSi (displayed on DispO) reflected by S, imaged, and detected by DetO. The 4 images IdOi are then processed by a processing unit (not shown) which determines, from these 4 detected images, the properties of the surface of the object Obj, and more particularly its relief, in order to typically identify surface defects.

[0007] In a typical deflectometry setup such as the one shown in Figure 1, the camera must be kept tilted relative to the part of the surface to be inspected in order to image the reflected light coming from the display. The display and the optical axis of the camera must therefore be positioned beyond a minimum angle relative to the part of the surface to be inspected. Indeed, without adding an angle, the camera would block the light from the screen or vice versa. To recover all the light, it is sufficient to reach the minimum angle from which visibility is total.

[0008] The angle of the ray reflected by the surface S depends on the local slope of the surface at the point of impact of the ray. We call (x,y) the coordinates of the displayed images IZ0i(x,y) (X,Y reference), and (x',y') the coordinates of the detected images ld0i(x',y'), there is typically a magnification factor between the two systems.

[0009] The idea is that when the surface S presents locally at a point P (x p ,y p ) a local slope p (a x p, a y p) relative to the flat reference surface, a fringe reflected by this surface S will be shifted on the detector by a shift dx' P in the x direction and dy'p in the y direction, these two quantities depending directly and respectively on the local slopes (a x p, ayp). Thus, knowing the geometric parameters of the system, from the shift dP(dx' P , dy'p) we can deduce the local slope ap(a x p, a y p) on the surface S at P. From these slopes ap we obtain by derivation the curvature of S at each point and by integration the altitude of S at each point (distribution of heights).

[0010] Thus, in the processing we compare the 4 detected IdOi images with 4 ldO images refi obtained by reflection of the images l£0i on a flat reference surface Sref positioned in place of the object Obj.

[0011] The ldO images re fi are undistorted sinusoidal patterns similar to the displayed images, except for the magnification factor.

[0012] We define a set called object made up of the 4 images IdOi and a set called reference made up of the 4 reference images ldO re fi-

[0013] For the comparison, we calculate a so-called absolute phase function for each of the two sets of object and reference images, respectively called absolute object phase function fapOs and absolute reference phase function fapÛRef, by applying a mathematical function gO on the 4 images corresponding to 4 variables that we will call for the formula f1, f2, f3 and f4, equal to:

[0014] gO = arctg((f4-f2) / (f 1 -f3)) (1 )

[0015] So :

[0016] fap0s (x',y') = g0(ld01 (x',y'), ld02(x',y'), ld03(x',y'), ld04(x',y'))

[0017] = arctan[(ld04(x',y') -ld02(x',y')) / (ld01 (x',y')-ld03(x',y'))].

[0018] fap0 Re f(x',y') = gO(ldO ref 1 (x',y'), ldO ref 2(x',y'), ldO ref 3(x',y'), ld0 ref 4(x',y') )

[0019] = arctan[(ld0ref4(x',y') -ldO re f2(x',y')) / (ld0 ref 1 (x',y')- ldO ref 3(x',y'))].

[0020] For illustration, the reference absolute phase function calculated with the 4 shifted sinusoidal patterns of Figure 2 is also shown in Figure 2. The reference absolute phase function calculated from the 4 shifted sinusoidal patterns is shown in Figure 2 (curve 20).

[0021] We note that this function is a ramp on intervals of 2% and that it is therefore bijective on an interval of 2K: to a value of x (or x') in this interval corresponds a unique value of y (or y'): the use of 4 images with a different phase shift allows to create at each point a bijective phase function.

[0022] The absolute object phase function fapOs is also calculated in the same way from the 4 detected deformed images ld0i(x',y').

[0023] We thus obtain a “mapping” of the surface in absolute object phase and in absolute reference phase.

[0024] From fapOs and fapÛRef, the paths of the different rays are reconstructed using an algorithm. The bijective character of the absolute phase functions reference and object makes it possible to connect a straight fringe of the reference images with the corresponding deformed fringe of the detected images, and thus to find the shift dP (measured in number of pixels in the sensor frame then transformed into distance) between these two fringes at a point P of the surface S. The bijective character is necessary to create a perfect "mapping" to correctly identify the fringes between them.

[0025] From this shift, we link this displacement / shift dP determined in the frame of the sensor x' and y' to angles seen by the optical imaging system coupled to the sensor. For this we use conjugation and / or geometric optics formulas. Once we know from which direction each absolute phase comes, we know that each ray strikes the surface S at a point, is reflected by the Snell-Descartes laws to a point on the screen. We thus determine, via the Snell-Descartes laws, the slope of the surface a P at point P of surface S.

[0026] The method is then repeated in the Y direction (the pattern of the four displayed images is MSi(y)) to have the slope information in both X and Y directions.

[0027] From the information on the slopes along X and Y, we deduce the curvature and / or the altitude as explained above.

[0028] The PSD method therefore processes at least 8 images in total, an object set of 4 images detected via a pattern shift along X and an object set of 4 images detected via a pattern shift along Y.

[0029] It has been shown that 4 phases as previously described per direction are necessary and sufficient to obtain the absolute phase function.

[0030] The classic PSD method as described above has drawbacks.

[0031] To make the best use of the camera dynamics, several fringes of the displayed pattern are used. This induces phase jumps in the absolute phase function corresponding to phase discontinuities over several periods (visible on ramp 20 of figure 2). To process them, it is necessary to "unroll the phase", that is to say to implement complex two-dimensional algorithms which search for the real phase jumps with respect to the calculation errors. In the case of several periods, the artan function of gO does not give the absolute phase; the phase must be unrolled to obtain it.

[0032] The implementation of this "phase progression" lengthens the analysis time and the complexity of the associated algorithms, and generates errors at discontinuities.

[0033] As the camera focus is set on the surface to be characterized, and not on the virtual image of the displayed image, this induces contrast problems (defocus blur) of the detected fringes. To overcome this in conventional PSDs, the imaging optics are closed (which increases the size of the Airy spot) and the integration times of the detector are increased, which limits the analysis speed.

[0034] Traditionally, PSD systems have an oblique incidence configuration. It is then difficult to be in focus on the entire surface. When trying to analyze very flat surfaces (such as "wafers" for example), not being in focus on the entire surface is a limitation. Indeed, if the depth of field decreases, the fact that we are in oblique incidence implies that a decreasing portion of the surface to be measured is found in the sharpness zone, and we then lose details on the edges. In addition, in oblique incidence, we must close the optical system to gain depth of field. In addition to increasing depth of field, closing the optical system reduces depth blur and this allows for more contrast when there are multiple fringes to distinguish on the screen. The cost is a longer exposure time since the system is closed and less light is collected. Finally, the pixels of the screens used for the implementation of the PSD do not emit an intensity transmitted in a linear way with respect to the initial information. Because of this non-linearity, the intensity emitted by the screen does not exactly present a sinusoidal variation: it is not a true sine that is generated. This induces at the time of the calculation of the absolute phase the appearance of a periodic noise called non-linearity that cannot be easily eliminated. To try to attenuate it, it is necessary: ​​to carry out a sophisticated calibration of the system or to finely characterize the non-linearity of the screen to send to the pixel a pre-deformed signal to try to correct the non-linearity and to emit a "true" sine.

[0035] Such an approach is for example described in the publication “Non linearity response correction in phase shifting deflectometry” by Nguyen et al (2018 Meas. Sci. Technol. 29,045012).

[0036] An object of the present invention is to overcome the aforementioned drawbacks by providing an improved method and system for analyzing a reflective surface by deflectometry, which does not have some of the aforementioned drawbacks and furthermore has better performance than a conventional phase shift deflectometry method. DESCRIPTION OF THE INVENTION

[0037] The present invention relates to a method for analyzing a reflective surface by deflectometry, with a system comprising a display arranged so that light images displayed on the display are reflected on said reflective surface and an imaging optic configured to image said surface on a matrix detector, the method comprising the steps of: A. successively display on the display n light images l / i indexed i with n>2, the n light images being obtained by n spatial shifts xi along a direction X of the same pattern, a light image l / i having a binarized light intensity obtained by screening the pattern M(x-xi), B. detect on the matrix detector n images ldi called detected images, obtained by reflection of the n light images l / i on the reflecting surface, C. determining a function called the object absolute phase function from the n detected images ldi, by applying a mathematical function g to said n detected images, the function g and the number of images n being determined so that the absolute phase function is bijective, the function g further verifying the relation: g(kM) = g(M) with k any real, D. compare the object absolute phase function to a so-called reference absolute phase function, determined by replacing the surface to be characterized by a plane mirror defining a so-called reference plane, and deduce information on the shape of said surface.

[0038] According to a variant, the pattern is a sinusoid, n=4, the four spatial shifts correspond to phase shifts respectively equal to 0, % / 2, %, 3% / 2.

[0039] According to one embodiment, the function g is defined by: g= arctg[(fc4-fc2) / (fc1 -fc3)] with fci corresponding to n=4 variables.

[0040] According to one embodiment, each light image displays only one period of the sinusoidal pattern.

[0041] According to another variant, the pattern is a Gaussian, n=2, a first spatial shift corresponding to a Gaussian centered on an edge of the light image 1 / 1, and a second spatial shift corresponding to a Gaussian centered on another edge of the image I / 2, and in which the function g is defined by:

[0042] g=Ln(fd ) - Ln(fc2) with fci corresponding to n=2 variables.

[0043] According to one embodiment, the pattern is invariant by Fourier transform.

[0044] According to one embodiment, the screening is carried out by the Floyd-Steinberg algorithm.

[0045] According to one embodiment, the imaging optics has an optical axis coincident with a normal to the reference plane, in which said light images illuminate said surface perpendicular to said reference plane, in which the following are defined: an optical center O of the imaging optics, a positive distance Ddp between the display and the reference plane Pref and a positive distance Dpo between the reference plane and the optical center O, and in which step D comprises the sub-steps consisting of: determining for points of the surface S, an angle determined from the offset between the object absolute phase function and the reference absolute phase function at said point of the surface, determining said slope a with the following formula:

[0046] According to another aspect, the invention relates to a system for analyzing a reflective surface by deflectometry comprising: a display arranged so that light images displayed on the display are reflected on said reflective surface, and configured to successively display n light images l / i indexed i with n>2, the n light images being obtained by n spatial shifts xi along a direction X of the same pattern M(x), a light image IZi(x,y) having a binarized light intensity obtained by rasterizing the pattern M(x-xi), an imaging optic and a matrix detector, the imaging optic being configured to image said surface on said matrix detector, the matrix detector being configured to detect n images ldi called detected images, obtained by reflection of the n light images l / i on the reflecting surface, a processing unit configured to: determine a function called the object absolute phase function, from the n detected images ldi, by applying a mathematical function g to said n detected images, the function g and the number of images n being determined so that the absolute phase function is bijective, the function g further verifying the relationship: g(kM) = g(M) with any real k, compare the object absolute phase function with a so-called reference absolute phase function, determined by replacing the surface to be characterized by a plane mirror defining a so-called reference plane, and deduce therefrom information on the shape of said surface.

[0047] According to one embodiment, the imaging optics has an optical axis arranged perpendicular to said reference plane, and in which the optical system further comprises a splitter plate configured to send said light images onto said surface perpendicular to said reference plane.

[0048] According to another aspect, the invention relates to a computer program comprising instructions which cause the system according to the invention to execute the steps of the method according to the invention.

[0049] The following description presents several exemplary embodiments of the device of the invention: these examples are not limiting of the scope of the invention. These exemplary embodiments present both the essential characteristics of the invention as well as additional characteristics linked to the embodiments considered.

[0050] The invention will be better understood and other characteristics, aims and advantages thereof will appear during the detailed description which follows and with reference to the appended drawings given as non-limiting examples and in which:

[0051] Figure 1 already cited illustrates a classic assembly of a phase shift deflectometry device.

[0052] Figure 2 already cited illustrates in A the sinusoidal pattern MS(x) and in B the four shifted patterns MSi(x) and the associated absolute phase function.

[0053] Figure 3 illustrates the method according to the invention.

[0054] Figure 4 illustrates the system according to the invention.

[0055] Figure 5 illustrates an example of a binarized image by dithering a sinusoidal pattern displayed on the display in the method / system according to the invention.

[0056] Figure 6 illustrates in A the intensity distribution of the displayed image in three successive planes during the propagation of light in space: I: on the display (d0=0); II: at a distance d1 from Disp for which the averaging is not yet sufficient; III: at a distance d2 sufficiently far from the screen Disp for the averaging to be successful. In B is illustrated, for the three situations, an example of the variation of the intensity I of the image along the X axis.

[0057] Figure 7 shows an example of the MTF of the detected image: in A in situation I and in B in situation III.

[0058] Figure 8 illustrates an embodiment of the invention in which each light image displays only one period of the sinusoidal pattern and the associated reference absolute phase function.

[0059] Figure 9 illustrates an example of a measurement carried out with a system according to the invention displaying a single period of the binarized sinusoidal pattern for the measurement of a concave surface S. The concavity was deduced to reveal the surface defects.

[0060] Figure 10 illustrates a measurement of the same concave surface (concavity inferred) made with a conventional PSD system.

[0061] Figure 11 A illustrates the measurement of a 2-inch silicon wafer carried out with the system according to the invention.

[0062] Figure 11 B illustrates the measurement of this same wafer with a commercial laser interference device (Zygo).

[0063] Figure 12 illustrates a second variant of the invention in which the pattern is a Gaussian and the associated absolute phase function is a reference. On an=2, the image 1 / 1 consists of the pattern M1(x) Gaussian function centered on one edge of the image, and the image I / 2 consists of the pattern M2(x) Gaussian function centered on the opposite edge of the image.

[0064] Figure 13 illustrates the shift dP corresponding to a slope a at a point C of the surface to be characterized.

[0065] Figure 14 is an optical diagram illustrating different quantities useful for understanding the invention. DETAILED DESCRIPTION OF THE INVENTION

[0066] The subject of the present invention is a method 100 for analyzing a reflective surface S by deflectometry, illustrated in FIG. 3, which constitutes an improvement of the conventional PSD method as described previously. According to another aspect, the invention also relates to a system 10 illustrated in FIG. 4 which implements the method 100. The system 10 comprises a display Disp arranged so that light images displayed on the display are reflected on the reflective surface S, and an imaging optic IO configured to image the surface on a matrix detector Det. The imaging optic / detector assembly forms, for example, a camera CA.

[0067] The method according to the invention is a generalization of the classical PSD in the sense that it does not only work with a sinusoidal M(x) pattern but also with other patterns, and makes it possible to solve certain problems inherent in the PSD, which improves its performance.

[0068] The method comprises a first step A in which n light images l / i indexed i with n>2 are successively displayed on the display Disp, the n light images being obtained by n spatial shifts xi along a direction X of the same pattern M(x). We define X and Y as the two directions of the frame of the image IZi(x,y).

[0069] Unlike a light image used in a conventional PSD, the light images l / i have a binarized light intensity obtained by dithering the pattern M(x-xi) also called Mi(x). After numerous experiments and simulations, the inventors established that such dithering was surprisingly compatible with a characterization of the surface by phase-shift deflectometry, significantly improving its performance while allowing the use of patterns other than a sinusoid (see below). The term "binarized image obtained by dithering" means the transformation of a grayscale image, typically coded between 1 and 255 (8 bits), into an image comprising only points having a non-zero intensity, preferably of maximum intensity (coded 1 or 255) and points having zero intensity (coded 0).The rasterization thus generates an image whose spatial density of points varies according to the pattern M(x) along the X direction. There are many rasterization algorithms and the inventors have tested several which give good results. We cite, without limitation: the algorithm consisting of generating a random image in which each pixel has a probability of the form (sin(x)+1) / 2 of being at 1 (or 0). the Floyd-Steinberg algorithm.

[0070] Other dithering algorithms are easily accessible on the internet.

[0071] Figure 5 illustrates an example of a binarized image by dithering a sinusoidal pattern of period T.

[0072] In a second step B, n images ldi(x',y') are detected on the matrix detector Det, called detected images, obtained by reflection of the n light images l / i on the reflecting surface S. The coordinates (x', y') of the detected image are linked to the coordinates (x, y) of the displayed image by a magnification factor. The directions of the reference frame of the detected image are always called (X, Y).

[0073] This step B is identical to what is classically practiced in PSD, except that classically we always have n=4 and M(x) sinusoid.

[0074] In a step C, a function called the absolute phase function faps object is determined from the n detected images ldi, by applying a mathematical function g to the n detected images, the function g and the number of images n being determined so that the absolute phase function is bijective, that is to say:

[0075] y' = faps(x') with y' unique for each x' (2)

[0076] When the pattern is sinusoidal and n=4 the mathematical function g is equal to gO given by the formula (1).

[0077] The function g further verifies the relation:

[0078] g(kM) = g(M) (3)

[0079] with any real k.

[0080] This condition (3) comes from the fact that the operator g must be insensitive to the reflectivity of the surface, the intensity reflected by the surface S and detected by the detector Det being proportional to this reflectivity. The function g applied to the images must therefore not keep this reflectivity which must cancel. An example is a cancellation of the reflectivity by means of a ratio between the images (see formula 1). When a pattern other than a sinusoid is used, the function g is different from formula (1).

[0081] In a step D, the object absolute phase function faps is compared to an absolute phase function fapMret called reference, determined by replacing the surface S to be characterized by a plane mirror Mref defining a plane Pref called reference illustrated in figure 4 and we deduce information on the shape of said surface, in the same spirit as what is done in classic PSD. The absolute reference phase function is obtained from the 4 detected images of references Idrefi.

[0082] Note that the IO imaging optics are configured to image the surface S and not the virtual image of the display (as well as for a Classic PSD). The image displayed on Disp is therefore not in focus on the Det detector, it is blurred.

[0083] As in the classic PSD, steps A to D are repeated along the Y axis to obtain slope information along the Y direction.

[0084] When the geometric parameters of the system are not changed, the same reference absolute phase function can be used for several measurements of different surfaces. If the parameters, for example the display-surface distance, and / or the surface-imaging optics distance, and / or the focal length of the imaging optics, are changed, the detection of the 4 images ld should be carried out. re fi (with the mirror Mref instead of S) and the determination of the absolute reference phase function from these 4 images in the new configuration.

[0085] The system 10 according to the invention illustrated in Figure 4 therefore comprises: a display Disp arranged so that light images displayed on the display are reflected on the reflective surface S, and configured to successively display the n binarized light images l / i, an imaging optic IO and a matrix detector Det, the imaging optic being configured to image the surface S on the detector Det, the matrix detector being configured to detect the n images ldi obtained by reflection of the n light images l / i on the reflective surface S, a processing unit (PU) configured to implement the steps C of determining the absolute object phase and D of comparing the absolute object and reference phase functions and determining information on the shape of S.

[0086] In a non-limiting manner, Figure 4 illustrates a normal incidence configuration which is preferred for implementing the method according to the invention. “Normal incidence” means a configuration in which the optical axis OA of the imaging optics IO is perpendicular to the reference plane Pref and in which the system comprises a beam splitter BS configured to send the light images onto the surface S perpendicular to the reference plane Pref. This configuration in normal incidence is rarely used in classical PSD. Since we are trying to determine very small slope angles a, the entire surface S is in focus on the detector.

[0087] The inventors have established that the binarization of the displayed image \L, combined with the defocusing of the image of \L carried out by 10, makes it possible to obtain on the surface S a light coming from the display corresponding to a "true" sine, rather than a degraded sine as is the case in classic PSD.

[0088] This is due to the fact that the binarized image averages itself as it propagates in space and gives, if the display is placed at a sufficient distance from the surface S, a sinusoidal function close to a perfect sine. Figure 6 illustrates in A the intensity distribution of the displayed image \L in three successive planes during the propagation of light in space: I: on the display (d0=0); II: at a distance d1 from Disp for which the averaging is not yet sufficient; III: at a distance d2 sufficiently far from the screen Disp for the averaging to be successful. In B is illustrated, for the three situations, an example of the variation of the intensity I of the image along the X axis (which oscillates between 1 (255) and 0) for a cross section along a 50 axis, showing the averaging as the propagation progresses. The Gaussian blur of the binarized image corresponds to the propagation of light in free space.

[0089] In other words, the I-image corresponds to what the detector detects when the camera is focused on the virtual image Ivir (the I-image here is a real image of the virtual image of the screen Ivir created by the surface S), and the III-image corresponds to what the detector detects when the camera is focused on the surface S, i.e. when the measurement is carried out.

[0090] Figure 7 shows an example of the MTF (for “Modulation Transfer Function” in English or modulation transfer function, a function of the spatial frequency fs in cycles / mm) of the image detected by Det: in A in situation I (focus on the virtual image of the display) for which the image has high spatial frequencies, and in B in situation III (focus on the surface S) for which the high spatial frequencies have been eliminated: the high spatial frequencies present in the binarized image are eliminated during propagation and a “true” sine is created on the surface S.

[0091] Thus, the binarization of the displayed image makes it possible to considerably reduce or even eliminate the non-linear periodic phase noise present in the classic PSD, which no longer exists here since the displayed image is binarized and no longer analog. This is true because LCD screens are very homogeneous for a given intensity, but are non-linear for intensity variations. This noise suppression avoids complex calibrations of the system and greatly simplifies its implementation.

[0092] For the measurement, the adjustment of the display-surface distance must be sufficient for propagation averaging to be effective, i.e. for the filtering of the high frequencies of the binarized image to take place. This adjustment is carried out, for example, by visually checking that the detected pattern presents a variation considered satisfactory or by characterizing the variation curve of the detected intensity along an axis parallel to X (see curves in figure 6 part B for II and HH).

[0093] To adjust the system's aperture, open it to the maximum to reduce the depth of field and maximize averaging (not too much, however, if the lens used is less efficient at maximum apertures).

[0094] In summary, the adjustment variables to properly average the "dither" are: take a screen with a higher pixel density, open the optical system, move the screen further away, possibly move the lens closer to the target, optionally stick a frosted glass on the screen in order to exacerbate the averaging in addition to the propagation.

[0095] The system 10 according to the invention with a normal incidence configuration makes it possible to bring the IO imaging optics closer to the surface to be characterize (see below). This makes it possible to increase the relative value of the difference between the straight fringe and the aforementioned curved fringe, directly linked to the value of the slope a sought, and therefore to measure smaller values ​​of a than with the classic PSD. The normal incidence configuration also allows focusing on the entire surface, which is very useful for characterizing very flat surfaces, i.e. with very low slopes a.

[0096] At a sufficient distance from the display, the propagation of the emitted wave is similar to a Fourier transform. Preferably, a pattern M(x) invariant by Fourier transform is chosen, to obtain on the surface S a pattern of the same nature as that displayed on Disp.

[0097] As explained above, according to a first variant, the pattern M(x) is a sinusoidal pattern (binarized). In this case we have an=4 and the four spatial shifts xi correspond to phase shifts respectively equal to 0, / 2, %, 3% / 2.

[0098] Preferably, the mathematical function g applied to the 4 detected images ldi (object) and to the 4 reference images Idæfi, corresponding to 4 variables called fci, is:

[0099] g= arctg[(fc4-fc2) / (fc1 -fc3)].

[0100] with fci = ldi (for the calculation of faps) and fci = ld re fi (for the calculation of fap re f)

[0101] This formula is identical to formula (1) used for a classic PSD process.

[0102] According to an embodiment of the method 100 and the system 10, according to the invention, each light image displays only one period of the pattern, as illustrated in figure 8 for the sinusoidal pattern: the spatial frequency of the sine of the pattern is reduced. Indeed, with the invention, the objective is opened, which optimizes the spatial frequencies near the sample to be characterized, and reduces the contrast of the fringes displayed on the screen. To recover good contrast on the display, it is therefore necessary to lower the spatial frequency of the fringes displayed.

[0103] The absolute object phase function calculated with formula (1) is equal to curve 80 which no longer presents discontinuities (phase jumps).

[0104] Using only one period means that you don't have to "unroll" the phase (see state of the art), which makes the algorithm for going back to the dy and slopes much less complex and faster. In addition, with a single fringe, you have more signal because you don't lose contrast on the detected fringes. Indeed, if you use several fringes, i.e. a higher spatial frequency on the display, as mentioned above, the contrast of high spatial frequencies decreases. A decrease in contrast implies a loss in the dynamic range of the camera. With a single fringe, looking at the MTF, you can see that low frequencies are much better transmitted than high frequencies, regardless of the focus. We therefore maintain good contrast, and we have more signal because max-min tends towards 1: we then exploit the camera's dynamic range to the maximum.

[0105] Figure 9 illustrates an example of a measurement carried out with a system according to the invention displaying a single period of the binarized sinusoidal pattern for the measurement of a concave surface S. The concavity has been deduced to reveal the surface defects. We see on the right-hand scale that the measurement sensitivity on the residual surface defects is approximately + / - 30 nm. The surface defects are clearly visible.

[0106] The system has the following characteristics: Optical center distance O of the imaging optics - sample: 47 cm Screen-Pref distance: 71 cm Imaging optics focal length: 50 mm Detector resolution: 4512x4512 pixels, pixel size 2.74 pm Imaging device aperture: N=2 Screen used: standard computer LCD screen

[0107] For comparison, Figure 10 illustrates a measurement of the same concave surface (concavity inferred) made with a conventional PSD system displaying one period of an analog pattern, without precorrection of the non-linearity of the display and with the same system as described above. We see on the right scale that the measurement sensitivity on the residual defects of the surface is approximately + / - 150 nm. This is due to the phase noise which adds a parasitic modulation. This modulation corresponds to the dark and light areas in the image. Because of this parasitic signal the measurement precision is lower and the defects are less visible.

[0108] Figure 11 A illustrates a measurement carried out with the system according to the invention of a 2-inch silicon wafer type surface (overall curvature deduced). The nanometric thickness polishing grooves are apparent and the image of the surface is complete. The measured thickness variation amplitude is + / - 100 nm or 200 nm (see scale on the right).

[0109] Figure 11 B illustrates a measurement of this same wafer (overall curvature deduced) carried out with a commercial device such as a Zygo laser interferometer. We see an area 11 without measurements corresponding to a measurement artifact. The object is in fact too curved for the measurement to be possible with the Zygo, which has a measurement dynamic of + / -80 nm, i.e. a maximum of 160 nm. The areas corresponding to a variation in thickness going beyond this are not processed and appear in white.

[0110] The system according to the invention is thus more efficient than the Zygo for this measurement: the dynamics are much greater and the details at high spatial frequencies (grooves) are better defined.

[0111] The inventors have shown that the method according to the invention is compatible with patterns other than the sinusoidal pattern.

[0112] According to a second variant, the pattern is a Gaussian and n=2. The image 1 / 1 consists of the pattern M1(x) Gaussian function centered on one edge of the image, and the image I / 2 consists of the pattern M2(x) Gaussian function centered on the opposite edge of the image, as illustrated in figure 12. The maximum of the Gaussian is coded at 1. The two Gaussians have the same parameters (amplitude, width).

[0113] The inventors have shown that a function g defined by formula (4) below is bijective and verifies condition (3):

[0114] g=Ln(fc1) - Ln(fc2) (4)

[0115] The reference absolute phase function calculated with the function g of formula (4) is also illustrated in Figure 12 (curve 12). It does not present any discontinuity. Note that the function g of formula (4) satisfies the condition g(kM) = g(M), and that a Gaussian function is invariant under Fourier transform.

[0116] It is important to ensure that the maximum of the Gaussian does not saturate the camera and that its minimum of the Gaussian is not below the noise level of the camera.

[0117] The advantage of this Gaussian pattern is that 2x2 images are necessary and sufficient for the implementation of the method according to the invention, compared to 2x4 images with the use of a sinusoidal pattern. This allows for faster acquisition, processing, and therefore measurement.

[0118] The system according to the invention has great flexibility because the geometric parameters can be modified according to the desired precision, i.e. the order of magnitude of the angle a of the local slope on the surface S. Figure 13 illustrates the shift dP corresponding to an angle a at a point C of S. This shift dP measured in the (x', y') frame of reference of the detector is the distance between the absolute phase of a fringe when a = 0 (reference) and the absolute phase of the same fringe when the surface C has an angle a locally. This shift is measured separately along x' (pattern displayed along x) and along y' (pattern displayed along y).

[0119] The optical center O of the imaging optics is defined and the angle corresponding to this shift dP measured relative to the center O is called 0 (O is the vertex of 0). Thus, the angle 0 is determined from the shift dP between the absolute object phase function and the absolute reference phase function at point C of the surface.

[0120] The inventors determined a relationship between a and 0 as a function of the system parameters for the preferred normal incidence configuration. This relationship involves only two quantities: a positive distance Ddp between the display and the reference plane Pref, and a positive distance Dpo between the reference plane Pref and the optical center O.

[0121] The diagram in Figure 14 illustrates these different quantities in an optical diagram for a numerical example with Ddp = 11 cm and Dpo = 31 cm. P DiS p is the plane in which the display Disp is arranged and Poet is the plane in which the detector Det is arranged.

[0122] Point A' is a point on the display.

[0123] Point A is the virtual image of A' when the reference mirror Mref is placed at Pref (perpendicular to OA). A ray from A' is reflected at point C (ray 3) and focused at point F in plane PDe t-

[0124] Point A” is the virtual image of A' when it is the surface S with a local slope a at C which reflects the ray coming from A'. This ray reflected by C (ray 4) is focused at point G in plane P Det This is valid for small angles. The ray is reflected by a point very close to point C. For small angles, and to establish the formula below, we considered that this point is C.

[0125] The distance FG corresponds to the offset dP.

[0126] Thus, the angle 0 is the angle formed between the points F, O (optical center-vertex) and G where F is the position of the absolute phase on the detector of a fringe of the screen (A') after reflection on the reference and G is the position of the absolute phase on the detector of the same fringe after reflection on the sample presenting an angle a.

[0127] The relationship established by the inventors is:

[0128] at 0.5.

[0129] This formula is of course to be applied according to X and Y independently.

[0130] The absolute phase of a reference fringe falls at F, the absolute phase of the same fringe after reflection from the sample falls at G. When the phase varies in the X direction, then F in the (x', y') frame is in X'F and G in X'G, and we have:

[0131] dx' = X' G -X'F, distance between F and G

[0132] For the simplified case of a thin lens we have:

[0133] px = arctan(dx' / f) f focal length of the imaging optics

[0134] For a more complex objective, the position of the main planes is taken into account.

[0135] ocx is then determined with formula (5).

[0136] Thus, according to an embodiment of the method 100, according to the invention in step D, the angle p is first determined then the angle a using formula (5).

[0137] It can be seen from this formula (5) that the relationship between oc and p can be adjusted according to the values ​​of the distances Dpo and Ddp chosen. This is an important advantage of the system / method according to the invention.

[0138] In a classical PSD system in oblique incidence, these two distances are classically equal and we therefore have a = p. See for example the publication “Review of phase measuring deflectometry” by Huang et al (Optics and Lasers Engineering, volume 107, August 2018, pages 247-257).

[0139] When we want to measure very small oc slopes, we try to increase the proportionality factor between a and p. A study of formula (5) shows that increasing this proportionality factor amounts to decreasing / minimizing the Dpo / Ddp coefficient. At constant focal length, this amounts to moving the camera closer (reducing Dpo) and moving the screen further away (increasing Ddp).

[0140] A measurement of very low oc slopes is also obtained by increasing the focal length of the imaging optics.

[0141] The paper "Phase measuring deflectometry for obtaining 3D shape of specular surface: a review of the state of the art" by Zhang et al (Optical Engineering, vol 60(2), 020903-1; 2021) describes a classic PSD method with these two different distances Dpo and Ddp. But it is then necessary to perform a very complex calibration in the camera space to ultimately obtain the correct values ​​(see §4 Error source analysis).

Claims

CLAIMS 1. Method for analyzing a reflective surface (S) by deflectometry, with a system comprising a display (Disp) arranged so that light images displayed on the display are reflected on said reflective surface (S) and an imaging optic (IO) configured to image said surface on a matrix detector (Det), the method comprising the steps of: To be displayed successively on the display (Disp) n light images l / i indexed i with n>2, the n light images being obtained by n spatial shifts xi along a direction X of the same pattern M(x), a light image l / i having a binarized light intensity obtained by screening the pattern M(x-xi), B detect on the matrix detector (Det) n images ldi called detected images, obtained by reflection of the n light images l / i on the reflecting surface (S), C determine a function called the object absolute phase function (faps) from the n detected images ldi, by applying a mathematical function g to said n detected images, the function g and the number of images n being determined so that the absolute phase function is bijective, the function g further verifying the relation: g(kM) = g(M) with k any real, D compare the object absolute phase function (faps) to an absolute phase function (fapMret) called reference, determined by replacing the surface (S) to be characterized by a plane mirror (Mref) defining a plane (Pref) called reference, and deduce information on the shape of said surface.

2. Method according to the preceding claim in which the pattern is a sinusoid, n=4, the four spatial shifts correspond to phase shifts respectively equal to 0, % / 2, %, 3% / 2.

3. Method according to the preceding claim in which the function g is defined by: g= arctg[(fc4-fc2) / (fc1 -fc3)] with fci corresponding to n=4 variables, fci corresponding to the images detected with said reflecting surface for the calculation of the object absolute phase function, and to the images detected with said reference mirror for the calculation of the reference absolute phase function.

4. Method according to one of claims 2 or 3 in which each light image displays only one period of the sinusoidal pattern.

5. Method according to claim 1 in which the pattern is a Gaussian, n=2, a first spatial shift corresponding to a Gaussian centered on an edge of the 1 / 1 light image and a second spatial shift corresponding to a Gaussian centered on another edge of the I / 2 image, and in which the function g is defined by: g=Ln(fc1) - Ln(fc2) with fci corresponding to n=2 variables, fci corresponding to the images detected with said reflecting surface for the calculation of the object absolute phase function, and to the images detected with said reference mirror for the calculation of the reference absolute phase function.

6. Method according to one of the preceding claims in which the pattern is invariant by Fourier transform.

7. Method according to one of the preceding claims in which the screening is carried out by the Floyd-Steinberg algorithm.

8. Method according to one of the preceding claims in which the imaging optics has an optical axis coincident with a normal to the reference plane, in which said light images illuminate said surface perpendicular to said reference plane, in which the following are defined: an optical center O of the imaging optics, a positive distance Ddp between the display and the reference plane Pref and a positive distance Dpo between the reference plane and the optical center O, and in which step D comprises the sub-steps consisting of: determine for points of the surface S, an angle p determined from the shift between the absolute phase function object and the absolute phase function referenced to said point of the surface, determine said slope a with the following formula: a = 0.

5.

9. System (10) for analyzing a reflective surface (S) by deflectometry comprising: a display (Disp) arranged so that light images displayed on the display are reflected on said reflective surface (S), and configured to successively display n light images l / i indexed i with n>2, the n light images being obtained by n spatial shifts xi along a direction X of the same pattern M(x), a light image l / i(x,y) having a binarized light intensity obtained by rasterizing the pattern M(x-xi), an imaging optic (IO) and a matrix detector (Det), the imaging optic being configured to image said surface (S) on said matrix detector, the matrix detector being configured to detect n images ldi called detected images, obtained by reflection of the n light images l / i on the reflective surface (S), a processing unit (PU) configured to: • determine a function called the object absolute phase function (faps), from the n detected images ldi, by applying a mathematical function g to said n detected images, the function g and the number of images n being determined so that the absolute phase function is bijective, the function g further verifying the relation: g(kM) = g(M) with k any real number, • compare the object absolute phase function (faps) to an absolute phase function (fapMret) called reference, determined by replacing the surface (S) to be characterized by a plane mirror (Mref) defining a plane (Pref) called reference, and deduce information on the shape of said surface.

10. System according to the preceding claim in which the imaging optics has an optical axis (OA) arranged perpendicular to said reference plane, and in which the optical system further comprises a splitter blade (BS) configured to send said light images onto said surface perpendicular to said reference plane.

11. Computer program comprising instructions which cause the system of claim 9 to execute the steps of the method according to one of claims 1 to 8.

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