SYSTEM AND METHOD FOR ANALYZING SURFACE QUALITY OF SUBSTRATES HAVING PARALLEL SURFACES - Patent application

Abstract

The present specification relates to a method for analyzing the surface quality of a substrate (100), comprising emitting a first light beam (221) incident on a first side (A) of the substrate, receiving the first reflected beam and a second reflected beam by a wavefront analysis means (240) to generate at least a first measurement signal indicative of a combined wavefront of a first reflected beam (222a) resulting from reflection of the first beam by the first side and a second reflected beam (222b) resulting from reflection by a second side (B) of the substrate, receiving a transmitted beam resulting from transmission of the substrate by the second light beam by the wavefront analysis means to generate a second measurement signal, and calculating from the first and second measurement signals a first signal and a second signal indicative of a deformation of the first side and the second side, respectively.

Description

[Technical field]

[0001] The present specification relates to systems and methods for analyzing the surface quality of substrates having parallel surfaces, and more particularly to analyzing deformations of the surfaces of such substrates. [Background technology]

[0002] The surface topography of parallel-sided materials, referred to herein simply as "substrates," is relevant in many fields and these materials may include, for example, glass substrates for computer hard disks, silicon photomasks and wafers for the semiconductor industry, flat screens and glass displays for mobile devices, windows, the optics of x-ray telescopes, optical filters, beam splitters, and protective domes.

[0003] Any deformations in the surfaces of such substrates can cause distortions in the systems that use those substrates, and so it is important to be able to study and quantify those deformations.

[0004] Non-contact optical methods are known for analyzing the surface quality of a substrate. One of the difficulties encountered by most methods in analyzing the surface quality of a substrate surface is the effect of reflection by the other surface (rear surface), especially in the case of substrates that are transparent in the spectral band of the light source used for the measurements.

[0005] Various metrology methods for analyzing the surface quality of thin transparent materials that can overcome the effects of reflections at the back surface are described, for example in the review article [Reference 1].

[0006] In particular, it is known to suppress reflection from the rear surface by applying a coating having an appropriate refractive index to the rear surface or a highly reflective coating to the front surface, but these methods require coating application and cleaning operations that may themselves cause surface deformation.

[0007] [Reference 1] also describes phase-shifting interferometry, where a white light source or a low-coherence light source is used to avoid parasitic interference due to reflections on both sides of the substrate. These methods, for example using a Michelson interferometer, are difficult to implement and are limited to substrates whose deformation is much smaller than their thickness.

[0008] Phase-shifting interferometry using a frequency-tunable laser source may also be considered, as described in [Reference 1]. For example, interferometric measurements on three surfaces (reference surface, front surface of the substrate, and rear surface) may be performed sequentially at two different wavelengths, followed by new interferometric measurements again at the two wavelengths, but with the substrate flipped over so that the rear surface faces the reference surface. The interference contributions of the planar and parallel surfaces of the material, and especially the interference contributions between the front surface and the reference surface, may then be mathematically separated. However, this method requires manipulation of the sample, which must be flipped to perform the two sets of measurements, which may be inconvenient for fragile and easily deformable materials. More generally, there are known methods using frequency-varying sources, where the profiles of the different surfaces can be extracted by Fourier analysis of the spectrum of the interference signal. Both of these methods require multiple data acquisitions and are therefore highly sensitive to environmental influences, especially vibrations.

[0009] [Reference 1] also describes methods for spatial separation of the reflections from the front and back surfaces, making it possible to block the reflection from the back surface by a shutter. These methods include, for example, interferometry with oblique or spherical illumination (also known as "grazing incidence interferometry"). However, these methods are very sensitive to the alignment of the components.

[0010] In addition to interference-based methods, [Reference 1] presents a method for analyzing the optical quality of surfaces of thin transparent materials using a Shack-Hartmann wavefront analyzer.

[0011] As shown in FIG. 1 taken from [Reference 1], the Shack-Hartmann wavefront analyzer includes an array of microlenses 20 and an array of elementary detectors 30. When a reference wavefront, for example a flat reference wavefront, is incident on the microlens array 20, each microlens (20i, 20j, ...) captures and focuses a portion of the wavefront without deflection, and the centroids of each focus are regularly located on the array of elementary detectors 30. In contrast, as shown in FIG. 1, when a wavefront 10 is incident deformed with respect to the flat reference wavefront, the microlenses (20i, 20j, ...) capture each portion of the wavefront (10i, 10j, ...) that has a locally non-zero slope. As a result, the centroids of each focus on the array of elementary detectors 30 are displaced. On the basis of the measurement signals thus determined, it is possible to determine a matrix of local tilts of the wavefront according to a two-dimensional matrix of displacements and to derive therefrom a matrix of values ​​of the wavefront measured at each microlens relative to a reference wavefront, for example by numerical integration of the values ​​of the local tilts. Since the local deformation of the analyzed surface is directly proportional to the local deformation of the wavefront, the deformation can thus be determined on the basis of the Shack-Hartmann measurement signals.

[0012] Compared to the above-mentioned interferometric techniques, measurement methods using a Shack-Hartmann wavefront analyzer, or more generally devices implementing a wavefront analyzer that directly analyzes the wavefront, make it possible to use light sources that are in particular temporally incoherent or have low temporal coherence, which are usually cheaper than lasers, and to operate in less controlled environments; in addition, these solutions are less costly.

[0013] However, as explained in [Reference 1], reflections from the back surface can interfere with the measurement of the surface quality of the front surface, especially when working with a light source that contains wavelengths for which the material is at least partially transparent. It has therefore been suggested that a spectral filter should be installed to filter out all wavelengths in the transparent regions of the material, or that a light source should be used that has wavelengths that are not transmitted by the material of the substrate being analysed.

[0014] Published patent application [Reference 2] describes the use of two wavefront analyzers, in this case lateral shift interferometers (or "shearing interferometers"), for simultaneous reflection and transmission measurements of a substrate to be measured for surface defects. Similar to the Shack-Hartmann wavefront analyzer, such a lateral shift interferometer may be used to measure the wavefront directly. The lateral shift interferometer does not use interference with a reference beam and is sensitive to the first derivative of the wavefront. The reflection measurement provides information about the topology of the surface, while the transmission measurement provides information about the thickness variations of the substrate. These two measurements can be combined to obtain information about the topology of both sides of the substrate. Although this method works well, its implementation is complicated, since the reflection measurement of one side of the substrate must not be interfered with by the reflection from the second side. To this end, it is proposed that wavelengths at which the substrate material is opaque, i.e. absorbing, should be used for this reflection measurement. This requires choosing wavelengths, for example in the UV or far infrared range, which requires special sensors and optics, thus imposing constraints on the choice of materials and costs.

[0015] One objective of the present specification is to propose a system and method for analyzing the surface quality of two surfaces of a substrate having parallel surfaces using a wavefront analyzer that allows the use of one or more light sources with low temporal coherence, without being restricted by the device and method described in [Reference 2]. Summary of the Invention [Means for solving the problem]

[0016] In this specification, "comprise" has the same meaning as "include" or "contain" and is inclusive or open and does not exclude other elements not stated or expressed.

[0017] Furthermore, as used herein, "about" or "substantially" are synonymous with (have the same meaning as) a margin of 10% above or below the respective value, such as a margin of 5%.

[0018] According to a first aspect, the present specification provides a method for analyzing a surface quality of a substrate having parallel surfaces, comprising emitting at least one first light beam with low temporal coherence by at least one first light source of an emitting means, said at least one first light beam being incident on said substrate, said substrate being at least partially transparent for at least one wavelength of said first incident light beam, and generating at least one first measurement signal characteristic of a combination of wavefronts of at least one first reflected beam resulting from reflection of said at least one first light beam by a first surface of said substrate and a second reflected beam resulting from a first transmission of said first light beam through said substrate and a second transmission through said substrate following a subsequent reflection by a second surface of said substrate. receiving the at least one first reflected beam and the second reflected beam by at least one first wavefront analyzer of a wavefront analysis means to generate a wavefront characteristic of at least one first transmitted beam resulting from at least one first transmission of a second light beam emitted by the emitting means into the substrate; and calculating from the at least one first measurement signal and the second measurement signal at least one first signal indicative of a deformation of the first surface of the substrate relative to a first reference surface and at least one second signal indicative of a deformation of the second surface of the substrate relative to a second reference surface.

[0019] In this specification, a "substrate having parallel surfaces" is understood to mean an optical element having a first surface and a second surface, the distance between the two surfaces measured along an axis perpendicular to the surfaces being substantially constant throughout the optical element, i.e., having a thickness variation of less than ±10%. A substrate having parallel surfaces may be flat, in which case the angle between the surfaces is less than about 5 minutes of arc. Other shapes of substrates having parallel surfaces may be considered in this specification, such as curved substrates, such as protective domes.

[0020] In the present specification, a light beam with low temporal coherence is a light beam with a sufficiently low temporal coherence to eliminate any interference effects between the reflected beams at each side of the substrate, which may cause problems in the measurement. For this purpose, it is advantageous in practice to make the length of temporal coherence of the first light beam less than about twice the optical thickness of the substrate with parallel faces to be analyzed, the optical thickness of the substrate being the thickness of the substrate multiplied by the average refractive index of the material of which the substrate is made. The temporal coherence of the first light beam is about 100 μm or less, or advantageously about 10 μm or less. Thus, for example, a first light beam with a temporal coherence of about 10 μm or less can analyze the surface of a very thin substrate, i.e. a substrate with a thickness of a few tens of microns. It should be noted that the length of temporal coherence of the first light beam sets a minimum thickness for the substrate to be analyzed, without imposing any further limitations. For example, a substrate with a thickness of a few tens of centimeters can also be analyzed by the same light source with a temporal coherence of about 10 μm or less.

[0021] According to one or more example embodiments, the at least one first light beam and the second light beam are spatially coherent.

[0022] For example, when a Shack-Hartmann wavefront analyzer is used, the first and second light beams have sufficient spatial coherence such that the resulting reflected or transmitted beam is incident on a microlens array to produce a focal spot having a size smaller than the size of the microlens that produces the focal spot.

[0023] It is known that in principle, when the spatial coherence of the light source generating the light beam decreases, i.e. when the angular size of the light source increases, the accuracy of the wavefront analyzer also decreases.The spatial coherence of the light beam must therefore be sufficient to allow the analyzer to measure with an accuracy that meets the requirements of the application.For example, as explained above for the Shack-Hartmann sensor, it is known that when the angular size of the light beam source extending into the space of the analyzer is less than the diffraction angle of the microlens, the accuracy of the measurement is not significantly affected.

[0024] According to one or more examples of embodiments, the at least one first light source for emitting the at least one first light beam with low temporal coherence is a light source selected from among an incandescent lamp, a light emitting diode (LED), a super-luminescent diode (SLED) that may be fiberized into a monomode fiber, and a laser diode used below its laser effect generation threshold that may be fiberized into a monomode fiber.

[0025] In this specification, a substrate is said to be at least partially transparent to at least one wavelength of a beam passing through it if the transmittance of said beam at said wavelength is at least equal to 10%, or advantageously at least equal to 30%.

[0026] In contrast to methods described in the prior art, such as for example the method described in [Reference 2], in this specification, by ensuring that a first light beam incident on the substrate to be analyzed is at least partially transmitted by the substrate, the combination of wavefronts of the beam reflected by the first and second surfaces of the substrate can be analyzed by the at least one first wavefront analyzer of the wavefront analysis means.

[0027] In this specification, the term "wavefront" of a light beam applies to a surface that has the same phase as the electromagnetic waves forming said beam. Thus, when a flat surface, for example of a defect-free substrate, is illuminated by a flat reference wave, the wavefront of the reflected beam is also flat. When the surface has a local deformation relative to the flat reference surface, the wavefront of the reflected beam is deformed relative to the flat reference wavefront. Thus, in this specification, wavefront analysis is the measurement of the deformation of said wavefront relative to a reference wavefront, which is for example, but not necessarily, a flat wavefront. For example, in the analysis of a curved substrate, the reference wavefront can be a spherical wavefront.

[0028] Thus, in this specification, the first measurement signal, the second measurement signal and the signal characteristic of the deformation of the first and second surfaces of the substrate are matrix signals, i.e. signals made up of a two-dimensional matrix of values.

[0029] A "wavefront analyzer" in this specification refers to a device for directly measuring the wavefront of a beam to be analyzed, as opposed to interferometric techniques that utilize the interference of the beam to be analyzed with a reference beam. Such devices generally allow the determination of the local slope of the wavefront (i.e. the first derivative of the wavefront), which is usually based on analyzing the angular variations of the movement of a light beam with a wavefront sensor that includes a set of one or more optical elements and a detector that is usually two-dimensional.

[0030] According to one or more example embodiments, the at least one first wavefront analyzer of the wavefront analysis means is selected from among a Hartmann and Shack-Hartmann wavefront analyzer as described, for example, in [Reference 3], a lateral shift interferometer as described, for example, in [Reference 4], a Moiré deflectometer as described, for example, in [Reference 5], and a Schlieren-based device as described, for example, in [Reference 6].

[0031] According to one or more exemplary embodiments, the at least one first light beam is incident on the substrate such that it is substantially perpendicular to the substrate. Although it is also possible to envisage an arrangement in which the first light beam is incident on the substrate at an incline with respect to the normal, a substantially perpendicular incidence is preferred, as it simplifies the optical assembly and makes it possible to avoid introducing any lateral shift between the first and second reflected beams, especially in the case of thick substrates.

[0032] According to one or more example embodiments, the second light beam is incident on the first surface of the substrate, and the method further includes positioning a reference mirror arranged substantially perpendicular to the second light beam for generating the second measurement signal, and the first transmitted beam is produced by a first transmission of the second light beam into the substrate, reflection by the reference mirror, and a second transmission of the beam reflected by the reference mirror into the substrate, and the first reflected beam is received by the first wavefront analyzer of the wavefront analysis means.

[0033] The method thus described may be implemented with a single wavefront analyzer and a single light emitting source, and the first light beam and the second light beam may be emitted from the same light source.

[0034] The reference mirror may be flat, for purposes of analysing flat substrates having parallel or curved surfaces, or may be, for example, spherical, for purposes of analysing substrates having non-zero curvature.

[0035] According to some example embodiments, the reference mirror may be arranged to be removable. In other example embodiments, the reference mirror may be maskable, for example by means of a shutter, or may be oriented by a motorized or non-motorized rotation system, such that the beam reflected by the mirror is not received by the wavefront analysis means. In both cases, this allows to obtain a first measurement signal characteristic of the combined wavefronts of the first and second reflecting mirrors when the mirror is not present or is masked or rotated, and a second measurement signal characteristic of the wavefront of the transmitted beam when the reference mirror is present and not masked or rotated.

[0036] According to one or more example embodiments, the second light beam is incident on the first surface of the substrate, the first transmitted beam is produced by a first transmission of the second light beam through the substrate, and the first transmitted beam is received by a second wavefront analyzer of the wavefront analysis means separate from the first wavefront analyzer.

[0037] The method thus described is implemented by wavefront analysis means comprising two separate wavefront analyzers which may be the same or different. Since the first and second light beams may be emitted simultaneously from the same light source, a first measurement signal characteristic of the combined wavefronts of the first and second reflected beams and a second measurement signal characteristic of the wavefront of the transmitted beam may be obtained simultaneously without manipulation of a reference mirror.

[0038] According to one or more examples of embodiments, the second light beam is emitted by a second light source of the emitting means separate from the first light source and is incident on the second surface of the substrate, and the first transmitted beam is produced by a first transmission of the second light beam into the substrate, and the first transmitted beam is received by the first wavefront analyzer of the measurement and analysis means.

[0039] The method thus described is carried out by an emission means that includes two separate emission sources, which may be the same or , different. This method allows a first measurement signal indicative of a combined wavefront characteristic of the first and second reflected beams and a second measurement signal indicative of a wavefront characteristic of the transmitted beam to be obtained without manipulating a reference mirror.

[0040] Thus, according to one or more example embodiments, in the case of different types of emission sources, the first light beam emitted by the first light source and the second light beam emitted by the second light source have at least one of different wavelengths and polarizations. The method further includes receiving the second transmitted beam by a second wavefront analyzer of the wavefront analysis means, separate from the first wavefront analyzer, to generate a third measurement signal indicative of a wavefront characteristic of the second transmitted beam resulting from a first transmission of the first incident light beam through the substrate; and comparing the second measurement signal indicative of a wavefront characteristic of the first transmitted beam with the third measurement signal indicative of a wavefront characteristic of the second transmitted beam to generate a signal indicative of a characteristic of the refractive index variation in the substrate.

[0041] According to a second aspect, the present description relates to a system for analyzing a surface quality of a substrate having parallel surfaces, for the implementation of an analysis method according to the first aspect.

[0042] Thus, the system according to the second aspect comprises at least one first support configured to receive the substrate to be analyzed, at least one first light source for emitting at least one first light beam with low temporal coherence having at least one wavelength for which the substrate is at least partially transparent, emitting means configured in operation for said at least one first light beam to be incident on the substrate, and wavefront analyzing means comprising at least one first wavefront analyzer, wherein in operation the system analyzes the wavefronts of at least one first reflected beam resulting from reflection of said at least one first light beam by a first surface of the substrate, and a second reflected beam resulting from a first transmission of said first light beam through the substrate and a second transmission through the substrate following a subsequent reflection by a second surface of the substrate. the wavefront analysis means configured to receive the at least one first reflected beam and the second reflected beam at an analysis surface of the first wavefront analyzer to generate a first measurement signal indicative of a combination of the at least one first transmitted beam by the wavefront analysis means to generate a second measurement signal indicative of a wavefront characteristic of at least one first transmitted beam resulting from at least one first transmission of the second light beam emitted by the emitting means into the substrate; and a processing unit configured to calculate from the first measurement signal and the second measurement signal at least one first signal indicative of a deformation of the first surface of the substrate relative to a first reference surface and at least one second signal indicative of a deformation of the second surface of the substrate relative to a second reference surface.

[0043] According to one or more example embodiments, the emitting means is configured such that, during operation, the at least one first beam is incident on the substrate substantially perpendicular to the substrate.

[0044] According to one or more example embodiments, the analysis surface of the first wavefront analyzer is optically conjugated with the substrate to be analyzed.

[0045] According to one or more example embodiments, the system further includes a second support configured to receive a reference mirror that is positioned substantially perpendicular to the second light beam during operation, and during operation: the first transmitted beam results from a first transmission of the second incident beam through the substrate, reflection by the reference mirror, and a second transmission of the beam reflected by the reference mirror through the substrate; The first and second reflected beams and the first transmitted beam are received by the first wavefront analyzer of the wavefront analyzing means.

[0046] According to one or more example embodiments, the wavefront analysis means includes a second wavefront analyzer separate from the first wavefront analyzer, the emission means is configured such that during operation the second light beam is incident on the first surface of the substrate, the first transmitted beam is provided by a first transmission of the second light beam into the substrate, and the wavefront analysis means is configured such that during operation the first transmitted beam is received by the second wavefront analyzer of the wavefront analysis means.

[0047] According to one or more example embodiments, the at least one first wavefront analyzer of the wavefront analysis means is selected from among a Hartmann and Shack-Hartmann wavefront analyzer as described, for example, in [Reference 3], a lateral shift interferometer as described, for example, in [Reference 4], a Moiré deflectometer as described, for example, in [Reference 5], and a Schlieren-based device as described, for example, in [Reference 6].

[0048] Other advantages and features of the invention will become apparent in the light of the following description illustrated by the drawings. [Brief description of the drawings]

[0049] [Figure 1] FIG. 1 above illustrates the principle of a prior art Shack-Hartmann analyzer. [Figure 2A]FIG. 2 illustrates a first step of an example method for analyzing the surface quality of a substrate according to the present specification using a first example system for analyzing the surface quality of a substrate according to the present specification. [Figure 2B] 2B shows a second step of an example of a method for analyzing the surface quality of a substrate according to the present specification using the system for analyzing the surface quality of a substrate shown in FIG. 2A. [Figure 3A] FIG. 3A illustrates the measurement of a signal characteristic of the combined wavefronts of the first and second reflected beams by a Shack-Hartmann analyzer in a step of a method for analyzing the surface quality of a substrate according to the present disclosure. [Figure 3B] FIG. 3B shows in more detail the measurement shown in FIG. 3A. [Figure 4A] FIG. 4A is a diagram illustrating an example of the deformation that a flat wavefront reflected from a first surface of a substrate undergoes when the first surface has a surface defect relative to a flat reference surface. [Figure 4B] FIG. 4B shows an example of the distortion experienced by a flat wavefront that is first transmitted through the substrate shown in FIG. 4A, then reflected from the second surface of the substrate, and then transmitted through the substrate a second time when the second surface has a surface defect. [Figure 4C] FIG. 4C illustrates an example of the deformations undergone by a planar wavefront that is transmitted through the substrate shown in FIG. 4B, then reflected from a reference mirror and transmitted through the substrate again. [Figure 5A] FIG. 13 illustrates a first step of an example method for analyzing the surface quality of a substrate according to the present specification using a second example system for analyzing the surface quality of a substrate according to the present specification adapted to analyze substrates with non-zero curvature. [Figure 5B] 5B illustrates a second step of an example of a method for analyzing the surface quality of a substrate according to the present specification using the system for analyzing the surface quality of a substrate illustrated in FIG. 5A. [Figure 6] 5A-5C are diagrams illustrating steps of an example method for analyzing the surface quality of a substrate according to the present specification, using a third example system for analyzing the surface quality of a substrate according to the present specification. [Figure 7] FIG. 11 illustrates steps of an example method for analyzing the surface quality of a substrate according to the present specification using a fourth example system for analyzing the surface quality of a substrate according to the present specification. [Figure 8] A diagram showing steps of an example method for analyzing the surface quality of a substrate according to the present specification using a fifth example system for analyzing the surface quality of a substrate according to the present specification. [Figure 9] FIG. 2C shows experimental images representing a matrix of deformations of the surface of a substrate obtained by the system shown in FIGS. 2A and 2B. [Figure 10A] A figure showing a first step of an example method for analyzing the surface quality of a substrate according to the present specification using a sixth example of a system for analyzing the surface quality of a substrate according to the present specification, adapted for incidence of a first light beam on the substrate having an inclined angle. [Figure 10B] 10B shows a second step of an example of a method for analyzing the surface quality of a substrate according to the present specification using the system for analyzing the surface quality of a substrate shown in FIG. 10A. [Figure 10C] FIG. 10B illustrates limitations to the implementation of a method for analyzing the surface quality of a substrate using the system for analyzing the surface quality of a substrate illustrated in FIG. 10A. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0050] For clarity, components in the drawings are not drawn to scale.

[0051] 2A and 2B show two steps for the implementation of an example of a method for analyzing the surface quality of a substrate 100 having substantially parallel surfaces, using a first example of a system for analyzing the surface quality of a substrate. The aim in this example is to analyze the quality of two surfaces of a flat substrate having substantially parallel surfaces.

[0052] The system for analyzing the surface quality of a substrate, shown in Figures 2A and 2B and referenced as 200, comprises at least one first support (not shown in the drawings) configured to receive the substrate 100 to be analyzed, and a second support (not shown in the drawings) configured to receive a mirror 250 (Figure 2B). The mirror may for example be removably arranged or maskable, for example by means of a shutter, or may be adjustable in direction, for example by means of a motorized or non-motorized rotation system, such that an incident light beam that is subsequently reflected from the mirror is not received by the wavefront analysis means.

[0053] The system 200 further comprises a light emitting means including a source 210 for light having at least one wavelength and low temporal coherence for which the substrate 100 is at least partially transparent.

[0054] In general, the light emitting source 210 may include an incandescent lamp, a light emitting diode (LED), a superluminescent light emitting diode (SLED), or a laser diode used below its threshold to create a laser effect.

[0055] The choice of light source may be adapted to the substrate to be analyzed, for example, when a spectral filter is to be analyzed, the light emitting source 210 may comprise a superluminescent diode (SLED) having a wavelength selected from the transmission spectral band of the interference filter.

[0056] The system 200 further includes a means for analyzing the wavefront, which in the example of FIGS. 2A and 2B includes a wavefront analyzer 240 (such as, but not limited to, a Shack-Hartmann analyzer).

[0057] The system 200 further includes a processing unit 260 configured to process the measurement signals transmitted by the wavefront analyzer 240, and may include a display unit (not shown).

[0058] In general, the processing unit referred to in this specification may include one or more physical entities or may be a combination of one or more computer elements. In this specification, when a calculation or processing step for performing a method step is specifically mentioned, it should be understood that each calculation or processing step may be performed by software, hardware, firmware, microcode, or any suitable combination of these technologies. When software is used, each calculation or processing step may be performed by computer program instructions or program code instructions. These instructions may be stored or transmitted in a storage medium readable by the processing unit, and may be executed by the processing unit to perform these calculations or processing steps, or both.

[0059] In this example, the light source 210 emits a first light beam 221. In this example, the emitting means is configured for incidence on the substrate such that during operation the light beam 221 is substantially perpendicular to the substrate (normal incidence). Although normal incidence is preferred, the analysis system may be adapted such that the first light beam is incident at an angle to the normal. Examples of this kind are shown in Figures 10A, 10B and 10C.

[0060] 2A and 2B, the objective is to analyze a substantially flat substrate with parallel faces, and the emitting means are configured such that during operation the light beam is incident on the substrate with a substantially flat wavefront. For example, the emitting means comprises, in addition to the light source 210, a set of optical lenses 211, 212, 215, which enable the light beam leaving the optical element 215 to be substantially parallel and to enable the size of said beam to be adapted to the size of the substrate to be analyzed, and deflection elements 213, 214. Advantageously, the set of optical lenses furthermore enables an optical conjugation to be substantially provided between the substrate to be analyzed and the analysis plane of the wavefront analyzer, for example the plane of the array of microlenses in the case of a Shack-Hartmann analyzer.

[0061] As shown in FIG. 2A, in a first step of the method implemented in this example, a first light beam 221 is reflected, on the one hand, from a first surface A of the substrate 100 to form a first reflected beam 222a, and, on the other hand, passes through the substrate and is reflected from a second surface B of the substrate 100, and then passes through the substrate again to form a second reflected beam 222b.

[0062] As described in more detail below, the wavefront analysis means is configured to receive the first and second reflected beams onto an analysis surface of the wavefront analyzer 240 to generate a first measurement signal indicative of a combined wavefront characteristic of the first reflected beam 222a and the second reflected beam 222b.

[0063] 2A and 2B, the wavefront analyzing means comprises a set of optical lenses 211, 212, 215 common to those of the emitting means and deflecting elements 213, 214 to direct the reflected beam towards the wavefront analyzer 240. The system 200 further comprises an optical beam splitting element 230 configured to separate the emitting means and the analyzing means. The optical element 230 comprises for example a beam splitting plate or a beam splitting cube or the like.

[0064] In this example, the set of optical lenses 211 , 212 , 215 and the deflection elements 213 , 214 make it possible to substantially adapt the size of the reflected beams 221 a and 221 b and the transmitted beam 223 to the size of the analysis surface of the wavefront analyzer 240 .

[0065] As shown in FIG. 2B, in the second step of the method implemented in this example, a reference mirror 250 is installed.

[0066] Mirror 250 is positioned in such a way that the second light beam incident on the substrate is incident on mirror 250 such that after transmitting through the substrate it is substantially perpendicular to mirror 250. In this example, the second light beam is also referred to as 221 because it is emitted from the same light source 210 as the first light beam, and the first and second beams have the same properties (coherence and wavelength), although the first and second beams are not emitted simultaneously.

[0067] The second incident beam is then first transmitted through the substrate 100, reflected by the reference mirror 250 and transmitted again through the substrate 100. The resulting transmitted beam 223 is sent to the wavefront analyzer 240 of the wavefront analysis means for generating a second measurement signal indicative of a wavefront characteristic of said transmitted beam.

[0068] As described below with reference to Figures 3A, 3B, 4A, 4B, and 4C, processing unit 260 can then calculate, based on the first measurement signal and the second measurement signal, at least one first signal indicating deformation of the first side A of the substrate relative to the first reference surface and at least one second signal indicating deformation of the second side B of the substrate relative to the second reference surface.

[0069] It should be noted that the optical elements of the system 200 may have manufacturing defects, which may be taken into account in the calibration step in order to avoid interfering with the quality of the measurements taken. A practical way of performing the calibration is to measure these defects by performing wavefront measurements in the configuration of Figure 2B, with the analyzed substrate 100 removed. The defects thus measured are subtracted from measurements made in the presence of the analyzed substrate 100 (described in more detail below).

[0070] In practice, the optical quality of the reference mirror 250 may be selected based on the desired accuracy of the deformation measurements on sides A and B of the analyzed substrate 100, since the accuracy of these measurements cannot be higher than the optical quality of the reference mirror 250.

[0071] The principle of the calculation is described below and illustrated in Figures 3A, 3B, 4A, 4B, and 4C.

[0072] The principle is described considering the example of a Shack-Hartmann wavefront analyzer, but is applicable to any type of wavefront analyzer, i.e. any type of measurement system that is able to measure the wavefront directly without interfering the measurement beam with a reference beam. A common feature of these analyzers is that they are sensitive to the derivative of the wavefront.

[0073] Thus, FIG. 3A shows a Shack-Hartmann analyzer identical to that shown in FIG. 1, in particular having an array 20 of microlenses and an array 30 of elementary detectors.

[0074] The principle is illustrated considering the example of a substrate to be analyzed having flat and substantially parallel faces. The objective is thus to find the deformation of faces A and B of the substrate relative to a flat reference plane. However, as will be explained in more detail below, the principle of calculation can also be applied to substrates of other shapes having parallel faces.

[0075] In a first step of the example method described with reference to Figures 2A and 2B, two reflected beams 222a and 222b are generated, resulting from reflections from faces A and B of the substrate, respectively. Thus, as shown in Figure 3A, the wavefront analyzer simultaneously receives wavefronts 310a and 310b of the reflected beams 222a and 222b, respectively. Each wavefront 310a, 310b may be deformed with respect to a reference wavefront, e.g., a flat wavefront.

[0076] As shown in FIG. 3A, each microlens (20i, 20j, ...) in the microlens array captures and focuses a wavefront portion (310a,i, 310a,j, ...) of wavefront 310a and captures and focuses a wavefront portion (310b,i, 310b,j, ...) of wavefront 310b.

[0077] As shown in Figure 3B, this results in, on the one hand, a shift in the center of gravity of the focal points (330a,i, 330a,j, ...) due to focusing of the wavefront portions (310a,i, 310a,j, ...) of the wavefront 310a by the microlenses (20i, 20j, ...), and, on the other hand, a shift in the center of gravity of the focal points (330b,i, 330b,j, ...) due to focusing of the wavefront portions (310b,i, 310b,j, ...) of the wavefront 310b by the microlenses (20i, 20j, ...).

[0078] In practice, the array of elementary detectors 30 detects a distribution of light energy (330i, 330j, ...), which is the sum of the energies of the focal points (330a,i, 330b,i, ...) and (330a,j, 330b,j, ...) for each microlens. To obtain the sum of the energies of the two focal points 330a,i and 330b,i, it is necessary to ensure that they do not interfere and are generated from two beams that are incoherent with each other. In the case of two beams resulting from reflections on two faces of a substrate with substantially parallel faces, this is made possible by an illumination source with a coherence length less than twice the optical thickness of the substrate.

[0079] In practice, the focal points (330a,i, 330b,i,...) and (330a,j, 330b,j,...) may be overlapped, partially overlapped, or discontinuous. In all cases, the shift of the resulting optical energy distribution (330i, 330j,...) relative to a nominal theoretical position (e.g., the position of the focal point resulting from a flat wavefront) indicates a local tilt of the weighted average wavefront of reflected beams 222a and 222b.

[0080] When multiple reflections on the substrate are ignored, the weighting coefficients for establishing said weighted average can be determined to be the reflection coefficient R1 of surface A for beam 222a and the reflection coefficient R2 of surface B for beam 222b multiplied by the square of the transmission coefficient T of the material forming the substrate and multiplied by the square of (1-R1), which is on the one hand the proportion of the illumination beam transmitted into the substrate at the interface between air and surface A and on the other hand the proportion of the beam reflected from surface B and transmitted into air at the interface between surface A and air.

[0081] Based on the measurement signals thus determined corresponding to the two-dimensional array of movements, it is possible to determine a matrix of local wavefront slopes corresponding to a weighted average of the reflected wavefronts 222a and 222b, and from there deduce a matrix of corresponding wavefront values ​​measured at each microlens.

[0082] 4A, 4B and 4C, a more detailed description is now given of how the deformation matrices α and β of surfaces A and B relative to a flat reference surface may be determined in a non-limiting example provided for illustrative purposes.

[0083] 4A and 4B correspond to the first step of the method described with reference to FIG. 2A.

[0084] FIG. 4A shows the local deformation α of surface A relative to a reference surface 401, which in this example is a flat surface.

[0085] Reflection of incident beam 221 by surface A results in a reflected beam 222a which is subject to a local variation δ of the optical path. [Number 1] δ=2α

[0086] FIG. 4B shows both sides A and B of the substrate 100.

[0087] In addition to the local deformation of surface A, FIG. 4B also shows the local deformation β of surface B relative to a reference surface 402, which in this example is a flat surface.

[0088] A reflected beam 222b resulting from reflection from face B following transmission through the substrate by the first light beam 221 experiences a local variation δ in the optical path before being transmitted through the substrate again. [Number 2] δ=2[α-nα+nβ]

[0089] where n is the refractive index of the substrate material, which is considered to be substantially constant in this example.

[0090] The reflected beams 222a and 222b, which have locally deformed wavefronts as described above due to the local deformation of surfaces A and B relative to the reference surface, are simultaneously received by a wavefront analyzer as shown in Figures 3A and 3B.

[0091] This results in a first measurement signal M1 in the form of a matrix characteristic of the weighted average of the wavefronts of the first reflected beam 222a and the second reflected beam 222b. The weighting coefficients are R1 and R2*T 2 *(1-R1) 2 It is. [Number 3] TIFF2025506571000002.tif13110

[0092] where R1 and R2 are the reflection coefficients of faces A and B, respectively, assumed to be constant, T is the transmission coefficient of the substrate material, assumed to be constant, and α and β are the deformation matrices of faces A and B.

[0093] FIG. 4C is described with reference to FIG. This corresponds to the second step of the method.

[0094] In this example, a transmitted beam 223 resulting from a first transmission of the second light beam through the substrate, reflection by a mirror 250 positioned substantially perpendicular to the light beam, and then a second transmission through the substrate is subject to a local variation δ of the optical path. [Number 4] δ=2(n-1)(β-α)

[0095] The transmitted beam 223 , which has a locally deformed wavefront as explained above due to the local deformations of surfaces A and B, is received by a wavefront analyzer 240 .

[0096] This results in a second measurement signal M2 in the form of a matrix representative of the wavefront characteristics of the transmitted beam. [Number 5] M2 = 2(n-1)(β-α) From the measurements M1 and M2, the deformation matrices α and β relative to their reference planes can be estimated. [Number 6] TIFF2025506571000003.tif1382 and [Number 7] TIFF2025506571000004.tif1238

[0097] Note that α and β are the deformations of surfaces A and B relative to a reference plane, and the profiles of surfaces A and B themselves can be found simply by applying the deformations α and β to the respective reference planes.

[0098] In the above calculations, it is assumed that the effect of multiple reflections in the substrate in the calculation of M1 is negligible. This is reasonable when the reflection coefficient of the substrate surface is about 10% or less, since the effect of multiple reflections on the measurement in this case is less than 1% of the signal received by the wavefront analyzer.

[0099] For reflection coefficients greater than 10%, multiple reflections can be taken into account in equation [mathematical formula 3] without any particular difficulty, resulting in a fairly complex equation, which will not be reproduced here.

[0100] Additionally, M2 is determined based on the assumption that the measurement is not disturbed by any signals resulting from reflections from each side of the substrate. This assumption is usually acceptable since the reflected signals are much weaker than the transmitted signals. However, the reflected signals can be eliminated in the measurement of M2 by tilting the substrate by a few degrees to eliminate reflections outside the measurement range. Alternatively, the reflected signals can be subtracted from the measurement signal generated from the transmitted beam. It is also possible without any difficulty to take into account the presence of reflections in the formula for the measured value M2 given by [Equation 5], again resulting in a more complicated formula for M2.

[0101] 5A and 5B show two steps for the implementation of an example of a method for analyzing the surface quality of a substrate 100 having parallel surfaces, using a second example of a system for analyzing the surface quality of a substrate. The aim in this example is to analyze the surface quality of a non-flat substrate, i.e. a substrate having at least locally a non-zero curvature.

[0102] Thus, in the example shown in Figures 5A and 5B, the objective is to analyze the surface quality of faces A and B of a parallel-sided substrate 100, where the faces of the substrate have a substantially constant finite radius of curvature. Such a substrate may be, for example, a protective dome. The radius of curvature of the faces of such a substrate is typically between a few centimeters and a few meters.

[0103] The system 500 for analyzing surface quality is substantially identical to that shown in Figures 2A and 2B, only the optical elements common to the emitting means and the wavefront analyzing means are adapted such that the first light beam 221 emitted by the light source 210 is incident on the substrate 100 substantially perpendicular to the surface of the substrate, which in this example is not flat. The reference wavefront for comparing the wavefront measurements is in this example a spherical wavefront. Similarly, the reference surface for analyzing the deformation of the surfaces A and B of the substrate is a spherical reference surface.

[0104] Thus, the emission means in this example includes an additional optical lens 216 for shaping the light beam 221 such that it is substantially perpendicular at all points to the analyzed substrate 100 and for substantially establishing an optical conjugate between the analyzed substrate and the analysis surface of the wavefront analyzer. In addition, the radius of curvature and the position of the reference mirror 550 are selected such that this mirror is substantially perpendicular at all points to the light beam 221.

[0105] In fact, the optical elements 216, 215, 230 and the mirrors 213 and 214 make the wavefronts of the reflected beams 222a and 222b received by the wavefront analyzer 240 substantially flat, as in the previous example, except for the deformation due to the deformation of faces A and B of the substrate 100, because the optical elements 216, 215, 230 and the mirrors 213 and 214 transform the spherical reference wavefront at the location of the substrate to be analyzed into a flat reference wavefront at the wavefront analyzer, as in the previous example. Therefore, a similar process can be performed to determine the deformation matrices of faces A and B.

[0106] It is also possible to directly receive a spherical wavefront in the wavefront analyzer, in which case the reference wavefront in the wavefront analyzer will be spherical.

[0107] It should be noted that the optical elements of the system 500 may have manufacturing defects, which may be taken into account in the calibration step in order to avoid interfering with the quality of the measurements taken. A practical way to do this is to measure these defects by performing wavefront measurements in the configuration of Figure 5B, with the analyzed substrate 100 removed. The defects measured in this way are subtracted from the measurements taken in the presence of the analyzed substrate 100.

[0108] In practice, the optical quality of the reference mirror 550 may be selected based on the desired accuracy of the deformation measurements on sides A and B of the analyzed substrate 100, since the accuracy of these measurements cannot be higher than the optical quality of the reference mirror 550.

[0109] 6 shows the implementation of another example of a method for analyzing the surface quality of a substrate 100 having parallel sides according to the present disclosure, using a second example of a system for analyzing the surface quality of a substrate. The objective in this example is to analyze the surface quality of a flat substrate 100 having parallel sides.

[0110] The system for analyzing the surface quality of a substrate shown in FIG. 6 and referenced as 600 includes a support (not shown in the drawing) configured to receive the substrate 100 to be analyzed, but does not require a reference mirror similar to the examples shown in FIGS. 2A, 2B, 5A, and 5B, except during a calibration step that may be performed, as described hereinafter.

[0111] The system 600 includes a light emitting means including a first emitting source 210a for light of low temporal coherence, in this example having at least one wavelength for which the substrate 100 is at least partially transparent. For example, the light emitting source 210a may include an incandescent lamp, an LED, an SLED, or a laser diode operating below the laser effect generation threshold as previously described.

[0112] The emission means also include a second emission source 210b having at least one wavelength for which the substrate 100 is at least partially transparent. Unlike the light source 210a, the light source 210b does not need to have a short coherence length, which opens up a range of possibilities. This light source 210b may thus, as before, include an incandescent lamp, an LED, an SLED, or a laser diode operating below the laser effect generation threshold, or indeed a laser or laser diode operating above its laser effect generation threshold.

[0113] Such light sources have the advantage of being spatially coherent.

[0114] In principle, a spatially coherent light source can be selected for the emission of the first and second light beams, since with a spatially coherent beam greater measurement accuracy for the wavefront analysis is achieved.

[0115] For example, when a Shack-Hartmann wavefront analyzer is used, the first and second light beams may have sufficient spatial coherence to produce a focal spot having a size smaller than the size of the microlenses at which the resulting reflected or transmitted beam is incident on the microlens array to produce the focal spot.

[0116] In the example of FIG. 6, the system 600 further includes a wavefront analysis means including a wavefront analyzer 240 (e.g., but not limited to, a Shack-Hartmann analyzer) and a processing unit 260 configured to process a measurement signal emitted from the wavefront analyzer 240.

[0117] In this example, the first light source 210a emits a first light beam 221a. The emission means are configured such that in operation the first light beam 221a is incident on one side of the substrate, in this example side A, advantageously substantially perpendicular to the substrate. The aim in the example of Fig. 6 is to analyze a substantially flat substrate having parallel faces, and the emission means are configured such that in operation the light beam is incident on the substrate with a substantially flat wavefront. For example, as in the previous example, the emission means comprises, in addition to the light source 210a, a set of optical lenses 211, 212, 215 and deflection elements 213, 214.

[0118] In this example, the second light source 210b emits a second light beam 221b. The emitting means are configured to make the second light beam 221b incident on the other side of the substrate (e.g., in this example, side B, but not necessarily) such that in operation the second light beam 221b is substantially perpendicular to the substrate. The objective in the example of Fig. 6 is to analyze a substantially flat substrate with parallel faces, and the emitting means are configured to make the second light beam incident on the substrate with a substantially flat wavefront in operation. For example, the emitting means comprises, in addition to the light source 210b, a set of optical lenses 615 for substantially collimating the beam and adapting its size to the size of the substrate to be analyzed, and deflection elements 613, 614.

[0119] As shown in FIG. 6, in a first step of the method implemented in this example, the light source 210a is activated and a first incident light beam 221a is reflected, on the one hand, from a first surface A of the substrate 100 to form a first reflected beam 222a, and, on the other hand, passes through the substrate and is reflected from a second surface B of the substrate 100, and passes through the substrate 100 again to form a second reflected beam 222b.

[0120] As described above, the wavefront analysis means is configured to receive the first and second reflected beams 222a and 222b to generate a first measurement signal indicative of a combined wavefront characteristic of said first and second reflected beams 222a and 222b.

[0121] 6, the wavefront analyzing means, as in the previous examples, includes a set of optical lenses 211, 212, 215 in common with those of the emitting means and deflecting elements 213, 214, so that the reflected beam is directed to a wavefront analyzer 240. The system 200 further includes an optical beam splitting element 230 configured to separate the emitting means and the analyzing means, as before.

[0122] In a second step of the method implemented in this example, light source 210b is activated while light source 210a is turned off and a second light beam 221b is transmitted through the substrate 100. The resulting transmitted beam 223 is sent to a wavefront analyzer 240 of the wavefront analysis means for generating a second measurement signal indicative of a wavefront characteristic of the transmitted beam.

[0123] Then, as described above with reference to Figures 3A, 3B, 4A, 4B, and 4C, the processing unit 260 can calculate, based on the first measurement signal and the second measurement signal, at least one first signal indicating deformation of the first side A of the substrate relative to the first reference surface and at least one second signal indicating deformation of the second side B of the substrate relative to the second reference surface. Since the passage of the substrate is simple, [Equation 5] becomes as follows: [Number 8] M2 = (n-1)(β-α)

[0124] As explained with reference to the previous examples, the optical elements of the system 600 may have manufacturing defects, which may be taken into account in the calibration step to avoid interfering with the quality of the measurements taken. Two calibration steps may be performed: a first calibration step for the transmitted beam and a second calibration step for the reflected beam. The actual way of performing the step of calibrating the transmitted beam is to measure the defects of the optical system by performing a wavefront measurement in the configuration of FIG. 6, with the substrate 100 to be analyzed removed and with the light source 210b switched on (light source 210a switched off). These defects measured in this way are then subtracted from the transmitted measurements made in the presence of the substrate 100 to be analyzed. The step of calibrating the reflected beam is identical to the calibration described with respect to FIGS. 2A and 2B, where the substrate is replaced by a reference mirror (light source 210a switched on and light source 210b switched off).

[0125] Although the case of the analysis of a flat substrate is shown, the method described with the aid of Fig. 6 can be applied to the analysis of curved substrates. For this purpose, the optical elements 615, 614, 613 must be particularly adapted so that, for example, the image of the source 210b formed by the optical elements 615, 614, 613 is located substantially in the centre of the curvature of the substrate to be analysed.

[0126] Compared to the example embodiments of Figures 2A, 2B, 5A, and 5B, a method for analyzing the surface quality of a substrate performed by a system such as that shown in Figure 6 may be faster because there is no need to install a reference mirror for the measurement itself, as the reference mirror is only useful for the calibration process.

[0127] In an example embodiment (not shown in the drawings), the system described in FIG. 6 may incorporate an additional light source in parallel with the second light source 210b, for example using a separating plate, a separating cube, or a dichroic plate. This additional light source may emit a third light beam having a different wavelength and / or polarization than the second light beam emitted to the light source 210b. This third light beam generates a second transmitted beam and follows the same optical path as the second light beam generating the first transmitted beam. The second transmitted beam is received by the analyzer 240, and a third measurement signal indicative of a wavefront characteristic of the second transmitted beam is generated. A comparison of the second measurement signal indicative of a wavefront characteristic of the first transmitted beam and the third measurement signal indicative of a wavefront characteristic of the second transmitted beam may be used to generate a signal indicative of a refractive index variation in the substrate.

[0128] 7 shows the implementation of another example of the method for analyzing the surface quality of a substrate 100 having parallel surfaces according to the present specification, using a third example of a system for analyzing the surface quality of a substrate. In this example, the two steps of the method for obtaining the first and second methods, respectively, may be performed simultaneously. The objective in this example is to analyze the surface quality of a substrate 100 having substantially flat parallel surfaces.

[0129] The system for analyzing the surface quality of a substrate shown in FIG. 7 and referenced as 700 includes a support (not shown in the drawing) configured to receive the substrate 100 to be analyzed, but does not require a reference mirror as in the examples shown in FIGS. 2A, 2B, 5A and 5B, except during calibration which may be performed as described hereinafter.

[0130] 2A, 2B, 5A, and 5B, the system 700 includes a light emitting means including a single emission source 210 for low temporal coherence light having at least one wavelength for which the substrate 100 is at least partially transparent. For example, the light emitting source 210 may include an incandescent lamp, an LED, an SLED, or a laser diode operating below the laser effect generation threshold, as previously described.

[0131] The system 700 further comprises wavefront analysis means, including in the example of Fig. 7 a first wavefront analyzer 240a and a second wavefront analyzer 240b separate from the first wavefront analyzer 240a, such as but not limited to a Shack-Hartmann analyzer, and a processing unit 260 configured to process the measurement signals emitted by the wavefront analyzers 240a and 240b. Advantageously, these wavefront analyzers are of the same type, although different types of wavefront analyzers may also be used.

[0132] In this example, the light source 210 emits a first light beam 221. The emitting means is configured such that in operation the first light beam 221 is incident on one side of the substrate, in this example side A, such that it is substantially perpendicular to the substrate. The aim in the example of Fig. 7 is to analyse substrates having substantially flat parallel surfaces, and the emitting means is configured such that in operation the light beam is incident on the substrate with a substantially flat wavefront. For example, as in the previous example, the emitting means comprises in addition to the light source 210 a set of optical lenses 211, 212, 215 and deflection elements 213, 214.

[0133] As shown in FIG. 7, in the first step of the method implemented in this example, the light source 210 is activated and a first incident light beam 221 is reflected, on the one hand, by a first surface A of the substrate 100 to form a first reflected beam 222a, and, on the other hand, passes through the substrate and is reflected by a second surface B of the substrate 100 and passes through the substrate 100 again to form a second reflected beam 222b.

[0134] As described above, the wavefront analysis means is configured to receive the first and second reflected beams 222a and 222b to generate a first measurement signal indicative of a combined wavefront characteristic of said first and second reflected beams 222a and 222b.

[0135] 7, the wavefront analyzing means includes a set of optical lenses 211, 212, 215 in common with those of the emitting means, and deflecting elements 213, 214, as in the previous examples, to direct the reflected beam towards the wavefront analyzer 240a and to substantially establish optical conjugation between the analyzed substrate 100 and the measurement surface of the wavefront analyzer 240a. The system 700 further includes an optical beam splitting element 230 configured to separate the emitting means and the wavefront analyzer 240a, as before.

[0136] In a second step of the method implemented in this example, which may be performed simultaneously with the first step, a transmitted beam 223 resulting from the transmission of a second light beam through the substrate, which may coincide with the first light beam 221, is sent to a second wavefront analyzer 240b of the wavefront analysis means to generate a second measurement signal indicative of the wavefront characteristics of the transmitted beam.

[0137] In the example of Figure 7, the wavefront analysis means includes a set of optical lenses 715, 712 and deflection elements 714, 713 to direct the transmitted beam 223 to the wavefront analyzer 240b and to substantially establish optical conjugation between the substrate 100 to be analyzed and the measurement surface of the wavefront analyzer 240b.

[0138] Then, as described above with reference to Figures 3A, 3B, 4A, 4B, and 4C, the processing unit 260 can calculate, based on the first measurement signal and the second measurement signal, at least one first signal indicating deformation of the first side A of the substrate relative to the first reference surface and at least one second signal indicating deformation of the second side B of the substrate relative to the second reference surface.

[0139] Similar to the example of FIG. 6, the second light beam simply passes through the substrate, so equation (8) is applicable.

[0140] As before, the optical elements of the system 700 may have manufacturing defects, which may be taken into account in the calibration step to avoid interference with the quality of the measurements taken. Two calibration steps may be provided: a calibration step for the transmitted beam and a calibration step for the reflected beam. The actual way of performing the step of calibrating the transmitted beam is to measure the defects of the optical system by the analyzer 240b, by performing a wavefront measurement in the configuration of FIG. 7 with the light source 210 switched on, with the substrate 100 to be analyzed removed. These defects measured in this way are then subtracted from the transmitted measurements made in the presence of the substrate 100 to be analyzed. The step of calibrating the reflected beam is identical to the calibration described for FIGS. 2A and 2B, where the substrate is replaced by a reference mirror.

[0141] Although the case of the analysis of a flat substrate is shown, the method described with the aid of Fig. 7 can be applied to the analysis of curved substrates. For this purpose, the optical elements 211-215 must be adapted, for example, so that the size of the beam 221 is adapted to the size of the substrate to be analyzed, in order to ensure that the beam 221 arrives substantially perpendicularly on the surface of the substrate to be analyzed and that an optical conjugation is substantially established between the substrate to be analyzed 100 and the measurement surface of the wavefront analyzer 240a. The optical elements 715, 714 and 713 must also be adapted, for example, so that the size of the transmitted beam at the substrate to be analyzed 100 is adapted to the size of the measurement surface of the analyzer 240b and that an optical conjugation is substantially established between the substrate to be analyzed 100 and the measurement surface of the wavefront analyzer 240b.

[0142] 2A, 2B, 5A and 5B, the method for analyzing the surface quality of a substrate implemented by a system such as that shown in Fig. 7 may be faster, since there is no need to install a reference mirror for the measurement itself, since the reference mirror is only useful for the calibration step. Furthermore, due to the presence of two wavefront analyzers, the first and second reflected beams 221a, 221b can be generated simultaneously from the light beam 221 together with the transmitted beam 223, so that measurements of M1 and M2 can be performed simultaneously.

[0143] Fig. 8 shows a system 800 including an emission means having a first emission source 210a and a second emission source 210b separate from the first emission source, similar to the example of Fig. 6. In addition, the system 800 includes a wavefront analysis means including a first wavefront analyzer 240a and a second wavefront analyzer 240b separate from the first wavefront analyzer 240a, similar to the example of Fig. 7. The system 800 further includes a processing unit 260 configured to process the measurement signals generated by the wavefront analyzers 240a and 240b.

[0144] Such a system has similar advantages to the system of FIG. 7, i.e. a single light beam 221a emitted by a first light source 210a can simultaneously generate reflected beams 222a and 222b that are detected by a first wavefront analyzer 240a to generate a first measurement signal indicative of the combined wavefront characteristics of the first and second reflected beams, and can generate a first transmitted beam 223a that is detected by a second wavefront analyzer 240b to generate a second measurement signal indicative of the wavefront characteristics of the transmitted beam.

[0145] As in the previous example, for this purpose the wavefront analyzing means may comprise a set of optical lenses 211, 212, 215 common to those of the emitting means and deflection elements 213, 214, so that the reflected beam is directed to the wavefront analyzer 240a and the optical conjugation between the substrate 100 to be analyzed and the measurement surface of the wavefront analyzer 240a is substantially established. The system 800 may further comprise an optical beam splitting element 230, as before, configured to separate the emitting means and the wavefront analyzer 240a. Additionally, in the example of Fig. 8, the wavefront analyzing means comprises a set of optical lenses 815, 812 and deflection elements 814, 813, so that the transmitted beam 223a is directed to the second wavefront analyzer 240b and the optical conjugation between the substrate 100 to be analyzed and the measurement surface of the wavefront analyzer 240b is substantially established.

[0146] Furthermore, in this example, the second light source 210b is configured to emit a second light beam 221b having a different wavelength and / or polarization than the first light beam 221a.

[0147] The method may then, in one example embodiment, include receiving the second transmitted beam resulting from the first transmission of the second light beam 221b through the substrate by a first wavefront analyzer 240a to generate a third measurement signal indicative of a wavefront characteristic of the second transmitted beam 223b. A comparison of the second measurement signal indicative of the wavefront characteristic of the first transmitted beam and the third measurement signal indicative of the wavefront characteristic of the second transmitted beam may be used to generate a signal indicative of a characteristic of the refractive index variation in the substrate.

[0148] As shown in FIG. 8, the emission means may include optical elements 811 and 812-815 in common with the analysis means, as well as a separation element 830, for directing the second light beam 221b towards the substrate 100, for example, by normal incidence, although this does not necessarily have to be the case.

[0149] A calibration process, such as that described in relation to the preceding figures, may be performed.

[0150] FIG. 9 shows experimental images illustrating the deformation of the surface of a flat substrate with parallel faces obtained by the method according to the present disclosure.

[0151] More precisely, in this example, the substrate is a 3 mm thick substrate with flat parallel faces produced by double-sided polishing, one of the two faces (face A) having a polishing defect.

[0152] The system used for the analysis is of the type shown in Figures 2A and 2B: the emission source is a laser diode coupled into a monomode fiber used below the laser effect generation threshold, and the wavefront analyzer is a Shack-Hartmann analyzer.

[0153] The deformation matrix is ​​determined using equations [6] and [7] based on a first measurement signal M1 characteristic of the combined wavefronts of the first and second reflected beams and a second measurement signal M2 characteristic of the wavefront of the transmitted beam, as described with reference to Figures 2A and 2B.

[0154] The substrate is analyzed and the matrices of deformations α and β of faces A and B relative to a flat reference plane are determined and shown in the left and right images of FIG. 9, respectively.

[0155] Polishing defects with a PV (peak to valley) amplitude of 0.315 μm are observed, especially on side A. This test demonstrates that the method clearly allows the two sides to be measured separately, since the measurement of side B shows no polishing defects, as would be expected for this substrate with polishing defects on only one side.

[0156] In the example embodiments described with reference to Figures 2A, 2B, 6, 7 and 8, a first light beam incident substantially perpendicularly on the substrate to be analysed has been considered.

[0157] Although this is an advantageous configuration, those skilled in the art will be able to envision other embodiments that are particularly suited to the use of tilted substrates.

[0158] Thus, Figure 10A shows a diagram illustrating a first step of an example of a method for analyzing the surface quality of a substrate according to the present disclosure, using an example of a system for analyzing the surface quality of a substrate according to the present disclosure adapted for a first light beam incident on the substrate at a non-zero tilt angle with respect to normal, and Figure 10B shows a diagram illustrating a second step of an example of a method for analyzing the surface quality of a substrate, in this example a reference mirror 250 is used, as in the example of Figures 2A and 2B.

[0159] The emitting means in this example comprises two light emitting sources, namely a light emitting source 210a for emitting a first light beam 221a (Figure 10A) having low temporal coherence and a light emitting source 210b for emitting a second light beam 221b (Figure 10B).

[0160] As shown in Figures 10A and 10B, the emission means also includes a set of optical lenses 1013, 1018, 1017, 1014 and deflection elements 1011, 1012, 1016, 1015 for directing the first light beam emitted from the first light source 210a and the second light beam emitted from the second light source 210b towards the substrate 100.

[0161] In this example, the analyzing means includes a set of optical lenses 1014, 1017, 1018 in common with the emitting means and deflecting elements 1015, 1016 to direct the reflected beams 222a, 222b to the first wavefront analyzer 240a and to substantially establish an optical conjugation between the analyzed substrate 100 and the measurement surface of the wavefront analyzer 240a. The splitting element 230 allows to separate the analyzing path from the emitting path.

[0162] As shown in Fig. 10C, the system described with reference to Fig. 10A and Fig. 10B can be used to analyze tilted substrates within certain limits. In particular, when the tilt angle θ of the first light beam 221a with respect to the normal to the substrate is too large, especially for thick substrates, this can result in a spatial offset, denoted d, between the footprints of defects of face B in the reflected beam 222b and their footprints in the transmitted beam, which can distort the calculation of the deformations of faces A and B from measurements in reflection and transmission. A person skilled in the art with knowledge in this field will be able to adapt the optical assembly to limit the tilt of the first light beam according to the thickness of the substrate, so that the offset d is small relative to the expected spatial periodicity of defects of face B and the spatial resolution of the wavefront analyzer.

[0163] While described in terms of a particular number of exemplary embodiments, the systems and methods herein embrace different variations, modifications, and improvements that will be apparent to those skilled in the art, and these different variations, modifications, and improvements are deemed to be within the scope of the invention as defined by the following claims. References

[0164] [References 1] Craig R. Forest et al., Metrology of thin transparent optics Shack-Hartmann wavefront sensing, Optical Engineering, 43(3), 2004, https: / / doi.org / 10.1117 / 1.1645256. [Reference 2] International Publication No. 2004 / 068088 [Reference 3] Principles and History of Shack-Hartmann, Journal of Refractive Surgery Volume 17, September / October 2001. [Reference 4] U.S. Patent No. 6,577,403 [Reference 5] U.S. Patent Application Publication No. 2010 / 0310130 [Reference 6] U.S. Patent Application Publication No. 2005 / 0036153

Claims

1. A method for analyzing the surface quality of a substrate (100) having parallel surfaces, comprising: - emitting at least one first light beam (221) with low temporal coherence by at least one first light source (210, 210a) of an emitting means, said at least one first light beam being incident on a first side (A) of said substrate, said substrate being at least partially transparent to at least one wavelength of said first light beam; receiving the at least one first reflected beam and the second reflected beam by at least one first wavefront analyzer (240, 240a) of a wavefront analysis means to generate at least one first measurement signal characteristic of a combination of wavefronts of at least one first reflected beam (222a) resulting from reflection of the at least one first light beam by the first surface (A) of the substrate and a second reflected beam (222b) resulting from a first transmission of the first light beam through the substrate and subsequent reflection by a second surface (B) of the substrate followed by a second transmission through the substrate; receiving, by said wavefront analysis means, at least one first transmitted beam (223, 223a) for generating a second measurement signal indicative of a wavefront characteristic of said at least one first transmitted beam (223, 223a) resulting from at least one first transmission of a second light beam emitted by said emitting means into said substrate; calculating at least one first signal indicative of a deformation of the first surface of the substrate relative to a first reference surface and at least one second signal indicative of a deformation of the second surface of the substrate relative to a second reference surface from the at least one first measurement signal and the second measurement signal.

2. The method of claim 1 , wherein the at least one first light beam is incident on the substrate substantially normal to the substrate.

3. 3. A method according to claim 1 or 2, comprising: The second light beam is incident on the first side (A) of the substrate, and the method includes, for generating the second measurement signal: positioning a reference mirror disposed substantially perpendicular to the second light beam; the first transmitted beam (223) results from a first transmission of the second light beam through the substrate, reflection by the reference mirror, and a second transmission of the beam reflected by the reference mirror through the substrate; The first and second reflected beams and the first transmitted beam are received by the first wavefront analyzer (240) of the wavefront analyzing means.

4. The method of claim 3 , wherein the first light beam and the second light beam are emitted by the first light source.

5. 3. A method according to claim 1 or 2, comprising: the second light beam is incident on the first surface (A) of the substrate; the first transmitted beam (223, 223a) results from a first transmission of the second light beam through the substrate; The method according to claim 1, wherein the first transmitted beam is received by a second wavefront analyzer (240b) of the wavefront analyzing means separate from the first wavefront analyzer.

6. 3. A method according to claim 1 or 2, comprising: the second light beam (221b) is emitted by a second light source of the emitting means, separate from the first light source, and is incident on the second face (B) of the substrate; the first transmitted beam (223b) results from a first transmission of the second light beam through the substrate; The method, wherein the first transmitted beam is received by the first wavefront analyzer (240) of the measurement and analysis means.

7. 7. The method of claim 6, The first light beam emitted by the first light source and the second light beam emitted by the second light source have at least one of different wavelengths and polarizations, and the method further comprises: receiving the second transmitted beam by a second wavefront analyzer (240b) of the wavefront analysis means, separate from the first wavefront analyzer, to generate a third measurement signal indicative of a wavefront characteristic of the second transmitted beam (223a) resulting from a first transmission of the first incident beam through the substrate; and comparing the second measurement signal indicative of a wavefront characteristic of the first transmitted beam to the third measurement signal indicative of a wavefront characteristic of the second transmitted beam to generate a signal indicative of a characteristic of a refractive index variation in the substrate.

8. 1. A system for analyzing a surface quality of a substrate having parallel surfaces, comprising: at least one first support configured to receive the substrate to be analyzed; - emitting means including at least one first light source for emitting at least one first light beam with low temporal coherence having at least one wavelength through which the substrate is at least partially transparent, the emitting means being configured such that during operation the at least one first light beam is incident on the substrate; A wavefront analysis means comprising at least one first wavefront analyzer (240, 240a), which during operation: receiving the at least one first reflected beam and the second reflected beam at an analysis surface of the first wavefront analyzer to generate a first measurement signal characteristic of a combination of wavefronts of at least one first reflected beam (222a) resulting from reflection of the at least one first light beam by a first surface (A) of the substrate and a second reflected beam (222a) resulting from a first transmission of the first light beam through the substrate and subsequent reflection by a second surface (B) of the substrate followed by a second transmission through the substrate; - wavefront analysis means configured to receive at least one first transmitted beam (223, 223a) by said wavefront analysis means in order to generate a second measurement signal indicative of a wavefront characteristic of said at least one first transmitted beam (223, 223a) resulting from at least one first transmission of the second light beam emitted by said emission means into said substrate; a processing unit (260) configured to calculate from the first measurement signal and the second measurement signal at least one first signal indicative of a deformation of the first surface of the substrate relative to a first reference surface and at least one second signal indicative of a deformation of the second surface of the substrate relative to a second reference surface.

9. 9. The system of claim 8, wherein the emitting means is configured such that, during operation, the at least one first light beam is incident on the substrate substantially normal to the substrate.

10. 10. A system according to claim 8 or 9, wherein the analysis surface of the first wavefront analyzer is substantially optically conjugate with the substrate to be analysed.

11. A system according to any one of claims 8 to 10, a second support configured to receive a reference mirror disposed substantially perpendicular to the second light beam during operation, the first transmitted beam (223) results from a first transmission of the at least one first incident beam to the substrate, reflection by the reference mirror, and a second transmission of the beam reflected by the reference mirror to the substrate; The first and second reflected beams and the first transmitted beam are received by the first wavefront analyzer (240) of the wavefront analysis means.

12. 11. A system according to claim 8, wherein the wavefront analysis means comprises a second wavefront analyzer separate from the first wavefront analyzer, the emitting means is configured such that, during operation, the second light beam is incident on the first side of the substrate, the first transmitted beam resulting from a first transmission of the second light beam through the substrate; The wavefront analyzing means is configured such that during operation the first transmitted beam is received by the second wavefront analyzer of the wavefront analyzing means.

13. 13. The system according to any one of claims 8 to 12, wherein the at least one first wavefront analyzer is selected from the group consisting of a Hartmann and Shack-Hartmann wavefront analyzer, a lateral-shift interferometer, a Moire deflectometer, and a Schlieren based device.

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