OPTICAL SYSTEM FOR MEASURING BRDF, BSDF AND BDTF

Description

[0001] The present invention relates to an optical system for measuring the bidirectional diffuse reflection and / or transmission functions BRDF, BTDF and BSDF of a reflective surface and / or operating in transmission of at least a portion of an object. Furthermore, the present invention also relates to a device for measuring the light intensity of a reflective surface and / or operating in transmission of at least a portion of an object.

[0002] Traditionally, the bidirectional reflectance distribution function (BRDF) or the bidirectional transmittance distribution function (BTDF) or the bidirectional scattering distribution function (BSDF) are measured with a two-axis goniometer. The intensity of the scattered light is measured point by point with a large articulated arm that can move in all directions. As a result, several hours are required to complete a measurement. In addition, the two-axis goniometer is bulky, heavy, and difficult to transport. It is only used in laboratories and is not suitable for on-site measurements.

[0003] It therefore seems appropriate to propose a system for measuring double conjugation BRDF, BTDF and BSDF which is compact, without moving parts, less expensive, and whose measurement is rapid.

[0004] Document FR2860869 (J.Delacour - OPTIS) describes a device for measuring the luminous intensity of an object which comprises a central dioptric part, for example consisting of a converging aspherical lens, and a catadioptric peripheral part such as a parabolic reflector pierced at its top. The converging aspherical lens and the parabolic reflector are arranged so that their optical axes H and their foci F1 coincide. The object whose luminous intensity or BRDF, BTDF or BSDF is to be measured is placed at this focus F1. The light diffused by the object is collected either by the converging aspherical lens (when the light rays are slightly inclined relative to the optical axis H), or by the parabolic reflector (when the light rays are strongly inclined relative to the optical axis H). The boundary between slightly inclined and strongly inclined is around 30 degrees of angle.Thus, document FR2860869 describes a measuring device that is less bulky than the goniometer, but this device does not allow good resolution to be obtained, particularly at large diffusion angles, because it is designed around a point object and it does not take into account all the aperture aberrations (coma) and field aberrations (field curvature). One consequence is that the resolution is not constant depending on the angle of the measurement taken. In addition, the discontinuity between the lens and the parabolic reflector creates an artifact that disrupts the measurement.

[0005] Document FR2749388 (T.Leroux - ELDIM) describes a BRDF measuring device which is limited to a small field angle. Indeed, the measuring objective performs the Fourier transform which implicitly induces a good correction of aperture aberrations and field aberrations but the fact that the diameter of the light beam always has the same section whatever the angle considered limits the opening angle to 40°. This implies that the sum of the angles of the incident light and the scattered light does not exceed the opening angle of the measuring objective, i.e. 40°. Consequently, surfaces whose diffusion angle exceeds 40°, in particular very diffuse surfaces, cannot be measured with this device.

[0006] One of the aims of the invention is to overcome one or more of these drawbacks. To this end, and according to a first aspect, the subject of the invention is an optical system, intended to measure the bidirectional diffuse BRDF, BTDF and BSDF functions of a reflective surface and / or operating in transmission of at least a part of an object, the system successively comprising in the direction of propagation of the diffused light: an aplanatic objective capable of projecting the image of an intensity diagram of the light diffused by the reflecting surface and / or operating in transmission onto an intermediate observation plane P downstream of the aplanatic objective, a converging field lens downstream of the plane P, an image-taking objective whose field angle is greater than or equal to the convergence angle of the beams of diffused light emerging from the field lens, and a video sensor, the aplanatic lens, the converging field lens, the image-taking lens and the video sensor being arranged so as to allow a first conjugation between the reflecting surface and / or operating in transmission and the entrance pupil of the image-taking lens and a second conjugation between a scattered light intensity diagram and the video sensor.

[0007] Thus, this configuration allows obtaining a clear image of an intensity diagram of the scattered light thanks to the two conjugations obtained by the system, when the focusing of the image capture objective is carried out.

[0008] The term 'aplanatic objective' means an objective having an angular resolution of between 10° and a value strictly greater than 0° and preferably between 5° and a value strictly greater than 0° and more preferably between 1° and a value strictly greater than 0° so that the correction of aperture aberrations is adapted to the angular resolution of the measurement.

[0009] When the objective is strictly aplanatic (or whose angular resolution is between 1° and a value strictly greater than 0°), the aperture aberrations of the first conjugation are corrected. Thus, the spherical aberration is corrected at all orders and the optical path between the object focus and the intermediate observation plane P is always identical. This condition (also called strict stigmatism) is expressed by the following formula: Σn i *ei =constant, where ei represents the thickness of material crossed by the light along a light ray, and ni the associated refractive index. On the other hand, the coma aberration is corrected at all orders, so that the height h between the emerging ray and the optical axis H can be defined by the equation "h= f' sinα" with f' denoting the focal length of the objective and α denoting the aperture angle of the ray considered.

[0010] In this way, the system according to the invention makes it possible to measure the BRDF, BTDF and BSDF of a wide variety of scattering surfaces, from weakly scattering surfaces to strongly scattering surfaces depending on the aperture angle considered. Furthermore, the measurement resolution is very good for small or large sizes of the studied surface such as 2 mm in diameter while offering a compact system, without moving parts and with a very short measurement time.

[0011] According to one embodiment of the invention, the converging field lens is aplanatic so that the first conjugation as a whole is aplanatic, so as to improve the resolution of the optical system and to properly delimit the actually measured surface of the diffusing object.

[0012] According to another embodiment, the converging field lens comprises at least two lenses arranged such that the converging field lens is aplanatic so as to simplify the optical design.

[0013] According to one possibility, the field lens has a thickness and a camber whose value is greater than 10% of the focal length of the converging field lens so as to be able to create a negative field curvature and compensate for the field curvature of the aplanatic objective. Indeed, the negative curvature of the field lens makes it possible to compensate for the positive field curvature of the aplanatic objective so as to correct the second conjugation of the field curvature and improve the angular resolution for large diffusion angles.

[0014] Alternatively, not forming part of the claimed invention, the converging field lens is a simple lens, of the biconvex or plano-convex type, spherical or aspherical, so as to save space and simplify production but in this case, the second conjugation is not corrected for field aberrations, in particular the field curvature because its field curvature is uncontrolled.

[0015] The aplanatic objective has, for example, an opening angle whose absolute value is between 0 and a value strictly less than 90°, preferably whose absolute value is between 45° and a value strictly less than 90°, and more preferably whose absolute value is between 60° and a value strictly less than 90°, and more preferably whose absolute value is between 85° and a value strictly less than 90° so as to be able to observe very varied diffusion surfaces and in particular very diffusing surfaces.

[0016] According to one embodiment, the aplanatic lens comprises at least one aspherical lens, preferably, the aplanatic lens comprises two aspherical lenses, and more preferably the aplanatic lens comprises two aspherical lenses each of whose surfaces has a deviation from the local radius of curvature measured at the center of its surface, which is greater than or equal to 10% of the focal length of the aplanatic lens.

[0017] Therefore, when the aplanatic lens is thus made up of two highly aspherical lenses, its aperture angle is very large. Thus, when the first and second conjugations are corrected for aperture and field aberrations, it is possible to observe a large surface (2 mm for example) and to have good angular resolution at the same time as a reduced size. In addition, the image of a Lambertian intensity diagram gives a uniform light distribution on the video sensor, which maximizes the dynamic range. Furthermore, all the scattered light is recovered by the video sensor and there is no vignetting, which limits sensitivity problems when measuring reflective surfaces and / or operating in transmission of dark objects.On the other hand, the apparent surface of the object seen by the sensor is always the same during the same measurement, regardless of the observation angle, so that the surface is always identical during the measurement. Finally, the measurement at high angles of incidence is done with good resolution.

[0018] In the alternative where the aplanatic objective consists of a simple aspherical lens, the cost and size are reduced, but the opening angle is limited to + / - 45° which limits the measurement to poorly diffusing surfaces.

[0019] According to an alternative embodiment, the aplanatic lens comprises at least two lenses arranged so as to correct the aperture aberrations of the aplanatic lens. Said at least two lenses can be any, spherical or aspherical, converging or diverging.

[0020] Advantageously, the aplanatic lens has an infinite focus type conjugation so that it is possible to image an intensity diagram located at infinity on an intermediate observation plane P and to match a direction of the intensity diagram with a pixel of the video sensor.

[0021] According to another embodiment, the image capture lens has a field angle of + / - 20°.

[0022] In particular, the image-taking lens is a camera lens.

[0023] The video sensor is for example chosen from a CMOS or CCD type sensor.

[0024] By the expression 'CCD' which is the English acronym of 'Charge-Coupled Device', we mean a charge transfer device.

[0025] The term 'CMOS video sensor' means a sensor with CMOS components, which is the English acronym for 'Complementary Metal Oxide Semiconductor'.

[0026] According to another aspect, the invention also relates to a device for measuring the bidirectional diffuse functions BRDF, BTDF and BSDF of a reflecting surface and / or operating in transmission of at least part of an object comprising: - an optical system as previously described, and a lighting channel capable of illuminating the reflective surface and / or operating in transmission at several angles of incidence i, so as to be able to measure the intensity diagram of the light diffused by the reflective surface and / or operating in transmission on the video sensor.

[0027] The term 'lighting path' means the propagation of light beams from the light source set to at least part of the object.

[0028] Advantageously, the measuring device comprises means for reconstructing the BRDF, BDTF and BSTF of the reflecting surface and / or operating in transmission and means for recording the measurements of the BRDF, BDTF and BSTF on a medium.

[0029] The reconstruction means can be software for example. The recording means make it possible to create a data library of the measured BRDF, BDTF and BSDF which can be used in the creation of a synthetic image to obtain a faithful reproduction of the object.

[0030] According to a particular embodiment, the measuring device is adapted to measure bidirectional diffuse functions BRDF and the lighting path comprises: a set of light sources of pre-collimated beams, a set of converging lenses arranged so as to form the image of the light sources on the intermediate observation plane P, and a semi-reflecting plate arranged at the intermediate observation plane P so that the pre-collimated beams are reflected towards at least a part of the object through the aplanatic objective while allowing the passage of the light diffused from the object or a part of the object towards the video sensor. Indeed, by focusing the beams of the light sources on the intermediate observation plane P, it is possible to address several given angles of incidence.

[0031] Other aspects, aims and advantages of the present invention will become more apparent upon reading the following description of an embodiment thereof, given by way of non-limiting example and with reference to the accompanying drawings. The figures do not necessarily respect the scale of all the elements represented so as to improve their readability. In the remainder of the description, for the sake of simplification, identical, similar or equivalent elements of the different embodiments bear the same numerical references. There figure 1 illustrates a block diagram of the optical system according to one embodiment of the invention. The figure 2 illustrates a ray tracing through an aplanatic objective and a field lens, from a source point located at the center of the object, to the imaging objective (C1 conjugation) according to an embodiment of the invention. figure 3 illustrates a ray tracing from the intensity diagram to the video sensor (conjugation C2), with the lighting paths superimposed according to one embodiment of the invention. The figure 1 illustrates an optical system 1 successively comprising an aplanatic lens 2, a converging field lens 3, an image capture lens 4 and a video sensor 5.

[0032] The substantially aplanatic objective 2, namely one whose angular resolution is between 1° and a value strictly greater than 0 or namely an objective 2 corrected for aperture aberrations (spherical and coma aberrations), has an infinite focus type conjugation. It is also equipped with a very large aperture angle which can range from 0 to a value close to + / -90° so as to measure surfaces which diffuse little or very much. To do this, the aplanatic objective 2 is made up of two aspherical lenses 6. It can also be made up of a single aspherical lens 6 so as to reduce costs but the aperture angle of such an objective 2 is limited to + / -45°.

[0033] When the aplanatic lens 2 comprises two aspherical lenses 6, their surfaces are difficult to determine, especially for large aperture angles. The parameterization requires solving a problem with two equations (spherical aberration and coma) and four unknowns (the four optical surfaces). In theory, we can therefore only define two of the four optical surfaces. In practice, the two free surfaces are adjusted to obtain a physically feasible geometry. The optimization calculation of a predefined geometry (polynomial or conical type) using optical calculation software does not give satisfactory results for obtaining a lens with good resolution at large aperture angles.On the other hand, analytical calculation allows the definition of a differential equation which can be solved numerically by software and leads to the complete definition of two of the four surfaces of the lenses 6 for a perfectly aplanatic objective 2, knowing that the other two surfaces are used as parameters. This differential equation is obtained by analytical calculation starting from the following two formulas: . - Σn i *ei =constant, where ei represents the thickness of material crossed by light along a light ray, from the object focus to the intermediate observation plane P (correction of spherical aberration), and ni the associated refractive index. h=f'sinα with f' designating the focal length of the objective, α designating the opening angle of an incident ray and h the height between the corresponding emerging ray and the optical axis H (coma correction).

[0034] Let (x1,y1,x2,y2) be the coordinates of the two surfaces that are not taken as parameters. By propagating a light ray through the lens from the focus to the intermediate observation plane P, it is possible to reformulate the two previous equations by introducing the unknowns (x1,y1,x2,y2). The result is a set of coupled equations that are functions of (x1,y1,x2,y2). One of these equations is a differential equation that can be solved numerically, using a ray with an opening angle of 0° as the initial condition.

[0035] The case of an aplanatic lens consisting of a single aspherical lens is treated in the same way, but this time there are two equations, two unknowns and no parameters left free.

[0036] According to a first conjugation C1 carried out by the optical system 1 (thinnest ray tracing), the light scattered by the reflecting surface 10 and / or operating in transmission of a part of the object 7 propagates through the aplanatic objective 2. This has the effect that an intensity diagram of the scattered light is projected onto an intermediate observation plane P located upstream of the converging field lens 3. This field lens 3 then converges the light beams of this image in the image-taking objective 4. The converging field lens 3 is an aplanatic lens so that the conjugation C1 as a whole is aplanatic. Alternatively, the lens 3 can consist of a single aspherical condenser type lens to limit costs.

[0037] According to a second C2 conjugation carried out by the optical system 1 (widest ray tracing), a direction of the intensity diagram located at infinity corresponds to a pixel of the video sensor 5. This second C2 conjugation is corrected for the field curvature aberrations induced by the aplanatic objective 2 using a field lens 3 whose thickness and curvature are significant. They are in fact greater than 10% of the focal length of the lens. The thickness and curvature of the field lens 3 are determined so as to introduce a negative field curvature which compensates for the positive field curvature of the aplanatic objective 2.

[0038] In reference to the figure 2 , a ray trace through aplanatic objective 2 and field lens 3 illustrates the first conjugation C1. The source point is located at the object focus of aplanatic objective 2. This figure illustrates in particular the intermediate observation plane P which in reality is curved due to the field aberrations of aplanatic objective 2, which are approximately corrected by the negative field curvature of the thick converging field lens 3.

[0039] In reference to the figure 3 A measuring device 8 of the BRDF is illustrated. In addition to the optical system 1 as previously described, the measuring device 8 comprises an illumination path 9 consisting of a set of four light sources of pre-collimated beams, such as 3 mm encapsulated LEDs, but a different number of light sources is possible. figure 3illustrates four converging lenses 11 corresponding to the light sources so as to focus the pre-collimated beams on the intermediate observation plane P thanks to a semi-reflecting blade 12 interposed between the aplanatic objective 2 and the field lens 3.

[0040] These converging lenses 11 are defined taking into account the intermediate observation plane P curvature so as not to degrade the angular resolution in the illumination path 9. The light thus propagates towards the reflective surface 10 of the part of the object 7 to be measured. Then the light diffused by the reflective surface 10 of the object 7 propagates from the object 7 to the video sensor 5.

[0041] According to a non-illustrated embodiment, when the measuring device 8 is applied to the measurement of the BTDF function, the light sources emit collimated beams upstream of the surface 10 operating in transmission. Thus, the surface 10 is illuminated with predetermined angles of incidence i, each light source having a divergence of less than 1° so as to correspond to the angular resolution of the measuring device (8). The angles of incidence obtained by the aplanatic system when the measuring device 8 is used to measure the BRDF are thus also obtained for the measurement of the BTDF.

[0042] It goes without saying that the invention is not limited to the embodiment described above as an example but that it includes all technical equivalents and variants of the means described as well as their combinations.

Claims

1. An optical system (1), intended to measure the bidirectional reflectance and / or transmittance distribution function BRDF (bidirectional reflectance distribution function), BTDF (bidirectional transmittance distribution function) and BSDF (bidirectional scattering distribution function) of a surface (10), reflecting and / or operating in transmission, of at least part of an object (7), the system comprising successively in the direction of propagation of the diffused light: - an aplanatic objective (2) capable of projecting the image of an intensity diagram of the light diffused by the surface (10), reflecting and / or operating in transmission, onto an intermediate observation plane P downstream of the aplanatic objective (2), - a converging field lens (3) downstream of the plane P, - an image pickup objective (4) whose field angle is greater than or equal to the convergence angle of the beams of the diffused light emerging from the field lens, and - a video sensor (5), the aplanatic objective (2), the converging field lens (3), the image pickup objective (4) and the video sensor (5) being arranged so as to allow a first conjugation C1 between the surface (10), reflecting and / or operating in transmission, and the entrance pupil of the image pickup objective (4) and a second conjugation C2 between an intensity diagram of the diffused light and the video sensor (5), characterized in that the aplanatic objective (2) has an angular resolution comprised between 10° and a value strictly greater than 0°, and comprises at least two lenses arranged so as to correct the aperture aberrations of the aplanatic objective (2), the aplanatic objective (2) having an aperture angle whose absolute value is comprised between 60° and a value strictly less than 90°, the aplanatic objective (2) comprising at least one aspherical lens; the converging field lens (3) being aplanatic, the first conjugation then being aplanatic.

2. The optical system (1) according to claim 1, characterized in that the aplanatic objective (2) has an aperture angle whose absolute value is comprised between 85° and a value strictly less than 90°.

3. The optical system (1) according to any of claims 1 and 2, characterized in that the aplanatic objective (2) comprises two aspherical lenses, and preferably the aplanatic objective (2) comprises two aspherical lenses each of whose surfaces has a deviation from the local radius of curvature measured at the center of its surface, which is greater than or equal to 10% of the focal length of the aplanatic objective.

4. The optical system (1) according to any of claims 1 to 3, characterized in that the aplanatic objective (2) has a conjugation of infinite focus type.

5. A measuring device (8) of the bidirectional reflectance and / or transmittance distribution function BRDF, BTDF and BSDF of a surface (10), reflecting and / or operating in transmission, of at least part of an object (7) comprising: - an optical system (1) according to any of claims 1 to 4 - an illumination path (9) capable of illuminating the surface (10), reflecting and / or operating in transmission, under several angles of incidence i.

6. The measuring device (8) according to claim 5, characterized in that it includes means for reconstructing the BRDF, BDTF and BSTF of the surface (10), reflecting and / or operating in transmission, and means for recording on a medium the measurements of the BRDF, BDTF and BSTF.

7. The measuring device (8) according to any of claims 5 or 6, characterized in that the measuring device (8) is adapted to measure the bidirectional reflectance distribution function BRDF and in that the illumination path (9) comprises: - a set of light sources of pre-collimated beams, - a set of converging lenses (11) arranged so as to focus the light sources on the intermediate observation plane P, and - a semi-reflecting blade (12) disposed at the intermediate observation plane P so that the pre-collimated beams are reflected in the direction of at least part of the object (7) through the aplanatic objective (2) while allowing the passage of the light diffused from the object (7) or part of the object (7) towards the video sensor (5).