Method for obtaining BRDF of diffuse reflection materials for laser spot measurement

Abstract

The present invention specifically relates to a method for obtaining the BRDF of a diffuse reflection material for laser spot measurement, which is used to solve the problem that the current BRDF scattering characteristic model and calculation method under laser irradiation have large errors, and the integration process of the existing model is complicated and time-consuming. The method for obtaining the BRDF of a diffuse reflection material for laser spot measurement comprises the following steps: step 1, obtaining the random rough surface height distribution function R and the spatial coherence function ρ of the diffuse reflection material according to the model; step 2, obtaining the micro-element orientation probability distribution R according to the random rough surface height distribution function W of the diffuse reflection material; step 3, calculating θ based on the reflection principle. a and φ a The expression of is obtained and substituted into the micro-element orientation probability distribution R to obtain the probability density distribution function P of the mirror reflection part of the material; step 4, substitute the probability density distribution function P of the mirror reflection part of the material into the corresponding model to derive the expression of the material BRDF; step 5, through the experimental data fitting, the specific expression of the material BRDF is obtained.

Description

Technical Field

[0001] The invention relates to a diffuse reflection material optical property measurement technology, and in particular to a method for obtaining a diffuse reflection material BRDF for laser spot measurement. Background Art

[0002] In common optical bands, almost all surfaces in nature, such as the ground and the sea, can be regarded as random rough surfaces, and their scattering properties have always been a hot topic of research. The analytical calculation model and method for accurately obtaining the material BRDF (bidirectional reflectance distribution function) are very important for remote sensing, lidar, computer imaging, virtual reality, and computer vision.

[0003] In the field of laser parameter measurement applications, using a camera to shoot the laser scattered light spot on the diffuse reflection screen is a common measurement method. Since the surface of the diffuse reflection screen is not an ideal Lambertian body in actual applications, the scattered light intensity in different directions is different, which introduces a large measurement error. It is urgent to establish an accurate and reliable BRDF scattering characteristic model and calculation method of the material under laser irradiation, which will provide a theoretical basis for subsequent research on improving the accuracy of parameter measurement, and can also be used to study the information of the rough surface itself. There are many models and many acquisition methods for describing the BRDF of a rough surface, which can basically be divided into empirical models, pure theoretical models and experimental models, but they are all relatively complicated in application. Although experimental data can be fitted based on existing models, the process is complicated and time-consuming. Summary of the invention

[0004] The present invention provides a method for obtaining the BRDF of a diffuse reflection material for laser spot measurement, which is used to solve the problem that the current BRDF scattering characteristic model and calculation method under laser irradiation have large errors, and the integration process of the existing model is complicated and time-consuming.

[0005] The present invention obtains a material BRDF analytical model based on the surface infinitesimal slope probability distribution function and the Torrance-Sparrow model theory, and verifies the model with experimental measurement to obtain the material BRDF characteristics, which can greatly improve the accuracy and cost-effectiveness of obtaining the BRDF characteristics of rough surfaces, reduce the complexity of the process, and meet the characteristics research and structural optimization design needs of complex rough diffuse reflection material structures.

[0006] In order to achieve the above object, the technical solution of the present invention is as follows:

[0007] The method for obtaining the BRDF of diffuse reflection materials for laser spot measurement is special in that it includes the following steps:

[0008] Step 1, according to the Torrance-Sparrow model, obtain the height distribution function W and spatial coherence function ρ of the random rough surface of the diffuse reflection material;

[0009] Step 2, according to the random rough surface height distribution function W of the diffuse reflection material, the micro-element orientation probability distribution R of the diffuse reflection material is obtained:

[0010] Step 3: Calculate θ based on the reflection principle a and φ a The expression of (θ a ,φ a ) is substituted into the microelement orientation probability distribution R to obtain the probability density distribution function P of the material's mirror reflection part;

[0011] Among them, θ a is the angle between the surface normal of the diffuse reflection material and the z-axis of the vertical coordinate system, φ a is the angle between the surface element normal and the xy plane of the vertical coordinate system;

[0012] Step 4, substitute the probability density distribution function P of the material's specular reflection part into the Torrance-Sparrow model to obtain the expression of the material's BRDF;

[0013] Step 5: Use the scattered light intensity measurement experimental platform to measure the incident light intensity E i (θ i ,φ i ) and the scattered light intensity E r (θ r ,φ r ) to obtain the specific value of the material BRDF;

[0014] Substitute the specific value of the material BRDF into the expression of the material BRDF obtained in step 4, and calculate the average slope r of the microelement surface and the value ρ of the scattering part of the microelement surface. d / π is fitted by the least square method. After multiple iterations of fitting, the average slope r of the diffuse reflection material microelement surface and the value ρ of the microelement surface scattering part in the expression of the material BRDF are obtained. d / π, and then obtain the specific expression of the material's BRDF.

[0015] Furthermore, in step 1, according to the Torrance-Sparrow model, it is assumed that the rough surface is composed of a series of symmetrical V-grooves whose scale is much larger than the wavelength of the incident laser, the height value of any point on the rough surface is normally distributed, and the average height value is selected as z=0. At this time, the expressions of the height distribution function W and the spatial coherence function ρ of the random rough surface of the diffuse reflection material are as follows:

[0016]

[0017]

[0018] in, is the mean square error of height distribution, D is the lateral scale of the diffuse reflector;

[0019] β represents the independent variable of the spatial coherence function;

[0020] z represents the height value of the scattering element, which is the z coordinate of the vertical coordinate system;

[0021] x represents the lateral scale of the scattering element and is the x-coordinate of the vertical coordinate system.

[0022] Furthermore, in step 2, assuming that the microelement surface distribution is uniform and isotropic, the expression of the microelement orientation probability distribution R is as follows:

[0023]

[0024] Among them, r = σ / τ is the average slope of the microelement surface;

[0025] τ is the autocorrelation length, and its value is the β value when the autocorrelation function ρ(β)=ρ(0) / e, which represents the lateral scale value of the V-groove microelement.

[0026] Further, in step 3, the θ a and φ a The expression is as follows:

[0027]

[0028]

[0029] The expression of the probability density distribution function P of the specular reflection part of the material is as follows:

[0030]

[0031] Among them, θ i is the angle between the incident light and the z-axis of the vertical coordinate system, φ i is the angle between the incident light and the xy plane of the vertical coordinate system, θ r is the angle between the reflected light and the z-axis of the vertical coordinate system, φ r is the angle between the incident light and the xy plane of the vertical coordinate system.

[0032] Furthermore, in step 4, it is assumed that the incident light is unpolarized and the incident light Reflected light and the microelement surface normal On the same plane, the material BRDF expression f is obtained by the following formula r (θ i ,φ i ,θr ,φ r as follows:

[0033]

[0034] Among them, GAF is the geometric occlusion factor of the microelement;

[0035]

[0036] R s is the material surface reflectivity;

[0037]

[0038] n+ik is the complex refractive index of the material surface; θ i ' is the local incident angle of the microelement;

[0039]

[0040] ρ d / π is the partial expression of the scattering of the material microelement surface;

[0041] r is the average slope of the material element surface.

[0042] Furthermore, in step 5, according to the scattered light intensity E r (θ r ,φ r ) and the incident light intensity E i (θ i ,φ i ) are as follows, and we get f r (θ i ,φ i ,θ r ,φ r )’s specific value:

[0043]

[0044] Among them, L is the distance from the measurement point to the infinitesimal element;

[0045] L r is the scattered irradiance per unit area. Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] 1. The present invention realizes the accurate acquisition of BRDF of diffuse reflection materials. The theoretical derivation is based on the surface microelement slope probability distribution function and Torrance-Sparrow model, comprehensively considering the characteristics of the light source and factors such as material specular reflection, scattering, absorption and occlusion, and combining a large amount of experimental data for fitting verification, thus realizing the acquisition of BRDF of diffuse reflection materials with high fidelity.

[0047] 2. The diffuse reflection material BRDF of the present invention can be applied to transparent medium materials, absorption materials and multi-layer transparent / absorption composite materials by simply changing the reflectivity expression.

[0048] 3. The BRDF of the diffuse reflection material of the present invention is theoretically derived based on non-polarized light. By changing the reflectivity expression of different polarization states, it can be applied to different polarization states.

[0049] 4. The diffuse reflection material BRDF of the present invention can be applied to the ultraviolet to infrared spectrum range by simply changing the reflectivity.

[0050] 5. The experimental data of the BRDF characteristics of the diffuse reflection material of the present invention are fitted using the least squares method, and the corresponding parameters are obtained through multiple iterations, which has high accuracy and a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the geometric relationship of the bidirectional reflection function BRDF of the diffuse reflection material in the present invention when the laser is incident;

[0052] Figure 2 This is a comparison diagram of the BRDF characteristic measurement and fitting results of a typical absorbing material in the present invention at a set angle;

[0053] Figure 3 This is a comparison chart of the BRDF characteristic measurement and fitting results of a typical transparent medium material in the present invention at a set angle. DETAILED DESCRIPTION

[0054] The present invention is further described with reference to the accompanying drawings and specific implementation modes.

[0055] A method for obtaining the BRDF of diffuse reflection materials for laser spot measurement. The bidirectional reflection function BRDF describes the distribution of reflected light intensity on a rough surface under different incident and reflection angles.

[0056] The scattering of light Figure 1 As shown, assuming that the light is incident on a plane with a normal of The surface element dA is reflected, and the incident light The angle is (θ i ,φ i ), reflecting light The angle is (θ r ,φ r ), surface elements The angle is (θ a ,φ a ). Among them, θ i is the angle between the incident light and the z-axis of the vertical coordinate system, φ iis the angle between the incident light and the xy plane of the vertical coordinate system, θ r is the angle between the reflected light and the z-axis of the vertical coordinate system, φ r is the angle between the incident light and the xy plane of the vertical coordinate system, θ a is the angle between the surface element normal and the z-axis of the vertical coordinate system, φ a is the angle between the surface element normal and the xy plane of the vertical coordinate system, then the BRDF can be defined as

[0057] In the above formula is the incident irradiance per unit area;

[0058] is the diffuse irradiance per unit area;

[0059] Φ i and Φ r are the incident laser power and the outgoing laser power on area dA respectively.

[0060] When the laser is incident on the surface of a diffuse reflective material, the steps for calculating the bidirectional reflectance function BRDF are as follows:

[0061] Step 1: According to the Torrance-Sparrow model, it is assumed that the rough surface is composed of a series of symmetrical V-grooves whose scale is much larger than the wavelength of the incident laser. The height value of any point on the rough surface is normally distributed, and the average height value is z = 0. At this time, the height distribution function W and the spatial coherence function ρ of the random rough surface of the diffuse reflection material can be expressed as:

[0062]

[0063]

[0064] in, is the mean square error of height distribution, D is the lateral scale of the diffuse reflector;

[0065] z represents the height value of the scattering element, which is the z coordinate of the vertical coordinate system;

[0066] x represents the lateral scale of the scattering element and is the x-coordinate of the vertical coordinate system.

[0067] Step 2, assuming that the surface distribution of the microelement is uniform and isotropic, derive formula 1 to obtain the microelement orientation probability distribution R:

[0068]

[0069] Among them, r = σ / τ is the average slope of the microelement surface, and the autocorrelation length τ is the β value when the autocorrelation function ρ(β) = ρ(0) / e, which represents the lateral scale value of the V-groove microelement.

[0070] Step 3: Based on the reflection principle, θ can be obtained by calculation. a and φ a The expression of the local microelement angle (θ a ,φ a ) is substituted into formula 3 to obtain the probability density distribution function P of the specular reflection part of the material:

[0071]

[0072]

[0073]

[0074] Step 4: Substitute Formula 4 into the Torrance-Sparrow model, assuming that the incident light is unpolarized and that Reflected light and the microelement surface normal On the same plane, the material BRDF distribution is obtained by theoretical derivation as follows:

[0075]

[0076] in,

[0077]

[0078] is the geometric occlusion factor of the microelement;

[0079]

[0080] is the material surface reflectivity;

[0081] n+ik is the complex refractive index of the material surface;

[0082] is the local angle of incidence on the microelement;

[0083] ρ d / π is the partial expression of the scattering of the material microelement surface;

[0084] r is the average slope of the material element surface.

[0085] Step 5, Experimental Fitting

[0086] Establish a scattered light intensity measurement experimental platform to measure the incident light intensity E i (θ i ,φ i ) and scattered light intensity E r (θ r ,φ r ) relationship, and calculate f according to Formula 6 r (θi ,φ i ,θ r ,φ r )

[0087]

[0088] Where L is the distance from the measurement point to the infinitesimal element dA.

[0089] In the experiment, the laser source irradiates the surface of the diffuse reflective material at different incident angles, and the scattering measurement system is used to obtain the intensity data of the scattered light in different angle directions. In the experiment, the incident light and the measured scattered light are in the same plane and perpendicular to the sample.

[0090] According to formula 6, we can get f r (θ i ,φ i ,θ r ,φ r ), the measurement results are fitted by the least square method based on the above formula 5, and the average slope r of the material microelement surface and the value ρ of the microelement surface scattering part are obtained after multiple iterations of fitting. d / π, and then obtain the BRDF characteristic parameter f of the material r (θ i ,φ i ,θ r ,φ r ).

[0091] Figure 2 and Figure 3 The theoretical and experimental results of the BRDF characteristics of typical absorbing materials and transparent dielectric materials at set angles are given, verifying that the data obtained by the reflection function is in good agreement with the experimental results.

[0092] In the diffuse reflection material BRDF for laser spot measurement, by replacing the reflectivity expression corresponding to the material, the BRDF can also be applied to the calculation of the corresponding material. For example, if the reflectivity expression is changed to transparent medium material, the BRDF is the bidirectional reflection distribution function of transparent medium material. Similarly, absorption materials and multi-layer transparent / absorption composite materials can also be directly replaced and used.

[0093] The diffuse reflection material BRDF for laser spot measurement can be applicable to the ultraviolet to infrared spectral range or different polarization states by only changing the reflectivity expression or the reflectivity expression of different polarization states.

Claims

1. A method for obtaining BRDF of diffuse reflection materials for laser spot measurement, characterized in that: The following steps are involved: Step 1, according to the Torrance-Sparrow model, obtain the height distribution function W and spatial coherence function ρ of the random rough surface of the diffuse reflection material; In step 1, according to the Torrance-Sparrow model, it is assumed that the rough surface is composed of a series of symmetrical V-shaped grooves whose scale is much larger than the wavelength of the incident laser, the height value of any point on the rough surface is normally distributed, and the average height value is selected as z=0. At this time, the expressions of the height distribution function W and the spatial coherence function ρ of the random rough surface of the diffuse reflection material are as follows: in, is the mean square error of height distribution, D is the lateral scale of the diffuse reflector; β represents the independent variable of the spatial coherence function; z represents the height value of the scattering element, which is the z coordinate of the vertical coordinate system; x represents the lateral scale of the scattering element, which is the x-coordinate of the vertical coordinate system; Step 2, according to the random rough surface height distribution function W of the diffuse reflection material, the micro-element orientation probability distribution R of the diffuse reflection material is obtained: In step 2, assuming that the microelement surface distribution is uniform and isotropic, the expression of the microelement orientation probability distribution R is as follows: Among them, r = σ / τ is the average slope of the microelement surface; τ is the autocorrelation length, and its value is the β value when the autocorrelation function ρ(β)=ρ(0) / e, which represents the lateral scale value of the V-shaped groove microelement; Step 3: Calculate θ based on the reflection principle a and φ a The expression of (θ a ,φ a ) is substituted into the microelement orientation probability distribution R to obtain the probability density distribution function P of the material's mirror reflection part; Among them, θ a is the angle between the surface normal of the diffuse reflection material and the z-axis of the vertical coordinate system, φ a is the angle between the surface element normal and the xy plane of the vertical coordinate system; In step 3, the θ a and φ a The expression is as follows: The expression of the probability density distribution function P of the specular reflection part of the material is as follows: Among them, θ i is the angle between the incident light and the z-axis of the vertical coordinate system, φ i is the angle between the incident light and the xy plane of the vertical coordinate system, θ r is the angle between the reflected light and the z-axis of the vertical coordinate system, φ r is the angle between the incident light and the xy plane of the vertical coordinate system; Step 4, substitute the probability density distribution function P of the material's specular reflection part into the Torrance-Sparrow model to obtain the expression of the material's BRDF; In step 4, it is assumed that the incident light is unpolarized and the incident light Reflected light and the microelement surface normal On the same plane, the material BRDF expression f is obtained by the following formula r (θ i ,φ i ,θ r ,φ r )as follows: Among them, GAF is the geometric occlusion factor of the microelement; R s is the material surface reflectivity; n+ik is the complex refractive index of the material surface; θ i ' is the local incident angle of the microelement; ρ d / π is the partial expression of the scattering of the material microelement surface; r is the average slope of the material microelement surface; Step 5: Use the scattered light intensity measurement experimental platform to measure the incident light intensity E i (θ i ,φ i ) and the scattered light intensity E r (θ r ,φ r ) to obtain the specific value of the material BRDF; In step 5, according to the scattered light intensity E r (θ r ,φ r ) and the incident light intensity E i (θ i ,φ i ) are as follows, and we get f r (θ i ,φ i ,θ r ,φ r )’s specific value: Among them, L is the distance from the measurement point to the infinitesimal element; L r is the diffuse irradiance per unit area; Substitute the specific value of the material BRDF into the expression of the material BRDF obtained in step 4, and calculate the average slope r of the microelement surface and the value ρ of the scattering part of the microelement surface. d / π is fitted by the least square method. After multiple iterations of fitting, the average slope r of the diffuse reflection material microelement surface and the value ρ of the microelement surface scattering part in the expression of the material BRDF are obtained. d / π, and then obtain the specific expression of the material's BRDF.

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