CN114974470A - Method for obtaining diffuse reflection material BRDF for laser spot measurement - Google Patents
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Abstract
The invention particularly relates to a method for acquiring a diffuse reflection material BRDF (bidirectional reflectance distribution function) for laser spot measurement, which is used for solving the problems that the existing BRDF scattering characteristic model and calculation method under laser irradiation have larger errors, and the process of integrating the existing model is complex and the consumed time is longer. The method for obtaining the diffuse reflection material BRDF for laser spot measurement comprises the following steps of 1, obtaining a height distribution function R and a spatial coherence function rho of a random rough surface of the diffuse reflection material according to a model; step 2, deducing and obtaining a infinitesimal orientation probability distribution R according to a height distribution function W of the random rough surface of the diffuse reflection material: step 3, based on the reflection principle, calculating theta a And phi a Substituting the expression of (A) into the infinitesimal orientation probability distribution R to obtain a probability density distribution function P of the specular reflection part of the material; step 4, substituting the probability density distribution function P of the specular reflection part of the material intoDeducing an expression of the BRDF material according to the corresponding model; and 5, fitting the test data to further obtain a BRDF specific expression of the material.
Description
Technical Field
The invention relates to a technology for measuring optical characteristics of a diffuse reflection material, in particular to a method for acquiring a diffuse reflection material BRDF for laser spot measurement.
Background
In the common optical wave band, almost all surfaces in nature such as the ground, the sea, etc. can be regarded as random rough surfaces, and the scattering property thereof is a continuous research focus. Analytical calculation models and methods for accurately obtaining a BRDF (bidirectional reflectance distribution function) are very important in the fields of remote sensing, laser radar, computer imaging, virtual reality, computer vision and the like.
In the field of laser parameter measurement application, a camera is adopted to shoot laser scattering light spots on a diffuse reflection screen, and the diffuse reflection screen surface is not an ideal lambertian body in practical application, so that scattering light intensities in different directions are different, and a larger measurement error is introduced. The description of the rough surface BRDF has a plurality of models and a plurality of obtaining methods, which can be basically divided into an empirical model, a pure theoretical model and an experimental model, but the application is complex. Although the experimental data can be fitted based on existing models, the process is complex and time consuming.
Disclosure of Invention
The invention provides a method for obtaining a diffuse reflection material BRDF (bidirectional reflectance distribution function) for laser spot measurement, which is used for solving the problems that the existing BRDF scattering characteristic model and calculation method under laser irradiation have larger errors, and the process of integrating the existing model is complex and the consumed time is longer.
The BRDF analytical model is obtained by derivation based on the surface infinitesimal slope probability distribution function and the Torrance-spark model theory, and the experimental measurement and verification model is combined to obtain the BRDF characteristics of the material, so that the acquisition precision and the cost-effectiveness ratio of the BRDF characteristics of the rough surface can be greatly improved, the process complexity is reduced, and the requirements of characteristic research and structure optimization design of the structure of the complex rough diffuse reflection material are met.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the method for obtaining the diffuse reflection material BRDF for measuring the laser spots is characterized by comprising the following steps of:
step 2, obtaining the micro-element orientation probability distribution R of the diffuse reflection material according to the height distribution function W of the random rough surface of the diffuse reflection material:
step 3, based on the reflection principle, calculating theta a And phi a Is expressed by (θ) a ,φ a ) Substituting the obtained solution into the infinitesimal orientation probability distribution R to obtain a probability density distribution function P of the specular reflection part of the material;
wherein, theta a Is the included angle phi between the normal of the surface infinitesimal of the diffuse reflection material and the z axis of a vertical coordinate system a Is the included angle between the normal of the surface infinitesimal and the xy plane of the vertical coordinate system;
step 4, substituting the probability density distribution function P of the specular reflection part of the material into a Torrance-spark model to obtain an expression of the BRDF;
step 5, respectively measuring the incident light intensity E through a scattered light intensity measurement experiment platform i (θ i ,φ i ) Specific value of (2) and scattered light intensity E r (θ r ,φ r ) Obtaining a specific value of the BRDF material;
substituting the specific value of the material BRDF into the expression of the material BRDF obtained in the step 4, and carrying out the average slope r of the obtained infinitesimal surface and the value rho of the scattering part of the infinitesimal surface d Performing least square fitting on the material/pi, and performing multiple iterative fitting to obtain the diffuse reflection material in the expression of the material BRDFMean slope r of surface of infinitesimal element and value rho of scattering part of surface of infinitesimal element d And the specific value of/pi, and further obtaining a BRDF specific expression of the material.
Further, in step 1, according to the Torrance-spark model, assuming that the rough surface is composed of a series of symmetrical V-shaped grooves with a size much larger than the wavelength of the incident laser, the height of any point on the rough surface is normally distributed, and the average height is selected to be 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 specifically as follows:
wherein the content of the first and second substances,
is the height distribution mean square error, D is the transverse dimension of the diffuse reflection material;
beta represents a spatial coherence function argument;
z represents the height value of the scattering infinitesimal and is the z coordinate of a vertical coordinate system;
and x represents the transverse dimension of the scattering infinitesimal and is the x coordinate of a vertical coordinate system.
Further, in the step 2, assuming that the distribution of the surface of the infinitesimal elements is uniform and isotropic, the expression of the infinitesimal orientation probability distribution R is as follows:
wherein r is sigma/tau is the infinitesimal surface average slope;
τ is an autocorrelation length, and a value thereof is a value β when the autocorrelation function ρ (β) is ρ (0)/e, and represents a lateral scale value of a V-groove infinitesimal.
Further, in step 3, θ a And phi a The expression of (c) is as follows:
the expression of the probability density distribution function P of the specular reflection part of the material is as follows:
wherein, theta i Is the angle between the incident ray and the z-axis of the vertical coordinate system i Is the angle between the incident ray and the xy-plane of the vertical coordinate system, theta r Is the angle between the reflected ray and the z-axis of the vertical coordinate system, phi r Is the angle between the incident ray and the xy plane of the vertical coordinate system.
Further, in step 4, it is assumed that the incident light is unpolarized, and the incident light is not polarized
Reflected light
And the surface normal of the infinitesimal element
On the same plane, obtaining the material BRDF expression f by the following formula r (θ i ,φ i ,θ r ,φ r The following were used:
wherein, GAF is a geometric occlusion factor of a infinitesimal element;
R s is the material surface reflectivity;
n + ik is the complex refractive index of the material surface; theta i ' is the local angle of incidence of the infinitesimal;
ρ d the/pi is a material infinitesimal surface scattering part expression;
and r is the average slope of the surface of the material element.
Further, in the step 5, according to the scattered light intensity E r (θ r ,φ r ) Specific value of (2) and incident light intensity E i (θ i ,φ i ) The following relationship between specific values of (A) to (B) yields f r (θ i ,φ i ,θ r ,φ r ) Specific values of (a):
wherein L is the distance from the measurement point to the infinitesimal;
L r is the scattered irradiance per unit area. Compared with the prior art, the invention has the following beneficial effects:
1. the invention realizes the accurate acquisition of the BRDF, the theoretical derivation is based on the probability distribution function of the surface infinitesimal slope and the Torrance-spark model, the factors such as the light source characteristic, the material specular reflection, the scattering, the absorption and the shielding are comprehensively considered, and the fitting verification is carried out by combining a large amount of experimental data, thereby realizing the acquisition of the BRDF with high fidelity.
2. The BRDF can be applied to transparent medium materials, absorption materials and multilayer transparent/absorption composite materials only by changing the reflectivity expression.
3. The BRDF is theoretically derived based on unpolarized light, and can be suitable for different polarization states by changing the reflectivity expressions of different polarization states.
4. The BRDF can be applied to the range from ultraviolet to infrared spectra only by changing the reflectivity.
5. According to the invention, the BRDF characteristic experiment data of the diffuse reflection material is fitted by adopting a least square method, and corresponding parameters are obtained through multiple iterations, so that the accuracy is high, and the application range is wide.
Drawings
FIG. 1 is a schematic diagram of the geometrical relationship of the bidirectional reflectance function BRDF of the diffuse reflection material of the present invention when laser is incident;
FIG. 2 is a graph comparing BRDF characterization and fit results at set angles for a typical absorbent material of the present invention;
fig. 3 is a graph comparing BRDF characteristics measurements and fitting results of typical transparent dielectric materials of the present invention at a set angle.
Detailed Description
The invention is further described with reference to the accompanying drawings and the detailed description.
A method for obtaining diffuse reflection material BRDF for laser spot measurement, the bidirectional reflection function BRDF describes the distribution of the reflection light intensity of the rough surface under different incidence and reflection angles.
Light is scattered as shown in FIG. 1, assuming that the light is incident on a normal line
Is reflected and incident light is reflected
Is (theta) i ,φ i ) Reflected light ray
Is (theta) r ,φ r ) Surface infinitesimal element
Is (theta) a ,φ a ). Wherein, theta i Is the angle between the incident ray and the z-axis of the vertical coordinate system, phi i Is the angle between the incident ray and the xy plane of the vertical coordinate system, theta r Is the angle between the reflected ray and the z-axis of the vertical coordinate system, phi r Is the angle between the incident ray and the xy-plane of the vertical coordinate system, theta a Is the angle between the normal of the surface infinitesimal and the z-axis of the vertical coordinate system, phi a Is the angle between the normal of the surface infinitesimal and the xy plane of the vertical coordinate system, the BRDF can be defined as
In the above formula
Is the incident irradiance per unit area;
Φ i and phi r The incident laser power and the outgoing laser power are respectively on the area dA.
The calculation steps of the bidirectional reflection function BRDF when laser is incident on the surface of the diffuse reflection material are as follows:
wherein the content of the first and second substances,
is the height distribution mean square error, and D is the transverse dimension of the diffuse reflection material;
z represents the height value of the scattering infinitesimal and is the z coordinate of a vertical coordinate system;
and x represents the transverse dimension of the scattering infinitesimal and is the x coordinate of a vertical coordinate system.
Step 2, assuming uniform and isotropic distribution of the surface of the infinitesimal, deducing a formula 1 to obtain the infinitesimal orientation probability distribution R:
where r ═ σ/τ is the mean slope of the surface of the infinitesimal, and the autocorrelation length τ is the value β when the autocorrelation function ρ (β) ═ ρ (0)/e, and represents the transverse scale value of the V-groove infinitesimal.
Step 3, based on the reflection principle, obtaining theta according to calculation a And phi a Expression of (a), the local infinitesimal angle (θ) a ,φ a ) Substituting into formula 3 and obtaining the probability density distribution function P of the specular reflection part of the material:
and 4, substituting the formula 4 into a Torrance-spark model, assuming that the incident light is unpolarized and the incident light is not polarized
Reflected light
And the surface normal of the infinitesimal element
In the same plane, the BRDF distribution of the material is obtained by theoretical derivation:
wherein the content of the first and second substances,
is the geometric occlusion factor of the infinitesimal;
is the material surface reflectivity;
n + ik is the complex refractive index of the material surface;
ρ d the/pi is a material infinitesimal surface scattering part expression;
and r is the average slope of the surface of the material element.
Step 5, fitting experiment
Establishing a scattered light intensity measurement experiment platform for respectively measuring incident light intensity E i (θ i ,φ i ) And intensity of scattered light E r (θ r ,φ r ) Relation, and calculating according to equation 6 to obtain f r (θ i ,φ i ,θ r ,φ r )
Where L is the distance of the measurement point from the infinitesimal dA.
In the experiment, the laser source irradiates the surface of the diffuse reflection material at different incidence angles, the scattering measurement system is utilized to obtain the intensity data of the scattering light in different angle directions, and the incident light and the measuring scattering light are in the same plane and perpendicular to the sample in the experiment.
F is obtained from equation 6 r (θ i ,φ i ,θ r ,φ r ) Based on the formula 5, least square fitting is carried out on the measurement result, and the average slope r of the material infinitesimal surface and the numerical value rho of the scattering part of the infinitesimal surface are obtained through multiple iterative fitting d Phi, and further obtaining BRDF characteristic parameter f of the material r (θ i ,φ i ,θ r ,φ r )。
Fig. 2 and fig. 3 show the BRDF characteristic theory and experimental results of typical absorbing materials and transparent dielectric materials under a set angle, and verify that the data obtained by the reflection function has a good fit with the experimental results.
In the diffuse reflection material BRDF for laser spot measurement, the reflectivity expression corresponding to the material is replaced, the BRDF can also be suitable for the calculation of the corresponding material, for example, the reflectivity expression is changed into a transparent medium material, and the BRDF is a bidirectional reflection distribution function of the transparent medium material. Similarly, the absorbing material and the multi-layer transparent/absorbing composite material can be directly replaced for use.
The diffuse reflection material BRDF for measuring the laser spots can be suitable for the ultraviolet to infrared spectrum range or the situations of different polarization states only by changing the reflectivity expression or the reflectivity expressions of the situations of different polarization states.
Claims (6)
1. The method for obtaining the diffuse reflection material BRDF for measuring the laser spots is characterized by comprising the following steps of:
step 1, obtaining a height distribution function W and a spatial coherence function rho of a random rough surface of a diffuse reflection material according to a Torrance-spark model;
step 2, obtaining the infinitesimal orientation probability distribution R of the diffuse reflection material according to the height distribution function W of the random rough surface of the diffuse reflection material:
step 3, based on the reflection principle, calculating theta a And phi a Is expressed by (θ) a ,φ a ) Substituting the obtained solution into the infinitesimal orientation probability distribution R to obtain a probability density distribution function P of the specular reflection part of the material;
wherein, theta a Is the included angle phi between the normal of the surface infinitesimal of the diffuse reflection material and the z axis of a vertical coordinate system a Is the included angle between the normal of the surface infinitesimal and the xy plane of the vertical coordinate system;
step 4, substituting the probability density distribution function P of the specular reflection part of the material into a Torrance-spark model to obtain an expression of the BRDF;
step 5, respectively measuring the incident light intensity E through a scattered light intensity measurement experiment platform i (θ i ,φ i ) Specific value of (2) and scattered light intensity E r (θ r ,φ r ) Obtaining a specific value of the BRDF material;
substituting the specific value of the material BRDF into the expression of the material BRDF obtained in the step 4, and carrying out the average slope r of the obtained infinitesimal surface and the value rho of the scattering part of the infinitesimal surface d Performing least square fitting on the/pi, and performing multiple iterative fitting to obtain the average slope r of the surface of the diffuse reflection material infinitesimal element and the value rho of the scattering part of the surface of the infinitesimal element in the expression of the material BRDF d And the specific value of/pi, and further obtaining a BRDF specific expression of the material.
2. The method according to claim 1, wherein in step 1, according to a torance-spark model, it is assumed that the rough surface is composed of a series of symmetrical V-shaped grooves whose dimensions are much larger than the wavelength of the incident laser, the height of any point on the rough surface is normally distributed, and the average height is selected to be z-0, and 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 specifically as follows:
wherein the content of the first and second substances,
is the height distribution mean square error, D is the transverse dimension of the diffuse reflection material;
beta represents a spatial coherence function argument;
z represents the height value of the scattering infinitesimal and is the z coordinate of a vertical coordinate system;
and x represents the transverse dimension of the scattering infinitesimal and is the x coordinate of a vertical coordinate system.
3. The method for acquiring the diffuse reflection material BRDF for laser spot measurement according to claim 1 or 2, wherein in the step 2, assuming that a surface distribution of the infinitesimal elements is uniform and isotropic, an expression of the infinitesimal element orientation probability distribution R is as follows:
wherein, r ═ σ/τ is the infinitesimal surface average slope;
τ is an autocorrelation length, and a value thereof is a value β when the autocorrelation function ρ (β) is ρ (0)/e, and represents a lateral scale value of a V-groove infinitesimal.
4. The diffuse reflection for laser spot measurement according to claim 3The method for obtaining the BRDF material is characterized in that in the step 3, the theta is a And phi a The expression of (a) is as follows:
the expression of the probability density distribution function P of the specular reflection part of the material is as follows:
wherein, theta i Is the angle between the incident ray and the z-axis of the vertical coordinate system i Is the angle between the incident ray and the xy-plane of the vertical coordinate system, theta r Is the angle between the reflected ray and the z-axis of the vertical coordinate system, phi r Is the angle between the incident ray and the xy plane of the vertical coordinate system.
5. The method for acquiring the diffuse reflection material BRDF for laser spot measurement according to claim 4, wherein in step 4, the incident light is assumed to be unpolarized, and the incident light is assumed to be unpolarized
Reflected light
And infinitesimal surface normals
On the same plane, obtaining the material BRDF expression f by the following formula r (θ i ,φ i ,θ r ,φ r ) The following were used:
wherein, GAF is a geometrical shielding factor of a infinitesimal element;
R s is the material surface reflectivity;
n + ik is the complex refractive index of the material surface; theta' i Is a local angle of incidence of the infinitesimal;
ρ d the/pi is a material infinitesimal surface scattering part expression;
and r is the average slope of the surface of the material element.
6. The method for acquiring the diffuse reflection material BRDF for laser spot measurement according to claim 5, wherein in step 5, the intensity E of the scattered light is determined according to the intensity of the scattered light r (θ r ,φ r ) Specific value of (2) and incident light intensity E i (θ i ,φ i ) The following relationship between specific values of (a) to (b) yields f r (θ i ,φ i ,θ r ,φ r ) Specific values of (a):
wherein L is the distance from the measurement point to the infinitesimal;
L r is a unit surfaceThe product scatter irradiance.
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