JP2003329586A - Method and apparatus for predicting specular glossiness - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate the refractive index of the surface of a sample in the case that the refractive index of the sample is not known in consideration of the heterogeneity of physical properties and to quantitatively estimate specular glossiness from both the surface structure of the sample and the estimated refractive index. <P>SOLUTION: The three-dimensional structure of the surface of the sample is measured to acquire height distribution data (step S1). A surface shape parameter is extracted on the basis of the height distribution data (step S2). A one- dimensional variable-angle reflectivity distribution is measured (step S4). A one-dimensional variable-angle reflectivity observed data is acquired, and the effective reflectivity of the surface of the sample is acquired on the basis of the surface shape parameter and the one-dimensional variable-angle reflectivity data (step S5). The specular glossiness is computed on the basis of the surface shape parameter and the effective reflectivity (step S6). <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a specular glossiness prediction method and a specular glossiness prediction device for estimating the reflectance of an object surface by a simulation technique based on a parameter representing the surface shape.

[0002]

[Prior art]

When the light reflection characteristic on an object having a rough surface such as a printed image is mainly caused by surface scattering, the surface roughness and the gradient distribution, which are the characteristic quantities related to the surface structure, are distributed. The dependence is known by the theory of rough surface scattering. In the surface scattering theory, it is assumed that the material surface has Fresnel reflection and is composed of an assembly of minute mirror surfaces oriented under a specific property. Derive rate distribution characteristics.

The reflectance is uniquely determined by giving the wavelength of the light source, the parameter relating to the surface structure, and the refractive index to the function representing the reflectance characteristic. Here, the surface structure can be directly measured by a three-dimensional structure measuring device such as a laser microscope, STM, and AFM. Regarding the refractive index, in the case of materials made of transparent materials, the method of obtaining from the Brewster angle (critical angle), the material is dipped in a transparent liquid of known refractive index, and the optical behavior at the refractive index interface is used to determine the refractive index. Can be obtained, and in the case of a sample whose surface is optically smooth, it can be obtained from the Fresnel reflectance.

However, the above method is not always applicable to an object having a rough surface that has a glossy feeling and is an object of measurement or analysis of specular gloss.

[0005]

In the method of estimating the refractive index of a rough surface object by the "refractive index measuring method and measuring device" disclosed in Patent Document 1, the area of the minute mirror surface to be formed is smaller than the wavelength of the light source. It can be applied only to a sample having a sufficiently large size and uniform properties. Therefore, since the refractive index is unknown and the surface properties of the object are not always uniform over the entire surface, the specular glossiness cannot be quantitatively predicted from the surface properties of the object.

The present invention has been made in view of the above problem, and when the refractive index of the sample is unknown, the refractive index of the sample surface is estimated by considering the non-uniformity of the physical properties of the sample, It is an object of the present invention to provide a specular glossiness prediction method and a specular glossiness prediction device capable of quantitatively estimating the specular glossiness from the surface structure of the sheet and the estimated refractive index and analyzing the glossiness of the printing surface and the like. .

[0007]

In order to achieve the above object, the first aspect of the present invention is to measure the three-dimensional structure of a sample surface to obtain height distribution data, and to obtain the height distribution data. Extracting surface shape parameters based on
The step of measuring the one-dimensional gonio-reflectance distribution and acquiring the one-dimensional gonio-reflectance actual measurement data, and acquiring the effective refractive index of the sample surface based on the surface shape parameter and the one-dimensional gonio-reflectance distribution data There is provided a specular glossiness prediction method comprising: a step; and a step of calculating a specular glossiness based on a surface shape parameter and an effective refractive index. In the first aspect of the present invention, the surface shape parameter is extracted based on the local height distribution data obtained by performing the inclination correction on the height distribution data in the vicinity of a predetermined position within a predetermined region of the sample surface. It is preferable. In addition to this, it is more preferable to extract the surface shape parameter based on height distribution data of a region having a size of 2 to 4 times the wavelength of the visible wavelength region near a predetermined location. This makes it possible to extract an effective feature amount (surface shape parameter) of the three-dimensional structure of the sample surface that affects the reflection characteristics in the wavelength region of the light source. Further, it is possible to obtain a more accurate surface shape parameter.

Further, in the above first aspect of the present invention,
Measures the one-dimensional gonio-reflectance distribution and acquires the one-dimensional gonio-reflectance distribution measurement data, acquires the one-dimensional gonio-reflectance distribution data based on the surface shape parameters, and measures the one-dimensional gonio-reflectance distribution measurement. It is preferable to acquire the effective refractive index based on the data and the one-dimensional variable-angle reflectance distribution data. In addition to this, the height distribution data is divided into a plurality of regions, and the one-dimensional goniogonal reflection is calculated based on the goniogonal reflection distribution function determined according to the surface shape parameter and the refractive index extracted for each region. More preferably, the rate distribution data is acquired.
By estimating the effective refractive index by comparing the calculated values of the one-dimensional variable-angle reflectance distribution data with the measured data of the one-dimensional reflectance distribution, the effective refractive index can be estimated even for a sample with an unknown refractive index. Is possible. In addition, for example, by calculating the one-dimensional gonio-reflectance based on the divided height distribution data and finally averaging it, the specular glossiness of the sample with non-uniform surface texture can be calculated using the one-dimensional gonio-reflectance data. It can be estimated.

In the first aspect of the present invention, the one-dimensional variable-angle reflectance distribution is measured to obtain the one-dimensional variable-angle reflectance distribution actual measurement data, and the Fresnel reflectance function and a plurality of parameters determined by the refractive index are obtained. The numerical value of the parameter variable is determined and determined based on the one-dimensional gonio-reflectance distribution data based on the gonio-reflectance distribution function represented by the product of the shape distribution functions having variables and the one-dimensional gonio-reflectance distribution data. It is preferable to obtain the effective refractive index based on the shape distribution function to which the numerical values of the parameter parameters are applied. By estimating the effective refractive index by comparing the calculated values of the one-dimensional variable-angle reflectance distribution data with the measured data of the one-dimensional reflectance distribution, the effective refractive index can be estimated even for a sample with an unknown refractive index. Is possible.

Further, in the above first aspect of the present invention,
The incident light flux having a predetermined aperture angle is incident on the sample surface from the light source at a predetermined incident angle, and is reflected by the sample surface in the specular reflection direction to be captured within the predetermined aperture angle. It is possible to obtain a predetermined refractive index and a surface shape parameter and a variable-angle reflection distribution function determined according to the surface shape parameter, and obtain a specular glossiness based on the light quantity of the incident light flux and the light quantity of the received light flux. preferable. In addition to this, it is more preferable to divide the height distribution data into a plurality of regions and acquire the specular glossiness based on the surface shape parameter extracted for each region. By calculating the specular glossiness based on the divided height distribution data and finally averaging the specular glossiness, it is possible to quantitatively estimate the specular glossiness even for a sample having a non-uniform surface texture.

In order to achieve the above object, as a second aspect of the present invention, a height distribution measuring means for measuring a three-dimensional structure of a sample surface and outputting height distribution data, and height distribution data are provided. Based on the surface shape parameter extraction means for extracting the surface shape parameter, a primary gonioreflectance distribution measuring means for measuring the one-dimensional gonioreflectance distribution, an effective refractive index acquisition means for acquiring the effective refractive index, and a mirror surface. A specular glossiness predicting apparatus having a specular glossiness acquisition means for acquiring glossiness. In the second aspect of the present invention, the surface shape parameter extraction means, based on the local height distribution data obtained by performing inclination correction on the height distribution data in the vicinity of a predetermined position in a predetermined region of the sample surface, It is preferable to extract the surface shape parameters. In addition to this, it is more preferable that the surface shape extraction means extracts the surface shape parameter based on height distribution data of a region having a size of 2 to 4 times the wavelength of the visible wavelength region near a predetermined location. . This makes it possible to extract an effective feature amount (surface shape parameter) of the three-dimensional structure of the sample surface that affects the reflection characteristics in the wavelength region of the light source. Further, it is possible to obtain a more accurate surface shape parameter.

In the second aspect of the present invention, the effective refractive index acquisition means is a one-dimensional variable angle reflectance distribution data calculating means for calculating the one-dimensional variable angle reflectance distribution data and the one-dimensional variable angle reflectance data. And a one-dimensional variable reflectance distribution means for measuring and obtaining the one-dimensional variable reflectance obtained by applying the surface shape parameter calculated by the surface shape parameter extracting means to the one-dimensional variable reflectance distribution data calculating means. It is preferable to acquire the effective refractive index based on the angular reflectance data and the one-dimensional variable angle reflectance distribution actual measurement data acquired by the one-dimensional variable angle reflectance distribution means. In addition to this, the one-dimensional gonio-reflectance distribution data calculation means divides the height distribution data into a plurality of areas, and is determined according to the surface shape parameter and the refractive index value extracted for each area. More preferably, the gonio reflectance distribution data is calculated based on the gonio reflectance distribution function. By estimating the effective refractive index by comparing the calculated values of the one-dimensional variable-angle reflectance distribution data with the measured data of the one-dimensional reflectance distribution, the effective refractive index can be estimated even for a sample with an unknown refractive index. Is possible. In addition, for example, by calculating the one-dimensional gonio-reflectance based on the divided height distribution data and finally averaging it, the specular glossiness of the sample with non-uniform surface texture can be calculated using the one-dimensional gonio-reflectance data. It can be estimated.

Further, in the second aspect of the present invention, the effective refractive index acquiring means actually measures and acquires the one-dimensional gonioreflectance distribution data, and obtains the Fresnel reflectance function and a plurality of parameter variables determined by the refractive index. The numerical values of the parameter variables were determined and determined based on the one-dimensional gonio-reflectance distribution data based on the gonio-reflectance distribution function represented by the product of the shape distribution functions and the one-dimensional gonio-reflectance distribution data. It is preferable to obtain the effective refractive index based on the shape distribution function to which the numerical value of the parameter variable is applied. By estimating the effective refractive index by comparing the calculated values of the one-dimensional variable-angle reflectance distribution data with the measured data of the one-dimensional reflectance distribution, the effective refractive index can be estimated even for a sample with an unknown refractive index. Is possible.

Further, in the second aspect of the present invention, the specular glossiness acquiring means causes an incident light beam having a predetermined opening angle to be incident on the sample surface from the light source at a predetermined incident angle in a specular reflection direction on the sample surface. The light quantity of the received light flux reflected and captured within the predetermined opening angle is obtained based on the effective refractive index or the predetermined refractive index, and the surface shape parameter and the variable-angle reflection distribution function determined according to the surface shape parameter. ,
It is preferable to acquire the specular glossiness based on the light quantity of the incident light flux and the light quantity of the received light flux. In addition to this, it is further preferable that the specular glossiness acquisition unit divides the height distribution data into a plurality of regions and acquires the specular glossiness based on the surface shape parameters extracted for each region.
By calculating the specular glossiness based on the divided height distribution data and finally averaging the specular glossiness, it is possible to quantitatively estimate the specular glossiness even for a sample having a non-uniform surface texture.

Further, the three-dimensional structure of the sample surface is measured to obtain height distribution data, surface shape parameters are extracted based on the height distribution data, and the extracted surface shape parameters and a predetermined effective refractive index are obtained. The specular glossiness may be calculated based on this.

When extracting this surface shape parameter,
Surface specular parameters can be extracted for each block under predetermined conditions based on the height distribution data of multiple blocks divided into predetermined sizes, and specular gloss can be quantitatively estimated even for samples with non-uniform surface properties. And

Further, the surface shape parameters are the RMS surface roughness which is the standard deviation of the height data in the area having the predetermined block size, and the neighboring area size around each coordinate in the area having the predetermined block size. It is desirable that the specular glossiness be calculated by using a set of RMS gradients that are root mean squares regarding a gradient distribution on a plane that fits the height distribution data.

Further, when calculating the surface glossiness, a reference value of a look-up table which uses as data the specular glossiness calculated by adding the surface shape parameter and the effective refractive index in a predetermined numerical value range and a predetermined step size. Based on, the surface shape parameter and the specular gloss for the effective refractive index may be acquired.

Furthermore, the block size, the neighborhood area size, and the effective refractive index are optimized based on the specular glossiness calculated for a plurality of samples and the specular glossiness measured for the same plurality of samples. It is advisable to acquire a specific block size, neighboring region size, and effective refractive index.

[0020]

BEST MODE FOR CARRYING OUT THE INVENTION A first embodiment in which the present invention is preferably implemented will be described. FIG. 1 shows an example of the processing flow of the specular glossiness prediction method according to the present invention. First, the three-dimensional structure of the sample surface is measured to measure height distribution data (step S1). Next, the surface shape parameter is extracted from the height distribution data (step S2). Subsequently, the one-dimensional variable angle reflectance distribution is measured to obtain one-dimensional variable angle reflectance distribution actual measurement data, and it is determined whether or not there is refractive index data (step S3). When the refractive index data of the sample does not exist (step S3 / no data), surface shape parameters and one-dimensional gonioreflectance distribution data are obtained (step S3).
4) Extract the effective refractive index of the sample surface (step S
5). Then, the specular glossiness is obtained based on the surface shape parameter and the effective refractive index (step S6). On the other hand, when the refractive index data of the sample exists (step S3 / with data), the specular glossiness is calculated based on the known refractive index data and the surface shape parameter (step S6).

Here, the variable angle reflectance distribution function model used during the series of processing shown in FIG. 1 will be described. As the variable-angle reflectance distribution function, for example, a variable-angle reflectance distribution function which is derived from the rough surface scattering theory by beckmann and is improved later can be applied. This is a combination of RMS surface roughness and gradient RMS as a pair of surface shape parameters that are the wavelength of the light source and the feature amount of the surface structure, or a combination of RMS surface roughness and autocorrelation length, incident angle, reflection angle (observation position). It is a function with the angle to the direction) and the refractive index as parameters. Specifically, the Fresnel reflectance considering the statistical properties of the rough surface,
It is expressed by the product of the scattering coefficient, which represents the attenuation of coherency due to the rough surface, and the attenuation factor of the attenuation rate due to shadowing. This function can also be applied to a scale in which the area of the micro mirror surface is equal to or smaller than the wavelength of the light source. For an unpolarized light source, this function is shown in equation (1).

[0022]

[Equation 1]

In this equation, ρ is a reflectance having a unit of [1 / Sr] (Sr: steradian). F is
It is the Fresnel reflectance for the average plane of the sample. F
The product of G and G represents the reflectance of the minute reflecting surface whose normal line is oriented in the dichotomous direction of the incident light vector and the observation direction vector. D is a scattering coefficient in the case where the minute reflection surface is formed according to a Gaussian distribution, and shows coherence attenuation due to the phase of the light source being disturbed by the unevenness of the surface. S is
The shadowing function, Smith (IEEE Transcations on
Antenas and Propergation, AP15 (5), 1967, 668-671). The shadowing function is a function in which the incident angle or the angle of the observation position becomes approximately 1 at an angle close to vertical, and can be replaced with a constant 1 when the 20-degree specular gloss is calculated by approximation.
Hereinafter, the variable-angle reflectance distribution function is indicated by R, and the surface shape parameter is indicated by f. As another example of the variable-angle reflectance distribution function, a Torrance-Sparrow model [Torance and Sp
arrow: Journal of the Optical Society of America, 57
(1967) 1105-1114], Cook-Torransce model [ACM Tran
Scatter on Graphics, 1 (1982) 7-24], etc., it is possible to approximate and apply any reflection model that requires parameters that characterize the surface shape of an object.

The process of extracting the surface shape parameter will be described. A three-dimensional shape measuring device such as a laser microscope is used to measure the three-dimensional structure of the sample surface, and height distribution data is obtained as multi-tone image data or array data extracted from the image data. When the sample surface has uniform statistical properties, a Gaussian distribution is obtained for the height distribution and a Rayleigh distribution is obtained for the gradient distribution. Since the length scale for glossiness is around the wavelength of the light source, the resolution in the depth (height) direction should be smaller than 1/4 of the wavelength range of the light source assumed in the calculation of specular glossiness described later. (For example, 0.05μ
m). The lateral magnification is set so that the actual scale between adjacent data elements of the height distribution data is at least the wavelength of the light source or less. For example, the height distribution scale is 1024 ×
In the case of the 768 rectangular data elements, if the magnification is set so that the actual scale of the long side is 300 μm, the actual scale interval between adjacent data elements will be about 0.3 μm, which satisfies the condition.

A set of surface shape parameters f is calculated from the height distribution data in a single region, taking the case where the surface shape parameter f in the variable angle reflectance distribution function is RMS surface roughness σ ₀ and RMS gradient μ as an example. A method for doing so will be described with reference to the flowchart shown in FIG. As preprocessing of the entire height distribution data, preprocessing such as noise removal depending on the properties of the three-dimensional shape measuring apparatus and inclination correction for the entire area is performed (step S21). The local inclination correction is performed by obtaining a plane that fits the height data near the N × N data element of the data element around each point (x, y) in the area where the surface shape parameter is to be extracted (step S22). ). Next, the local RMS surface roughness and the local gradient are obtained (step S23). Step S
22 and step S23 are repeated a predetermined number of times, and then the average value of the local RMS surface roughness in the entire region is calculated to obtain the RMS surface roughness σ ₀ , and the average value of the local RMS gradient in the entire region is calculated. The RMS slope μ is calculated and calculated (step S24). The surface shape parameter extraction method described above makes it possible to accurately extract the surface shape parameter of the sample surface.

The effect of making the actual size of the region near the target for the local inclination correction twice or four times the wavelength used for the light source will be described. For example, if the wavelength of the light source is 550 nm
In this case, if the actual size of the neighborhood area is set to 1.5 μm, when the actual scale between adjacent data elements of the height distribution data is 0.3 μm, the size of the neighborhood of N × N data elements should be N = 5. . According to the definition of RMS surface roughness (σ ₀ ), in an extreme case, when a locally optically smooth curved surface has a large waviness structure or a step, an excessively large value compared with the wavelength of the light source. May be obtained. However, if the size of the neighboring region is set to the above condition and the parameters of the surface shape are extracted, an effective value can be obtained.

An example of processing for extracting the effective refractive index will be described with reference to the flowchart of FIG. Bending angle reflectance distribution measuring device (diffusion rate meter or BR
When a given incident angle, for example, a specular gloss of 60 degrees is obtained by a DF measuring device), a one-dimensional reflected light intensity distribution obtained by one-dimensionally scanning the reflection angle with respect to the incident angle of 60 degrees. The data R _meas (θ _r ) is obtained (step S31). For example, 1.2 is given as an initial value to the unknown refractive index (step S32), and the known surface shape parameter f is subjected to the one-dimensional variable angle by the calculation method of the one-dimensional variable angle reflectance distribution data described later. The reflectance distribution data R _calc (θ _r ) is obtained at intervals of a predetermined reflection angle, for example, at intervals of 1 degree (step S33). This is compared with the one-dimensional variable angle reflection intensity distribution data R _meas (θ _r ) obtained by the measurement (step S34). R _meas (θ _r ) and R _calc
If it is not determined that (θ _r ) matches (step S34 / mismatch), the refractive index is reset (step S3).
5) and proceeds to step S33. On the other hand, if R _meas (θ _r ) and R _calc (θ _r ) match (step S34 /
Matching), the current refractive index is output as the effective refractive index (step S36), and the process ends.

As a criterion for determining the coincidence between R _meas (θ _r ) and R _calc (θ _r ), for example, the sum of squares of the differences between the one-dimensional variable angle reflectance distribution data for each reflection angle is minimized. To determine the unknown refractive index, an optimization method such as the Marquardt method may be applied. However, if the calculated effective refractive index is out of the preset range as the common sense value of the refractive index of the object, an error message is output and all the processes are terminated, or the default value is preset as a default. Alternatively, the value of the refractive index may be a temporary effective refractive index.

An example of processing for calculating the one-dimensional variable-angle reflectance distribution data will be described with reference to the flowchart shown in FIG. The area A of the given height distribution data is divided into m areas which do not overlap each other, and the divided areas A (k) (k =
1 to m) are obtained (step S41). For example, when the height data has a data size of 1024 × 768 and the actual scale of the long side is 300 μm, 8 × 6 rectangular areas (each 1
28 × 128 (30 μm square) rectangular area).
Next, the surface shape parameter f (k) (k = 1 to m) for the divided area A (k) is extracted (step S4).
2).

Subsequently, each surface shape parameter f (k), given incident angle (θ _i , φ _i ) and effective refractive index nef.
The gonioreflectance distribution function with f and f as parameters, R (θ _i , φ _i , θ _r , φ _r , f (k), neff,
λ) φ _i = 180 °, φ _r = 0 °, one-dimensional gonio-reflectance data in which the reflectance θ _r is changed at an angle step Δθ, R _k (θ _j ) = R (θ _i , φ _i , θ _r = θ _j , φ _r , f
(K), neff, λ) (k = 1 to _m , θ _j = jΔθ) is calculated (step S43).

Then, the arithmetic mean for each angle in the entire region is calculated by the equation (2), and is output as step S44) and the one-dimensional variable angle reflectance distribution data R (θ _j ) of the sample surface (step S45). .

[0032]

[Equation 2]

According to the above processing, a more accurate reflectance distribution can be estimated by performing the averaging operation when the reflection characteristics or geometrical statistical properties of the sample surface are not uniform.

An example of processing for extracting the effective refractive index will be described. The one-dimensional variable angle reflectance distribution is measured to obtain the one-dimensional variable angle reflectance distribution measured data. Next, one-dimensional gonio-reflectance data based on the gonio-reflectance distribution function represented by the product of the Fresnel reflectance function having the refractive index as a parameter and the shape distribution function having a plurality of parameter variables The numerical value of the parameter variable given to the shape distribution function is obtained from the relationship with the actual data of the rate distribution. Further, the effective refractive index is obtained based on the determined shape distribution function. For example, according to the refractive index measuring method according to Patent Document 1, the Fresnel reflectance function F (θ) of the formula (3) and the shape distribution function G of the formula (4).
(Φ) is applied.

[0035]

[Equation 3]

[0036]

[Equation 4]

Here, θ is the incident angle and reflection angle in specular reflection, φ is the angle in the normal direction of the micro rough surface on the sample surface, and n is the refractive index. Further, g and σ are shape distribution functions G
(Φ) Fitting parameter, which determines the specific shape.

The gonioreflectance distribution function R (θ, φ) is given by F
An example will be described in which the product of (θ) and G (φ) is defined as R (θ, σ) = F (θ) G (φ). First, the fitting parameters g and σ are obtained based on the one-dimensional variable angle reflection distribution measurement data for a plurality of incident angles. Next, from the relationship between the shape distribution function G (φ) determined by g and σ, the variable-angle reflectance distribution function R (θ, φ), and the one-dimensional variable-angle reflectance distribution actual measurement data, fitting is performed. The refractive index in the Fresnel reflectance function F (θ) is calculated. By the above processing, the effective refractive index can be estimated when the surface shape is unknown.

An example of processing for calculating the specular gloss will be described. JISZ8 is shown in FIGS. 5 (a), (b), and (c).
The geometrical conditions in the measuring device in the specular glossiness measuring method defined by 741 are shown. The light flux passing from the light source 51 through the light source side opening 52 (AI) having a predetermined opening angle is collimated by the lenses 53 a and 53 b and reaches the sample surface 54. Reflected light including specular reflected light and diffused light from the sample surface 54 is condensed by the lens 55.
Of the collected light, the light that has passed through the light receiver side opening 56 (AR) having a predetermined opening angle reaches the light receiver 57.
At that time, the image of the light source aperture 52 is defined by the lens 55 so as to form a predetermined opening angle on the aperture surface of the light receiver side aperture 56 (FIG. 5B). For example, in FIG.
As shown in (c), the opening angle of the aperture determined in the case of 60-degree specular gloss is α1 ′ = 0.75 ± 0.10 ° β1 ′ = 2.5 ± 0.1 ° α2 = 4.4 ± 0.1 ° β2 = 11.7 ± 0.1 °.

A method of obtaining the light intensity of the light flux reaching the light receiver 57 under the above geometric conditions will be described. Here, since the solid angle α1 ′ formed by the light source side opening 52 is sufficiently small, the light beam emitted from the light source is approximated by a light beam having no width. Further, the light flux passing through the light receiver side opening 56 and reaching the light receiver 57 is approximated by the light flux directly reaching the light receiver side opening 56 without passing through the lens 55. Since the light reaching the sample surface 54 actually has a finite area, it is necessary to consider all the scattered light having different positions in the irradiation region, but the opening angle α2 of the light receiver side opening 56 is small. Is approximated by a light beam scattered from one point on the sample surface 54 and reaching the light receiver 57 at a solid angle formed by the light receiver side opening 56. Under the above approximation, the variable-angle reflection distribution function R (θ _i , for a given set of shape parameters and effective refractive index,
φ _i , θ _r , φ _r , f, n, λ)
The light intensity P _s detected by the light receiver 57 is obtained by integrating the light flux reflected from one point and passing through the light receiver side opening 56 as shown in equation (5).

[0041]

[Equation 5]

The light intensity of the light source 51 is arbitrary, and the light receiver 57
Based on the relationship between the light intensity Ps detected by (1) and the specular reflection light intensity P _0s from the reference surface, a predetermined incidence
The specular gloss G _s (θ) with respect to the reflection angle (θ) is obtained.

[0043]

[Equation 6]

The reference specular reflectance G _0s (θ) is a Fresnel reflectance having a specific refractive index independent of wavelength, specifically, a refractive index of 1.567. For example, in the case of 60-degree specular gloss, approximately G _0s (θ) = 0.1. The above process yields a set of shape parameters extracted from a given sample and specular reflectance for the effective index of refraction.

An example of processing for calculating the specular gloss will be described with reference to the flowchart shown in FIG. First, the area A of the given height distribution data is divided into n areas that do not overlap each other, and the divided areas A (k) (k = 1 to
n) is obtained (step S61). Next, the divided area A
The surface shape parameter for (k) is extracted (step S62). Then, the surface shape parameter f (n)
(N = 1 to m) and the specular gloss G based on the effective refractive index
_n (θ) is calculated (step S63). Then, the arithmetic mean value is calculated as shown in Expression (7) (step S6).
4) and outputs the result as the specular glossiness estimated for the entire area A.

[0046]

[Equation 7]

On an actual sample surface, the surface structure is not uniform even within a region of 1 mm square or less, the height distribution data is not always ideal, and Gaussian distribution may be superimposed. Therefore, by averaging, an accurate estimated value of specular gloss can be obtained. When the surface shape parameter f (k) is extracted for the divided area (FIG. 4, step S41) equivalent to the processing for calculating the one-dimensional variable reflectance distribution data, the surface shape parameter obtained in step S42 is used. By using f (k) as it is, the processes of step S61 and step S62 can be omitted.

FIG. 7 shows the structure of the specular glossiness prediction apparatus according to the present invention and the data flow during operation. The specular gloss predicting apparatus according to the present invention includes a height distribution measuring unit 1 (for example,
Laser microscope, three-dimensional shape measuring device such as AFM and STM), surface shape extraction parameter 2, effective refractive index extracting means 3, one-dimensional gonio-reflectance distribution measuring means 4 (for example, diffusion distribution meter or BRDF measuring device) (Reflectance measuring device), specular specular glossiness calculating means 5 and refractive index data selecting means 6. The operation when the specular glossiness prediction device performs the process of the flow of FIG. 1 will be described. The height distribution data measuring means 1 obtains height distribution data 11 on the sample surface (step S1). The surface shape parameter 12 is obtained by the surface shape parameter extraction means 2 based on the height distribution data 11 (step S2). The refractive index data selecting means 17 determines whether or not the refractive index data of the sample exists (step S3). When the refractive index of the sample exists (step S3 / with data), the specular gloss calculation unit 5 calculates the specular gloss 15 based on the known refractive index data 16 and the surface shape parameter 12, and the process ends. (Step S6). On the other hand, when there is no refractive index data (step S3 / no data), the one-dimensional variable-angle reflectance distribution measuring means 4 obtains the one-dimensional variable-angle reflectance distribution data 14 for a specific incident angle (step S).
4). Then, the effective refractive index extracting unit 3 calculates the effective refractive index 13 based on the shape parameter 12 and the one-dimensional variable angle reflectance distribution data 14 (step S5). Then, the specular gloss 15 is calculated based on the obtained effective refractive index 13 and the surface shape parameter 12 (step S
6), the process ends. As a result, even if the sample has an unknown refractive index, the specular gloss can be estimated using the refractive index estimated based on the surface shape parameter.

When estimating the specular glossiness, the three-dimensional structure of the sample surface is measured to measure height distribution data, surface shape parameters are extracted from the measured height distribution data, and the extracted surface shape is measured. The specular glossiness may be obtained based on the parameter and a predetermined effective refractive index.

The processing in this case will be described with reference to the flowchart of FIG. First, the area A of the measured height distribution data is equally divided into N areas which do not overlap each other, and are set as blocks B (k) (k = 1 to N) as shown in FIG. 9 (step S72). Next, the surface shape parameter for the block B (k) is extracted (step S73). The surface shape parameters are RMS surface roughness σ (k) and RM.
It consists of a set of S gradients μ (k).

This surface shape parameter σ (k), μ
As shown in the flowchart of FIG. 10, the process of extracting (k) is, as preprocessing for the height distribution data of the target region A, noise removal depending on the property of the three-dimensional shape measuring apparatus and inclination correction for the entire region. Such pre-processing is performed (step S81), the standard deviation of the height data in the target area B (k) is calculated, and the RMS surface roughness σ is extracted (step S82). Next, a predetermined height distribution data area B
For each point (x, y) in (k), the slope Slope of the plane that fits the height data of the neighborhood area of the predetermined size L _N
(X, y) is calculated (step S83), and Slope (x, y
The square of y) is sequentially added to calculate the sum of squares (step S84). The calculation of the sum of squares of Slope (x, y) is repeatedly executed for all points (x, y) in the target area B (k), and then the average square root of the sum of squares of Slope (x, y) is calculated. The RMS gradient μ is calculated and extracted (step S85).

The advantages of extracting the RMS gradient μ in this way will be described. When calculating the slope Slope (x, y), the data resolution (Δx, Δy), for example, Δx =
Height data H sampled at Δy = 0.3 μm intervals
By the difference method based on (x, y), for example, the following equation (8),

[0053]

[Equation 8]

When the specular glossiness is calculated by the RMS gradient μ obtained for the gradient distribution calculated by, the value is considerably lower than the actually measured value. This is because the gradient obtained by the method based on the equation (8) is estimated to be larger than the effective gradient sensitive to light, and as a result, the specular glossiness is calculated to be low. Each point when calculating Slope (x, y)
Obtaining a plane that fits the height distribution in the neighborhood of a predetermined size L _N around (x, y) and setting the slope of the plane as the target Slope (x, y) means that the resolution is the size L.
It corresponds to the reduction to _N, and corresponds to the scattering of light with respect to the slope distribution of the slope having such a size. Further, the RMS surface roughness σ changes in the extracted value depending on the block size L _B of the extraction target area and the statistical characteristics of the height data, and the RMS gradient μ indicates the extraction target area. Block size L _B and the neighborhood size L
_{Since N} and the value extracted depending on the statistical characteristics of the height data have the property of changing, the block size L _B and the neighboring region size L _N are given a degree of freedom, and optimized for the measured specular glossiness. By doing so, highly accurate surface shape parameters can be obtained.

This extracted surface shape parameter σ
The specular gloss G (k) is calculated based on (k), μ (k) (k = 1 to N) and the effective refractive index n _E (step S7).
4). After repeating the same processing for all blocks B (k) (loop L71), the arithmetic mean value is calculated as shown in Expression (9) (step S75), and the result is estimated for the entire area A. It is output as the specular glossiness (step S75).

[0056]

[Equation 9]

The effect of dividing the height distribution data into a plurality of blocks having a predetermined block size L _B and calculating the specular gloss will be described. The height distribution data of the data size S is transferred to the block B of the area S (k).
(K), and RMS surface roughness σ (k) and RMS gradient μ are used as surface shape parameters for each block B (k).
(K) is extracted, the specular glossiness G _S (k) is calculated based on the extracted surface shape parameter, and the area weight is added as shown in Expression (9) to add the specular glossiness. obtained average value <G _S>, even if the statistical properties of the surface state or the height distribution data of the specimen is not uniform, it is possible to obtain a highly precise specular gloss. Further, in the process of calculating the specular glossiness of the block B (k), if an inappropriate result is obtained due to measurement noise or the like, or an error due to it is generated, the block is rejected and is subjected to averaging. By performing processing such as not performing, it is possible to obtain a more accurate result.

Further, when the specular gloss is calculated, the RMS surface roughness σ and RMS are determined by a predetermined numerical range and numerical interval.
A specular surface obtained by applying a three-dimensional vector (σ (i _X ), μ (i _Y ), n _E (i _Z )) having the MS gradient μ and the effective refractive index n _E as elements to specular gloss calculation. A three-dimensional lookup table T _G (σ (i _X ), μ (i _Y ), n _E (i
_Z )) should be created in advance. Then, when the specular glossiness is calculated, a lookup table T _G (σ is set for predetermined three-dimensional vector data (σ, μ, n _E ).
(i _X ), μ (i _Y ), n _E (i _Z )) is referred to and three-dimensional interpolation processing is performed to obtain specular gloss data. As this interpolation processing method, a linear interpolation method such as a trilinear method or a higher-order interpolation method such as a cubic spline method can be applied. Here, the predetermined three-dimensional vector data (σ,
When μ, n _E ) exceeds the numerical range given in advance, the specular glossiness may be calculated directly without referring to the look-up table. The specular glossiness calculated when creating this lookup table changes gently with respect to numerical changes in the surface shape parameters and effective refractive index, so even if linear interpolation is applied, the specular glossiness can be achieved with high accuracy and at high speed. It is possible to get the degree.

Next, the effective refractive index n_EAnd block size L
_BAnd neighborhood area size L_NAs an example of the process to obtain the optimization of
Based on the flowchart shown in FIG. 11 and FIG.
explain. For example, the data element whose height data is 1024 × 768
If there is a height data, as shown in Fig. 3 (a)
Length of one side (block size) L_BEqually divided into squares
Then L_BTo the power of 2 L_B= 2^PBAnd later
Processing becomes easy. L _BFor example, the range of 16 to 1
28 (P_B= 4 to 7) (loop L91). next,
Neighborhood area size L_NAs the minimum value to the closest element
Distance L_N= 1 or more, the maximum value of the adjacent block
One side size L_BUp to Even if the shape of the neighborhood area is
If one side length L_NIf the square area of is
Is L_N= 3, the maximum value is L_N= 2L_BYou can set it to +1
(Loop L92). The shape of the neighborhood is limited to square
However, as shown in FIG. 3B, the radius L
_NIt can be a circle. In this case, the neighborhood area size L_NMaximum of
Value is L_BIt should be done. Block size L_B(Loop L
91) and the neighborhood area size L_N(Loop L92) and multiple
Loops that sequentially give height data for each sample (loop
L93), a subroutine SUB1 (step
S94) for processing the height data of a given sample
Block size L_BAnd the neighborhood area size L_NAnd effective refraction
Rate n_EGet the specular gloss under. Next, regarding each sample
Calculated specular gloss and the measured specular gloss
The error is evaluated more (step S95). In particular,
Specular gloss G measured for N samples_MEAS 
(i) (i = 1 to N) and calculated for the corresponding sample
Specular gloss G_CALCFor (i) (i = 1 to N)
Then, as the error evaluation function E, for example, as an absolute error,
The mean square error shown in the following formula (10) is used as the error evaluation function.
To calculate.

[0060]

[Equation 10]

As the error evaluation function, the RMS ratio error represented by the following equation (11) or (1
You may employ | adopt the average absolute value ratio error shown in Formula (2). This error evaluation function may be appropriately selected as a target accuracy scale.

[0062]

[Equation 11]

Finally, all block sizes L_BAnd the neighborhood
Area size L_NAnd the effective refractive index n _EPair of
The error evaluation function E is minimized.
Is L_BAnd the neighborhood area size L_NAnd the effective refractive index n_EDecided
Set (step S96).

Next, the processing in the subroutine SUB1
An example will be described based on the flowchart shown in FIG.
Height data is size L_BDivided into blocks (step
S102), regarding height data of each block B (k)
The surface shape parameters (σ (k), μ (k)) of
(Step S103). For all divided blocks
After repeated processing (loop L101), the effective bending
Folding rate n_EIncrement value Δn _EAs a small enough value, for example
Δn_E= 0.01, n_E= 1 + Δn_EIn the range of ~ 2.00
Shake (loop L105). Effective refractive index n_EThe upper limit of
It is not limited to 2. This effective refractive index n_ENomono
And the shape parameters (σ (k), μ
(K)) repeated (loop L104), specular light
Calculate the roughness (step S106), and finally specular gloss
Are averaged and the processing of the subroutine SUB1 ends (
Step S107).

Here, the height data at a plurality of locations within the area where the glossiness was measured for the same sample is measured, and the glossiness calculated for each height data is arithmetically averaged to obtain the glossiness. The influence of variations such as unevenness can be suppressed. In addition, by the method described above, the specular glossiness is calculated for a plurality of samples made of the same kind of material and having different glossinesses, and the error is minimized by comparing with the specular glossiness obtained by actual measurement. By obtaining the so-called optimized effective refractive index n _E , block size L _B, and neighboring region size L _N , and calculating the specular gloss under these conditions, the actual refractive index The specular gloss can be acquired without measurement.

[0066]

As is clear from the above description, according to the present invention, the refractive index of the sample surface is estimated when the refractive index of the sample is unknown while considering the non-uniformity of the physical properties of the object. ,
The specular gloss can be quantitatively estimated from the surface structure of the sample and the estimated refractive index. For example, in electrophotography, it becomes possible to predict the specular glossiness from the working conditions such as fixing temperature, fixing pressure, fixing speed, etc., and it is used for gloss analysis as part of the function of the total simulator of the image forming apparatus. Can be applied.

When estimating the specular gloss, the three-dimensional structure of the sample surface is measured to measure the height distribution data,
The surface shape parameter is extracted from the measured height distribution data, and the specular glossiness is calculated based on the extracted surface shape parameter and a predetermined effective refractive index, thereby considering the non-uniformity of the physical properties of the sample surface. The effective refractive index is extracted without directly measuring the refractive index of, and the specular glossiness can be quantitatively estimated from the surface structure of the sample and the extracted effective refractive index. Furthermore, it becomes possible to estimate the local specular glossiness for a small area where the specular glossiness cannot be measured, for example, a small area of 1 mm ² or less, and it can be used for analyzing uneven glossiness of printed matter and the like.

[Brief description of drawings]

FIG. 1 is a flowchart showing a processing flow of a specular glossiness prediction method according to the present invention.

FIG. 2 is a flowchart showing an example of processing for measuring height distribution data.

FIG. 3 is a flowchart showing an example of processing for extracting an effective refractive index.

FIG. 4 is a flowchart showing an example of processing for calculating one-dimensional variable-angle reflectance distribution data.

FIG. 5 is a diagram showing geometrical conditions in a measuring device in a specular glossiness measuring method defined in JIS Z8741.

FIG. 6 is a flowchart showing an example of a process of calculating a specular glossiness.

FIG. 7 is a diagram showing a configuration and a data flow during operation of the specular glossiness prediction device according to the present invention.

FIG. 8 is a flowchart showing another process of specular glossiness prediction.

FIG. 9 is a schematic diagram showing divided areas of height distribution data.

FIG. 10 is a flowchart showing an RMS gradient calculation process.

FIG. 11 is a flowchart showing an optimization process of an effective refractive index, a block size, and a neighboring region size.

FIG. 12 is a flowchart showing a subroutine process of an optimization process.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1; Height distribution measuring means, 2; Surface shape extracting means, 3; Effective refractive index extracting means, 4; One-dimensional variable angle reflectance distribution measuring means, 5; Specular gloss calculating means, 6; Refractive index data selecting means , 51; light source, 52; light source side aperture, 53a, 53b, 55; lens, 54; sample surface, 56;
Light receiving side aperture, 57; light receiver

Claims (23)

[Claims] 1. A step of measuring a three-dimensional structure of a sample surface to obtain height distribution data, extracting a surface shape parameter based on the height distribution data, and measuring a one-dimensional gonio-reflectance distribution. A step of acquiring one-dimensional variable-angle reflectance measured data; a step of acquiring an effective refractive index of the sample surface based on the surface shape parameter and the one-dimensional variable-angle reflectance distribution data; And a step of calculating a specular gloss on the basis of the effective refractive index. 2. The surface shape parameter is extracted based on local height distribution data obtained by subjecting height distribution data in the vicinity of a predetermined position in a predetermined region of the sample surface to inclination correction. The specular glossiness prediction method according to claim 1. 3. The surface shape parameter is extracted based on height distribution data of a region having a size that is twice to four times the wavelength of a visible wavelength region near a predetermined location. Specular gloss prediction method. 4. The one-dimensional variable-angle reflectance distribution is measured to obtain the one-dimensional variable-angle reflectance distribution actual measurement data, and the one-dimensional variable-angle reflectance distribution data is acquired based on the surface shape parameter. The specular glossiness prediction method according to claim 1, wherein the effective refractive index is acquired based on the one-dimensional variable angle reflectance distribution actual measurement data and the one-dimensional variable angle reflectance distribution data. 5. The height distribution data is divided into a plurality of regions, and the one-dimensional shape is calculated based on the variable-angle reflection distribution function determined according to the surface shape parameter and the refractive index extracted for each region. The specular glossiness prediction method according to claim 4, wherein the variable angle reflectance distribution data is acquired. 6. The one-dimensional variable-angle reflectance distribution is measured to obtain the one-dimensional variable-angle reflectance distribution actual measurement data, and a Fresnel reflectance function determined by a refractive index and a shape distribution function having a plurality of parameter variables are obtained. One-dimensional gonio reflectance distribution data based on the gonio reflectance distribution function represented by the product, and determine the numerical value of the parameter variable based on the one-dimensional gonio reflectance distribution data, of the confirmed parameter variable The specular glossiness prediction method according to claim 1, wherein the effective refractive index is acquired based on the shape distribution function to which a numerical value is applied. 7. A received light flux which is reflected in the specular reflection direction on the sample surface by being incident on the sample surface from a light source with an incident light flux having a predetermined opening angle and is captured within the predetermined opening angle. The amount of light is acquired based on the effective refractive index or a predetermined refractive index, and the surface shape parameter and the variable-angle reflection distribution function determined according to the surface shape parameter, and the amount of light of the incident light flux and the amount of light of the received light flux. The specular gloss prediction method according to claim 1, wherein the specular gloss is acquired based on the following. 8. The height distribution data is divided into a plurality of areas, and the specular glossiness is acquired based on the surface shape parameter extracted for each area. Specular gloss prediction method. 9. A step of measuring a three-dimensional structure of a sample surface to obtain height distribution data and extracting a surface shape parameter based on the height distribution data, the surface shape parameter and a predetermined effective refractive index. And a step of calculating a specular glossiness based on the above. 10. The measured height distribution data is divided into a plurality of blocks of a predetermined size, and a surface shape parameter is extracted for each of the height distribution data of the plurality of divided blocks,
The specular gloss prediction method according to claim 9, wherein the specular gloss is calculated based on the extracted surface shape parameter. 11. The surface topography parameter comprises a set of RMS surface roughness and RMS slope, where RMS surface roughness is the standard deviation for height data in a region having a given block size, and RMS slope is 11. The specular glossiness prediction method according to claim 10, wherein the specular glossiness prediction is a root mean square of a gradient distribution of a plane that fits height distribution data of neighboring area sizes around each coordinate in an area having a predetermined block size. 12. When the surface glossiness is calculated, a look-up table whose data is specular glossiness calculated by adding a surface shape parameter and an effective refractive index in a predetermined numerical value range and a predetermined step size is referred to. The specular glossiness prediction method according to claim 9, wherein the specular glossiness with respect to the surface shape parameter and the effective refractive index is acquired based on the value. 13. The block size, the neighborhood area size, and the effective refractive index are based on the specular glossiness calculated for a plurality of samples and the specular glossiness measured for the same plurality of samples, The specular glossiness prediction method according to any one of claims 9 to 12, wherein an optimum block size, a neighboring region size, and an effective refractive index are acquired. 14. Height distribution measuring means for measuring a three-dimensional structure of a sample surface and outputting height distribution data; surface shape parameter extracting means for extracting surface shape parameters based on the height distribution data; It is characterized by having a first-order gonio-reflectance distribution measuring means for measuring a one-dimensional gonio-reflectance distribution, an effective refraction index acquiring means for acquiring an effective refractive index, and a specular glossiness acquiring means for acquiring a specular glossiness. Specular glossiness prediction device. 15. The surface shape parameter extraction means,
15. The surface shape parameter is extracted based on local height distribution data obtained by performing inclination correction on height distribution data near a predetermined position in a predetermined region of the sample surface. The specular glossiness prediction device described. 16. The surface shape extraction means extracts the surface shape parameter based on height distribution data of a region having a size of 2 to 4 times the wavelength of a visible wavelength region near a predetermined location. The specular glossiness prediction device according to claim 15, which is characterized in that. 17. The one-dimensional variable angle reflectance distribution data calculating means for calculating one-dimensional variable angle reflectance distribution data, and the effective refractive index acquisition means for actually measuring and acquiring the one-dimensional variable angle reflectance data. One-dimensional variable angle reflectance data obtained by applying the surface shape parameter calculated by the surface shape parameter extracting means to the one-dimensional variable angle reflectance distribution data calculating means. The specular glossiness prediction apparatus according to claim 14, wherein the effective refractive index is acquired based on the one-dimensional variable-angle reflectance distribution actual measurement data acquired by the one-dimensional variable-angle reflectance distribution means. 18. The one-dimensional gonio-reflectance distribution data calculation means divides the height distribution data into a plurality of regions, and obtains the surface shape parameter and the refractive index value extracted for each region. 18. The specular glossiness prediction device according to claim 17, wherein the variable angle reflectance distribution data is calculated based on the variable angle reflectance distribution function determined accordingly. 19. The effective refractive index acquisition means measures and acquires one-dimensional variable-angle reflectance distribution data, and represents the product of a Fresnel reflectance function determined by the refractive index and a shape distribution function having a plurality of parameter variables. The one-dimensional gonio-reflectance distribution data based on the gonio-reflectance distribution function, and the numerical value of the parameter variable is determined based on the one-dimensional gonio-reflectance distribution data, and the numerical value of the confirmed parameter variable is applied. The specular glossiness prediction apparatus according to claim 14, wherein the effective refractive index is acquired based on the shape distribution function that has been obtained. 20. The specular glossiness acquiring unit reflects an incident light beam having a predetermined opening angle from the light source to the sample surface at a predetermined incident angle, and is reflected in a specular reflection direction on the sample surface to have a predetermined opening angle. The light quantity of the received light flux that is supplemented within is obtained based on the effective refractive index or a predetermined refractive index, and the surface shape parameter and the variable-angle reflection distribution function determined according to the surface shape parameter, and the incident light flux. 15. The specular glossiness prediction device according to claim 14, wherein the specular glossiness is acquired based on the light intensity of the received light flux and the light intensity of the received light flux. 21. The specular glossiness acquisition unit divides the height distribution data into a plurality of areas, and acquires the specular glossiness based on the surface shape parameter extracted for each area. 21. The specular glossiness prediction device according to claim 20. 22. Surface shape parameter extracting means for measuring a three-dimensional structure of a sample surface to obtain height distribution data, and extracting a surface shape parameter based on the height distribution data, the surface shape parameter and a predetermined value. A specular glossiness prediction device, comprising: a specular glossiness calculating means for calculating a specular glossiness based on an effective refractive index. 23. The surface shape parameter extraction means,
The surface shape parameter is extracted based on the height distribution data of a plurality of blocks divided into a predetermined size for each block under a predetermined condition, and the specular glossiness calculation means is based on the extracted surface shape parameter. 23. The specular glossiness prediction device according to claim 22, wherein the specular glossiness is calculated.