JPH07140070A - Method for determining optical characteristic value of recording material - Google Patents

Abstract

PURPOSE:To make it possible to determined the optical characteristic values, e.g. PSF, of recording materials having single layer and multilayer structures easily and correctly as compared with a conventional method. CONSTITUTION:Reflectance R and and transmittance T are measured for the incident light to a recording material. Basic optical characteristic values, e.g. scattering coefficient AS and reflection coefficient PR, are then determined for each layer of the recording material from the measurements by an approximate method, e.g. Monte Carlo method, and then other optical characteristic values, e.g. point-spread-function(PSF), are determined.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optical characteristic value of a recording material used in a printing machine, especially a color copying machine, for example,
The present invention relates to a spread function (hereinafter abbreviated as PSF) measurement method.

[0002]

2. Description of the Related Art Optical characteristics of a recording material such as a scattering coefficient,
The absorption coefficient and the like are emphasized in relation to printing suitability, especially color printing suitability, and the property known as PSF is particularly emphasized. As a method for measuring the PSF, conventionally, a method described in "Optical Technology Handbook" (Asakura Shoten) P250 to P251, that is, a thin light beam is vertically or obliquely incident on the recording material, and the intensity of reflected light on the surface of the recording material is measured. There has been a method in which the distribution is captured as an image such as a CCD or a photograph and deconvoluted with the intensity distribution of incident light to obtain the distribution.

[0003]

A recording material made of paper or the like, which is commonly used at present, is made of fibers such as vegetation. Since incident light is multiple-scattered inside the recording material structure, the light flux is tentatively changed. Even if virtual light having an infinitely small width is incident on the surface of the recording material, the incident light is spread from the surface of the recording material with a spread centering on that position. The intensity distribution of the emitted light at that time on the surface of the recording material is generally called PSF.

The cause of dot gain when printing on a recording material and color bleeding and unnecessary color mixing during color printing is the spread of light due to the above-mentioned internal scattering. Therefore, if the PSF of the recording material can be known, it is possible to predict the dot gain after printing and the degree of color bleeding, and thus the optical characteristics of the recording material, in other words, the printability.

However, the above-mentioned measuring method has a drawback that the optical system is complicated, and the measurement is time-consuming, and the same measurement must be repeated every time the distribution of the measurement angle of the PSF or the incident angle is changed. . In actual measurement, if the angular distribution of reflected light intensity is not symmetrical with respect to the axis perpendicular to the surface of the recording material, or if the angular distribution differs depending on the position, it is difficult to measure, and the optical properties of the recording material are easy to measure. And it was very difficult to grasp accurately.

Many recording materials such as recording sheets or OHP sheets currently used have a multi-layer structure such as a layer having a so-called coat layer on a base material layer, and particularly, With respect to these recording materials, it is extremely difficult to accurately measure various optical characteristic values by the conventional method including the method described above.

The present invention has been made in view of the above circumstances, and its problem is that P is applied to all recording materials.
It is to provide a method of more accurately and easily obtaining optical characteristic values such as SF.

[0008]

According to the present invention, the reflectance (hereinafter referred to as R) and / or the transmittance (hereinafter referred to as T) of a recording material with respect to incident light is measured, and then an approximate calculation is performed from the measured values. Provided is a method for obtaining an optical characteristic value of a recording material, which comprises a step (hereinafter referred to as a first step) of obtaining a basic optical characteristic value of the recording material by an optimization method. Further, according to the present invention, the basic optical characteristic value is further weighted with factors such as the thickness of the entire recording material and the thickness of each layer, if necessary, and further approximate calculation is performed based on these values (hereinafter, the second step). (Hereinafter referred to as a “recording material”).

The method of the present invention comprises one layer, or a base layer and a coat layer such as a coated paper (base layer: fibrous material) or an OHP sheet (base layer: transparent resin layer). The present invention can be applied not only to those having a two-layer structure but also to recording materials having a multilayer structure of three or more layers.

The basic optical characteristic value of the recording material to be obtained in the first step of the method of the present invention is, for example, a scattering coefficient (hereinafter referred to as AS) or a reflection coefficient (hereinafter referred to as PR).
However, the optical characteristic value of the recording material may be either the characteristic of the entire recording material or the characteristic value of each layer, such as the above-mentioned PSF, optical dot gain, spectral reflectance, spectral transmittance, Examples include transparency and whiteness.

The approximate calculation used in the present invention is to reproduce the behavior of light inside the recording material using, for example, the Monte Carlo method or the diffusion equation to calculate the reflectance (R), the transmittance (T), the PSF.
It is for calculating optical characteristic values such as.

FIG. 10 is a conceptual diagram showing the relationship between the basic optical characteristic value, the optical characteristic value and the approximate calculation described above.

The light incident on the surface of the recording material propagates inside the recording material, and in the process, it collides with the internal structure of the recording material many times and is absorbed and scattered. The scattered light is bent in its direction, part of which is emitted again from the front surface of the recording material, and the rest is emitted from the rear surface of the recording material.

As an example, the optical behavior of a recording material having a two-layer structure in the case of front incidence will be described. FIG. 7 shows how light enters the recording material from the front side (FIG. 7A) and then exits (FIG. 7B). The emission on the front side is reflected light, and the emission on the back side is transmitted light. In the example shown in FIG. 7A, 12 light rays are incident. Assuming that the intensities of the respective light rays are equal at the time of incidence and at the time of emission, in this case, 9 out of 12 rays are reflected and 3 out of them are transmitted (FIG. 7 (b)), so that the reflectance is 75%, The transmittance is 25%. FIG. 8 is a diagram showing the orbit in the recording material for one of the light rays in FIG.

The process shown in this example is reproduced as follows by an approximate calculation such as the Monte Carlo method. now,
In the recording material in the model space, the direction in which the incident light collides with a certain recording material structure and is scattered, and the distance traveled until it collides with the next structure are determined using random numbers. It shall decrease at a certain rate. This is repeated in the computer until the light beam is emitted from the recording material, and finally the position, intensity, and
Record the exit angle. By making the number of incident light rays very large, it is possible to obtain a PSF having an arbitrary angular distribution of the recording material.

FIG. 1 shows the outline of the procedure of the method of the present invention, and FIG. 2 shows a concrete example of measurement of R and T.

For example, as shown in FIG. 2, the measurement of R and T is performed by making a light ray 23 vertically incident on the recording material 21 and using the integrating sphere 22 for the reflected light 24 and the transmitted light 25. Next, as the first step in FIG. 1, what actually occurs in the recording material having optical properties represented by R and T is Monte Carlo method, diffusion equation, etc. (optical behavior calculation)
Reproduced by the approximate calculation of A, which is the basic optical characteristic of the recording material.
Find S and PR. In this case, AS is an amount that represents how many times a light beam can be reflected on the inside of the recording material on average while traveling a unit distance, and PR is a case where the light beam collides with the structure inside the recording material and is scattered. Represents the reflectance of. R and T are functions of AS and PR of the recording material, and have a relationship as shown in the following formula.

[0018]

[Equation 1] R = f (AS, PR)

[0019]

## EQU2 ## T = g (AS, PR) In this case, if the recording material has a single-layer structure, there are one AS and one PR, respectively.
If the structure consists of multiple layers, AS and P are provided for each layer.
R is different, and R and T are also different depending on whether the incident light beam is from the recording front surface side or the recording back surface side. Therefore, for example, in FIG.
In the case of such a two-layer structure, the relationship is as in the following equation.

[0020]

## EQU3 ## R ₁ = f ₁ (AS _a , AS _b , PR _a , PR _b )

[0021]

## EQU4 ## R ₂ = f ₂ (AS _a , AS _b , PR _a , PR _b )

[0022]

## EQU5 ## T ₁ = g ₁ (AS _a , AS _b , PR _a , PR _b )

[0023]

## EQU6 ## T ₂ = g ₂ (AS _a , AS _b , PR _a , PR _b ) where AS _a , PR _a , AS _b, and PR _b are AS, PR, and b of the a layer in FIG. 8, respectively. AS and PR of the layer,
R ₁ and T ₁ are R and T for front incidence, and R ₂ and T ₂ are R and T for back incidence. In the case of a structure having three or more layers, the number of characteristic values to be considered increases, but the concept is the same.

However, the functional form (in the above case, f,
Since f ₁ , f ₂ , g, g ₁ and g ₂ ) are unknown, AS and PR cannot be directly obtained from R and T. Therefore, these values are obtained by approximation calculation and optimization methods.

The optical behavior calculation using the Monte Carlo method will be described below as an example of the approximate calculation.

The distance L that a light ray travels before striking one structure and striking the next structure is determined by the following equation.

[0027]

## EQU7 ## L = -log ((RAN) / AS) where RAN is a uniform scattering of 0 to 1. This is a general formula for handling scattering by the Monte Carlo method, but in addition to this, it is also possible to determine the distance using a probability distribution that considers the state of the scatterer.

The traveling direction of the light beam after the collision is randomly determined by a random number. This is one example in which isotropic scattering is modeled, and the direction can be determined by using a probability distribution in which the angular dependence of scattering intensity is taken into consideration.

Next, absorption will be described. a, b, ...
In a recording material composed of m layers of m, when the intensity of the incident light beam is I ₀ , the intensity I of the outgoing light beam is determined using the following formula.

[0030]

[Equation 8] Here, n _a , n _b , ... N _m are the total number of scatterings in each layer of a, b ,. Other than this, an absorption determination method or the like using the total orbital distance can be used.

Next, regarding the optimization method of the first stage, 1
An example in which a recording material having a layered structure is used as an object will be described.

The number of incident light rays is made very large, and the above operation is performed for each light ray. The value R ^* obtained by dividing the total intensity of the light rays emitted from the surface of the recording material by the total intensity of the incident light rays is equal to R, and the total intensity of the light rays emitted from the back through the recording material having the thickness L. Divided by the total intensity of the incident ray, T ^* is T
There is only one set of AS and PR values that match
Therefore, by obtaining this value, AS and PR, which are values representative of the optical properties of the recording material, are determined.

As an example of the method of obtaining AS and PR, given these initial values, appropriate initial values AS ^* and PR ^* are given ^.
The above-mentioned first step work is performed before and after minute changes in the values of and PR ^* , and the change rates ΔR and ΔT of R ^* and T ^* obtained at that time are obtained.

Next, an optimization method such as a linear approximation least squares method, a Lagrange multiplier method, or a simulated annealing from ΔR and ΔT is used, and R ^* =
Estimate AS ^** and PR ^** satisfying the condition of R, T ^* = T,
Perform the above-mentioned work to confirm whether or not R ^* = R and T ^* = T are actually satisfied. When this condition is not satisfied, R ^** and T ^** are obtained by using AS ^** and PR ^** as initial values, and the difference between R and R ^** and T and T ^** is obtained to obtain the above. Make an evaluation. Such an operation is repeated until the difference becomes equal to or less than the measurement error of R and T.

Further, as a second step, which is the next work of FIG. 1, a ray of light incident from an arbitrary direction on one point of the recording material having the optical property determined by AS and PR obtained in the first step is used. The distribution of reflected light intensity and angle is obtained using the Monte Carlo method. That is, in the computer, a very large number of infinitely small light rays are made incident on one specific point on the surface of the recording material from an arbitrary direction, each light ray is traced by the Monte Carlo method, and the position, intensity, and emission angle of the emitted light ray are calculated. To record. An example of the intensity distribution of the emitted light thus obtained, that is, the PSF is shown in FIGS. 3 and 4. FIG. 3 is a PSF obtained by the Monte Carlo method in which 10,000 light rays are vertically incident on the laser printer paper. In the figure, the vertical axis represents the reflected light intensity when the incident light intensity is 1.0, and the horizontal axis represents the scale of 300 μm on each side. Figure 4
Is an example where light is obliquely incident at an incident angle of 20 degrees, and the scale on the horizontal axis is 100 μm on a side.

Next, the procedure of the method of the present invention will be described in detail with reference to the drawings, taking a recording material having a two-layer structure as an example.

FIG. 6 shows the outline of the procedure for obtaining the characteristic values for the recording material having the two-layer structure as shown in FIG. 5, and FIG. 9 is a flow chart showing the flow of the first step of FIG.

In FIG. 9, the reflectance and the transmittance of the recording material are measured by the spectrophotometer 1. The measurement is performed under both conditions of front incidence and back incidence, and four measurement values of T ₁ , R ₁ , T ₂ , and R ₂ are obtained. The front side here is the layer a side in FIG. 5, and the back side is the layer b side.

The approximate calculation unit 3 includes the optical behavior reproduction calculation unit 4 and
It is divided into other parts. Four light behavior reproduction calculation units 4
Basic optical characteristic value AS_a ^*, PR_a ^*, AS_b ^*, PR_b ^*To
As an input parameter, the optical behavior such as the Monte Carlo method described above
By the reproduction calculation, T₁ ^*, R ₁ ^*, T₂ ^*, R₂ ^*The four anti
Obtain the output of emissivity and transmittance.

In the first time, AS _a ^* , which is appropriate as an initial value,
PR _a ^* , AS _b ^* , and PR _b ^* are given, and the optical behavior reproduction calculation such as the Monte Carlo method may be performed.

The comparison / accuracy determining means 10 has four values of T ₁ , R ₁ , T ₂ and R ₂ obtained by the measurement and T ₁ ^* , R ₁ ^* and T obtained by the optical behavior reproduction calculation section. The 4 values of ₂ ^* and R ₂ ^* are compared, and if they match with each other with sufficient accuracy, AS _a ^* , PR _a ^* , AS
_b ^* , PR _b ^* are the basic optical characteristic values AS _a , P of this recording material
R _a, AS _b, and outputs a PR _b.

If they do not coincide with each other with sufficient accuracy, the new parameter determining means 11 causes new AS _a ^* , P
R _a ^*, AS _b ^*, determines a PR _b ^*, repeated light behavior reproduced calculation.

The comparison / accuracy determination means 10 and the new parameter determination means 11 are the above-mentioned linear approximation least squares method, Lagrange multiplier method, and simulated annealing (simu).
A so-called optimization method such as a plated annealing) method can be used.

Subsequently, the obtained basic optical characteristic value A
Based on S _a , PR _a , AS _b , and PR _b , approximation calculation is further performed as described above (second step) to obtain the optical characteristic value of the recording material such as PSF.

All the basic optical characteristic values and the entire optical characteristic values of each layer of the recording material treated in the present invention are usually dependent on the wavelength of light. Therefore, it is originally desirable to perform the method of the present invention for each wavelength, but an average value or the like of a certain wavelength section can be used.

[0046]

EXAMPLES The present invention will be specifically described below with reference to examples.

Example 1 Optical characteristic values were obtained using a recording paper such as white recycled paper EW-500 manufactured by Sanyo Kokusaku Pulp Co., Ltd. as a recording material.

First, the reflectance R and the transmittance T were measured using a Shimadzu self-recording spectrophotometer UV-3100S manufactured by Shimadzu Corporation. As a result, the average visible wavelength was R = 0.74, T = 0.1.
It was 3. The optical condition at the time of measurement is total diffused light measurement using an integrating sphere. Based on this value, the scattering coefficient AS and the reflection coefficient PR of the paper are applied with the Monte Carlo method so as to satisfy the conditions of R = 0.74 and T = 0.13, and AS = 84.9 /
mm, PR = 0.9887 was determined.

Next, using this value, the line spread function of the above paper (hereinafter abbreviated as LSF) was obtained by calculation by the Monte Carlo method. Here, LSF is a kind of convolution of PSF. FIG. 11 shows calculated values by the Monte Carlo method, and FIG. 12 shows measured LSF values of the above paper. 11 and 12, the horizontal axis represents the position of the central portion of the slit-shaped detection area, and the vertical axis represents the reflected light intensity (%) (the reflected light from the paper surface at a position sufficiently separated from the knife edge is 100). Yes). The measurement is performed by arranging the knife edge of the mirror surface on the paper surface and illuminating a sufficiently wide range at an angle of 45 degrees from diagonally above, width about 10 μm and length 250 μ
The measurement was performed by detecting the reflected light from the minute slit-shaped area of m. FIG. 12 shows the result of operating the measurement area for 200 μm across the edge in the direction perpendicular to the edge under the above conditions.

Note that the maximum value in FIG. 12 exceeds 100% because of variations in the actual measurement values.

Comparing FIG. 11 and FIG. 12, it is clear that the two correlate well and that the method of the present invention is useful as a method for determining the optical characteristic value of the recording material.

(Embodiment 2) Next, as shown in FIG.
The ray tracing of the present invention was performed on 10,000 coated rays in a coated paper having a layered structure and comprising a coated layer and a paper layer, and calculations were performed. When PSF was calculated from the obtained characteristic values and compared with the actual measurement results, a good agreement was found between the two, and the optical characteristic values obtained by the method of the present invention showed that the actual measurement results were good. It turned out to reflect.

[0053]

As described above, in the present invention, the PSF can be obtained by an approximate calculation such as the Monte Carlo method based on the measured values of the transmittance and the absorptance of the recording material. Therefore, a complicated optical system and an image processing device are not required, and once the values of AS and PR are obtained, the PSF at an arbitrary incident angle and an arbitrary angular distribution can be repeatedly calculated without any troublesome measurement. You can ask. Further, the method of the present invention is effective not only for the recording material having a single layer or two layers but also for determining the characteristic value in the recording material having a multilayer structure of three or more layers, and it is possible to easily obtain a more accurate value than the conventional method. You can

[Brief description of drawings]

FIG. 1 is a schematic diagram showing a flow of a method for estimating an optical characteristic value of a recording material of the present invention.

FIG. 2 is a schematic diagram showing an example of a method for measuring reflectance and absorptance.

FIG. 3 is a diagram showing an example of PSF obtained by carrying out the present invention.

FIG. 4 is a diagram showing another example of PSF obtained by carrying out the present invention.

FIG. 5 is a diagram showing basic optical characteristic values of each layer of a recording material having a two-layer structure.

FIG. 6 is a schematic diagram showing a flow of an optical characteristic value estimation method for a recording material having a two-layer structure of the present invention.

FIG. 7 is a diagram schematically showing incidence and emission of light rays on a two-layer recording material.

FIG. 8 is a schematic diagram showing trajectory tracking and absorption of one ray in a two-layer recording material.

9 is a flowchart showing a procedure of a first step of the present invention in FIG.

FIG. 10 is a schematic diagram showing a relationship between a basic optical characteristic value, an approximate calculation, and an optical characteristic value in the present invention.

FIG. 11 is a graph showing LSF calculated values according to the present invention.

FIG. 12 is a graph showing measured LSF values in the present invention.

[Explanation of symbols]

 1 Spectrophotometer 2 Reflectance and transmittance data 3 Approximate calculation part 4 Light behavior calculation part 5 Light incident part 6 Scattering absorption part 7 Light emission part 8 Reflectance and transmittance data 9 Basic optical characteristic value parameter 10 Comparison / accuracy Judgment means 11 New parameter determination means 12 Basic optical characteristics 21 Recording material 22 Integrating sphere 23 Incident light 24 Reflected light 25 Transmitted light

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Tatsuya Nakai 1-6-1, Nishino 1-chome, Nishi-ku, Sapporo-shi, Hokkaido

Claims (10)

[Claims] 1. A reflectance of an incident light of a recording material and //
Alternatively, the optical characteristic value of the recording material is obtained, which comprises a step of measuring the transmittance and then obtaining the basic optical characteristic value of the recording material by an approximate calculation and an optimization method from the measured values. Method. 2. The reflectance of the recording material for incident light and / or
Alternatively, a step of measuring the transmittance, and then obtaining the basic optical characteristic value of the recording material by an approximate calculation and an optimization method from the measured values, and further, from the basic optical characteristic value, the approximate calculation of the recording material of the recording material. A method for obtaining an optical characteristic value of a recording material, the method comprising: obtaining an optical characteristic value. 3. The basic optical characteristic values are a scattering coefficient and / or
The method according to claim 1 or 2, which is also a reflection coefficient. 4. The method according to claim 1, wherein the finally obtained optical characteristic value is a point spread function. 5. The recording material comprises one layer.
The method according to any one of 1. 6. The method according to claim 1, wherein the recording material comprises a plurality of layers. 7. The method according to claim 6, wherein a basic optical characteristic value is determined for each layer of the recording material, and the optical characteristic value is determined using the basic optical characteristic value. 8. The method according to claim 7, wherein the recording material comprises two layers. 9. The method according to claim 7, wherein a measured value of incident light on the recording front surface and / or the back surface of the recording material is used as the measured value of the reflectance and / or the transmittance. 10. The measurement value of the reflectance and / or the transmission rate, a plurality of measurement values of a plurality of incident light having different incident angles to the recording front surface and / or the back surface of the recording material is used. the method of.