JP2017032293A - Method for calibrating a spectroscopic device and method for producing a calibrated spectroscopic device - Google Patents

Abstract

Provided is a calibration method for suppressing the difference in spectral characteristics output for each individual spectroscopic device. First-order calibration of each of a plurality of first individuals that are individuals of a spectroscopic device 1000 is performed. In the primary calibration, measured light 1020 for primary calibration including a bright line component is measured by the first individual. The measured light 1020 for secondary calibration is measured by each of the plurality of first individuals, and spectral characteristics are output. The plurality of output spectral characteristics are averaged to obtain an average spectral characteristic. Secondary calibration of the second individual that is the individual of the spectroscopic device 1000 is performed. In the secondary calibration, the second calibration target light 1020 for secondary calibration is measured, and the output spectral characteristic is brought close to the average spectral characteristic. In each of the primary calibration and the secondary calibration, calibration parameters that determine the spectral sensitivity of the sensor 1031 are adjusted. [Selection] Figure 1

Description

  The present invention relates to calibration of spectroscopic devices.

  A spectroscopic device including a polychromator includes a sensor that outputs a signal indicating the amount of energy of each of a plurality of wavelength components. Spectral characteristics such as spectral reflectance, spectral transmittance, and spectral radiance are obtained from a plurality of signals output by a plurality of sensors.

  The spectral sensitivity of the sensor varies depending on the arrangement, shape, size, and the like of the light receiving sensor, and varies depending on the arrangement, shape, size, etc. of the slit plate, diffraction grating, and the like provided in the polychromator. For this reason, the spectral sensitivity of the sensor that is the basis of the spectral characteristics must be calibrated for each individual spectroscopic device.

  In the wavelength calibration method of the spectrocolorimeter described in Patent Document 1, the difference from the reference value of the center wavelength of the spectral sensitivity is given by a linear function of the pixel number (paragraph 0026), and the half width of the spectral sensitivity is calculated. The ratio to the reference value is given by a linear function of the pixel number (paragraph 0028), and a corrected spectral sensitivity table is created using the ratio of the spectral sensitivity center wavelength and the spectral sensitivity half-width to the reference value (paragraph 0029). Coefficients included in each of the linear functions of the pixel numbers are determined so that the calculated relative output calculated from the corrected spectral sensitivity table and the emission line wavelength and the measured relative output are closest to each other (paragraph 0033). When wavelength calibration is performed, the spectrocolorimeter measures the emitted light of the bright line light source (paragraph 0032). In order to make the calculated relative output and the measured relative output close to each other, the evaluation function is made smaller than the threshold (paragraph 0041).

Japanese Patent No. 4660694

  When the wavelength calibration is performed using the emitted light of the bright line light source as in the wavelength calibration method of the spectrocolorimeter described in Patent Document 1, the spectral sensitivity is accurately obtained in the wavelength band close to the wavelength of the bright line. However, in other wavelength bands, the spectral sensitivity may not be accurately obtained. This causes the measurement results to be different for each spectrocolorimeter. When wavelength calibration is performed using an evaluation function as in the wavelength calibration method of the spectrocolorimeter described in Patent Document 1, the evaluation function may approach a minimum value that is not the minimum value. This causes the measurement result to become an outlier. These problems also apply to spectroscopic devices other than spectrocolorimeters.

  The invention described in the detailed description of the invention is made to solve these problems. The problem to be solved by the invention described in the detailed description of the invention is to suppress the difference in spectral characteristics output for each individual spectroscopic device.

  The spectroscopic device includes an optical system that converts measured light into a spectrum, a plurality of light receiving sensors that output signals indicating the amounts of energy of a plurality of wavelength components included in the spectrum, and a plurality of light outputs that are output by the plurality of sensors. And a signal processing mechanism for obtaining spectral characteristics using the spectral sensitivity of the signal and the sensor.

  Primary calibration is performed on the plurality of first spectroscopic devices. In the primary calibration, when the light to be measured for primary calibration from the bright line light source is measured by the first spectroscopic device, the spectral sensitivity of the sensor provided in the spectroscopic device is output by the sensor provided in the spectroscopic device. Calibration parameters that determine the spectral sensitivity of the sensor are adjusted to match the signal.

  With respect to the plurality of first spectroscopic devices, after the primary calibration is performed, when the light to be measured for secondary calibration is measured by the first spectroscopic device, spectral characteristics output by the first spectroscopic device are obtained. Thereby, a plurality of spectral characteristics are obtained.

  All or some of the obtained plurality of spectral characteristics are averaged to obtain an average spectral characteristic.

  Secondary calibration is performed on the second spectroscopic device. In the secondary calibration, the spectral characteristics output by the second spectroscopic device when the light to be measured for secondary calibration is measured by the second spectroscopic device are average spectroscopic values obtained by the plurality of first spectroscopic devices. Calibration parameters that determine the spectral sensitivity of the sensor provided in the second spectroscopic device are adjusted so as to approach the characteristics.

  Spectral sensitivity of the spectroscopic device is adjusted so that the spectral characteristic output by the spectroscopic device approaches the average spectral characteristic measured by a plurality of spectroscopic devices, and the spectral characteristic output for each individual spectroscopic device is different. It is suppressed.

It is a schematic diagram showing a spectrocolorimeter and a calibration device for primary calibration. It is a schematic diagram which shows the spectrophotometer and the calibration apparatus for secondary calibration. It is a schematic diagram which shows a spectroscopy unit. It is a schematic diagram which shows a linear array sensor. It is a block diagram which shows a signal processing mechanism. It is a graph which shows spectral sensitivity and the spectral intensity of to-be-measured light. It is a schematic diagram which shows the calibration procedure of a spectrocolorimeter. It is a schematic diagram which shows the relationship between a reference | standard spectral sensitivity and the spectral sensitivity of each spectroscopy apparatus. Placement errors a ₁ is a graph showing the shift of the center wavelength of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₁ is a graph showing the shift amount of the half-value width of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₂ is a graph showing the shift of the center wavelength of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₂ is a graph showing the shift amount of the half-value width of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₃ is a graph showing the shift of the center wavelength of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₃ is a graph showing the shift amount of the half-value width of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Manufacturing tolerances a ₄ is a graph showing the shift of the center wavelength of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Manufacturing tolerances a ₄ is a graph showing the shift amount of the half-value width of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₅ is a graph showing the shift of the center wavelength of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. Placement errors a ₅ is a graph showing the shift amount of the half-value width of the spectral sensitivity of each channel of the sensor when the deviation ± 1 unit. It is a graph which shows the example of spectral sensitivity and the spectral intensity of a bright line light source. It is a graph which shows the relationship between each channel of a sensor at the time of bright line light source measurement, and a sensor output signal. It is a graph which shows the spectral reflectance of a red tile. It is a graph which shows the spectral reflectance of a green tile. It is a graph which shows the spectral reflectance of a blue tile. It is a graph which shows the shift | offset | difference of the average spectral reflectance after the primary calibration of a some 1st spectroscopic apparatus about the red tile, and the spectral reflectance after the primary calibration of a 2nd spectroscopic apparatus. It is a graph which shows the shift | offset | difference of the average spectral reflectance after the primary calibration of the some 1st spectroscopic apparatus about the green tile, and the spectral reflectance after the primary calibration of the 2nd spectroscopic apparatus. It is a graph which shows the shift | offset | difference of the average spectral reflectance after the primary calibration of a some 1st spectroscopic apparatus about the blue tile, and the spectral reflectance after the primary calibration of a 2nd spectroscopic apparatus. It is a flowchart which shows the procedure of the secondary calibration of a spectrophotometer. It is a schematic diagram which shows the calibration procedure of a spectrocolorimeter. It is a schematic diagram which shows the calibration procedure of a spectrocolorimeter. It is a graph which shows the shift | offset | difference between the average spectral reflectance after the primary calibration of the plurality of first spectroscopic devices and the spectral reflectance after the secondary calibration of the second spectroscopic device for the red tile. It is a graph which shows the shift | offset | difference of the average spectral reflectance after the primary calibration of the some 1st spectroscopic apparatus about the green tile, and the spectral reflectance after the secondary calibration of the 2nd spectroscopic apparatus. It is a graph which shows the shift | offset | difference of the average spectral reflectance after the primary calibration of the some 1st spectroscopic apparatus about the blue tile, and the spectral reflectance after the secondary calibration of the 2nd spectroscopic apparatus. It is a flowchart which shows the procedure which produces the calibrated spectral colorimeter.

1 Spectral Colorimeter The schematic diagram of FIG. 1 shows a spectrocolorimeter and a calibration device for primary calibration. The schematic diagram of FIG. 2 shows a spectrocolorimeter and a calibration device for secondary calibration. Each of FIGS. 1 and 2 shows a cross section of a spectroscopic unit provided in a spectrocolorimeter.

  The spectrocolorimeter 1000 includes a spectroscopic unit 1010 and a signal processing mechanism 1011 as shown in FIGS.

  When the spectrocolorimeter 1000 performs measurement, the spectroscopic unit 1010 receives the light to be measured 1020, and the first wavelength component, the second wavelength component included in the received light to be measured 1020,. A first signal, a second signal,..., A 40th signal each indicating the energy amount of the 40th wavelength component are output. The signal processing mechanism 1011 obtains the spectral reflectance using the first signal, the second signal,..., The 40th signal, and outputs the obtained spectral reflectance.

In the spectrocolorimeter 1000, when the object to be measured is irradiated with light, the light reflected by the object to be measured becomes the measured light 1020, and the spectral reflectance is obtained. Spectral characteristics other than the spectral reflectance may be obtained. For example, spectral transmittance, colorimetric values, and the like may be obtained. When the spectral transmittance is obtained, the light that has passed through the object to be measured becomes the light to be measured 1020. The colorimetric values are expressed in Munsell color system, L ^* a ^* b ^* color system, L ^* C ^* h color system, Hunter Lab color system, XYZ color system, and the like. The spectrocolorimeter 1000 may be replaced with another type of spectroscopic device. For example, the spectral colorimeter 1000 may be replaced with a spectral luminance meter. In the spectral luminance meter, the light emitted from the light source to be measured becomes the measured light 1020, and the spectral radiance is obtained. When spectral characteristics other than the spectral reflectance are required, calibration similar to the calibration described later is possible.

2 Spectroscopic Unit The schematic diagram of FIG. 3 is a perspective view showing the spectral unit.

  The spectroscopic unit 1010 includes an optical system 1030 and a linear array sensor 1031 as shown in FIGS. The optical system 1030 is a polychromator and includes a slit plate 1040 and a concave diffraction grating 1041.

  The schematic diagram of FIG. 4 is a plan view showing a linear array sensor.

  As shown in FIG. 4, the linear array sensor 1031 includes sensors (light receiving sensors) 1050-1, 1050-2,.

  When the spectrocolorimeter 1000 performs measurement, the light to be measured 1020 is guided to a rectangular slit 1060 formed in the slit plate 1040. The light to be measured 1020 guided to the slit 1060 passes through the slit 1060. The light to be measured 1020 that has passed through the slit 1060 travels from the slit 1060 to the diffraction surface 1070 of the concave diffraction grating 1041 and is reflected by the diffraction surface 1070. The light to be measured 1020 is converted into a spectrum by being reflected by the diffraction surface 1070. The measured light 1020 converted into a spectrum travels from the diffraction surface 1070 of the concave diffraction grating 1041 to the light receiving surface 1080 of the linear array sensor 1031, forms an image on the light receiving surface 1080, and is received by the linear array sensor 1031. The sensors 1050-1, 1050-2,..., 1050-40 are linearly arranged in the direction 1100 on the light receiving surface 1080. The slit plate 1040, the concave diffraction grating 1041, and the linear array sensor 1031 are arranged such that the wavelength of light that forms an image on the light receiving surface 1080 changes according to the position in the direction 1100. Therefore, when the linear array sensor 1031 receives the light to be measured 1020 converted into a spectrum, the sensors 1050-1, 1050-2,..., 1050-40 are different from each other in the spectrum. A first signal, a second signal,..., A 40th signal respectively indicating the energy amount of the wavelength component, the second wavelength component,. The output first signal, second signal,..., 40th signal are input to the signal processing mechanism 1011. The signal processing mechanism 1011 obtains the spectral reflectance using the input first signal, second signal,..., 40th signal.

  The optical system 1030 has an optical axis 1110 extending from the slit 1060 to the diffraction surface 1070 and an optical axis 1111 extending from the diffraction surface 1070 to the light receiving surface 1080.

  The optical system 1030 may be replaced with another type of optical system. For example, the concave diffraction grating 1041 may be replaced with a plane diffraction grating and a concave mirror. The slit plate 1040 and the concave diffraction grating 1041 may be replaced with a slit plate having a circular slit, a cylindrical lens, and a linear variable filter. The light to be measured that has passed through the circular slit passes through the cylindrical lens. When the light to be measured passes through the cylindrical lens, the cross-sectional shape of the light to be measured is converted from a circular shape to a linear shape. The light to be measured that has passed through the cylindrical lens passes through the linear variable filter. The light to be measured is converted into a spectrum by passing through a linear variable filter.

  The linear array sensor 1031 may be replaced with another type of light receiving sensor. For example, the linear array sensor 1031 may be replaced with a linear array sensor including 39 or less or 41 or more sensors. Depending on the optical system, the linear array sensor 1031 may be replaced with an area sensor.

3 Signal Processing Mechanism The block diagram of FIG. 5 shows the signal processing mechanism.

  As shown in FIG. 5, the signal processing mechanism 1011 includes an A / D conversion mechanism 1120 and an arithmetic mechanism 1121.

  When the first signal, the second signal,..., The 40th signal is input to the signal processing mechanism 1011, the first signal, the second signal,. / D conversion mechanism 1120. The first signal, the second signal,..., The 40th signal input to the A / D conversion mechanism 1120 are the first signal value, the second signal value,. Each value is analog / digital converted. The first signal value, the second signal value,..., The 40th signal value are input to the calculation mechanism 1121. The calculation mechanism 1121 includes the input first signal value, second signal value,..., 40th signal value, and spectral sensitivities 1130-1, 1130-2,. , 1130-40 to obtain the spectral reflectance. Spectral sensitivities 1130-1, 1130-2,..., 1130-40 are spectral sensitivities of the sensors 1050-1, 105-2,. Instead of the spectral sensitivities 1130-1, 1130-2,..., 1130-40, information derived from the spectral sensitivities 1130-1, 1130-2,. Information necessary for this may be stored in the calculation mechanism 1121.

  The calculation mechanism 1121 is a computer and operates according to an installed program. All or part of the processing performed by the calculation mechanism 1121 may be performed by an electronic circuit without a program. All or part of the processing performed by the calculation mechanism 1121 may be performed manually.

4 Example of Spectral Sensitivity of Sensor The graph of FIG. 6 shows an example of the spectral sensitivity of the sensor and the spectral intensity of light to be measured for primary calibration.

  The central wavelength of the spectral sensitivity 1140-1 of the sensor 1050-1, the central wavelength of the spectral sensitivity 1140-2 of the sensor 1050-2, ..., the central wavelength of the spectral sensitivity 1140-40 of the sensor 1050-40 are shown in FIG. As shown, they are different from each other and are about 352 nm, about 363 nm,..., About 740 nm, respectively. Accordingly, the sensors 1050-1, 1050-2,..., 1050-40 indicate the energy amounts of the first wavelength component, the second wavelength component,. The first signal, the second signal,..., The 40th signal are output.

5 Necessity of Calibration of Spectral Colorimeter Each of the spectral sensitivities 1140-1, 1140-2,..., 1140-40 has the arrangement, shape, and size of the slit plate 1040, the concave diffraction grating 1041, and the linear array sensor 1031. It depends on the situation. Therefore, in order to obtain the spectral reflectance with high accuracy, the spectral sensitivities 1130-1, 1130-2,..., 1130-40 stored in the calculation mechanism 1121 are replaced with the slit plate 1040, the concave diffraction grating 1041 and It must be changed according to the arrangement, shape, size, etc. of the linear array sensor 1031 and close to the true spectral sensitivities 1140-1, 1140-2, ..., 1140-40, respectively. In the following, the spectral sensitivities 1130-1, 1130-2,..., 1130-40 stored in the calculation mechanism 1121 are brought close to the true spectral sensitivities 1140-1, 1140-2,. This is called calibration of the spectrocolorimeter 1000. The calibration of the spectrocolorimeter 1000 includes a primary calibration and a secondary calibration.

6. Calibration Device for Primary Calibration The calibration device 1150 for primary calibration includes an HgCd lamp 1160 and a control calculation mechanism 1161, as shown in FIG.

  When primary calibration of the spectrocolorimeter 1000 is performed using the calibration device 1150 for primary calibration, the control calculation mechanism 1161 causes the HgCd lamp 1160 to emit the measurement light 1170 for primary calibration. The emitted measurement light 1170 for primary calibration is measured by the spectrocolorimeter 1000. When the measurement light 1170 for primary calibration is measured by the spectrocolorimeter 1000, the first signal value, the second signal value corresponding to the spectral intensity of the measurement light 1170 for primary calibration, ... The 40th signal value is input to the calculation mechanism 1121. The input first signal value, second signal value,..., 40th signal value are transferred from the calculation mechanism 1121 to the control calculation mechanism 1161. The control arithmetic mechanism 1161 uses the transferred first signal value, second signal value,..., 40th signal value, the spectral sensitivity of the sensor 1050-1, the spectral sensitivity of the sensor 1050-2, ..., the spectral sensitivity of the sensor 1050-40 is obtained. The obtained spectral sensitivity of the sensor 1050-1, the spectral sensitivity of the sensor 1050-2,..., The spectral sensitivity of the sensor 1050-40 are transferred from the control calculation mechanism 1161 to the calculation mechanism 1121, and each is newly added to the calculation mechanism 1121. , 1130-40 are stored in the spectral sensitivities 1130-1, 1130-2,. Thereby, after the primary calibration of the spectrocolorimeter 1000 is performed, the calculation mechanism 1121 performs the first signal, the second signal,..., The 40th signal and the newly obtained sensor 1050-. Spectral reflectance can be obtained using the spectral sensitivity of 1, the spectral sensitivity of the sensor 1050-2, ..., the spectral sensitivity of the sensor 1050-40.

  The control operation mechanism 1161 is a computer and operates according to an installed program. All or part of the processing performed by the control arithmetic mechanism 1161 may be performed by an electronic circuit without a program. All or part of the processing performed by the control arithmetic mechanism 1161 may be performed manually. A control calculation mechanism 1161 may be built in the spectrocolorimeter 1000.

7 Wavelength of Bright Line Component The measured light 1170 for primary calibration includes bright line components 1180-1, 1180-2, 1180-3, 1180-4, 1180-5 and 1180-6 as shown in FIG. Including. The wavelengths of the bright line components 1180-1, 1180-2, 1180-3, 1180-4, 1180-5 and 1180-6 are 404.55 nm, 435.84 nm, 508.58 nm, 546.07 nm, 578 nm and 647. 85 nm. The bright line components 1180-1, 1180-2, 1180-3, 1180-4, 1180-5 and 1180-6 are used for the primary calibration of the spectrocolorimeter 1000.

  Bright line components other than the bright line components 1180-1, 1180-2, 1180-3, 1180-4, 1180-5 and 1180-6 may be used for the primary calibration of the spectrocolorimeter 1000. Five or less or seven or more bright line components may be used for the primary calibration of the spectrocolorimeter 1000. The light emitted from the bright line light source other than the HgCd lamp 1160 may be measured light 1170 for primary calibration.

8 Calibration Device for Secondary Calibration The calibration device 1190 for secondary calibration includes an irradiation mechanism 1200, a tile 1201, a temperature sensor 1202, and a control calculation mechanism 1203, as shown in FIG.

  When secondary calibration of the spectrocolorimeter 1000 is performed using the calibration device 1190 for secondary calibration, the control calculation mechanism 1203 causes the irradiation mechanism 1200 to irradiate the tile 1201 with light. The light reflected by the tile 1201 becomes the measurement light 1210 for secondary calibration, and is measured by the spectrocolorimeter 1000. When the measurement light 1210 for secondary calibration is measured by the spectrocolorimeter 1000, the spectral reflectance is output by the calculation mechanism 1121. The output spectral reflectance is transferred from the calculation mechanism 1121 to the control calculation mechanism 1203. The control arithmetic mechanism 1203 corrects the spectral reflectance transferred using the temperature of the tile 1201 measured by the temperature sensor 1202, and uses the spectral reflectance corrected for temperature to detect the spectral sensitivity of the sensor 1050-1. The spectral sensitivity of 1050-2, ..., the spectral sensitivity of the sensor 1050-40 is obtained. The obtained spectral sensitivity of the sensor 1050-1, the spectral sensitivity of the sensor 1050-2,..., The spectral sensitivity of the sensor 1050-40 are transferred from the control arithmetic mechanism 1203 to the arithmetic mechanism 1121, and are newly added to the arithmetic mechanism 1121, respectively. , 1130-40 are stored in the spectral sensitivities 1130-1, 1130-2,. As a result, after the secondary calibration of the spectrocolorimeter 1000 is performed, the calculation mechanism 1121 causes the first signal, the second signal,..., The 40th signal, and the newly obtained sensor 1050-. Spectral reflectance can be obtained using the spectral sensitivity of 1, the spectral sensitivity of the sensor 1050-2, ..., the spectral sensitivity of the sensor 1050-40.

  The tile 1201 may be replaced with another type of object. When the spectrocolorimeter 1000 is replaced with a spectral luminance meter, the tile 1201 is replaced with a light source.

9 Calibration Procedure of Spectral Colorimeter The schematic diagram of FIG. 7 shows the calibration procedure of the spectrocolorimeter.

  In the calibration of the spectrocolorimeter 1000, as shown in FIG. 7, the individuals 1220-1,..., 1220-S sequentially pass through the calibration sites 1240 and 1241. Each of the individuals 1220-1,..., 1220-S is an individual of the spectrocolorimeter 1000. Each of the individuals 1220-1,..., 1220-S passes through the calibration site 1241 after passing through the calibration site 1240. The individual 1220-j in the calibration site 1240 is subjected to primary calibration using the calibration device 1150 for primary calibration. The individual 1220-i in the calibration site 1241 is subjected to secondary calibration using the calibration device 1190 for secondary calibration. Thus, each of the individuals 1220-1,..., 1220-S is subjected to secondary calibration after being subjected to primary calibration. The individuals 1220-1,..., 1220-S to be subjected to the secondary calibration are the same as the individuals 1220-1,. Each of the individuals 1220-1,..., 1220-S is shipped as a product after the primary calibration and the secondary calibration are performed.

  The average spectral reflectance 1250 used for the secondary calibration of the individual 1220-i is the average of the spectral reflectance output by the individual 1220-i, ..., the spectral reflectance output by the individual 1220-k.

10 Details of the primary calibration of the spectrocolorimeter 10.1 Model used in the primary calibration of the spectrocolorimeter In the primary calibration of the spectrocolorimeter 1000, the first model, the second model, or the third model The model is used.

10.2 Index indicating the spectral sensitivity of the sensor In each of the first model, the second model, and the third model, the sensors 1050-1, 1050-2, ..., 1050-40 are identified by the position i. Is done. The position i takes one of 40 different values i ₁ , i ₂ ,..., I ₄₀ . The sensors 1050-1, 1050-2, ..., 1050-40 may be identified by an index other than the position. For example, the sensors 1050-1, 1050-2,..., 1050-40 may be identified by the center wavelength of the reference spectral sensitivity described later, the sensor number, and the like.

In each of the first model, the second model, and the third model, the spectral sensitivity of the sensor at the position i has a center wavelength λ _G (i) of the spectral sensitivity of the sensor at the position i and a half-value width FWHM ( i). Each of the center wavelength λ _G (i) and the full width at half maximum FWHM (i) is a function of the position i.

The spectral sensitivity of the sensor at position i is well approximated by a Gaussian function where the independent variable is wavelength and the dependent variable is sensitivity. The shape of the Gaussian function is determined by the center wavelength and the half width. For this reason, the center wavelength λ _G (i) and the full width at half maximum FWHM (i) are suitable as indices indicating the spectral sensitivity of the sensor at the position i. However, the index indicating the spectral sensitivity of the sensor at position i may be changed. The index indicating the spectral sensitivity of the sensor at the position i can be composed of one variable or three or more variables.

10.3 First Model When the first-order calibration of the spectrocolorimeter 1000 is performed using the first model, the equation (1) in which the center wavelength λ _G (i) is represented by the n-order function of the position i ) Is created.

  Further, Expression (2) in which the half width FWHM (i) is expressed by an m-th order function at the position i is created.

The first model consists of equations (1) and (2). Coefficients _a n, ···, _{a 0} and _b n, ···, _{b 0} is the spectral sensitivity of the sensor at position _{i 1,} the spectral sensitivity of the sensor at position _{i 2,} · · ·, to the position _{i 40} A calibration parameter that determines the spectral sensitivity of a sensor.

When primary calibration of the spectrocolorimeter 1000 is performed using the first model, a signal output from the sensor with the spectral sensitivity of the sensor indicated by the center wavelength λ _G (i) and the half-value width FWHM (i). to fit the calibration parameter coefficients _a n, ···, _{a 0} and _b n, ···, _{b 0} is adjusted. Details will be described in the description of the case where the primary calibration of the spectrocolorimeter 1000 is performed using the third model.

Subsequently, the center wavelength λ _G (i) is obtained using the created equation (1) and the adjusted calibration parameter coefficients a _n ,..., A ₀ , and the created equation (2) and adjusted The full width at half maximum FWHM (i) is obtained using the calibration parameters b _n ,..., B ₀ .

Subsequently, the spectral sensitivity of the sensor at the position i is obtained using the obtained center wavelength λ _G (i) and the half-value width FWHM (i). The spectral sensitivity of the sensor at the required position i is the spectral sensitivity indicated by the determined center wavelength λ _G (i) and half width FWHM (i).

10.4 Second Model When the first calibration of the spectrocolorimeter 1000 is performed using the second model, the arrangement, shape, size, etc. of the slit plate 1040, the concave diffraction grating 1041, and the linear array sensor 1031 Is ideal spectral colorimeter 1000 that matches the design goal, and the reference spectral sensitivity of the sensor at position i provided in the assumed spectral colorimeter 1000 is obtained by optical simulation. The reference spectral sensitivity of the sensor at position i is a function of position i.

Subsequently, the center wavelength λ _G0 (i) and the half-value width FWHM ₀ (i) of the reference spectral sensitivity of the sensor at the position i are obtained.

The center wavelength λ _G0 (i) and the full width at half maximum FWHM ₀ (i) are suitable as indices indicating the reference spectral sensitivity of the sensor at the position i.

Subsequently, expression center wavelength lambda _G0 center wavelength from (i) λ _G deviation [Delta] [lambda] _G of (i) (i) is represented by a linear function of position i (3) is created.

Further, Expression (4) is created in which the ratio ratio (i) of the half-value width FWHM (i) to the half-value width FWHM ₀ (i) is expressed by a linear function of the position i.

The second model consists of equations (3) and (4). The coefficients a ₁ , a ₀ , b ₁ and b ₀ are calibrations that determine the spectral sensitivity of the sensor at position i ₁ , the spectral sensitivity of the sensor at position i ₂ , ..., the spectral sensitivity of the sensor at position i _40. Become a parameter.

The center wavelength λ _G (i) is obtained using Expression (5) derived from Expression (3).

When the first calibration of the spectrocolorimeter 1000 is performed using the second model, a signal output from the sensor with the spectral sensitivity of the sensor indicated by the center wavelength λ _G (i) and the half-value width FWHM (i). The calibration parameters a ₁ , a ₀ , b ₁ and b ₀ are adjusted to meet Details will be described in the description of the case where the primary calibration of the spectrocolorimeter 1000 is performed using the third model.

Subsequently, the deviation Δλ _G (i) is obtained using the created equation (3) and the adjusted calibration parameter coefficients a ₁ and a ₀ , and the created equation (4) and the adjusted calibration parameter b _{1 are obtained.} And the ratio ratio (i) is determined using b ₀ .

Subsequently, the spectral sensitivity of the sensor at the position i is obtained using the obtained deviation Δλ _G (i) and the ratio ratio (i).

  The schematic diagram of FIG. 8 shows the relationship between the reference spectral sensitivity of the sensor at position i and the spectral sensitivity of the sensor at position i.

As shown in FIG. 8, the spectral sensitivity of the sensor at the position i is increased by the ratio of the reference spectral sensitivity of the sensor at the position i by ratio (i) times around the center wavelength λ _G0 (i) in the wavelength axis direction. The enlarged reference spectral sensitivity is moved by Δλ _G (i) in the wavelength axis direction.

10.5 Third Model When primary calibration of the spectrocolorimeter 1000 is performed using the third model, the arrangement, shape, size, etc. of the slit plate 1040, the concave diffraction grating 1041, and the linear array sensor 1031 Is ideal spectral colorimeter 1000 that matches the design goal, and the reference spectral sensitivity of the sensor at position i provided in the assumed spectral colorimeter 1000 is obtained by optical simulation. The reference spectral sensitivity of the sensor at position i is a function of position i.

Subsequently, the center wavelength λ _G0 (i) and the half-value width FWHM ₀ (i) of the reference spectral sensitivity of the sensor at the position i are obtained. Each of the center wavelength λ _G0 (i) and the full width at half maximum FWHM ₀ (i) is a function of the position i.

The center wavelength λ _G0 (i) and the full width at half maximum FWHM ₀ (i) are suitable as indices indicating the reference spectral sensitivity of the sensor at the position i.

Subsequently, placement errors _a 1, _{a 2} and _{a 3} of the shift of the center wavelength λ _G (i) from the center wavelength λ _G0 (i) is a linear array sensor 1031, the fabrication of the width of the slit 1060 error _{a 4} and the concave diffraction expression represented by a linear function of the placement error _{a 5} grid 1041 (6) is created. Further, the deviation of the half-value width FWHM (i) from the half-value width FWHM ₀ (i) causes the placement errors a ₁ , a ₂ and a _{3 of} the linear array sensor 1031, the manufacturing error a ₄ of the width of the slit 1060, and the concave diffraction grating 1041. the placement error a represented formula by the primary function of the ₅ (7) is created. Each of the center wavelength λ _G0 (i) and the full width at half maximum FWHM ₀ (i) is a function of the position i. The errors a ₁ , a ₂ , a ₃ , a ₄ and a ₅ are indices indicating the mechanical errors of the spectrocolorimeter 1000.

Placement errors _{a 1} linear array sensor 1031, sensor 1050-1,1050-2, ..., a placement error of the linear array sensor 1031 in the direction 1100 1050-40 are arranged. Placement error _{a 2} of the linear array sensor 1031 is a placement error of the linear array sensor 1031 in the direction 1101 in which the optical axis 1111 extends. Placement error _a linear array sensor 1031 _3, about a central axis 1116 of the linear array sensor 1031 extending in a direction forming each vertical directions 1100 and 1101 in the arrangement error of the linear array sensor 1031 for travel around the rotation direction 1102 is there. The manufacturing error a ₄ of the width of the slit 1060 is a manufacturing error of the width of the slit 1060 in the direction 1103 parallel to the main cross section 1260 of the concave diffraction grating 1041 and perpendicular to the optical axis 1110. The arrangement error a ₅ is an arrangement error of the concave diffraction grating 1041 in the rotation direction 1104 around the central axis 1115 of the concave diffraction grating 1041 perpendicular to the main cross section 1260 of the concave diffraction grating 1041. The main cross section 1260 of the concave diffraction grating 1041 is a surface perpendicular to the score line formed on the diffraction surface 1070.

The third model consists of equations (6) and (7). Errors a ₁ , a ₂ , a ₃ , a ₄ and a ₅ are the spectral sensitivity of the sensor at position i ₁ , the spectral sensitivity of the sensor at position i ₂ ,..., The spectral sensitivity of the sensor at position i _40. Calibration parameter that determines

Since the calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ are expected to be small, the deviation of the center wavelength λ _G (i) from the center wavelength λ _G0 (i) is determined by the calibration parameters a ₁ , a _The linear function of ₂ , a ₃ , a ₄ and a ₅ is a good approximation, and the deviation of the half-value width FWHM (i) from the half-value width FWHM ₀ (i) is a calibration parameter a ₁ , a ₂ , It is also a good approximation that can be expressed by a linear function of a ₃ , a ₄ and a ₅ . For this reason, when the primary calibration of the spectrocolorimeter 1000 is performed using the third model, the spectral sensitivity is accurately obtained.

The calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ have a large influence on the center wavelength λ _G (i) or the half-value width FWHM (i), and have an influence on the spectral sensitivity of the sensor at the position i. large. For this reason, the calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ are suitable as an index indicating the mechanical error of the spectrocolorimeter 1000. However, the index indicating the mechanical error of the spectrocolorimeter 1000 may be changed. The number of calibration parameters included in the index indicating the mechanical error of the spectrocolorimeter 1000 is limited to the number of bright line components included in the measurement light 1170 for primary calibration, but is 4 or less or 6 It may be the above.

In the primary function of the calibration parameters _{a 1, a 2, a 3} , a 4 and _{a 5} included in the formula (6), the calibration parameters _{a 1, a 2, a 3} , a 4 and _{a 5,} coefficient δλ _G1 (i), δλ _G2 (i), δλ _G3 (i), δλ _G4 (i) and δλ _G5 (i) are respectively multiplied. The coefficients δλ _G1 (i), δλ _G2 (i), δλ _G3 (i), δλ _G4 (i), and δλ _G5 (i) are the calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a _{5 respectively.} This is the shift amount of the center wavelength λ _G (i) when shifted by a unit amount, and is obtained by optical simulation. Each of the coefficients δλ _G1 (i), δλ _G2 (i), δλ _G3 (i), δλ _G4 (i) and δλ _G5 (i) is a function of position i.

In the primary function of the calibration parameters _{a 1, a 2, a 3} , a 4 and _{a 5} included in the formula (7), the calibration parameters _{a 1, a 2, a 3} , a 4 and _{a 5,} coefficient δFWHM ₁ (i), δFWHM ₂ (i), δFWHM ₃ (i), δFWHM ₄ (i) and δFWHM ₅ (i) are respectively multiplied. The coefficients δFWHM ₁ (i), δFWHM ₂ (i), δFWHM ₃ (i), δFWHM ₄ (i) and δFWHM ₅ (i) have calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a _{5 respectively.} The amount of deviation of the full width at half maximum FWHM (i) in the case of deviation by a unit amount, which is obtained by optical simulation. Each of the coefficients δFWHM ₁ (i), δFWHM ₂ (i), δFWHM ₃ (i), δFWHM ₄ (i) and δFWHM ₅ (i) is a function of position i.

  The channel Ch in each of FIGS. 9 to 18 is a sensor number for identifying the sensors 1050-1, 1050-2,..., 1050-40.

The shift amount 1270 shown in FIG. 9 indicates the shift amount δλ _G of the center wavelength of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₁ is shifted by +1 unit from 0, and the shift amount 1271 shown in FIG. indicates a shift amount [delta] [lambda] _G of the center wavelength of the sensor spectral sensitivity of each channel Ch when placement error a ₁ is shifted -1 unit from 0. The deviation amounts 1270 and 1271 are obtained by optical simulation. The coefficient δλ _G1 (i) is obtained using, for example, the shift amounts 1270 and 1271.

The shift amount 1280 shown in FIG. 10 indicates the shift amount δFWHM of the half-value width of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₁ is shifted by +1 unit. The shift amount 1281 shown in FIG. , The amount of deviation δFWHM of the half-value width of the spectral sensitivity of the sensor of each channel Ch when the arrangement error a ₁ is deviated from 0 by −1 unit. The deviation amounts 1280 and 1281 are obtained by optical simulation. The coefficient δFWHM ₁ (i) is obtained using, for example, the deviation amounts 1280 and 1281.

The shift amount 1290 shown in FIG. 11 indicates the shift amount δλ _G of the center wavelength of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₂ is shifted from +1 unit, and the shift amount 1291 shown in FIG. indicates a shift amount [delta] [lambda] _G of the center wavelength of the sensor spectral sensitivity of each channel Ch when placement error a ₂ is shifted -1 unit from 0. The shift amounts 1290 and 1291 are obtained by optical simulation. The coefficient δλ _G2 (i) is obtained using, for example, the shift amounts 1290 and 1291.

The shift amount 1300 shown in FIG. 12 indicates the shift amount δFWHM of the half-width of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₂ is shifted from +1 unit. The shift amount 1301 shown in FIG. , The shift amount δFWHM of the half-value width of the spectral sensitivity of the sensor of each channel Ch when the arrangement error a ₂ is shifted by −1 unit from 0. The shift amounts 1300 and 1301 are obtained by optical simulation. The coefficient δFWHM ₂ (i) is obtained using, for example, the shift amounts 1300 and 1301.

The shift amount 1310 shown in FIG. 13 indicates the shift amount δλ _G of the center wavelength of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₃ is shifted from +1 unit, and the shift amount 1311 shown in FIG. indicates a shift amount [delta] [lambda] _G of the center wavelength of the sensor spectral sensitivity of each channel Ch when placement error a ₃ is shifted -1 unit from 0. The deviation amounts 1310 and 1311 are obtained by optical simulation. The coefficient δλ _G3 (i) is obtained by using the deviation amounts 1310 and 1311, for example.

The shift amount 1320 shown in FIG. 14 indicates the shift amount δFWHM of the half-value width of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₃ is shifted by +1 unit from 0. The shift amount 1321 shown in FIG. , The shift amount δFWHM of the full width at half maximum of the spectral sensitivity of the sensor of each channel Ch when the arrangement error a ₃ is shifted by −1 unit from 0. The deviation amounts 1320 and 1321 are obtained by optical simulation. The coefficient δFWHM ₃ (i) is obtained, for example, using the deviation amounts 1320 and 1321.

The shift amount 1330 shown in FIG. 15 indicates the shift amount δλ _G of the center wavelength of the spectral sensitivity of the sensor of each channel Ch when the manufacturing error a ₄ is shifted from +1 unit, and the shift amount 1331 shown in FIG. indicates a shift amount [delta] [lambda] _G of the center wavelength of the sensor spectral sensitivity of each channel Ch when manufacturing errors a ₄ is shifted -1 unit from 0. The deviation amounts 1330 and 1331 are obtained by optical simulation. The coefficient δλ _G4 (i) is obtained using the deviation amounts 1330 and 1331, for example.

The shift amount 1340 shown in FIG. 16 indicates the shift amount δFWHM of the half-value width of the spectral sensitivity of the sensor of each channel Ch when the manufacturing error a ₄ is shifted from +1 unit, and the shift amount 1341 shown in FIG. shows a half-value width of the shift amount δFWHM sensor spectral sensitivity for each channel Ch when manufacturing errors a ₄ is shifted -1 unit from 0. The shift amounts 1340 and 1341 are obtained by optical simulation. The coefficient δFWHM ₄ (i) is obtained using, for example, the shift amounts 1340 and 1341.

Shift amount 1350 of FIG. 17 shows the shift amount [delta] [lambda] _G of the center wavelength of the sensor spectral sensitivity of each channel Ch when placement error a ₅ is shifted +1 units from 0, shift amount 1351 of FIG 17 indicates a shift amount [delta] [lambda] _G of the center wavelength of the sensor spectral sensitivity of each channel Ch when placement error a ₅ is shifted -1 unit from 0. The deviation amounts 1350 and 1351 are obtained by optical simulation. The coefficient δλ _G5 (i) is obtained using the deviation amounts 1350 and 1351, for example.

The shift amount 1360 shown in FIG. 18 indicates the shift amount δFWHM of the half-value width of the spectral sensitivity of the sensor of each channel Ch when the placement error a ₅ is shifted by +1 unit from 0, and the shift amount 1361 shown in FIG. , The shift amount δFWHM of the full width at half maximum of the spectral sensitivity of the sensor of each channel Ch when the arrangement error a ₅ is shifted by −1 unit from 0. The shift amounts 1360 and 1361 are obtained by optical simulation. The coefficient δFWHM ₅ (i) is obtained using, for example, the shift amounts 1360 and 1361.

When primary calibration of the spectrocolorimeter 1000 is performed using the third model, a signal output from the sensor with the spectral sensitivity of the sensor indicated by the center wavelength λ _G (i) and the half-value width FWHM (i). The calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ are adjusted so that Adapting the spectral sensitivity to the signal is output by the sensor when the true spectral sensitivity of the sensor at position i is that of the sensor indicated by the center wavelength λ _G (i) and the full width at half maximum FWHM (i). This means that the signal assumed to be close to the signal actually output by the sensor. Objective variables are used to assess suitability.

For the primary calibration, the wavelengths λ _HgCd (1), λ _HgCd (2),..., Λ _HgCd (K ₀ ) of the bright line components of the sensors 1050-1, 1050-2,. The signal output by the sensitive sensor is used.

Then, using the calibration parameters _{a 1, a 2, a 3} , a 4 and _{a 5,} which is created Equation (6) and adjusting the center wavelength of the center wavelength _{λ G0 (i) λ G (} i) Deviation is required. Also, the deviation of the half-value width FWHM (i) from the half-value width FWHM ₀ (i) using the created equation (7) and the adjusted calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ Is required.

Subsequently, the reference spectral sensitivity of the sensor at the determined position i, the shift of the center wavelength λ _G (i) from the center wavelength λ _G0 (i), and the half width FWHM (i) from the half width FWHM ₀ (i). Is used to determine the spectral sensitivity of the sensor at position i.

As shown in FIG. 8, the spectral sensitivity of the sensor at the required position i has been expanded by expanding the reference spectral sensitivity by a ratio (i) times around the center wavelength λ _G0 (i) in the wavelength axis direction. The reference spectral sensitivity is shifted by Δλ _G (i) in the wavelength axis direction.

  The ratio ratio (i) is expressed by equation (8).

When the first calibration of the spectrocolorimeter 1000 is performed using the third model, each of the center wavelength λ _G0 (i) and the half-value width FWHM ₀ (i) is a calibration parameter a ₁ , a ₂ , a ₃ , a _4, and a ₅ are expressed by a linear function, and therefore, when the calibration parameters a ₁ , a ₂ , a ₃ , a _4, and a ₅ are changed, the suitability of the spectral sensitivity to the signal changes greatly. do not do. For this reason, calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ are appropriately determined, and the spectral sensitivity after calibration of the sensor is appropriately determined.

Further, when the spectrocolorimeter 1000 is calibrated using the third model, the center wavelength λ _G (i) and the half-value width FWHM (i) each have a common calibration parameter a ₁ , a ₂ , Since it is represented by a ₃ , a _4, and a ₅ , the number of calibration parameters is reduced as compared with the case where the calibration parameter representing the center wavelength λ _G (i) is different from the calibration parameter representing the full width at half maximum FWHM (i). As a result, the number of bright line components necessary for the primary calibration of the spectrocolorimeter 1000 is reduced.

Further, when the primary calibration of the spectrocolorimeter 1000 is performed using the third model, the center wavelength λ _G (i) and the half-value width FWHM (i) are common calibration parameters a ₁ , a ₂ , Since it is represented by a ₃ , a ₄ and a ₅ , the relationship between the center wavelength λ _G (i) and the half width FWHM (i) does not become inappropriate, and the center wavelength λ _G (i) and the half width FWHM (I) is appropriately determined.

In the following, it is _assumed that the bright line component having the wavelength λ _HgCd (k) is incident on the sensor at the position I _k and the sensor at the position I _{k + 1} . The center wavelength of the reference spectral sensitivity of the sensor at position I _{k + 1} is adjacent to the center wavelength of the reference spectral sensitivity of the sensor at position I _k . It is assumed that the identification number k of the bright line component takes any value of 1, 2,..., K ₀ .

  The graph of FIG. 19 shows an example of the spectral sensitivity of the sensor and the spectral intensity of the measured light for primary calibration. The graph of FIG. 19 is an enlarged view of the range where the wavelength of the graph of FIG. 6 is from 390 nm to 420 nm.

  The emission line component 1180-1 having a wavelength of 404.54 nm is incident across a sensor having a spectral sensitivity 1140-5 having a center wavelength of about 396 nm and a sensor having a spectral sensitivity 1140-6 having a center wavelength of about 407 nm. . Therefore, each of the sensor having the spectral sensitivity 1140-5 and the sensor having the spectral sensitivity 1140-6 has sensitivity to the bright line component 1180-1, as shown in FIG.

  The graph of FIG. 20 shows the relationship between the sensor channel and the signal output by the sensor.

  Each of the channel 5 sensor and the channel 6 sensor is sensitive to the bright line component 1180-1, each of the channel 8 sensor and the channel 9 sensor is sensitive to the bright line component 1180-2, Each of the sensor of channel 15 and the sensor of channel 16 is sensitive to the bright line component 1180-3, and each of the sensor of channel 19 and the sensor of channel 20 is sensitive to the bright line component 1180-4, The channel 22 sensor and the channel 23 sensor are sensitive to the bright line component 1180-5, and the channel 29 sensor and the channel 30 sensor are each sensitive to the bright line component 1180-6. As a result, a signal as shown in FIG. 20 is obtained.

1 of the spectrocolorimeter 1000 using an emission line component having a wavelength of λ _HgCd (1), an emission line component having a wavelength of λ _HgCd (2),..., An emission line component having a wavelength of λ _HgCd (K ₀ ). When the next calibration is completely performed, the spectral sensitivity Response (i, λ) of the sensor at the position i and the signal value Count () obtained by analog / digital conversion of the signal output from the sensor at the position i i) satisfies the relationships shown in equations (9) and (10) for each of k = 1, 2,..., K ₀ .

Equations (9) and (10) show for each k = 1, 2,..., K ₀ a sensor at position I _k and a sensor at position I _{k + 1} that is sensitive at wavelength λ _HgCd (k). If you choose, the signal value indicating the signal sensitivity Response at the wavelength lambda _HgCd (k) of the spectral sensitivity of the sensor in the position _{I k (I k, λ HgCd} (k)) is output by the sensor in the position _{I k} Count _{(I k)} to match the signal position _{I k + 1} sensitivity at the wavelength lambda _HgCd (k) of the spectral sensitivity of the sensor on the _{Response (I k + 1, λ} HgCd (k)) is output by the sensor in the position _{I k + 1} The signal value Count (I _{k + 1} ) indicating

_{Adapting the} spectral sensitivity to the signal brings the relationship between the sensitivity Response (I _k , λ _HgCd (k)) and the signal value Count (I _k ) closer to the relationship shown in Equation (9), and the sensitivity Response (I _{k + 1} , It means that the relationship between λ _HgCd (k)) and the signal value Count (I _{k + 1} ) is brought close to the relationship shown in Expression (10).

For this reason, the first method for adapting the spectral sensitivity to the signal is to obtain calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ that minimize the objective variable F shown in Equation (11). is there.

Target variable F represented by formula (11), the signal value Count _{(I k)} Sensitivity Response from the sensitivity from the square and the signal value Count _{(I k + 1)} of the deviation of _{(I k,} lambda _HgCd (k)) Response The sum of squares of deviations of (I _{k + 1} , λ _HgCd (k)) for k = 1, 2,..., K ₀ .

  The square of the deviation may be replaced with another factor whose absolute value increases as the absolute value of the deviation increases. For example, the square of the deviation may be replaced with the absolute value of the deviation.

For a certain k, if the sensor at position I _k−1 , the sensor at position I _k and the sensor at position I _{k + 1} are sensitive at wavelength λ _HgCd (k), then from the signal value Count (I _k−1 ) The square of the deviation of the sensitivity Response (I _k−1 , λ _HgCd (k)) may be added to the objective function F.

  In addition, Expression (12) is derived from Expressions (9) and (10).

_{Adapting the} spectral sensitivity to the signal is related to the sensitivity Response (I _k , λ _HgCd (k)) and Response (I _{k + 1} , λ _HgCd (k)) and the signal values Count (I _k ) and Count (I _{k + 1} ). Is approximated to the relationship shown in the equation (12).

Therefore, the second method for adapting the spectral sensitivity to the signal is to obtain calibration parameters a ₁ , a ₂ , a ₃ , a ₄ and a ₅ that minimize the objective variable F shown in the equation (13). is there.

Objective function F as shown in equation (13), the signal value Count sensitivity Response from the ratio of _{(I k)} signal values for Count _{(I k + 1)} sensitivity to _{(I k, λ HgCd (k} )) Response (I k + 1, λ _HgCd (k)) is the sum of the deviations in the ratio for k = 1, 2,..., K ₀ .

According to the objective function F shown in Equation (13), the sensitivity Response (I _k , λ _HgCd (k)) and Response (I _{k + 1} , λ _HgCd (k)) are converted into signal values Count (I _k ) and Count (I _It is not necessary to normalize the spectral sensitivity Response (i, λ) so that it can be compared with _{k + 1} ).

If a sensor at position I _k−1 , a sensor at position I _k and a sensor at position I _{k + 1} for a certain k is sensitive at wavelength λ _HgCd (k), the signal for signal value Count (I _k−1 ) sensitivity Response from the ratio of the value Count _{(I k)} sensitivity Response for _{(I k-1, λ HgCd} (k)) deviation of the ratio of _{(I k, λ HgCd (k} )) is also added to the objective function F Good.

11 Details of secondary calibration of spectrocolorimeter 11.1 Necessity of secondary calibration of spectrocolorimeter The graph of FIG. 21 shows the spectral reflectances r _RED (λ, 1), r _RED (λ, 2),..., R _RED (λ, N) is shown as an example. The graph of FIG. 22 shows an example of spectral reflectances r _GREEN (λ, 1), r _GREEN (λ, 2),..., R _GREEN (λ, N) of the green tile. The graph of FIG. 23 shows an example of spectral reflectances r _BLUE (λ, 1), r _BLUE (λ, 2),..., R _BLUE (λ, N) of the blue tile. The spectral reflectances r _RED (λ, 1), r _RED (λ, 2),..., R _RED (λ, N) are the individual numbers 1, 2,. It is output by each individual. The spectral reflectances r _GREEN (λ, 1), r _GREEN (λ, 2),..., R _GREEN (λ, N) are the individual numbers 1, 2,. It is output by each individual. The spectral reflectances r _BLUE (λ, 1), r _BLUE (λ, 2),..., R _BLUE (λ, N) are the individual numbers 1, 2,. It is output by each individual.

Graph of Figure 24, for the red tiles, the average spectral reflectance _{r RED} from the spectral reflectance (lambda, 1) deviation of Δr _{RED (λ,} 1), the spectral reflectance from the average spectral reflectance _{r RED} (lambda, 2) A deviation Δr _RED (λ, 2),..., A deviation Δr _RED (λ, N) of the spectral reflectance r _RED (λ, N) from the average spectral reflectance. Graph of Figure 25, for the green tiles, the average spectral reflectance _{r GREEN} from spectral reflectance (lambda, 1) the deviation [Delta] r _GREEN of (lambda, 1), the spectral reflectance from the average spectral reflectance _{r GREEN} (lambda, 2) A deviation Δr _GREEN (λ, 2),..., A deviation Δr _GREEN (λ, N) of the spectral reflectance r _GREEN (λ, N) from the average spectral reflectance. Graph of Figure 26, for the blue tiles, the average spectral reflection spectral reflectance from the ratio _{r BLUE (λ,} 1) the deviation [Delta] r _BLUE of (lambda, 1), the spectral reflectance from the average spectral reflectance _{r BLUE} (lambda, 2) A deviation Δr _BLUE (λ, 2),..., A deviation Δr _BLUE (λ, N) of the spectral reflectance r _BLUE (λ, N) from the average spectral reflectance.

As shown in FIGS. 24, 25 and 26, due to the calibration error in the primary calibration, the red tile spectral reflectances r _RED (λ, 1), r _RED (λ, 2),... , R _RED (λ, N) varies around the average spectral reflectance of the red tile, and the spectral reflectances of green tiles r _GREEN (λ, 1), r _GREEN (λ, 2),..., R _GREEN (Λ, N) varies around the average spectral reflectance of the green tile, and the spectral reflectances r _BLUE (λ, 1), r _BLUE (λ, 2),..., R _BLUE (λ, N) varies around the average spectral reflectance of the blue tile. In addition, an outlier (outlier) may occur in the spectral reflectance as shown by a shift 1365 shown in FIG.

  When the primary calibration is performed using the bright line components 1180-1, 1180-2, 1180-3, 1180-4, 1180-5 and 1180-6, the bright line components 1180-1, 1180-2, 1180- Spectral sensitivity is accurately obtained in a wavelength band close to the wavelength of 3,1180-4, 1180-5, or 1180-6, but spectral sensitivity may not be accurately obtained in other wavelength bands. This is the main cause of the above variation. In addition, when the primary calibration is performed, the calibration parameter is adjusted so that the objective function takes the minimum value, but the calibration parameter is erroneously adjusted so that the objective function takes a minimum value that is not the minimum value. There is a case. This causes the occurrence of the above outlier.

  The secondary calibration is performed to alleviate such a calibration error in the primary calibration.

11.2 Procedure for secondary calibration of spectrocolorimeter In the following, it is assumed that the primary calibration of the spectrocolorimeter 1000 is performed using the third model. The primary calibration of the spectrocolorimeter 1000 may be performed using the first model or the second model.

  The flowchart of FIG. 27 shows the procedure of secondary calibration.

  When secondary calibration of the spectrocolorimeter 1000 is performed, the measured light 1210 for secondary calibration is assigned to the individual number of the spectrocolorimeter 1000 for each of n = 1,... When n individuals are measured, the spectral reflectance output from the individual with individual number n is obtained. Since the obtained spectral reflectance is a spectral reflectance output after the primary calibration of the individual is performed, it already has a certain degree of accuracy. Thereby, the spectral reflectances r (λ, 1), r (λ, 2),... Output from the individual with the individual number 1, the individual with the individual number 2,. r (λ, N) is obtained.

A deviation Δr (λ, n ₀ ) of the spectral reflectance r (λ, n ₀ ) from the average spectral reflectance is obtained by the equation (14). The second term on the right side of Equation (14) indicates the average spectral reflectance.

  Subsequently, in step S <b> 2, the temperature of the tile 1201 is measured by the temperature sensor 1202.

  Subsequently, in step S3, the obtained spectral reflectances r (λ, 1), r (λ, 2),..., R (λ, N) are corrected using the measured temperatures. Thereby, even when the spectral reflectance of the tile 1201 changes depending on the temperature, the secondary calibration of the spectrocolorimeter 1000 is accurately performed. When the temperature change of the spectral reflectance of the tile 1201 is small, the temperature measurement and the spectral reflectance correction may be omitted.

  Subsequently, in step S4, the corrected spectral reflectances r (λ, 1), r (λ, 2),..., R (λ, N) are averaged to obtain an average spectral reflectance. The number of spectral reflectances to be averaged is not limited, but is, for example, 30.

  The average spectral reflectance may be obtained by averaging all of the spectral reflectances r (λ, 1), r (λ, 2),..., R (λ, N). It may be obtained by averaging a part of r (λ, 1), r (λ, 2), ..., r (λ, N).

  When the average spectral reflectance is obtained by averaging a part of the spectral reflectances r (λ, 1), r (λ, 2),..., R (λ, N), the spectral reflectance r ( All of λ, 1), r (λ, 2)..., r (λ, N) are averaged to obtain a provisional average spectral reflectance, and the spectral reflectance r (λ , 1), r (λ, 2)..., R (λ, N), two or more spectral reflectances are averaged to obtain an average spectral reflectance. The excluded spectral reflectance is a spectral reflectance that has a deviation from the temporary average spectral reflectance larger than the reference.

Subsequently, in step S5, for each of n = 1,..., N, the individual number n is set so that the spectral reflectance r (λ, n) output by the individual with the individual number n approaches the average spectral reflectance. Calibration parameters a ₁ , a ₂ , a ₃ , a _4, and a ₅ that determine spectral sensitivities 1130-1,..., 1130-40 stored in individual individuals are calibration parameters a ₁ (n), a ₂ (N), a ₃ (n), a ₄ (n) and a ₅ (n) are adjusted.

When the calibration parameters a ₁ (n), a ₂ (n), a ₃ (n), a ₄ (n) and a ₅ (n) are adjusted, for example, the calibration parameters a ₁ (n), a ₂ (N), a ₃ (n), a ₄ (n) and a ₅ (n) are calibrated with the calibration parameters a ₁ (n) + δa ₁ , a ₂ (n) + δa ₂ , a ₃ (n) + δa ₃ , a ₄ Calibration parameters that are replaced with (n) + δa ₄ and a ₅ (n) + δa ₅ are corrected. Subsequently, the corrected calibration parameters a ₁ (n) + δa ₁ , a ₂ (n) + δa ₂ , a ₃ (n) + δa ₃ , a ₄ (n) + δa ₄ and a ₅ (n) + δa _{5 are} determined. Spectral reflectance is calculated using the spectral sensitivity, and an objective function comprising the sum of squares of the difference between the calculated spectral reflectance and the obtained average spectral reflectance is obtained. Then, the calibration parameters a ₁ (n), a ₂ (n), a ₃ (n), a ₄ (n) and a ₅ (n) are adjusted so that the objective function takes the minimum value. For example, correction of calibration parameters and calculation of spectral reflectance are repeated until the objective function has a minimum value. The spectral reflectance used is temperature corrected using the measured temperature. An objective function other than the objective function consisting of other than the sum of squares of the difference between the calculated spectral reflectance and the obtained average spectral reflectance may be obtained. Depending on the objective variable, the calibration parameters a ₁ (n), a ₂ (n), a ₃ (n), a ₄ (n) and a ₅ (n) may be set so that the objective function takes a target value other than the minimum value. May be adjusted. For example, if the objective function is obtained by inverting the sign of the sum of squares of the difference between the calculated spectral reflectance and the obtained average spectral reflectance, the calibration parameter is set so that the objective function takes the maximum value. a ₁ (n), a ₂ (n), a ₃ (n), a ₄ (n) and a ₅ (n) are adjusted.

  An individual that outputs spectral reflectance that becomes an outlier when measuring the measurement light 1210 for secondary calibration is selected from the individual of individual number 1,..., The individual of individual number N, and only the selected individual is selected. May be subject to secondary calibration. When only the selected individual is to be subjected to the secondary calibration, the individual with individual number 1,..., Each individual with individual number N is given as a candidate for secondary calibration, and becomes the outlier spectral reflection. The average spectral reflectance is obtained by averaging two or more spectral reflectances excluding the reflectance from the spectral reflectances r (λ, 1), r (λ, 2)..., R (λ, N). .

  A plurality of tiles are prepared so that the spectral reflectances output from the spectrocolorimeter 1000 are different from each other when measured by the spectrocolorimeter 1000, and when measured by the spectrocolorimeter 1000, the spectrocolorimeter 1000 is measured. Lights having different spectral reflectances output by the above are used as light to be measured for secondary calibration, and the plurality of tiles of the sum of squares of the difference between the spectral reflectance and the average spectral reflectance for each of the plurality of tiles May be the objective function. Thereby, the spectral reflectance is accurately calibrated over a wide range of wavelengths.

For example, a red tile, a green tile, and a blue tile are prepared, and the sum of squares of the difference between the spectral reflectance and the average spectral reflectance for the red tile, the spectral reflectance for the green tile, as shown in Equation (15). The sum of the square sum of the difference between the average reflectance and the average spectral reflectance and the sum of the square sum of the difference between the spectral reflectance and the average spectral reflectance for the blue tile may be set as the objective function F (n ₀ ). The number of color tiles may be increased or decreased. All or part of the red tile, green tile, and blue tile may be replaced with other color tiles.

Spectral reflectances r _RED (λ (j), n ₀ ), r _GREEN (λ (j), n ₀ ) and r _BLUE (λ (j), n ₀ ) are each determined by secondary calibration parameters. This is the spectral reflectance of the red tile, green tile, and blue tile output from the individual with the individual number n ₀ when the spectral sensitivity is used.

Spectral reflectances r _{0, RED} (λ (j), n), r _{0, GREEN} (λ (j), n) and r _{0, BLUE} (λ (j), n ₀ ) are the primary calibration parameters, respectively. Is the spectral reflectance of the red tile, green tile and blue tile output from the individual with individual number n when the spectral sensitivity determined by is used.

Instead of the objective function F _{(n 0)} represented by the formula (15), the objective function F _{(n 0)} may be used which is represented by the formula (16).

In the objective function F (n ₀ ) expressed by Expression (16), the weighting factor w _RED (j), is the square of the difference between the spectral reflectance and the average spectral reflectance for the red tile, the green tile, and the blue tile. Each of w _GREEN (j) and w _BLUE (j) is multiplied. The weighting factors w _RED (j), w _GREEN (j) and w _BLUE (j) are the objective functions F (n ₀₎ of the difference between the spectral reflectance and the average spectral reflectance for the red tile, green tile and blue tile, respectively. ) To vary the wavelength for each wavelength. The weighting factors w _RED (j), w _GREEN (j), and w _BLUE (j) are increased in the wavelength band where the change in the spectral reflectance of the red tile, the green tile, and the blue tile is increased, respectively. Increases in the wavelength band where the change in the spectral intensity of the measured light 1210 increases. This increases the contribution of the difference between the spectral reflectance and the average spectral reflectance to the objective function F (n ₀ ) in the wavelength band where the change in spectral intensity of the measurement light 1210 for secondary calibration becomes large.

12 Procedure for Calibration of Spectral Colorimeter The schematic diagrams of FIGS. 28 and 29 show another example of the calibration procedure.

  Calibration of the spectrocolorimeter 1000 may be performed according to the procedure shown in FIGS.

  The average spectral reflectance 1400 used for the secondary calibration of the individual 1370-i is the spectral reflectance output by the primary calibrated master individual 1400-1, ..., the spectrum output by the master individual 1400-M. This is the average reflectance.

  In the procedure for obtaining the average spectral reflectance 1400, as shown in FIG. 29, the master individuals 1400-1, ..., 1400-M sequentially pass through the calibration sites 1410 and 1411. Each of the master individuals 1400-1, ..., 1400-M is an individual of the spectrocolorimeter 1000. Each of the master individuals 1400-1, ..., 1400-M passes through the calibration site 1411 after passing through the calibration site 1410. The master individual 1400-j in the calibration site 1410 is subjected to primary calibration using a calibration device 1150 for primary calibration. The master individual 1400-i in the calibration site 1411 is a target of spectral reflectance measurement using the calibration device 1190 for secondary calibration. The master individual 1400-i in the calibration site 1411 does not need to be subjected to the secondary calibration. As a result, each of the master individuals 1400-1,..., 1400-M is set as a target for spectral reflectance measurement after being subjected to primary calibration, and is output by the master individual 1400-1. Spectral reflectance,..., Average spectral reflectance output from the master individual 1400-M is obtained to obtain an average spectral reflectance. The master individuals 1400-1,..., 1400-M are not shipped as products after the primary calibration and the spectral reflectance measurement are performed, but are stored as standard individuals.

  The primary calibration of each of the master individuals 1400-1, ..., 1400-M may be performed only once, or may be performed twice or more. When the primary calibration of each of the master individuals 1400-1,..., 1400-M is performed twice or more, the master individuals 1400-1,. , 1400-M is subjected to primary calibration. As a result, the secondary calibration is less susceptible to the change over time of the master individuals 1400-1, ..., 1400-M.

  Individuals 1370-1,..., 1370-S sequentially pass through the calibration site 1380 as shown in FIG. Each of the individual 1370-1,..., 1370-S is an individual of the spectrocolorimeter 1000. The individual 1370-i at the calibration site 1380 is subjected to secondary calibration using the calibration device 1190 for secondary calibration. Thereby, each of the individual 1370-1,..., 1370-S is subjected to the secondary calibration. Each of the individuals 1370-1,..., 1370-S to be subjected to the secondary calibration is different from any of the master individuals 1400-1,. Each of the individual 1370-1, ..., 1370-S is shipped as a product after the secondary calibration is performed.

Individuals 1370-1 to 1370-S may pass through the site of FIG. Even if calibration parameters a ₁ (n), a ₂ (n), a ₃ (n), a ₄ (n) and a ₅ (n) obtained by primary calibration are used as initial values of calibration parameters for secondary calibration Good.

Alternatively, the individual 1370-1 to 1370-S performs primary calibration through the site of FIG. Using the calibration parameters a ₁ (n), a ₂ (n), a ₃ (n), a ₄ (n) and a ₅ (n) obtained by the primary calibration, red, green, Measure the spectral reflectance of the blue tile. The secondary calibration may be performed only when the spectral reflectance of the same tile measured by the master deviates by a certain threshold value or more.

  In these procedures, the objective function shown in Expression (17) is used instead of the objective function shown in Expression (15).

Spectral reflectances r ^* _RED (λ (j), m), r ^* _GREEN (λ (j), m) and r ^* _BLUE (λ (j), m) are the individual numbers m after primary calibration, respectively. Spectral sensitivity of red tile, green tile and blue tile output from the master individual.

The graph of FIG. 30 shows deviations Δr _RED (λ, 1), Δr _RED (λ, 2),..., Δr _RED (λ, N) after calibration is performed by this procedure.

The graph of FIG. 31 shows deviations Δr _GREEN (λ, 1), Δr _GREEN (λ, 2),..., Δr _GREEN (λ, N) after calibration is performed by this procedure.

The graph of FIG. 32 shows deviations Δr _BLUE (λ, 1), Δr _BLUE (λ, 2),..., Δr _BLUE (λ, N) after calibration is performed by this procedure.

  As shown in FIGS. 30, 31, and 32, when calibration is performed by this procedure, the output spectral reflectance variation is reduced.

13 Procedure for Producing Calibrated Spectral Colorimeter When a calibrated spectral colorimeter 1000 is produced, as shown in FIG. 33, the spectrocolorimeter 1000 is prepared in step S11, and in step S12. The prepared spectrocolorimeter 1000 is calibrated. In step S <b> 11, an operator who calibrates the spectrocolorimeter 1000 may prepare the spectrocolorimeter 1000 by manufacturing the spectrocolorimeter 1000, or a business that calibrates the spectrocolorimeter 1000. A spectrocolorimeter 1000 may be prepared by a person purchasing a spectrocolorimeter 1000 from another company.

1000 Spectral Colorimeter 1010 Spectroscopic Unit 1011 Signal Processing Mechanism 1031 Linear Array Sensor 1050-1, 1050-2,..., 1050-40 Sensor 1150 Calibration Device for Primary Calibration 1190 Calibration Device for Secondary Calibration

Claims (12)

a) an optical system that converts measured light into a spectrum, a plurality of light receiving sensors that output signals indicating the amounts of energy of a plurality of wavelength components included in the spectrum, and a plurality of signals output by the plurality of sensors And a signal processing mechanism for obtaining spectral characteristics using spectral sensitivity of the sensor, and a step of subjecting each of a plurality of first individuals to primary calibration, each of which is an individual of a spectroscopic device,
b) For the plurality of first individuals, when the first individual is measured with light to be measured for primary calibration including a bright line component, the spectral sensitivity of the sensor provided in the first individual is the first individual. Performing a primary calibration to adjust calibration parameters that determine the spectral sensitivity of the sensor provided to the first individual to match the signal output by the sensor provided to the single individual;
c) Obtaining spectral characteristics output from the first individual when the first individual is measured with the light to be measured for secondary calibration after the first calibration is performed on the first individual. Obtaining a plurality of spectral characteristics for the plurality of first individuals,
d) calculating a mean spectral characteristic by averaging all or some of the plurality of spectral characteristics obtained in step c);
e) subjecting a second individual, which is an individual of the spectroscopic device, to a secondary calibration target;
f) The average spectrum obtained in step d) for the second individual when the second individual measured light for secondary calibration is measured by the second individual. Performing a secondary calibration for adjusting a calibration parameter for determining a spectral sensitivity of a sensor provided in the second individual so as to approach a characteristic;
A method for calibrating a spectroscopic device comprising: In step d), all of the plurality of spectral characteristics obtained in step c) are averaged to obtain a temporary average spectral characteristic, and a spectral characteristic whose deviation from the temporary average spectral characteristic is larger than the reference is obtained in step c). The method of calibrating the spectroscopic device according to claim 1, wherein two or more spectral characteristics excluded from the plurality of spectral characteristics are averaged to obtain an average spectral characteristic. Step e) selects an individual that outputs a spectral characteristic whose deviation from the average spectral characteristic obtained in step d) is larger than the reference from the second individual candidates when measuring the light to be measured for secondary calibration. A method of calibrating the spectroscopic device according to claim 2, wherein the second individual is used.   4. The method for calibrating a spectroscopic device according to claim 1, wherein the second individual is different from any of the plurality of first individuals.   The method for calibrating the spectroscopic device according to claim 1, wherein the second individual in the first period is one of the plurality of first individuals. 6. The method of calibrating a spectroscopic apparatus according to claim 1, wherein step b) performs the primary calibration at each of a plurality of calibration periods. 7. The spectroscopic device according to claim 1, comprising: a plurality of lights having different spectral characteristics output from the spectroscopic device when the light to be measured for secondary calibration is measured by the spectroscopic device. how to. Step f) is the difference between the spectral characteristics output by the second individual and the average spectral characteristics determined in step d) when the second individual is measured with the second calibration target light. A method for calibrating a spectroscopic apparatus according to any one of claims 1 to 7, wherein a calibration parameter is adjusted so that the objective function becomes a target value. Step f) is the difference between the spectral characteristics output by the second individual and the average spectral characteristics determined in step d) when the second individual is measured with the second calibration target light. 9. The method for calibrating the spectroscopic device according to claim 8, wherein the magnitude of the contribution to the objective function is increased in a wavelength band where the change in the spectral intensity of the light to be measured for secondary calibration increases. The light to be measured for primary calibration is emitted from an HgCd lamp and has an emission line component having a wavelength of 404.55 nm, an emission line component having a wavelength of 435.84 nm, an emission line component having a wavelength of 508.58 nm, and a wavelength of 546.nm. 10. The method for calibrating a spectroscopic device according to claim 1, comprising an emission line component having a wavelength of 07 nm, an emission line component having a wavelength of 578 nm, and an emission line component having a wavelength of 647.85 nm. Light to be measured for secondary calibration is light reflected by an object,
g) measuring the temperature of the object;
h) correcting each of the plurality of spectral characteristics obtained in step c) using the temperature measured in step g);
Further comprising
Step f) uses the temperature measured in step g) to correct the spectral characteristics output by the second individual when the second individual is measured with light to be measured for secondary calibration. A method for calibrating a spectroscopic device according to claim 1. i) preparing a spectroscopic device;
j) calibrating the spectroscopic device prepared in step i) by the method of calibrating any spectroscopic device according to claim 1;
To produce a calibrated spectroscopic device comprising:

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