Solar Spectral Radiation Correction Method and Related Equipment Based on Downlink Optical Sensor
By establishing a light intensity value model and solving it using the least squares method, the light intensity value of the downlink optical sensor was corrected, solving the problem of inaccurate spectral measurement of the sensor when the angle changes, and realizing accurate spectral measurement at different angles.
Patent Information
- Application Number
- CN202211291337.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-20
- Publication Date
- 2026-01-30
- Estimated Expiration
- 2042-10-20
AI Technical Summary
Existing downlink optical sensors are inaccurate in measuring light intensity and spectrum when the sun's position changes, and are easily affected by the acquisition angle, leading to errors in solar spectrum measurements.
A light intensity model is established, and the correlation parameters are solved by the least squares method. The optimal solution is used for correction to overcome the influence of angle changes.
Under different angles of sunlight incidence, the sensor can accurately measure the intensity of sunlight, providing a basis for accurate spectral data and ensuring the accuracy of material spectral identification.
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Figure CN115641274B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of solar spectral radiation correction technology, and particularly relates to a solar spectral radiation correction method and related equipment based on a downlink optical sensor. Background Technology
[0002] Under natural sunlight, ground objects reflect sunlight, and the reflected flux and its spectral distribution vary with changes in solar radiation flux and its spectrum. Related studies show that low-to-mid-level clouds have a significant impact on ground solar radiation flux and its spectral distribution, while high-level clouds have a relatively small impact. Sensitivity experiments with water vapor and ozone indicate that water vapor has a greater impact on near-infrared radiation, while ozone has a greater impact on visible and ultraviolet radiation. Aerosols have the second greatest impact on ground solar radiation, after atmospheric absorption. Furthermore, the solar zenith angle and surface albedo also significantly affect ground solar radiation flux and its spectral distribution. Generally, under natural sunlight, ground object spectra can be collected using airborne or outdoor spectroscopic cameras. Accurate solar spectra are crucial for obtaining accurate ground object reflectance spectra for subsequent analysis and applications. Therefore, how to acquire solar spectra in real-time and accurately is a key issue in ground object spectral research and applications.
[0003] Currently available downlink optical sensors contain sensor units covering 18 wavelengths from visible light to near-infrared, capable of measuring light intensity data across these 18 wavelengths to obtain the solar spectrum. However, due to the sensor's structure, changes in the relative position of the sun and the sensor significantly alter the measured light intensity, leading to errors in solar spectrum measurements. Since the sun constantly changes position throughout the day, if the sensor is used on an aircraft, its position relative to the angle of sunlight will be even more prone to change, further increasing the likelihood of errors in the measured solar spectrum and causing inaccurate light intensity correction for photographs. Therefore, the main drawback of existing solar spectrum acquisition methods using downlink optical sensors is the inaccuracy of solar intensity and spectrum measurements, further exacerbated by the susceptibility to the influence of the acquisition angle. Summary of the Invention
[0004] This invention provides a solar spectral radiation correction method and related equipment based on a downlink optical sensor, aiming to solve the problems of inaccurate solar intensity and spectral measurement and susceptibility to the influence of the acquisition angle in traditional downlink optical sensor-based solar spectrum acquisition methods.
[0005] In a first aspect, embodiments of the present invention provide a solar spectral radiation correction method based on a downlink optical sensor, the solar spectral radiation correction method comprising the following steps:
[0006] A light intensity value model is established with the light intensity value collected by the downlink optical sensor as a correlation parameter and the rotation angle of the downlink optical sensor relative to the sun, the tilt angle of the downlink optical sensor relative to the sun, the sunlight intensity, and the ambient light.
[0007] Acquire a set of actual data collected by the downlink optical sensor, and calibrate the light intensity value model based on the actual data to obtain the undetermined parameter values of the light intensity value model;
[0008] Substitute the actual data and the undetermined parameter values into the light intensity value model, and solve the light intensity value model using the least squares method to obtain the optimal solution for the associated parameters;
[0009] The light intensity value collected by the downlink optical sensor is corrected using the light intensity value model that incorporates the optimal solution of the correlation parameters, and the corrected light intensity value is output.
[0010] Furthermore, the light intensity value collected by the downlink optical sensor is defined as y, the rotation angle of the downlink optical sensor relative to the sun direction is α, the tilt angle of the downlink optical sensor relative to the sun direction is β, the sunlight intensity is e, the ambient light is b, and the undetermined parameter value is P, wherein the rotation angle α and the tilt angle β have an angular function relationship g, and the light intensity value model satisfies the following relationship (1):
[0011] y=f(α,β,e,b)=e·g(α,β|P)+b (1).
[0012] Furthermore, the rotation angle α and the tilt angle β are cosines of each other, and the angle function g satisfies the following relationship (2):
[0013] g(α,β|P)=cos(α+p1)+cos(β+p2) (2);
[0014] In relation (2), p1 and p2 are constants after the decomposition of the undetermined parameter value P.
[0015] Furthermore, the method used to calibrate the light intensity value model based on the actual data is curve fitting.
[0016] Furthermore, in the step of correcting the light intensity value collected by the downlink optical sensor using the light intensity value model with the optimal solution of the correlation parameters, the rotation angle α is set to 0° and the tilt angle β is set to 90°.
[0017] Furthermore, in the optimal solution of the associated parameters, the optimal solution for the solar intensity is defined as follows: The optimal solution for the ambient light is The corrected light intensity value is y adj The corrected light intensity value y adj The following relation (3) must be satisfied:
[0018]
[0019] Furthermore, the downlink optical sensor is a three-channel downlink optical sensor, and when calculating the corrected optical intensity value based on the optical intensity value, the calculation is performed using a group of 18 optical intensity values.
[0020] Secondly, embodiments of the present invention also provide a solar spectral radiation correction system based on a downlink optical sensor, comprising:
[0021] The modeling module is used to establish a light intensity value model with the light intensity value collected by the downlink optical sensor as a correlation parameter and the rotation angle of the downlink optical sensor relative to the sun direction, the tilt angle of the downlink optical sensor relative to the sun direction, the sunlight intensity, and the ambient light.
[0022] The calibration module is used to acquire a set of actual data collected by the downlink optical sensor, and to calibrate the light intensity value model based on the actual data to obtain the undetermined parameter values of the light intensity value model.
[0023] The solution module is used to substitute the actual data and the values of the parameters to be determined into the light intensity value model, and to solve the light intensity value model using the least squares method to obtain the optimal solution of the associated parameters;
[0024] The correction module is used to correct the light intensity value collected by the downlink optical sensor using the light intensity value model with the optimal solution of the correlation parameters, and output the corrected light intensity value.
[0025] Thirdly, embodiments of the present invention also provide a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps in the solar spectral radiation correction method based on a downlink optical sensor as described in any of the above embodiments.
[0026] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps in the solar spectral radiation correction method based on a downlink optical sensor as described in any of the above embodiments.
[0027] The beneficial effects achieved by this invention are that, by correcting the data collected by the downlink optical sensor, the sensor can accurately measure the solar intensity under different incident angles of sunlight, thus providing a data basis for tasks such as reconstructing spectral curves and ensuring the accuracy of material spectral identification. Attached Figure Description
[0028] Figure 1 This is a flowchart illustrating the steps of the solar spectral radiation correction method based on a downlink optical sensor provided in this embodiment of the invention.
[0029] Figure 2 This is a schematic diagram illustrating the relationship between the downlink optical sensor coordinate system and the solar coordinate system provided in an embodiment of the present invention;
[0030] Figure 3 This is a schematic diagram of model calibration provided in an embodiment of the present invention;
[0031] Figure 4 This is a schematic diagram of the structure of the solar spectral radiation correction system based on a downlink optical sensor provided in an embodiment of the present invention;
[0032] Figure 5 This is a schematic diagram of the structure of a computer device provided in an embodiment of the present invention. Detailed Implementation
[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0034] Please refer to Figure 1 , Figure 1 This is a flowchart of the steps of the solar spectral radiation correction method based on downlink optical sensors provided in the embodiments of the present invention. Specifically, in the embodiments of the present invention, each downlink optical sensor used is a three-channel downlink optical sensor, each sensor has 6 independent optical filters, and there are a total of 18 channels in the three channels, which can collect light intensity values of 18 different wavelengths. In the calculation, the correction calculation is performed in groups of 18 light intensity values.
[0035] The solar spectral radiation correction method specifically includes the following steps:
[0036] S101. Establish a light intensity value model with the light intensity value collected by the downlink optical sensor as a correlation parameter and the rotation angle of the downlink optical sensor relative to the sun direction, the tilt angle of the downlink optical sensor relative to the sun direction, the sunlight intensity, and the ambient light.
[0037] Specifically, in this embodiment of the invention, the light intensity value collected by the downlink optical sensor is a dependent function, and the corresponding independent function variables are the rotation angle of the downlink optical sensor relative to the sun, the tilt angle of the downlink optical sensor relative to the sun, the sunlight intensity, and the ambient light.
[0038] Furthermore, the light intensity value collected by the downlink optical sensor is defined as y, the rotation angle of the downlink optical sensor relative to the sun direction is α, the tilt angle of the downlink optical sensor relative to the sun direction is β, the sunlight intensity is e, the ambient light is b, and the undetermined parameter value is P, wherein the rotation angle α and the tilt angle β have an angular function relationship g, and the light intensity value model satisfies the following relationship (1):
[0039] y=f(α,β,e,b)=e·g(α,β|P)+b (1).
[0040] For example, please refer to Figure 2 , Figure 2 This is a schematic diagram illustrating the relationship between the downlink optical sensor coordinate system and the solar coordinate system provided in an embodiment of the present invention. Figure 2 In the diagram, the circle represents the downlink optical sensor. In the top view on the left, the sky direction where the sun is located is above the top view. A positive direction is defined for the downlink optical sensor and its own coordinate system. The angle between the two is the rotation angle α relative to the sun direction. In the front view on the right, a coordinate system is defined for the downlink optical sensor. The angle between the system and the positive direction of sunlight is defined as the tilt angle β relative to the sun direction.
[0041] This invention embodiment uses indoor experiments to simulate sunlight with halogen lamps to control the intensity of sunlight e and ambient light b. Through experimental data analysis, it is found that the light intensity value y collected by the downlink light sensor has a cosine relationship with the rotation angle α and the tilt angle β relative to the sun.
[0042] Furthermore, the rotation angle α and the tilt angle β are cosines of each other, and the angle function g satisfies the following relationship (2):
[0043] g(α,β|P)=cos(α+p1)+cos(β+p2) (2);
[0044] In relation (2), p1 and p2 are constants after the decomposition of the undetermined parameter value P.
[0045] S102. Obtain a set of actual data collected by the downlink optical sensor, and calibrate the light intensity value model based on the actual data to obtain the undetermined parameter values of the light intensity value model.
[0046] Furthermore, the method used to calibrate the light intensity value model based on the actual data is curve fitting.
[0047] Specifically, even slight differences in the manufacturing process during the integration and installation of downlink optical sensors can result in slightly different light intensity values collected by different downlink optical sensors. Therefore, the light intensity value model parameters used for each set of three downlink optical sensors are also different. The actual data mentioned are existing illumination data that serve as a reference. The actual data collected through a set of experiments can be used to calibrate the undetermined parameter value P of a set of three downlink optical sensors, and the undetermined parameter value P is solved by curve fitting.
[0048] For example, during curve fitting, by keeping the sunlight intensity e and ambient light b constant, the rotation angle α and tilt angle β are brought closer to the actual data. Using a specific set of rotation angle α and tilt angle β as an example, such as... Figure 3 As shown, Figure 3 This is a schematic diagram of model calibration provided in an embodiment of the present invention. Through model calibration, the undetermined parameter P is obtained. The known rotation angle α relative to the sun, the tilt angle β relative to the sun, and the calculated undetermined parameter value P are substituted into the angle function relationship g to obtain the fitted light intensity value after model calibration, as shown below. Figure 3 As shown by the broken line in the figure, it can be seen that the light intensity value fitted after model calibration is extremely similar to the light intensity value collected by the downlink optical sensor, indicating that the model calibration method using curve fitting in this embodiment of the invention is successful and effective.
[0049] S103. Substitute the actual data and the undetermined parameter values into the light intensity value model, and use the least squares method to solve the light intensity value model to obtain the optimal solution of the associated parameters.
[0050] Least squares is a mathematical optimization algorithm that finds the optimal solution for data by minimizing the sum of squared errors. In this embodiment of the invention, after calculating the undetermined parameter value P in step S102, the light intensity values y and P collected by the downlink optical sensor are input into the light intensity value model. The least squares method is used to continuously find the value of the associated parameter with the smallest error relative to the undetermined parameter value P, and then output it.
[0051] S104. The light intensity value collected by the downlink optical sensor is corrected using the light intensity value model that incorporates the optimal solution of the correlation parameters, and the corrected light intensity value is output.
[0052] In this embodiment of the invention, the meaning of the corrected light intensity value is the light intensity value of sunlight incident perpendicularly received by the three downlink optical sensors. Furthermore, in the step of correcting the light intensity value collected by the downlink optical sensors using the light intensity value model incorporating the optimal solution of the correlation parameters, the rotation angle α is set to 0° and the tilt angle β is set to 90°, so as to correct the value collected by the sensor at any angle to the value of the angle at which sunlight is incident perpendicularly on the sensor.
[0053] Furthermore, in the optimal solution of the associated parameters, the optimal solution for the solar intensity is defined as follows: The optimal solution for the ambient light is The corrected light intensity value is y adj The corrected light intensity value y adj The following relation (3) must be satisfied:
[0054]
[0055] The beneficial effects achieved by this invention are that, by correcting the data collected by the downlink optical sensor, the sensor can accurately measure the solar intensity under different incident angles of sunlight, thus providing a data basis for tasks such as reconstructing spectral curves and ensuring the accuracy of material spectral identification.
[0056] This invention also provides a solar spectral radiation correction system based on a downlink optical sensor, please refer to... Figure 4 , Figure 4 This is a schematic diagram of the structure of the solar spectral radiation correction system based on a downlink optical sensor provided in an embodiment of the present invention. Specifically, the solar spectral radiation correction system 200 based on a downlink optical sensor includes:
[0057] Modeling module 201 is used to establish a light intensity value model with the light intensity value collected by the downlink optical sensor as a correlation parameter and the rotation angle of the downlink optical sensor relative to the sun direction, the tilt angle of the downlink optical sensor relative to the sun direction, the sunlight intensity, and the ambient light.
[0058] The calibration module 202 is used to acquire a set of actual data collected by the downlink optical sensor, and calibrate the light intensity value model according to the actual data to obtain the undetermined parameter values of the light intensity value model.
[0059] The solution module 203 is used to substitute the actual data and the undetermined parameter values into the light intensity value model, and use the least squares method to solve the light intensity value model to obtain the optimal solution of the associated parameters;
[0060] The correction module 204 is used to correct the light intensity value collected by the downlink optical sensor using the light intensity value model with the optimal solution of the correlation parameters, and output the corrected light intensity value.
[0061] The solar spectral radiation correction system 200 based on the downlink optical sensor can implement the steps in the solar spectral radiation correction method based on the downlink optical sensor in the above embodiments, and can achieve the same technical effect. Refer to the description in the above embodiments, which will not be repeated here.
[0062] This invention also provides a computer device, please refer to... Figure 5 , Figure 5 This is a schematic diagram of the structure of a computer device provided in an embodiment of the present invention. The computer device 300 includes: a memory 302, a processor 301, and a computer program stored in the memory 302 and executable on the processor 301.
[0063] The processor 301 calls the computer program stored in the memory 302 to execute the steps in the solar spectral radiation correction method based on a downlink optical sensor provided in this embodiment of the invention. Please refer to... Figure 1 Specifically, it includes:
[0064] S101. Establish a light intensity value model with the light intensity value collected by the downlink optical sensor as a correlation parameter and the rotation angle of the downlink optical sensor relative to the sun direction, the tilt angle of the downlink optical sensor relative to the sun direction, the sunlight intensity, and the ambient light.
[0065] S102. Obtain a set of actual data collected by the downlink optical sensor, and calibrate the light intensity value model according to the actual data to obtain the undetermined parameter values of the light intensity value model.
[0066] S103. Substitute the actual data and the undetermined parameter values into the light intensity value model, and use the least squares method to solve the light intensity value model to obtain the optimal solution of the associated parameters.
[0067] S104. The light intensity value collected by the downlink optical sensor is corrected using the light intensity value model that incorporates the optimal solution of the correlation parameters, and the corrected light intensity value is output.
[0068] Furthermore, the light intensity value collected by the downlink optical sensor is defined as y, the rotation angle of the downlink optical sensor relative to the sun direction is α, the tilt angle of the downlink optical sensor relative to the sun direction is β, the sunlight intensity is e, the ambient light is b, and the undetermined parameter value is P, wherein the rotation angle α and the tilt angle β have an angular function relationship g, and the light intensity value model satisfies the following relationship (1):
[0069] y=f(α,β,e,b)=e·g(α,β|P)+b (1).
[0070] Furthermore, the rotation angle α and the tilt angle β are cosines of each other, and the angle function g satisfies the following relationship (2):
[0071] g(α,β|P)=cos(α+p1)+cos(β+p2) (2);
[0072] In relation (2), p1 and p2 are constants after the decomposition of the undetermined parameter value P.
[0073] Furthermore, the method used to calibrate the light intensity value model based on the actual data is curve fitting.
[0074] Furthermore, in the step of correcting the light intensity value collected by the downlink optical sensor using the light intensity value model with the optimal solution of the correlation parameters, the rotation angle α is set to 0° and the tilt angle β is set to 90°.
[0075] Furthermore, in the optimal solution of the associated parameters, the optimal solution for the solar intensity is defined as follows: The optimal solution for the ambient light is The corrected light intensity value is y adj The corrected light intensity value y adj The following relation (3) must be satisfied:
[0076]
[0077] Furthermore, the downlink optical sensor is a three-channel downlink optical sensor, and when calculating the corrected optical intensity value based on the optical intensity value, the calculation is performed using a group of 18 optical intensity values.
[0078] The computer device 300 provided in this embodiment of the invention can implement the steps in the solar spectral radiation correction method based on downlink optical sensor as described in the above embodiments, and can achieve the same technical effect. Refer to the description in the above embodiments, which will not be repeated here.
[0079] This invention also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the various processes and steps of the solar spectral radiation correction method based on a downlink optical sensor provided in this invention, and can achieve the same technical effect. To avoid repetition, it will not be described again here.
[0080] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.
[0081] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.
[0082] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.
[0083] The embodiments of the present invention have been described above with reference to the accompanying drawings. The disclosed embodiments are merely preferred embodiments of the present invention. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many equivalent changes in form without departing from the spirit and scope of the claims of the present invention, and all such changes are within the protection scope of the present invention.
Claims
1. A method for correcting solar spectrum irradiance based on a downwelling optical sensor, characterized in that, The solar spectrum radiation correction method comprises the following steps: A light intensity value model is established, in which the light intensity value collected by a downlink light sensor is correlated with the rotation angle of the downlink light sensor relative to the sun direction, the inclination angle of the downlink light sensor relative to the sun direction, the solar intensity and the ambient light; A set of actual data collected by the downlink light sensor is obtained, and the light intensity value model is calibrated according to the actual data to obtain the undetermined parameter value of the light intensity value model; The actual data and the undetermined parameter value are substituted into the light intensity value model, and the light intensity value model is solved by using the least square method to obtain the optimal solution of the correlated parameters; The light intensity value collected by the downlink light sensor is corrected by using the light intensity value model with the optimal solution of the correlated parameters, and the corrected light intensity value is output.
2. The downwelling light sensor based solar spectral irradiance correction method of claim 1, wherein, The light intensity value collected by the downlink light sensor is defined as y, the rotation angle of the downlink light sensor relative to the sun direction is α, the inclination angle of the downlink light sensor relative to the sun direction is β, the solar intensity is e, the ambient light is b, and the undetermined parameter value is P, wherein the rotation angle α and the inclination angle β have an angle function relationship g, and the light intensity value model satisfies the following relationship (1): y=f(α,β,e,b)=e·g(α,β|P)+b (1).
3. The downwelling light sensor based solar spectral irradiance correction method of claim 2, wherein, The rotation angle α and the inclination angle β are cosine relationship, and the angle function relationship g satisfies the following relationship (2): g(α,β|P)=cos(α+p1)+cos(β+p2) (2). In the relationship (2), p1 and p2 are constants after the undetermined parameter value P is decomposed.
4. The downwelling light sensor based solar spectral irradiance correction method of claim 1, wherein, The method used for calibrating the light intensity value model according to the actual data is a curve fitting method.
5. The downwelling light sensor based solar spectral irradiance correction method of claim 3, wherein, In the step of correcting the light intensity value collected by the downlink light sensor by using the light intensity value model with the optimal solution of the correlated parameters, the rotation angle α is taken as 0° and the inclination angle β is taken as 90°.
6. The downwelling light sensor based solar spectral irradiance correction method of claim 5, wherein, The optimal solution of the correlation parameter is defined as follows: the optimal solution of the sunlight intensity is The optimal solution of the ambient light is The corrected light intensity value is y adj The corrected light intensity value y adj satisfies the following relationship (3):
7. The downwelling light sensor based solar spectral irradiance correction method recited in claim 1, wherein, The downlink light sensor is a three-way downlink light sensor, and when the corrected light intensity value is calculated according to the light intensity value, 18 light intensity values are taken as a group of data for calculation.
8. A downwelling light sensor based solar spectral irradiance correction system, characterized in that, It comprises: A modeling module is configured to establish a light intensity value model in which the light intensity value collected by a downlink light sensor is correlated with the rotation angle of the downlink light sensor relative to the sun direction, the inclination angle of the downlink light sensor relative to the sun direction, the solar intensity and the ambient light; A calibration module is configured to obtain a set of actual data collected by the downlink light sensor, and calibrate the light intensity value model according to the actual data to obtain the undetermined parameter value of the light intensity value model; A solving module is configured to substitute the actual data and the undetermined parameter value into the light intensity value model, and solve the light intensity value model by using the least square method to obtain the optimal solution of the correlated parameters; A correction module is configured to correct the light intensity value collected by the downlink light sensor by using the light intensity value model with the optimal solution of the correlated parameters, and output the corrected light intensity value.
9. A computer device, comprising: It comprises: The memory, the processor and the computer program stored on the memory and capable of running on the processor, the processor implementing the steps of the downwelling light sensor based solar spectral irradiance correction method according to any one of claims 1 to 7 when executing the computer program.
10. A computer-readable storage medium, characterized in that, The computer program is stored on the computer readable storage medium and capable of being executed by the processor, the processor implementing the steps of the downwelling light sensor based solar spectral irradiance correction method according to any one of claims 1 to 7 when executing the computer program.
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