Aerosol particle size distribution measurement system and method based on long-wave infrared laser radar

Abstract

The invention belongs to the technical field of atmospheric environment monitoring, and discloses an aerosol particle size distribution measurement system based on a long-wave infrared laser radar, a long-wave infrared laser emission module generates a stable long-wave infrared laser signal, a light beam expansion and emission module carries out light beam shaping and divergence angle compression on the laser signal, and the long-wave infrared laser radar generates a long-wave infrared laser signal; the receiving and detecting module captures back scattering light of aerosol in the atmosphere and converts the back scattering light into electric signals, the signal processing module carries out noise reduction and analysis on the electric signals output by the receiving and detecting module to obtain aerosol optical parameters, and the Mie scattering theory calculation module calculates extinction efficiency factors of aerosol particles under different particle sizes based on the Mie scattering theory. And the particle size distribution inversion module is combined with the extinction coefficient and the extinction efficiency factor, and aerosol particle size distribution is obtained through inversion. According to the invention, through combination of long-wave infrared laser detection and a precise inversion algorithm, high-precision measurement of the particle size distribution of the large-particle aerosol is realized.

Description

Technical Field

[0001] This invention belongs to the field of atmospheric environment monitoring technology, and relates to an aerosol particle size distribution measurement system and method based on long-wave infrared lidar, which is suitable for the accurate detection of particle size parameters of large particle aerosols (including bioaerosols) in the atmosphere. Background Technology

[0002] Atmospheric aerosols, as an important component of the atmospheric system, directly affect climate radiative forcing, atmospheric visibility, and human respiratory health through their particle size distribution. They are key parameters for assessing atmospheric environmental quality and conducting climate modeling research. Among current mainstream aerosol particle size measurement technologies, visible light and near-infrared lidar are limited by wavelength. When detecting large particles (greater than 5 μm, such as pollen, dust particles, and bioaerosol spores), they are prone to problems such as extinction signal saturation and excessive particle size inversion errors, making it difficult to meet the monitoring needs of large particles in complex atmospheric environments.

[0003] Long-wave infrared (9-11 μm) lasers possess unique advantages such as strong penetration and sensitivity to large particle scattering, theoretically offering a viable solution to the challenge of large particle measurement. However, current long-wave infrared lidar technologies primarily focus on atmospheric composition concentration detection and have not yet developed a mature measurement system for aerosol particle size distribution. On one hand, there is a lack of quantitative correlation models between extinction efficiency factors and particle size in the long-wave infrared band; on the other hand, traditional inversion algorithms are ill-suited to the characteristics of long-wave infrared signals, resulting in measurement accuracy that fails to meet practical application requirements. Therefore, developing an aerosol particle size distribution measurement system based on long-wave infrared lidar to fill the gap in high-precision large particle measurement technology has significant scientific value and application prospects. Summary of the Invention

[0004] (a) Purpose of the invention The purpose of this invention is to overcome the shortcomings of existing lidar in measuring the particle size of large aerosols, and to provide a long-wave infrared lidar system and measurement method that balances measurement range and accuracy, so as to achieve efficient and accurate detection of aerosol particle size distribution.

[0005] (II) Technical Solution To address the aforementioned technical problems, this invention provides an aerosol particle size distribution measurement system based on a long-wave infrared lidar, comprising: a long-wave infrared laser emitting module 1, a beam spreading and emitting module 2, a receiving and detecting module 3, a signal processing module 4, a Mie scattering theory calculation module 5, and a particle size distribution inversion module 6. The long-wave infrared laser emitting module 1 generates a stable long-wave infrared laser signal; the beam spreading and emitting module 2 performs beam shaping and divergence angle compression on the laser signal; the receiving and detecting module 3 captures the backscattered light from aerosols in the atmosphere and converts it into an electrical signal; the signal processing module 4 performs noise reduction and analysis on the electrical signal output by the receiving and detecting module to obtain aerosol optical parameters; the Mie scattering theory calculation module 5 calculates the extinction efficiency factor of aerosol particles at different particle sizes based on Mie scattering theory; and the particle size distribution inversion module 6 combines the extinction coefficient and the extinction efficiency factor to invert the aerosol particle size distribution.

[0006] Long-wave infrared laser emitting module: used to generate stable long-wave infrared laser signals, including a tunable long-wave infrared laser and a laser frequency stabilization unit; the tunable long-wave infrared laser can output 60 branch lasers in the 9-11μm band, with a laser repetition frequency of 20Hz, a pulse width of less than 100ns, and a maximum single pulse energy of 100mJ; the laser frequency stabilization unit uses phase-locked loop technology to control the laser frequency stability within ±1MHz, ensuring the consistency of the laser signal wavelength.

[0007] Beam spreading and emission module: used for beam shaping and divergence angle compression of laser signals, including a 5x laser beam expander and a high-precision optical collimator; the 5x laser beam expander compresses the laser divergence angle output by the laser emission module from 4.5mrad to 1mrad, reducing energy loss during atmospheric transmission; the high-precision optical collimator 22 ensures the parallelism of the laser beam and ensures the accuracy of the detection direction.

[0008] The receiving and detection module is used to capture backscattered light from aerosols in the atmosphere and convert it into an electrical signal. It includes a large-aperture receiving telescope, a long-wave infrared filter, and an infrared photodetector. The large-aperture receiving telescope (aperture ≥ 200 mm) improves the collection efficiency of backscattered light. The long-wave infrared filter only allows scattered light in the 9-11 μm band to pass through, filtering out ambient stray light interference. The infrared photodetector (detectivity ≥ 10¹² cm·Hz^(1 / 2) / W) converts the scattered light signal into a weak electrical signal and performs preliminary amplification.

[0009] The signal processing module is used to reduce noise and analyze the electrical signal output by the receiving and detection module to obtain aerosol optical parameters. It includes a preamplifier, a signal denoising unit, and a radar equation calculation unit. The preamplifier amplifies the weak electrical signal to a processable range. The signal denoising unit uses a wavelet transform denoising algorithm to remove background noise and electromagnetic interference from the electrical signal. The radar equation calculation unit combines parameters such as laser emission energy and receiving optical efficiency to calculate the extinction coefficient and backscattering coefficient of the aerosol using the lidar equation.

[0010] The Mie scattering theory calculation module is used to calculate the extinction efficiency factor of aerosol particles with different particle sizes based on Mie scattering theory. It includes a particle size range setting unit, an optical parameter input unit, and an extinction efficiency factor calculation unit. The particle size range setting unit can set a particle size calculation range of 0.1-100 μm according to measurement requirements, with a minimum particle size step of 0.01 μm. The optical parameter input unit can input parameters such as the refractive index (real and imaginary parts) and laser wavelength of the aerosol particles. The extinction efficiency factor calculation unit calculates the extinction efficiency factor for the corresponding particle size using the Mie scattering theory formula and outputs the extinction efficiency factor-particle size relationship curve (as shown in Figure 2).

[0011] The particle size distribution inversion module is used to invert the aerosol particle size distribution by combining the extinction coefficient and the extinction efficiency factor. It includes an integral equation construction unit, a regularization solution unit, and a particle size distribution output unit. The integral equation construction unit constructs a first-type Fredholm integral equation based on the relationship between the aerosol extinction coefficient and the extinction efficiency factor. The regularization solution unit uses a generalized cross-validation regularization method to solve the integral equation to avoid oscillations in the solution. The particle size distribution output unit outputs the inversion results as particle size distribution curves, characteristic particle sizes (such as median particle size and geometric mean particle size), and calculates the fitting error between the inversion results and the standard model.

[0012] According to the measurement system, the present invention also provides a method for measuring aerosol particle size distribution based on long-wave infrared lidar, comprising the following steps: 1. Laser signal emission: The long-wave infrared laser emission module is activated, and the tunable long-wave infrared laser generates a laser signal in the 9-11μm band. The laser frequency stabilization unit stabilizes the laser frequency. After the laser signal is compressed by the beam expander and the 5x laser beam expander of the emission module to compress the divergence angle, and collimated by the high-precision optical collimator, it is emitted into the atmospheric detection area.

[0013] 2. Backscattered light reception and conversion: Aerosol particles in the atmosphere backscatter the laser signal. The large-aperture receiving telescope of the receiving and detection module captures the backscattered light. After the long-wave infrared filter filters out stray light, the infrared photodetector converts the scattered light signal into an electrical signal and transmits it to the signal processing module.

[0014] 3. Optical parameter calculation: The preamplifier of the signal processing module amplifies the electrical signal, and the signal noise reduction unit uses wavelet transform algorithm to remove noise; the radar equation calculation unit substitutes parameters such as laser emission energy, receiving telescope aperture, and atmospheric transmission distance, and calculates the extinction coefficient σ(λ,z) ​​and backscattering coefficient β(λ,z) ​​of the aerosol through the lidar equation (where λ is the laser wavelength and z is the detection distance).

[0015] 4. Extinction Efficiency Factor Calculation: The particle size range setting unit of the Mie scattering theory calculation module sets the target particle size range (e.g., 1-50μm), and the optical parameter input unit inputs the aerosol particle refractive index (e.g., the real part of the refractive index of sand particles is 1.53, and the imaginary part is 0.001) and the laser wavelength; the extinction efficiency factor calculation unit calculates the extinction efficiency factor Q_ext(d) (where d is the particle size) corresponding to each particle size in the range based on the Mie scattering theory, and generates the extinction efficiency factor-particle size relationship curve.

[0016] 5. Particle Size Distribution Inversion: The integral equation construction unit of the particle size distribution inversion module constructs a first-type Fredholm integral equation based on the relationship between the extinction coefficient and the extinction efficiency factor: σ(λ,z)=∫(d_min)^(d_max) Q_ext(d)·n(d,z)·π(d / 2)²dd (where n(d,z) is the particle size distribution function, and d_min and d_max are the upper and lower limits of the particle size interval, respectively); the regularization solution unit solves the integral equation using the generalized cross-validation method to obtain the particle size distribution function n(d,z); the particle size distribution output unit outputs the particle size distribution curve and characteristic parameters, and calculates the fitting error (such as the fitting error with the unimodal log-normal distribution model).

[0017] 6. Result verification and optimization: If the fitting error is greater than the preset threshold (e.g., 7.5%), adjust the optical parameters of the Mie scattering theory calculation module or the regularization parameters of the particle size distribution inversion module, and repeat steps 4-5 until the error meets the requirements; if the error is less than or equal to the threshold, output the final aerosol particle size distribution result.

[0018] (III) Beneficial Effects The aerosol particle size distribution measurement system and method based on long-wave infrared lidar provided by the above technical solution achieves high-precision measurement of large particle aerosol particle size distribution by combining long-wave infrared laser detection with a precise inversion algorithm, and has the following beneficial effects: 1. Breakthrough in measurement range: It adopts a 9-11μm long-wave infrared laser, which effectively solves the problem of insufficient measurement capability of traditional visible light / near infrared lidar for large particles (>5μm), and can cover the measurement needs of large-diameter aerosols such as bioaerosols, dust, and cloud particles.

[0019] 2. High-precision measurement: Through laser frequency stabilization, wavelet transform noise reduction, and generalized cross-validation regularization, the measurement error of aerosol particle size distribution is controlled within 7.5%, which is significantly better than existing similar measurement technologies (the error is mostly between 10% and 15%).

[0020] 3. Technological Innovation: For the first time, a quantitative correlation model between extinction efficiency factor and particle size in the long-wave infrared band was established. Combined with lidar technology, the direct inversion of large particle size distribution was achieved, filling a technological gap in this field.

[0021] 4. Wide range of applications: The system has a compact structure and can be adapted to various scenarios such as ground-based fixed monitoring and mobile vehicle-mounted monitoring. It is not only suitable for conventional atmospheric environmental monitoring, but can also provide technical support for special fields such as early warning of biochemical terrorist attacks and agricultural pollen monitoring. Attached Figure Description

[0022] Figure 1 is a schematic diagram of the aerosol particle size distribution measurement system based on long-wave infrared lidar provided by the present invention. Figure 2 shows the relationship between the extinction efficiency factor at different wavelengths and the particle size provided by the present invention. Detailed Implementation

[0023] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0024] Reference Figure 1 As shown, the aerosol particle size distribution measurement system based on long-wave infrared lidar in this embodiment includes: a long-wave infrared laser emitting module 1, a beam spreading and emitting module 2, a receiving and detection module 3, a signal processing module 4, a Mie scattering theory calculation module 5, and a particle size distribution inversion module 6; the long-wave infrared laser emitting module 1 is used to generate a stable long-wave infrared laser signal, including a tunable long-wave infrared laser and a laser frequency stabilization unit; In this embodiment, the long-wave infrared laser emitting module 1 uses a tunable quantum cascade laser as the tunable long-wave infrared laser. Its output band covers 60 branch lasers in the range of 9-11μm, with a repetition frequency of 20Hz, a pulse width of 80ns, and a single pulse energy of 100mJ. At the same time, it is equipped with a laser frequency stabilization unit using rubidium atomic clock phase-locked loop technology to precisely control the laser frequency stability within ±0.5MHz, ensuring the stability and consistency of the laser signal.

[0025] In the beam expansion and emission module 2, the 5x laser beam expander adopts a refractive optical structure and selects germanium (Ge) as the material to ensure high transmittance in the long-wave infrared band. The high-precision optical collimator is set with a focal length of 100mm and collimation accuracy controlled within ≤0.1mrad, achieving effective shaping and divergence angle compression of the laser signal.

[0026] The receiving and detection module 3 is equipped with a large-aperture receiving telescope with a Cassegrain structure, which has an aperture of 250mm and a focal length of 2000mm. It is paired with a long-wave infrared filter with a center wavelength of 10μm and a bandwidth of 1μm, as well as a mercury cadmium telluride (MCT) infrared photodetector with a detectivity of 1.5×10¹²cm·Hz^(1 / 2) / W and a response time of ≤10ns, which efficiently captures backscattered light and completes photoelectric conversion.

[0027] Signal processing module 4 uses a low-noise operational amplifier as a preamplifier with a gain of 1000 times and a noise figure of ≤1.5dB. The signal noise reduction unit uses a dB4 wavelet basis and a layer decomposition combined with a soft threshold noise reduction algorithm to remove noise. The radar equation calculation unit presets parameters such as laser emission energy, receiving telescope area, and optical transmittance, and calculates aerosol optical parameters based on the standard lidar equation.

[0028] In the Mie scattering theory calculation module 5, the particle size range setting unit sets the particle size range to 0.5-100μm with a particle size step of 0.01μm. The optical parameter input unit can input the refractive index of typical aerosol particles (such as the real part of the refractive index of biological aerosol spores is 1.58 and the imaginary part is 0.002, and the real part of the refractive index of dust particles is 1.53 and the imaginary part is 0.001). The extinction efficiency factor calculation unit calculates Q_ext(d) for the corresponding particle size based on the Mie scattering theory code.

[0029] The integral equation construction unit of particle size distribution inversion module 6 constructs an integral equation based on the relationship between the extinction coefficient and Q_ext(d). The regularization solution unit uses generalized cross-validation to determine the regularization parameters and solve the integral equation. The particle size distribution output unit outputs the particle size distribution curve in Origin format and calculates the median particle size (D50), geometric standard deviation (σg), and fitting error, laying a precise system foundation for subsequent measurement work.

[0030] (II) Actual Measurement Process Taking the measurement of cloud particle size distribution (a typical example of large aerosol particles) under cloudy weather conditions as an example, the specific steps are as follows: 1. System startup and warm-up: Turn on the entire system and warm up for 30 minutes to ensure that the laser emission module, detector and other components are working stably; calibrate the laser frequency through the laser frequency stabilization unit to stabilize the output laser wavelength at 10μm.

[0031] 2. Laser emission and scattered light reception: The long-wave infrared laser emission module 1 generates a 10μm laser signal, which is then compressed to a divergence angle of 1mrad by the beam expansion and emission module before being vertically emitted into the cloud region; the large-aperture receiving telescope of the receiving and detection module is aligned with the laser emission direction to capture the backscattered light of cloud particles, which is then converted into an electrical signal by a filter and detector and transmitted to the signal processing module.

[0032] 3. Optical Parameter Calculation: The preamplifier of the signal processing module amplifies the electrical signal to 1-5V; the signal noise reduction unit removes atmospheric turbulence and electromagnetic interference noise through wavelet transform; the radar equation calculation unit substitutes the laser energy (100mJ) and the receiving telescope area (0.049m²) into the calculation. 2 Based on parameters such as detection distance (2km), the extinction coefficient of cloud particles σ(10μm,2km) was calculated to be 0.15km. -1 .

[0033] 4. Extinction efficiency factor calculation: The Mie scattering theory calculation module inputs the refractive index of the cloud particles (real part 1.33, imaginary part 0), sets the particle size range to 5-50μm, and calculates the extinction efficiency factor Q_ext (d) within this range, where Q_ext=2.1 when d=20μm and Q_ext=2.3 when d=30μm.

[0034] 5. Particle size distribution inversion: The particle size distribution inversion module constructs the integral equation: 0.15=∫(5)^(50) Q_ext(d)·n (d,2km)·π(d / 2)² dd; the generalized cross-validation regularization method is used to solve the equation, and the cloud particle size distribution function n (d,2km) is obtained. The distribution is a unimodal log-normal distribution with a median particle size D50=25μm and a geometric standard deviation σg=1.2.

[0035] 6. Result verification: The particle size distribution obtained by inversion was compared with the standard unimodal log-normal distribution model. The fitting error was calculated to be 6.8% (less than the 7.5% threshold), which verified the high accuracy of the measurement results. The particle size distribution curve and characteristic parameters were output to complete this cloud particle size distribution measurement.

[0036] like Figure 2 As shown, the horizontal axis represents particle size (unit: μm), and the vertical axis represents extinction efficiency factor (dimensionless). Curves 1-3 correspond to the trends of extinction efficiency factor at wavelengths of 8μm, 10μm, and 12μm, respectively. As can be seen from the figure, as the particle size increases, the fluctuation of extinction efficiency factor at each wavelength gradually becomes smoother and approaches the average value. Furthermore, wavelength is positively correlated with extinction efficiency factor, that is, the larger the wavelength, the larger the extinction efficiency factor, which verifies the high sensitivity of the long-wave infrared band to large particles.

[0037] (III) System Performance Testing To verify the system's stability and accuracy, multiple repeatability tests and comparative tests were conducted: Repeatability test: At the same time and the same detection point (cloud layer at 2km), 10 consecutive measurements were taken. The median particle size D50 fluctuated between 24.8 and 25.2 μm, with a relative standard deviation of 1.6%, which proves that the system has good repeatability.

[0038] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An aerosol particle size distribution measurement system based on long-wave infrared lidar, characterized in that, include: The system comprises a long-wave infrared laser emitting module, a beam spreading and emitting module, a receiving and detection module, a signal processing module, a Mie scattering theory calculation module, and a particle size distribution inversion module. The long-wave infrared laser emitting module generates a stable long-wave infrared laser signal. The beam spreading and emitting module performs beam shaping and divergence angle compression on the laser signal. The receiving and detection module captures backscattered light from aerosols in the atmosphere and converts it into an electrical signal. The signal processing module reduces noise and analyzes the electrical signal output by the receiving and detection module to obtain the aerosol optical parameters. The Mie scattering theory calculation module calculates the extinction efficiency factor of aerosol particles at different particle sizes based on Mie scattering theory. The particle size distribution inversion module combines the extinction coefficient and the extinction efficiency factor to invert the aerosol particle size distribution.

2. The aerosol particle size distribution measurement system based on long-wave infrared lidar as described in claim 1, characterized in that, The long-wave infrared laser emitting module includes a tunable long-wave infrared laser and a laser frequency stabilization unit. The tunable long-wave infrared laser outputs 60 branch laser lines in the 9-11μm band, with a laser repetition frequency of 20Hz, a pulse width of less than 100ns, and a maximum single-pulse energy of 100mJ. The laser frequency stabilization unit uses phase-locked loop technology to control the laser frequency stability within ±1MHz, ensuring the consistency of the laser signal wavelength.

3. The aerosol particle size distribution measurement system based on long-wave infrared lidar as described in claim 2, characterized in that, The beam expansion and emission module includes a 5x laser beam expander and a high-precision optical collimator; the 5x laser beam expander compresses the laser divergence angle output by the laser emission module from 4.5 mrad to 1 mrad; the high-precision optical collimator 22 adjusts the parallelism of the laser beam.

4. The aerosol particle size distribution measurement system based on long-wave infrared lidar as described in claim 3, characterized in that, The receiving and detection module includes a large-aperture receiving telescope, a long-wave infrared filter, and an infrared photodetector. The large-aperture receiving telescope with an aperture of ≥200mm improves the collection efficiency of backscattered light. The long-wave infrared filter allows scattered light in the 9-11μm band to pass through while filtering out ambient stray light interference. The infrared photodetector with a detectivity of ≥10¹²cm·Hz^(1 / 2) / W converts the scattered light signal into a weak electrical signal and performs preliminary amplification.

5. The aerosol particle size distribution measurement system based on long-wave infrared lidar as described in claim 4, characterized in that, The signal processing module includes a preamplifier, a signal denoising unit, and a radar equation calculation unit. The preamplifier amplifies weak electrical signals to a processable range. The signal denoising unit uses a wavelet transform denoising algorithm to remove background noise and electromagnetic interference from the electrical signals. The radar equation calculation unit combines parameters such as laser emission energy and receiving optical efficiency to calculate the extinction coefficient and backscattering coefficient of aerosols using the lidar equation.

6. The aerosol particle size distribution measurement system based on long-wave infrared lidar as described in claim 5, characterized in that, The Mie scattering theory calculation module includes a particle size range setting unit, an optical parameter input unit, and an extinction efficiency factor calculation unit. The particle size range setting unit sets a particle size calculation range of 0.1-100 μm according to measurement requirements, with a minimum particle size step of 0.01 μm. The optical parameter input unit inputs the refractive index of the aerosol particles and the laser wavelength. The extinction efficiency factor calculation unit calculates the extinction efficiency factor for the corresponding particle size using the Mie scattering theory formula and outputs the extinction efficiency factor-particle size relationship curve.

7. The aerosol particle size distribution measurement system based on long-wave infrared lidar as described in claim 6, characterized in that, The particle size distribution inversion module includes an integral equation construction unit, a regularization solution unit, and a particle size distribution output unit. The integral equation construction unit constructs a first-type Fredholm integral equation based on the relationship between the aerosol extinction coefficient and the extinction efficiency factor. The regularization solution unit uses a generalized cross-validation regularization method to solve the integral equation to avoid oscillations in the solutions. The particle size distribution output unit outputs the inversion results as particle size distribution curves and characteristic particle sizes, and calculates the fitting error between the inversion results and the standard model.

8. A method for measuring aerosol particle size distribution based on a long-wave infrared lidar using the measurement system described in claim 7, characterized in that, Includes the following steps: S1: Laser signal emission; S2: Backscattered light reception and conversion; S3: Calculation of optical parameters; S4: Extinction efficiency factor calculation; S5: Particle size distribution inversion; S6: Result verification and optimization.

9. The method for measuring aerosol particle size distribution based on long-wave infrared lidar as described in claim 8, characterized in that, In step S1, the long-wave infrared laser emitting module is activated, and the tunable long-wave infrared laser generates a laser signal in the 9-11μm band. The laser frequency stabilization unit stabilizes the laser frequency. After the laser signal is compressed by the beam expander and the 5x laser beam expander of the emitting module, and collimated by the high-precision optical collimator, it is emitted into the atmospheric detection area. In step S2, aerosol particles in the atmosphere backscatter the laser signal. The large-aperture receiving telescope of the receiving detection module captures the backscattered light. After the long-wave infrared filter filters out stray light, the infrared photodetector converts the scattered light signal into an electrical signal and transmits it to the signal processing module. In step S3, the preamplifier of the signal processing module amplifies the electrical signal, and the signal noise reduction unit uses a wavelet transform algorithm to remove noise. The radar equation calculation unit substitutes the laser emission energy, the receiving telescope aperture, and the atmospheric transmission distance parameters, and calculates the extinction coefficient σ(λ,z) ​​and backscattering coefficient β(λ,z) ​​of the aerosol through the lidar equation, where λ is the laser wavelength and z is the detection distance.

10. The method for measuring aerosol particle size distribution based on long-wave infrared lidar as described in claim 9, characterized in that, In step S4, the particle size range setting unit of the Mie scattering theory calculation module sets the target particle size range, and the optical parameter input unit inputs the refractive index of aerosol particles and the laser wavelength. The extinction efficiency factor calculation unit calculates the extinction efficiency factor Q_ext(d) for each particle size within the specified particle size range based on Mie scattering theory, where d is the particle size, and generates an extinction efficiency factor-particle size relationship curve. In step S5, the integral equation construction unit of the particle size distribution inversion module constructs a first-type Fredholm integral equation based on the relationship between the extinction coefficient and the extinction efficiency factor: σ(λ,z)=∫(d_min)^(d_max)Q_ext(d)·n(d,z)·π(d / 2)²dd, where n(d,z) is the particle size distribution function, and d_min and d_max are the upper and lower limits of the particle size range, respectively. The regularization solution unit solves the integral equation using the generalized cross-validation method to obtain the particle size distribution function n(d,z). The particle size distribution output unit outputs the particle size distribution curve and characteristic parameters, and calculates the fitting error. In step S6, if the fitting error is greater than a preset threshold, the Mie scattering is adjusted. Repeat steps S4-S5 for the optical parameters of the scattering theory calculation module or the regularization parameters of the particle size distribution inversion module until the error meets the requirements; if the error is less than or equal to the threshold, output the final aerosol particle size distribution result.

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