Water vapor Raman laser radar beam splitting system and method based on photon sieve array
Through the photon sieve array design, the optical path of the water vapor Raman lidar spectroscopic system is simplified, and efficient filtering and collection of signals of different wavelengths are achieved, which solves the problem of high complexity of the existing system, promotes the lightweight and miniaturization of the system, and improves the detection performance.
Patent Information
- Application Number
- CN202511111077.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-08
- Publication Date
- 2025-10-14
AI Technical Summary
The existing water vapor Raman lidar spectroscopic system has a complex optical path design, which results in a large system size and heavy weight, which is not conducive to lightweighting and miniaturization.
A photon sieve array design is adopted, and through the combination of optical fiber, collimating beam expansion lens, photon sieve array and CMOS imaging device, efficient filtering and collection of atmospheric backscattered echo signals of different wavelengths are achieved. The photon sieve array is used to focus and filter signals of different wavelengths, and the pinhole and CMOS imaging device are combined to achieve synchronous signal collection.
The optical path of the spectroscopic system is simplified, the system complexity is reduced, which is conducive to lightweight and miniaturization. At the same time, it realizes the effective separation and filtering of atmospheric Mie-Rayleigh scattering, nitrogen Raman scattering and water vapor Raman scattering signals, and improves the practical performance of the lidar.
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Figure CN120779427A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of laser radar atmospheric remote sensing detection methods, and particularly relates to a water vapor Raman laser radar spectrometer based on a photon sieve array, and also relates to a spectrometer method of the spectrometer. BACKGROUND
[0002] In meteorology, atmospheric water vapor is an important atmospheric physical parameter and a basic parameter for fine structure atmospheric observation. Atmospheric water vapor is an important part of the earth's water cycle and has a profound impact on climate, weather and ecological systems. Laser radar, as an active remote sensing detection technology, has the advantages of continuous measurement, real-time, high spatial resolution and high detection sensitivity. Raman laser radar is an optical detection method that uses the Raman scattering effect of laser and atmospheric medium to obtain medium density information through detection of the backscattering Raman spectrum of the medium. Laser radar using molecular vibration Raman scattering of molecules with high concentration such as nitrogen and water vapor can obtain effective fine detection of atmospheric water vapor. At present, Raman laser radar is getting more and more attention and application, and has become one of the main methods for fine detection of atmospheric water vapor.
[0003] The structure of a Raman laser radar generally includes a transmitting system, a receiving system, a spectrometer system and a data processing system. The research on high-precision and high-reliability spectrometer systems has always been the core problem of water vapor detection Raman laser radar technology. The spectrometer system uses spectrometer devices to realize efficient extraction of Raman scattering signals and suppresses and filters out elastic scattering signals and solar background light, and its composition and structure directly affect the detection performance of atmospheric detection laser radar. At present, the spectrometer devices used at home and abroad mainly include narrow-band optical filters, Fabry-Perot etalons and gratings, etc. These traditional spectrometer devices provide hardware support for high temporal and spatial resolution atmospheric water vapor vertical profile detection, but also face new challenges, including high cost, system complexity and being not conducive to lightweight and small design. The Raman laser radar spectrometer system needs to separate and detect multiple Raman scattering wavelengths at the same time, which usually relies on complex optical filters, prisms, gratings or beam splitters, resulting in complex optical paths and large volume. And the signals after spectrometry need to be received by multiple detectors such as photodiode arrays, photomultiplier tubes or CCD arrays, and the arrangement of multiple detectors and their circuit integration increase the volume and weight. SUMMARY
[0004] The first object of the present application is to provide a water vapor Raman laser radar spectrometer based on a photon sieve array, which solves the problem of complex optical path design of the existing water vapor Raman laser radar spectrometer.
[0005] The second object of the present application is to provide a water vapor Raman laser radar spectrometer method based on a photon sieve array.
[0006] The first technical solution adopted by the present application is a water vapor Raman lidar spectral system based on a photon sieve array, comprising a fiber, an L1 lens, a photon sieve array, a pinhole and a CMOS imaging device arranged in sequence along an optical axis; The L1 lens is arranged in the light path of the exit end of the fiber, and the exit end surface of the fiber coincides with the front focal plane of the L1 lens; The photon sieve array is arranged in the exit light path of the L1 lens; The pinhole is arranged at the back focal plane of the photon sieve array, and the center of the pinhole coincides with the main focal point of the photon sieve array on the optical axis; The CMOS imaging device is arranged in the exit light path of the pinhole.
[0007] The first technical solution of the present application is further characterized in that, The L1 lens is a collimating and expanding lens.
[0008] The second technical solution adopted by the present application is a water vapor Raman lidar spectral method based on a photon sieve array, which uses a water vapor Raman lidar spectral system based on a photon sieve array, and the specific steps are as follows: S1: using a fiber to couple the atmospheric backscattering echo signal received by a telescope to the subsequent optical path; S2: converting the subsequent light into a parallel light beam with a half aperture of 20mm through a collimating and expanding lens; S3: making the collimated and expanded parallel light beam incident to the photon sieve array, and using the photon sieve array to filter the atmospheric backscattering echo signal of different wavelengths, so that the photon sieve is focused at different spatial positions of the focal plane; S4: setting a pinhole at the focal plane of the photon sieve array, and screening the focused light signal corresponding to the target wavelength through the pinhole; S5: using a CMOS imaging device to convert the light signal screened through the pinhole into an electrical signal, and completing the collection and processing of the atmospheric backscattering signal.
[0009] The second technical solution of the present application is further characterized in that, The photon sieve array in S3 has a size of 40x40mm, and is composed of a first photon sieve, a second photon sieve and a third photon sieve with different center wavelengths.
[0010] The center positions of the first photon sieve, the second photon sieve and the third photon sieve are defined in the focal plane coordinate system as follows: the center position of the first photon sieve is (0, 5) mm; the center position of the second photon sieve is (7, -5) mm; and the center position of the third photon sieve is (-7, -5) mm; The first photon sieve, the second photon sieve and the third photon sieve are all set to be coated with SiO2 film layers, and the thickness of the SiO2 film layers are 372.8 nm, 410.0 nm and 434.2 nm respectively; The focal lengths of the first, second, and third photon sieves are all 100 mm, and their central wavelengths are 354.7 nm, 386.7 nm, and 407.5 nm, respectively; The apertures of the first photon sieve, the second photon sieve and the third photon sieve are 11.4 mm, 12.2 mm and 12.6 mm respectively.
[0011] The first photon sieve (0, 5) mm corresponds to focusing the atmospheric backscattered echo signal of 354.7 nm; The second photon sieve (7, -5) mm corresponds to focusing the atmospheric backscattered echo signal of 386.7 nm; The third photon sieve (-7, -5) mm corresponds to the focused atmospheric backscattered echo signal of 407.5 nm; The focusing spot sizes of the first photon sieve, the second photon sieve and the third photon sieve are 6.8um, 7.0um and 7.2um respectively, realizing the synchronous acquisition of 354.7nm, 386.7nm and 407.5nm signals.
[0012] The original method for selecting the wavelength of any photon sieve is: When the minimum aperture of any photon sieve is larger than the wavelength of the incident wave, according to the Fresnel-Kirchhoff scalar diffraction theory, n The amplitude of the small hole at any point on the imaging plane U n (X,Y) for: (1) Where, , , , A n is the light field amplitude at the center of the pinhole, L n =0, g n =0, h n =0,( x n , y n ) is the n The coordinates of the center of the small hole, r n For the n The radius of the small hole on the first ring is n Aperture positions on the ring Rn Concerning, k For wave number, J1 is the first Bessel function.
[0013] In formula (1) r n And R n The expression is: (2) (3) In the formula, f The focal length of the photon sieve to the focal plane is represented by f, λ The incident wavelength is represented by λ, and the number of holes on the first ring can be represented by N1. n Wherein , wherein α =1.0, β =5.0, N ring The total number of rings of the photon sieve holes is represented by N. The different spatial positions of the photon sieve focusing on the focal plane are specifically: The light field on the focal plane is the superposition of the diffraction light fields of numerous small holes, so the light field distribution of the entire photon sieve on the focal plane is U ( X,Y ): (4) Wherein m The number of all small holes of the photon sieve is represented by N.
[0014] In S4, the small aperture diaphragm is arranged at the focal plane of the photon sieve array, specifically: The small aperture diaphragm is arranged at the focal plane of the photon sieve array, and the aperture size is 10um, which is respectively located at (0, 5) mm, (7, -5) mm and (-7, -5) mm.
[0015] Compared with the prior art, the beneficial effects of the present application are: The application provides a water vapor Raman lidar spectrometer system and method based on a photon sieve array. Through the design of three photon sieves, the spectral transmission of a very small full width at half maximum (FWHM) is realized, and the signal intensity of other wavelengths can be inhibited, and the required spectral signal can be obtained at the corresponding spatial position of the photon sieve array diffraction focal plane. At the same time, the simultaneous acquisition of Mie-Rayleigh scattering signals, nitrogen vibration Raman scattering signals and water vapor Raman scattering signals is realized by using a CMOS detector. The method of simultaneously acquiring signals by using a single detector after the photon sieve array focal plane simplifies the complex optical path of the existing spectrometer system. The method not only significantly reduces the complexity of the traditional spectrometer system, is conducive to lightweight and miniaturized design, but also can complete the effective separation and filtering extraction of atmospheric Mie-Rayleigh scattering, nitrogen Raman scattering and water vapor Raman scattering echo signals, and improves the practical performance of the Raman lidar. BRIEF DESCRIPTION OF DRAWINGS
[0016] Figure 1 is a structural schematic diagram of the water vapor Raman lidar spectrometer system based on the photon sieve array of the application; Figure 2 is a laser wavelength of 354.7nm laser lidar atmospheric echo signal spectrum distribution graph Figure 3 is a spectral transmission curve diagram of the first photon sieve, the second photon sieve and the third photon sieve of the application; Figure 4 is a distribution schematic diagram of the photon sieve array of the application; Figure 5 is a light intensity distribution diagram of the 354.7nm, 386.7nm and 407.5nm optical signals on the focal plane of the photon sieve array respectively; Figure 6 is a light intensity distribution diagram of the mixed light signals of 354.7nm, 386.7nm and 407.5nm on the focal plane of the photon sieve array; Figure 7 is a flow schematic diagram of the water vapor Raman lidar spectrometer method based on the photon sieve array in the embodiment 5 of the application.
[0017] In the figure, 1. optical fiber; 2. L1 lens; 3. photon sieve array; 4. pinhole; 5. CMOS imaging device. DETAILED DESCRIPTION
[0018] The application will be described in detail below in combination with the drawings and specific embodiments.
[0019] Embodiment 1 This embodiment provides a water vapor Raman lidar spectrometer system based on a photon sieve array, as shown in Figure 1As shown, it comprises optical fiber 1, L1 lens 2, photon sieve array 3, pinhole 4 and CMOS imaging device arranged in sequence along the optical axis.
[0020] Wherein, L1 lens 2 is arranged in the light path of the exit end of the optical fiber, and the exit end surface of the optical fiber coincides with the front focal plane of L1 lens 2; the photon sieve array 3 is arranged in the exit light path of L1 lens 2; the pinhole 4 is arranged in the back focal plane of the photon sieve array 3, and the center of the pinhole 4 coincides with the main focal point of the photon sieve array 3 on the optical axis; the CMOS imaging device 5 is arranged in the exit light path of the pinhole 4; L1 lens 2 is a collimating and expanding lens.
[0021] Embodiment 2 The embodiment provides a water vapor Raman laser radar spectral method based on a photon sieve array, and the specific steps are as follows: S1: Utilize the optical fiber 1 to couple the atmospheric backscattering echo signal received by the telescope to the subsequent optical path; The core diameter of the optical fiber in S1 is 0.8 mm, and the numerical aperture NA is 0.22.
[0022] S2: Convert the subsequent light into a parallel light beam with a half aperture of 20 mm through a collimating and expanding lens; S3: Make the collimated and expanded parallel light beam incident to the photon sieve array 3, filter the atmospheric backscattering echo signals of different wavelengths by using the photon sieve array 3, and focus the photon sieve on different spatial positions of the focal plane; S4: Arrange the pinhole 4 at the focal plane of the photon sieve array 3, and screen out the focused light signals corresponding to the target wavelength through the pinhole 4; S5: Convert the light signals screened through the pinhole 4 into electrical signals by using the CMOS imaging device 5, and complete the collection and processing of the atmospheric backscattering signals.
[0023] Embodiment 3 On the basis of embodiment 2, as shown in Figure 2 Figure 2 It is an atmospheric backscattering signal spectrum diagram when the laser with a central wavelength of 354.7 nm interacts with atmospheric matter, and different central wavelengths and line widths of the rotational-vibrational spectrum of atmospheric molecules such as nitrogen and water vapor molecules are generated, mainly including atmospheric aerosol Mie scattering and atmospheric molecular Rayleigh scattering with a central wavelength of 354.7 nm, and nitrogen molecule and water vapor molecule vibration Raman scattering signals with central wavelengths of 386.7 nm and 407.5 nm.
[0024] The first photon sieve, the second photon sieve and the third photon sieve are all provided with a SiO2 film layer, and the thicknesses of the SiO2 film layers are 372.8 nm, 410.0 nm and 434.2 nm in sequence; the apertures of the first photon sieve, the second photon sieve and the third photon sieve are 11.4 mm, 12.2 mm and 12.6 mm respectively.
[0025] Example 4 Based on Example 3, Figure 3 (a) The light intensity spectrum curve of the first photon sieve with 450 rings and focal length f = 100 mm. The central wavelength of the spectrum is 354.7 nm and the full width at half maximum (FWHM) is 0.739 nm. Figure 3 (b) is the light intensity spectrum curve of the second photon sieve with 475 rings and focal length f = 100 mm. The central wavelength of the spectrum is 386.7 nm and the half-height width is about 0.764 nm. Figure 3 (c) is the light intensity spectrum curve of photon sieve 3 with 485 rings and focal length f=100mm. The central wavelength of the spectrum is 407.5nm and the half-maximum width is 0.788nm.
[0026] like Figure 4 The figure shows the distribution diagram of the photon sieve array designed in S3. The photon sieve array is on a 40×40mm substrate. The first photon sieve with a central wavelength of 354.7nm is located at (0, 5)mm, the second photon sieve with a central wavelength of 386.7nm is located at (7, -5)mm, and the third photon sieve with a central wavelength of 407.5nm is located at (-7, -5)mm.
[0027] Figure 5 These are the intensity distributions of the 354.7nm, 386.7nm, and 407.5nm optical signals on the focal plane of the photon sieve array. Figure 5 (a) When 354.7 nm light is incident on the photon sieve array, the 355 nm wavelength light is focused at (0, 5) mm in the center of the focal plane, and there is almost no high-intensity light spot in other areas; Figure 5 (b) When 386.7nm light is incident on the photon sieve array, the 386.7nm wavelength light is focused at (7, -5) mm, and there is no significant light intensity at other positions; Figure 5 (c) When 407.5nm light is incident on the photon sieve array, the 407.5nm wavelength light is focused at (-7, -5) mm, and no obvious high-intensity light spot is received in other areas of the focal plane.
[0028] Figure 6 It is the light intensity distribution of the mixed light signal of 354.7nm, 386.7nm and 407.5nm in the focal plane of the photon sieve array, and synchronous focusing of 354.7nm, 386.7nm and 407.5nm is obtained at the positions of (0, 5), (7, -5) and (-7, -5) (unit: mm).
[0029] The focusing spot sizes of the first, second and third photon sieves are 6.8 um, 7.0 um and 7.2 um respectively, and the synchronization acquisition of 354.7 nm, 386.7 nm and 407.5 nm signals is realized.
[0030] Embodiment 5 On the basis of embodiment 4, the wavelength selection principle method of any photon sieve provided in the embodiment is: When the minimum transmission aperture of the photon sieve is greater than the wavelength of the incident wave, the polarization property of the incident light can be ignored, that is, the focusing and imaging of the photon sieve can be analyzed by using the scalar diffraction theory. According to the Fresnel-Kirchhoff scalar diffraction theory, the amplitude of the light field at any point on the imaging plane of the first small hole is: n U n (X,Y) (1) In the formula, , , , A n is the amplitude of the light field at the center of the small hole, L n =0, g n =0, h n =0, x n , y n is the coordinate of the center of the first small hole, n r n is the radius of the small hole on the first ring, and the aperture position on the first ring is related to n n R n , k is the wave number, , and J1 is the first Bessel function.
[0031] In formula (1), r n and R n The expression of (2) (3) In the formula, f represents the focal length of the photon sieve to the focal plane, λ is the incident wavelength, and the number of holes on the first ring can be expressed as n wherein α = 1.0, β = 5.0, N ring is the total number of rings of the pinhole; The different spatial positions of the pinhole array focused on the focal plane are specifically: The light field on the focal plane is the superposition of the diffraction light field of a large number of pinholes, so the light field distribution of the entire pinhole array on the focal plane is U X,Y ): (4) wherein m is the number of all pinholes of the pinhole array.
[0032] Based on the scalar diffraction theory of the pinhole array, the diffraction light field distribution on the focal plane of the pinhole array is obtained, and then combined with spectral scanning, the spectral light intensity distribution curve is obtained. A single pinhole array has a sharp energy distribution near the central wavelength, and the focal plane light energy rapidly decreases as the wavelength increases and decreases. The spectral range of the pinhole array involves the light wave bands that the traditional catadioptric optical devices are difficult to cover, including visible light, infrared light, soft X-ray and extreme ultraviolet light.
[0033] Embodiment 6 This embodiment provides a water vapor Raman lidar spectral system and method based on a pinhole array, as shown in Figure 7 , the specific steps are: Step 1: Use the optical fiber F1 to couple the atmospheric backscattering echo signal received by the telescope into the subsequent optical path. The numerical aperture of the optical fiber is NA=0.22, and the core size is 0.8mm.
[0034] Step 2: Set the collimating and expanding lens L1 to convert the subsequent light into a parallel light beam with a half aperture of 20mm. The lens aperture is 50.8mm, and the focal length is 100mm.
[0035] Step 3: The collimated and expanded parallel light beam is incident to the pinhole array (PSA), and the pinhole array acts as a filter device to focus the atmospheric backscattering echo signals of different wavelengths at different spatial positions on the focal plane. The center positions of the pinhole arrays 1-3 are (0, 5), (7, -5) and (-7, -5) (unit: mm), respectively, and the synchronous focusing of the atmospheric backscattering echo signals of 354.7nm, 386.7nm and 407.5nm is obtained at the positions (0, 5), (7, -5) and (-7, -5) (unit: mm).
[0036] Step 4: A pinhole diaphragm is arranged at the focal plane of the pinhole array, with an aperture size of 10um, respectively located at (0, 5)mm, (7, -5)mm and (-7, -5)mm.
[0037] Step 5, finally, the STC-MCS122BPOE type CMOS camera with 4096x3000 effective pixels, pixel size is 3.45umx3.45um, the light signal is converted into electrical signal on CMOS, and the synchronous collection of 354.7nm, 386.7nm and 407.5nm signals is realized at the corresponding pixel position of CMOS.
[0038] The water vapor Raman laser radar spectral system and method based on the photon sieve array provided by the application are based on the wavelength selection principle of the single-wavelength photon sieve, and a photon sieve array capable of working at three wavelengths is designed for the central wavelength of the water vapor Raman laser radar echo signal, and a single detector is used for synchronous collection behind the photon sieve array focal plane, so that the complex optical path of the existing spectral system is simplified.
Claims
1. The water vapor Raman lidar spectroscopic system based on the photon sieve array is characterized by: It includes an optical fiber (1), an L1 lens (2), a photon sieve array (3), a small hole (4) and a CMOS imaging device (5) arranged in sequence along the optical axis; The L1 lens (2) is arranged in the optical path of the output end of the optical fiber, and the output end face of the optical fiber coincides with the front focal plane of the L1 lens (2); The photon sieve array (3) is arranged in the outgoing light path of the L1 lens (2); The small hole (4) is arranged on the rear focal plane of the photon sieve array (3), and the center of the small hole (4) coincides with the main focus of the photon sieve array (3) on the optical axis; The CMOS imaging device (5) is arranged on the outgoing light path of the small hole (4).
2. The water vapor Raman lidar spectroscopic system based on the photon sieve array according to claim 1 is characterized in that: The L1 lens (2) is a collimating beam expanding lens.
3. A water vapor Raman lidar spectrometry method based on a photon sieve array is characterized by: Using the water vapor Raman lidar spectroscopic system based on the photon sieve array as claimed in claim 2, the specific steps are as follows: S1: using the optical fiber (1) to couple the atmospheric backscattered echo signal received by the telescope to a subsequent optical path; S2: converting the subsequent light into a parallel beam with a semi-aperture of 20 mm through the collimating beam expander lens; S3: allowing the collimated and expanded parallel light beam to be incident on the photon sieve array (3), and using the photon sieve array (3) to filter atmospheric backscattered echo signals of different wavelengths, so that the photon sieve is focused on different spatial positions of the focal plane; S4: providing a small hole (4) at the focal plane of the photon sieve array (3), and screening out a focused light signal corresponding to a target wavelength through the small hole (4); S5: Utilize the CMOS imaging device (5) to convert the optical signal filtered by the pinhole (4) into an electrical signal, thereby completing the collection and processing of the atmospheric backscattering signal.
4. The water vapor Raman lidar spectrometry method based on a photon sieve array according to claim 3, characterized in that: The photon sieve array (3) in S3 is 40×40 mm in size and consists of a first photon sieve, a second photon sieve, and a third photon sieve with three different central wavelengths.
5. The water vapor Raman lidar spectrometry method based on a photon sieve array according to claim 4, characterized in that: The center positions of the first photon sieve, the second photon sieve, and the third photon sieve are defined in the focal plane coordinate system as follows: the center position of the first photon sieve is (0, 5) mm; the center position of the second photon sieve is (7, -5) mm; and the center position of the third photon sieve is (-7, -5) mm. The first photon sieve, the second photon sieve and the third photon sieve are all configured to be coated with a SiO2 film layer, and the thickness of the SiO2 film layer is 372.8 nm, 410.0 nm and 434.2 nm respectively; The focal lengths of the first, second and third photon sieves are all 100 mm, and the central wavelengths are 354.7 nm, 386.7 nm and 407.5 nm respectively; The apertures of the first photon sieve, the second photon sieve and the third photon sieve are 11.4 mm, 12.2 mm and 12.6 mm respectively.
6. The water vapor Raman lidar spectrometry method based on a photon sieve array according to claim 5, characterized in that: The first photon sieve (0, 5) mm corresponds to focusing the atmospheric backscattered echo signal of 354.7 nm; The second photon sieve (7, -5) mm corresponds to focusing the atmospheric backscattered echo signal of 386.7 nm; The third photon sieve (-7, -5) mm corresponds to focusing the atmospheric backscattered echo signal of 407.5 nm; The focusing spot sizes of the first photon sieve, the second photon sieve and the third photon sieve are 6.8um, 7.0um and 7.2um respectively, realizing the synchronous acquisition of 354.7nm, 386.7nm and 407.5nm signals.
7. The water vapor Raman lidar spectrometry method based on a photon sieve array according to claim 5, characterized in that: The wavelength selection method for any photon sieve is: When the minimum aperture of any photon sieve is larger than the wavelength of the incident wave, according to the Fresnel-Kirchhoff scalar diffraction theory, n The amplitude of the small hole at any point on the imaging plane U n (X,Y) for: (1) Where, , , , A n is the light field amplitude at the center of the pinhole, L n =0, g n =0, h n =0,( x n , y n ) is the n The coordinates of the center of the small hole, r n For the n The radius of the small hole on the first ring is n Aperture positions on the ring R n related, k is the wave number, , J1 is a first-order Bessel function.
8. The water vapor Raman lidar spectrometry method based on a photon sieve array according to claim 7, characterized in that: In formula (1) r n and R n The expression is: (2) (3) Where, f represents the focal length from the photon sieve to the focal plane, λ is the incident wavelength, n The number of holes on a ring can be expressed as ,in α =1.0, β =5.0, N ring is the total number of photon sieve holes; The photon sieve focuses on different spatial positions of the focal plane as follows: The light field on the focal plane is the superposition of the diffraction light fields of many small holes, so the light field distribution of the entire photon sieve on the focal plane is U ( X,Y ): (4) in m is the number of all small holes in the photon sieve.
9. The water vapor Raman lidar spectrometry method based on a photon sieve array according to claim 3, characterized in that: The arrangement of the small hole (4) at the focal plane of the photon sieve array described in S4 is specifically as follows: Small holes (4) are set at the focal plane of the photon sieve array (3), with an aperture size of 10 μm, and are located at (0, 5) mm, (7, -5) mm and (-7, -5) mm respectively.
