High-precision measuring device for bidirectional reflection distribution function of low-scattering coating

文档序号:1797168 发布日期:2021-11-05 浏览:22次 中文

阅读说明:本技术 一种低散射涂层双向反射分布函数高精度测量装置 (High-precision measuring device for bidirectional reflection distribution function of low-scattering coating ) 是由 霍熠炜 张玉涛 王彪 朱凌轩 高伟 于 2021-08-02 设计创作,主要内容包括:本发明提供一种低散射涂层双向反射分布函数高精度测量装置,其包含:激光发射模块、光子模态探测接收模块、半球空间滑动测量系统;所述激光发射模块可产生两路激光光束,一路为探测光束,另一路为泵浦光束,分别通过两路不同的光纤通道传输给光子模态探测接收模块;所述半球空间滑动测量系统,其设置有低散射涂层平面,使探测光束产生半球空间的散射光束,采用不同类型的圆形轨道以实现低散射涂层半球空间双向反射分布函数的测量;所述光子模态探测接收模块包含:光子模态转换晶体,利用光子模态转换晶体滤除与泵浦光束不同的噪声光子,从根本上滤除噪声,提升测量精度。本发明具有测量精度高,测量速度快,准确率高,测试成本低等优势。(The invention provides a high-precision measuring device for a bidirectional reflection distribution function of a low-scattering coating, which comprises: the device comprises a laser emission module, a photon mode detection receiving module and a hemispherical space sliding measurement system; the laser emission module can generate two laser beams, one is a detection beam, and the other is a pumping beam, and the two laser beams are respectively transmitted to the photon mode detection receiving module through two different optical fiber channels; the hemispherical space sliding measurement system is provided with a low scattering coating plane, so that the detection light beam generates a scattering light beam in a hemispherical space, and different types of circular tracks are adopted to realize the measurement of a bidirectional reflection distribution function in the hemispherical space of the low scattering coating; the photon modal detection receiving module comprises: the photon mode conversion crystal is used for filtering noise photons different from the pumping light beams, so that noise is filtered fundamentally, and the measurement precision is improved. The invention has the advantages of high measurement precision, high measurement speed, high accuracy, low test cost and the like.)

1. A high-precision measurement device for a bidirectional reflectance distribution function of a low-scattering coating, comprising:

the device comprises a laser emission module, a photon mode detection receiving module and a hemispherical space sliding measurement system;

the laser emission module generates two laser beams, one is a detection beam, and the other is a pumping beam, and the two laser beams are transmitted to the photon mode detection receiving module through the detection beam transmission channel and the pumping beam transmission channel respectively;

the hemispherical space sliding measurement system is provided with a low-scattering coating plane (14), so that a detection beam generates a scattering beam in a hemispherical space, and different types of circular tracks are adopted for placing a laser emission module and a photon mode detection receiving module, so that the measurement of a bidirectional reflection distribution function in the hemispherical space of the low-scattering coating is realized;

the photon modal detection receiving module comprises: the photon mode conversion crystal (8) is used for filtering noise photons in the scattered light beam, which are different from the pump light beam, by the photon mode conversion crystal (8), so that the noise is filtered fundamentally, and the measurement precision is improved.

2. The low-scattering coating double-reflection profile high-accuracy measuring device as claimed in claim 1, wherein said laser emitting module comprises:

an MLL (1) for generating a light source of a desired wavelength band;

and the 50-50 optical fiber beam splitter (2) is connected with the MLL (1) and can split laser emitted by the MLL (1) into two beams, wherein one beam is a probe beam, and the other beam is a pumping beam.

3. The low-scattering coating two-way reflection profile high-accuracy measurement apparatus of claim 2, wherein the probe beam transmission channel comprises:

one end of the optical fiber-free space collimator (3) containing a polaroid is connected with the detection light beam split by the 50-50 optical fiber beam splitter (2) through an optical fiber, the other end of the optical fiber-free space collimator is provided with the polaroid, and the optical fiber-free space collimator (3) can collimate the detection light beam in the optical fiber and then enables the detection light beam to enter a low-scattering coating plane (14);

the anti-reflection coating aspheric collimating lens (4) is used for receiving the scattered light beam scattered by the low-scattering coating plane (14) and reducing the Fresnel reflection in the photon mode detection receiving module to the minimum;

and the angle polishing optical fiber connector (5) is connected with the anti-reflection coating aspheric collimating lens (4) and is used for transmitting the scattered light beam.

4. The device for high-precision measurement of the bi-directional reflection distribution function of low-scattering coating as claimed in claim 3, wherein the pump beam transmission channel comprises an ODL (6) which is connected with the pump beam split by the 50-50 fiber splitter (2) through an optical fiber and is used for receiving the pump beam and adjusting the time delay of the pump beam to ensure the optical path consistency of the scattered beam and the pump beam.

5. The low-scattering coating bi-directional reflection profile high-accuracy measurement device of claim 4, the photonic mode detection receiving module comprising:

the optical fiber coupling connector (7) is respectively connected with the angle polishing optical fiber connector (5) and the ODL (6) through optical fibers and is used for connecting the scattered light beam and the pumping light beam;

a mode conversion crystal (8) for selecting scattered photons in the scattered light beam in the same mode as the pump photons in the pump light beam, changing the frequency mode of the scattered light beam, and distinguishing noise mode photons from the mode of the scattered photons;

a scattered light filter (9) connected with the mode conversion crystal (8) through an optical fiber and used for further processing the mode of the scattered photons;

and the InGaAs photodetector (10) is used for carrying out signal processing on the scattered photons subjected to mode conversion by the scattered light filter (9) to obtain a final scattered light signal.

6. The device for high-precision measurement of the bidirectional reflectance distribution function of a low-scattering coating according to claim 5, wherein the photonic mode conversion crystal (8) is LiNbO3And the quasi-phase matching with the corresponding laser detection wavelength is required in the manufacturing process of the artificial crystal.

7. The low-scattering coated two-way reflection profile high-accuracy measuring device according to claim 5, wherein the scattered light filter (9) comprises: a dichroic mirror, a short pass filter and a double grating filter;

the dichroic mirror and the short-pass filter separate the scattered photons from the pumping photons after the modal conversion of the modal conversion crystal (8) and filter other noise modal photons;

the double grating filter is used for introducing separated scattered photons and eliminating any external band noise mode photons.

8. The low-scattering coated bi-directional reflection profile high accuracy measurement device of claim 5, wherein said hemispherical spatial sliding measurement system comprises:

the rotating support (13) is provided with the low-scattering coating plane (14) which is used for generating a scattered light beam in a hemispherical space so as to perform hemispherical space detection;

a quarter-circle track (12) on which a fiber-free space collimator (3) including a polarizer is disposed to be movable along the quarter-circle track (12), and the quarter-circle track (12) is fixedly connected to a rotating bracket (13) so that a low-scattering coating can be irradiated in a 90-degree range;

the circular track (11) is provided with a vertical upright rod which can move along the circular track (11) and is used for fixedly connecting the anti-reflection coating aspheric collimating lens (4) so as to measure the range of 360 degrees.

9. The device for measuring the bidirectional reflection distribution function with high precision of the low scattering coating according to any one of claims 1 to 8, wherein the MLL (1) generates a light source with a required waveband, transmits the light source to a 50-50 fiber beam splitter (2), and obtains a probe beam and a pump beam after beam splitting; the detection light beam is transmitted to a fiber-free space collimator (3) with a polaroid through an optical fiber and then enters a low-scattering coating plane (14), after the detection light beam is scattered by the low-scattering coating plane (14), the scattering light beam enters an anti-reflection coating aspheric collimating lens (4), and then is transmitted to a fiber coupling connector (7) through an angle polishing fiber connector (5).

10. The device for measuring bi-directional reflection distribution function with high precision of low scattering coating according to claim 9, wherein the pump beam is transmitted to the ODL (6) through an optical fiber, the optical path lengths of the scattered beam and the pump beam are kept consistent after the time delay is adjusted by the ODL (6), and then the pump beam and the pump beam are transmitted to the optical fiber coupling connector (7) and merged with the scattered beam, the merged beam is filtered by the photon mode conversion crystal (8) to remove noise mode photons in the scattered beam, which are different from the noise mode photons in the pump beam, and then the filtered scattered beam is transmitted to the scattered light filter (9), and finally the scattered photons after the mode conversion by the scattered light filter (9) are processed by the InGaAS photodetector (10) to obtain the final scattered beam signal.

Technical Field

The invention relates to the technical field of optical scattering transmission testing, in particular to a measuring device for improving the measurement precision of a bidirectional reflection distribution function of a low-scattering coating.

Background

The bi-directional reflection distribution function is used to describe the spatial light reflection characteristics of the target object surface. The method is used for describing the characteristic that the light reflection characteristic of the surface of an object has uniqueness, and the determined reflection characteristic only depends on the characteristic of the surface of the object, and represents the reflection characteristic of the surface of the object at any observation angle under different incidence conditions. It is mainly determined by the factors of surface roughness, dielectric constant, radiation wavelength, polarization and the like. The bidirectional reflection distribution function can well unify the reflection and the scattering of the surface of the material in the same concept, and can describe the directional scattering and the radiation characteristics of the surface.

In the existing measurement research on the bidirectional scattering distribution function of a coating and a target, for example, laser with specific laser wavelength is used as an irradiation source, a polytetrafluoroethylene standard white board is used as a reference standard, and the bidirectional reflection distribution function of stealth coating samples with different infrared emissivities is measured by adopting a relative method, but the establishment of a measurement scheme of a low-scattering target is not carried out, and a corresponding solution is not provided for the improvement of detection precision. In addition, 1064nm laser is used as an emission source to measure the bidirectional reflection distribution function of the camouflage coating with different colors, and parameter modeling is carried out on the measurement result, but the low-scattering coating sample is not measured, and the adopted bidirectional reflection distribution function measurement system is also similar to the traditional system.

In order to solve the above problems of the low-scattering coating in the bidirectional reflection distribution function measurement, a measuring device is provided for receiving the scattered light of the low-scattering coating by using a photon mode selection technology, so as to improve the measurement precision of the bidirectional reflection distribution function measurement system of the low-scattering coating. The traditional test method usually has larger measurement error for the scattering coating, only can measure the target coating with stronger scattering light, and does not optimize the detection precision of the bidirectional reflection distribution function from the angle of improving the detection end. For example, the prior art provides a device for measuring a spatial undersampled bidirectional reflection distribution function of a surface, the device adopts three sensors to receive light reflected in different directions, so as to represent a first appearance attribute of a target surface, but the system cannot realize high-precision detection of scattered light of a low-scattering target, and cannot detect the scattered light if the scattered light is weak and does not reach the sensitivity of a detector; in addition, a system for collecting bidirectional reflection distribution function data of the unmanned aerial vehicle by adopting a hyperspectral imager is provided in the prior art, the hyperspectral imager is used as a detection end to measure and acquire hyperspectral data of a target, and whether a measurement method for a low-scattering unmanned aerial vehicle is applicable or not is not mentioned, and a precision improvement measure for the measurement data is not taken. Meanwhile, in the prior art, a traditional laser light source or natural light is generally used as incident light, and a traditional photoelectric detector or a hyperspectral imager is used as a receiving end to receive reflected signals. If the prior art is adopted to measure the bidirectional reflection distribution function of the ground scattering coating, the signal obtained by a receiving end is very weak, and the signal-to-noise ratio is poor, so that the precision of the measured data of the bidirectional reflection distribution function is greatly influenced.

Disclosure of Invention

The invention aims to provide a high-precision measuring device for a bidirectional reflection distribution function of a low-scattering coating, which aims to solve the problem that a bidirectional reflection distribution function measuring system in the prior art does not have the high-precision measuring capability for the low-scattering coating.

In order to achieve the above object, the present invention provides a high-precision measurement device for bidirectional reflectance distribution function of a low-scattering coating, comprising: the device comprises a laser emission module, a photon mode detection receiving module and a hemispherical space sliding measurement system; the laser emission module generates two laser beams, one is a detection beam, and the other is a pumping beam, and the two laser beams are transmitted to the photon mode detection receiving module through the detection beam transmission channel and the pumping beam transmission channel respectively; the hemispherical space sliding measurement system is provided with a low scattering coating plane, so that the detection light beam generates a scattering light beam in a hemispherical space, and different types of circular tracks are adopted for placing a laser emission module and a photon mode detection receiving module, so as to realize the measurement of a bidirectional reflection distribution function of the low scattering coating hemispherical space; the photon modal detection receiving module comprises: the photon mode conversion crystal is used for filtering noise photons in scattered light beams, which are different from the pump light beams, so that noise is filtered fundamentally, and the measurement precision is improved.

Wherein the laser emission module includes: an MLL for generating a light source of a desired wavelength band; and the 50-50 optical fiber beam splitter is connected with the MLL and can split laser emitted by the MLL into two beams, wherein one beam is a probe beam, and the other beam is a pump beam.

Wherein the probe beam transmission channel includes: one end of the optical fiber-free space collimator containing the polaroid is connected with the detection light beam split by the 50-50 optical fiber beam splitter through an optical fiber, the other end of the optical fiber-free space collimator is provided with the polaroid, and the optical fiber-free space collimator can collimate the detection light beam in the optical fiber and then enables the detection light beam to be incident to a low-scattering coating plane; the anti-reflection coating aspheric collimating lens is used for receiving the scattered light beam scattered by the low-scattering coating plane, so that the fresnel reflection in the photon mode detection receiving module is reduced to the minimum; and the angle polishing optical fiber connector is connected with the anti-reflection coating aspheric collimating lens and is used for transmitting the scattering light beam.

The pump beam transmission channel comprises an ODL, the ODL is connected with the pump beam split by the 50-50 optical fiber beam splitter through an optical fiber and used for receiving the pump beam and adjusting the time delay of the pump beam, and the consistency of the optical paths of the scattered beam and the pump beam is ensured.

Wherein the photon modal detection receiving module comprises: the optical fiber coupling connector is respectively connected with the angle polishing optical fiber connector and the ODL through optical fibers and is used for connecting the scattered light beam and the pumping light beam; the mode conversion crystal is used for selecting scattered photons in a scattered light beam with the same mode as that of pump photons in the pump light beam, changing the frequency mode of the scattered light beam and distinguishing noise mode photons from the mode of the scattered photons; the scattered light filter is connected with the mode conversion crystal through an optical fiber and is used for further processing the mode of the scattered photons; and the InGaAs photodetector is used for performing signal processing on the scattered photons subjected to the mode conversion of the scattered light filter to obtain a final scattered light signal.

Preferably, the photon mode conversion crystal is made of LiNbO3And the quasi-phase matching with the corresponding laser detection wavelength is required in the manufacturing process of the artificial crystal.

Wherein the scattered light filter comprises: a dichroic mirror, a short pass filter and a double grating filter; the dichroic mirror and the short-pass filter separate the scattered photons from the pumping photons after the modal conversion of the modal conversion crystal, and filter other noise modal photons; the double grating filter is used for introducing separated scattered photons and eliminating any external band noise mode photons.

Wherein the hemispherical space sliding measurement system comprises: the low-scattering coating plane is arranged on the rotating support and used for generating a scattering light beam in a hemispherical space so as to perform hemispherical space detection; the quarter-circle track is provided with a fiber-free space collimator which can move along the quarter-circle track and contains a polaroid, and the quarter-circle track is fixedly connected to the rotating bracket, so that the low-scattering coating can be irradiated in a 90-degree range; the circular track is provided with a vertical upright rod which can move along the circular track and is used for fixedly connecting the anti-reflection coating aspheric collimating lens, so that 360-degree range measurement is carried out.

The MLL generates a light source with a required waveband, transmits the light source to a 50-50 optical fiber beam splitter, and obtains a probe beam and a pump beam after beam splitting; the detection light beam is transmitted to a fiber-free space collimator containing a polaroid through an optical fiber and then enters a low-scattering coating plane, after the detection light beam is scattered through the low-scattering coating plane, the scattering light beam enters an anti-reflection coating aspheric collimating lens and then is transmitted to an optical fiber coupling connector through an angle polishing optical fiber connector.

The pump light beam is transmitted to the ODL through an optical fiber, the optical paths of the scattered light beam and the pump light beam are kept consistent after the time delay is adjusted by the ODL, then the scattered light beam and the pump light beam are transmitted to the optical fiber coupling connector and converged with the scattered light beam, the converged light beam is filtered by the photon mode conversion crystal to remove noise mode photons different from the pump light beam in the scattered light beam, then the filtered scattered light beam is transmitted to the scattered light filter, and finally the scattered light photons subjected to mode conversion by the scattered light filter are subjected to signal processing by the InGaAs photoelectric detector to obtain a final scattered light beam signal.

In summary, compared with the prior art, the high-precision measurement device for the bidirectional reflection distribution function of the low-scattering coating provided by the invention has the following beneficial effects: the invention adopts a photon mode selection technology, filters other noise photons by matching the photon modes of the pump light and the scattered light, and receives the scattered light of the low-scattering coating, thereby improving the measurement precision of the bidirectional reflection distribution function measurement system for the low-scattering coating.

Drawings

FIG. 1 is a schematic diagram of a high-precision measurement device for a bidirectional reflection distribution function of a low-scattering coating according to the present invention.

Detailed Description

The technical solution, the structural features, the achieved objects and the effects of the embodiments of the present invention will be described in detail with reference to the attached drawings 1 of the embodiments of the present invention.

It should be noted that the drawings are simplified in form and not to precise scale, and are only used for convenience and clarity to assist in describing the embodiments of the present invention, but not for limiting the conditions of the embodiments of the present invention, and therefore, the present invention is not limited by the technical spirit, and any structural modifications, changes in the proportional relationship, or adjustments in size, should fall within the scope of the technical content of the present invention without affecting the function and the achievable purpose of the present invention.

It is to be noted that, in the present invention, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.

The invention provides a high-precision measuring device for a bidirectional reflection distribution function of a low-scattering coating, as shown in figure 1, the high-precision measuring device for the bidirectional reflection distribution function comprises: the device comprises a laser emission module, a photon mode detection receiving module and a hemispherical space sliding measurement system; the laser emission module can generate two laser beams, one is a detection beam, and the other is a pumping beam which are transmitted to the photon mode detection receiving module through the detection beam transmission channel and the pumping beam transmission channel respectively; the hemisphere space sliding measurement system is provided with a low scattering coating plane 14, and different types of circular tracks are used for placing a laser emission module and a photon mode detection receiving module so as to realize the measurement of a low scattering coating hemisphere space bidirectional reflection distribution function; the photon modal detection receiving module comprises: the photon mode conversion crystal 8 is used for filtering noise mode photons in scattered light beams, which are different from the pump light beams, by the photon mode conversion crystal 8, so that noise is filtered fundamentally, and the measurement precision is improved.

Wherein the laser emission module includes: an MLL (femtosecond mode-locked laser) 1 that can generate a light source with a band of 1550 nm; the 50-50 optical fiber beam splitter 2 is connected with the MLL1, can split laser emitted by the MLL1 into two beams, one beam is a probe beam, the other beam is a pump beam, and uses an optical fiber for transmission; specifically, the probe beam is used to illuminate a low-scattering coating plane 14 in a sliding measurement system arranged in a hemisphere space, so that the probe beam generates a scattered beam in the hemisphere space.

Wherein the probe beam transmission channel includes: one end of the optical fiber-free space collimator 3 containing a polaroid is connected with the detection light beam split by the 50-50 optical fiber beam splitter 2 through an optical fiber, the other end of the optical fiber-free space collimator 3 is provided with the polaroid, and the optical fiber-free space collimator 3 can collimate the detection light beam in the optical fiber and then emits the detection light beam to the low-scattering coating plane 14; the anti-reflection coating aspheric collimating lens 4 is used for receiving the scattered light beam scattered by the low-scattering coating plane 14, so that the fresnel reflection in the photon mode detection receiving module is reduced to the minimum; an angle-polished optical fiber connector 5 connected with the anti-reflection coating aspheric collimating lens 4 for transmitting the scattered light beam; the invention selects the optical fiber-free space collimator 3 containing the polaroid, can change the polarization state of an incident light source and improve the measurement precision.

Wherein the pump beam transmission channel comprises: and the ODL (optical delay system) 6 is connected with the pump light beams split by the 50-50 optical fiber beam splitter 2 through optical fibers and is used for receiving the pump light beams and adjusting the time delay of the pump light beams, so that the optical path consistency of the scattered light beams and the pump light beams is ensured, and the pump light beams and the scattered light beams simultaneously reach the optical fiber coupling connector 7.

Wherein the photon modal detection receiving module comprises: an optical fiber coupling connector 7 respectively connected to the angle polished optical fiber connector 5 and the ODL6 through optical fibers for connecting the scattered beam and the pump beam; a mode conversion crystal 8 for selecting a photon (scattered photon) in the scattered light beam having the same mode as a photon (pump photon) in the pump light beam, changing a frequency mode of the scattered light beam, and distinguishing a mode of a noise photon from a mode of a scattered photon, in which a mode of a noise photon is completely different from modes of the pump light and the scattered light; a scattered light filter 9 connected with the mode conversion crystal 8 through an optical fiber and used for further processing the mode of the scattered photons; and the InGaAs photodetector 10 is used for performing signal processing on the scattered photons subjected to the mode conversion by the scattered light filter 9 to obtain a final scattered light signal.

Preferably, the material adopted by the photon mode conversion crystal 8 is LiNbO3And the quasi-phase matching with the corresponding laser detection wavelength is required in the manufacturing process of the artificial crystal.

Specifically, the scattered light filter 9 includes: a dichroic mirror, a short pass filter and a double grating filter; the dichroic mirror and the short-pass filter separate the scattered photons from the pumping photons after the mode conversion of the mode conversion crystal 8, and filter other noise mode photons; the double grating filter is used for introducing the separated scattered photons, thereby eliminating any out-band noise mode photons and ensuring that the scattered photons transmitted to the InGaAs photodetector 10 do not contain any out-band noise mode photons.

Hemisphere space slip measurement system includes: the rotating support 13 is provided with a low-scattering coating plane (14) which is used for generating a scattered light beam in a hemispherical space so as to perform hemispherical space detection; the quarter-circular track 12 is provided with a fiber-free space collimator 3 containing a polaroid, the fiber-free space collimator 3 containing the polaroid can slide along the quarter-circular track 12 so as to irradiate the low-scattering coating plane 14 within 90 degrees, and the quarter-circular track 12 is fixedly connected to the rotating bracket 13; circular track 11 is provided with a vertical pole setting on it for fixed connection antireflection coating aspheric surface collimating lens 4, and the pole setting can slide along circular track 11, and then drives antireflection coating aspheric surface collimating lens 4 and carry out 360 degrees range measurements.

It should be noted that, when the low-scattering coating bidirectional reflection distribution function high-precision measuring device of the present invention is used, MLL1 generates a 1550nm light source, which is split by 50-50 optical fiber beam splitter 2 to obtain a probe beam and a pump beam; the detection light beam is transmitted to a fiber-free space collimator 3 containing a polaroid through an optical fiber and then enters a low-scattering coating plane 14, after the detection light beam is scattered by the low-scattering coating plane 14, the scattering light beam enters an anti-reflection coating aspheric surface collimating lens 4 and then is transmitted to a fiber coupling connector 7 through an angle polishing fiber connector 5; the pump beam is transmitted to the ODL6 through an optical fiber, the optical paths of the scattered beam and the pump beam are kept consistent after the time delay is adjusted by the ODL6, the scattered beam and the pump beam are transmitted to the optical fiber coupling connector 7 and merged with the scattered beam, the merged beam is filtered by the photon mode conversion crystal 8 to remove noise mode photons different from the pump beam in the scattered beam, the filtered scattered beam is transmitted to the scattered light filter 9, and finally the scattered photons subjected to mode conversion by the scattered light filter 9 are subjected to signal processing by the InGaAS photodetector 10 to obtain a final scattered light signal.

In summary, compared with the prior art, the high-precision measuring device for the low-scattering coating bidirectional reflection distribution function provided by the invention has the advantages of high measuring precision, high measuring speed, high accuracy, low measuring cost and the like, overcomes the disadvantages of low measuring precision, limited measuring target range and the like of the traditional bidirectional reflection distribution function measuring system, and improves the measuring precision of the low-scattering coating bidirectional reflection distribution function.

While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

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