A parabolic mirror multi-pass cell design method for a TDLAS system

Abstract

This invention relates to the field of optical detection technology, specifically to a design method for a parabolic mirror multi-pass cell for a TDLAS system. The multi-pass cell consists of two identical and coaxially opposed parabolic mirrors. The design method includes: calculating the reflected ray parameters of the incident ray each time it passes through the multi-pass cell mirrors using a ray tracing method between the two parabolic mirrors; projecting the light spots at all intersections of the ray with the two parabolic mirrors onto the x-y plane to generate a light spot pattern; changing the parameters of the parabolic mirrors, the center distance between the two mirrors, the position and direction cosine of the incident ray, and the number of reflections of the ray until the desired light spot pattern is generated; after generating the desired light spot pattern, keeping the direction cosine and number of reflections of the incident ray constant, adjusting the mirror parameters, the center distance between the two mirrors, and the position of the incident ray to adjust the density and size of the light spot pattern, thus obtaining the final multi-pass cell. This invention adjusts the optical path length and volume of the multi-pass cell by adjusting the relevant parameters of the parabolic mirrors and the incident ray.

Description

Technical Field

[0001] This invention relates to the field of optical detection technology, and specifically to a design method for a parabolic mirror multi-pass cell for a TDLAS system. Background Technology

[0002] Tunable semiconductor laser absorption spectroscopy (TDLAS) is a non-destructive gas concentration detection technique characterized by fast response, high sensitivity, and high resolution. It utilizes a narrow-bandwidth, tunable laser to selectively measure the absorption of gas molecules, accurately acquiring parameters such as concentration, temperature, and pressure of the analyte. A multi-pass cell is a crucial component of a TDLAS system, especially important for detecting weak absorption in trace gases. This cell provides the optical path length for light propagation within the chamber, enhancing detection sensitivity.

[0003] The early multipass cell based on spherical mirrors developed by White and Heriot is still used in laser-based spectral trace gas sensors due to its simplicity, reliability, and operability. However, the White and Heriot multipass cell cannot produce dense spot patterns on the mirror surface and has a relatively large size, which limits its application.

[0004] In 2017, S. Ozharar et al. introduced a mirror with a focal length inversely proportional to its off-axis distance into a multipass cell. Applying the paraxial approximation theory, they derived a numerical expression for ray tracing and obtained various spot patterns in mirror simulations. However, for non-paraxial rays, as the curvature of the reflecting mirror and the number of reflections increase, the deviations between the angles and optical path lengths of the rays obtained by the paraxial approximation theory and the actual rays also increase. Since the paraxial approximation theory does not consider these errors, these errors accumulate and are amplified, making it impossible to calculate the actual ray trajectory. The actual spot pattern deviates significantly from the spot pattern obtained by the paraxial approximation theory.

[0005] To address the problems of existing methods based on paraxial approximation theory, Chinese Patent Publication No. CN114065321A discloses a "Design Method for a Spherical Mirror Multipass Cell with Dense Light Spot Patterns," which includes: determining the initial incident point coordinates and incident direction vector of the light beam; obtaining different ray parameters for each pass through the multipass cell using a reflection ray equation algorithm, wherein the ray parameters include the reflection point coordinates, the reflected ray direction vector, and the number of reflections; projecting all the light spots of the beam passing through the two mirrors onto the xy plane and observing the light spot pattern; changing the number of reflections, the distance between the spherical mirrors, and the initial incident point coordinates and incident direction vector of the beam, and repeating the calculation until the desired light spot pattern is obtained. This scheme can generate rich light spot patterns by numerically simulating the reflection and free propagation of light in a multipass cell composed of a pair of spherical mirrors, thereby improving the utilization efficiency of the mirror surface.

[0006] However, the applicant found that the existing solutions for multi-pass cells composed of spherical mirrors have the following problems: 1) The existing solutions do not provide a method for calculating the optical path length and volume of the multi-pass cell, making it impossible to evaluate the sensitivity and structural compactness of the designed multi-pass cell, and thus failing to obtain a multi-pass cell with both high sensitivity and a compact structure, resulting in insufficient performance. 2) After obtaining the spot pattern, the existing solutions cannot adjust the spot density and pattern size according to actual needs, i.e., they cannot effectively adjust the performance of the multi-pass cell, resulting in limited application scenarios. Therefore, how to provide a multi-pass cell design method that can improve the application scenarios and performance of multi-pass cells is an urgent technical problem to be solved. Summary of the Invention

[0007] To address the shortcomings of the existing technology, the technical problem to be solved by this invention is: how to provide a design method for a parabolic mirror multi-pass cell for a TDLAS system, by adjusting the relevant parameters of the parabolic mirror and the incident light to adjust the optical path length and volume of the multi-pass cell, thereby obtaining a multi-pass cell with high sensitivity and compact structure, and improving the performance of the multi-pass cell; at the same time, a method for adjusting the spot density and pattern size of the spot pattern is provided, so that the multi-pass cell can adapt to different measurement requirements and gas sample characteristics, thereby improving the versatility and flexibility of the multi-pass cell.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A design method for a parabolic mirror multipass cell for a TDLAS system, wherein the multipass cell consists of two identical and coaxially opposed parabolic mirrors, the design method comprising the following steps:

[0010] S1: Determine the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, and the position (x1, y1, z1) and direction cosine (sx1, sy1, sz1) of the incident light rays entering the multipass cell.

[0011] S2: Calculate the parameters of the reflected rays of the incident ray each time it passes through the multi-pass mirror using a ray tracing method between two parabolic mirrors; the reflected ray parameters include the three-dimensional coordinates of the intersection point of the incident ray and the parabolic mirror and the direction cosine of the reflected ray.

[0012] S3: Project the light spots at all intersections of the light rays with the two parabolic mirrors onto the xy plane to generate a light spot pattern;

[0013] S4: Change the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, the position and direction cosine of the incident light, and the number of reflections n of the light. Repeat steps S2 and S3 until the desired light spot pattern is generated.

[0014] S5: After generating the required light spot pattern, keep the direction cosine and reflection number of the incident light unchanged, and adjust the light spot density and pattern size by adjusting the parameters of the parabolic mirror, the distance L between the centers of the two mirrors, and the position of the incident light to obtain the final multipass cell.

[0015] Preferably, in step S1, in the Cartesian coordinate system, the multipass pool is composed of two identical and coaxially opposite parabolic mirrors M1 and M2, and the distance between the centers O1 and O2 of the two mirrors is L.

[0016] The formulas F1(x,y,z) and F2(x,y,z) for two parabolic mirrors are expressed as follows:

[0017] M1:F1(x,y,z)=x 2 +y 2 -2pz = 0;

[0018] M2:F2(x,y,z)=x 2 +y 2 +2p(zL) = 0;

[0019] In the formula: M1 and M2 represent two parabolic mirrors.

[0020] Preferably, in step S2, the incident light ray enters from the parabolic mirror M1, and the position and direction cosines of the incident light ray are (x1, y1, z1) and (sx1, sy1, sz1), respectively; the incident light ray is transmitted and reflected in the multi-pass cell, and the position and direction cosines of the nth incident light ray are (x1, y1, z1) and (sx1, sy1, sz1), respectively. n ,y n ,z n ) and (sx n ,sy n ,sz n );

[0021] The formula for the nth incident ray is expressed as:

[0022] x = x n +sx n ·d;

[0023] y = y n +sy n ·d;

[0024] z = z n +sz n ·d;

[0025] In the formula: d represents the length of the incident ray.

[0026] Preferably, in step S2, the formula for the reflecting surface of the nth incident ray is expressed as:

[0027]

[0028] Preferably, in step S2, the optical path length d of the nth incident ray is calculated using the following formula. n :

[0029]

[0030] in:

[0031] A n =sx n 2 +sy n 2 ;

[0032] B n =x n ·sx n +y n ·sy n +(-1) n+1 p·sz n ;

[0033]

[0034] Preferably, in step S2, after calculating the length of the incident ray, the three-dimensional coordinates (x, y, y) of the intersection point between the nth incident ray and the parabolic mirror are further calculated. n+1 ,y n+1 ,z n+1 The calculation formula is expressed as follows:

[0035] x n+1 =x n +sx n ·d n ;

[0036] y n+1 =y n +sy n ·d n ;

[0037] z n+1 =z n +sz n ·d n .

[0038] Preferably, in step S2, according to the vector reflection theorem:

[0039]

[0040] In the formula: and Let represent the direction cosine vectors of the incident and reflected rays of the parabolic mirror, respectively; The normal vector of the reflecting mirror is expressed by the formula:

[0041]

[0042] Preferably, in step S2, the direction cosine vector of the reflected ray is calculated.

[0043] Preferably, in step S4, the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, the position and direction cosine of the incident light, and the number of reflections of the light are adjusted, and ray tracing is performed according to the existing conditions of the light to generate the desired light spot pattern.

[0044] Preferably, in step S5, after generating the desired light spot pattern, the direction cosine (sx1, sy1, sz1) and reflection number n of the incident light rays initially incident on the parabolic mirror M1 are kept unchanged; the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, and the position (x1, y1, z1) of the incident light rays initially incident on the parabolic mirror M1 are multiplied by the expected gain factor to adjust the size and density of the light spot pattern.

[0045] Compared with existing technologies, the parabolic mirror multi-pass cell design method for TDLAS systems in this invention has the following advantages:

[0046] This invention utilizes two identical, coaxially opposed parabolic mirrors to form a multi-pass cell. Compared to existing multi-pass cells composed of spherical mirrors, this invention offers several advantages: First, parabolic mirrors possess unique focusing characteristics, converging parallel light rays to their focal point, while spherical mirrors exhibit aberrations, particularly at large angles of light reflection. Therefore, the multi-pass cell using parabolic mirrors more effectively focuses incident light and reflects it multiple times within the cell, reducing light divergence and energy loss, and improving the optical path utilization and intensity distribution uniformity. Second, the focusing effect of parabolic mirrors makes the light reflection path within the cell more compact and efficient, allowing for more reflections within the same physical space. This increases the interaction time between light and the analyte gas, enhancing the detection sensitivity of the TDLAS system. Finally, spherical mirrors can cause spot distortion during reflection, affecting the uniformity of the spot pattern and intensity distribution. The parabolic mirrors of this invention effectively reduce this distortion, maintaining a circular or near-circular spot, resulting in a more uniform energy distribution and improving the accuracy and reliability of the multi-pass cell measurement results.

[0047] This invention adjusts the optical path length and volume of a multi-pass cell by changing the parameters of the parabolic mirror, the incident position and direction cosine of the incident light, and the number of reflections. First, by increasing the optical path length of the multi-pass cell, the interaction time between the light and the analyte gas within the cell is prolonged, thereby improving the system's detection sensitivity (especially important for detecting low-concentration gases). Second, by optimizing the parameters of the parabolic mirror and the mirror distance (i.e., the distance between the centers of the two mirrors), the volume of the multi-pass cell can be reduced while increasing the optical path length, making the multi-pass cell structure more compact, which is particularly important for space-constrained applications. The compact structure helps reduce the impact of external factors on system performance (such as vibration, temperature changes, etc.) and also helps reduce production and transportation costs. This patented solution easily yields a small-volume multi-pass cell; a smaller volume also means reduced material usage and potential failure points, improving system stability and reliability.

[0048] Using the method of this invention, the spot density and size of the light spot pattern can be further adjusted by modifying the parameters of the parabolic mirror, the mirror distance, and the incident position of the incident light. Firstly, increasing the spot density means that more light interacts with the gas to be measured per unit volume, thereby improving the system's detection sensitivity. Simultaneously, optimizing the spot pattern ensures that more light paths pass through the gas sample, increasing signal strength. Secondly, adjusting the size and shape of the spot pattern helps optimize the uniformity of gas mixing within the cell, reducing measurement errors caused by uneven gas concentrations (especially when using multi-component gas analysis, a uniform spot pattern ensures that each gas can be effectively detected), thus improving the performance of the multi-pass cell. Finally, different application scenarios may require different spot patterns. By flexibly adjusting the spot density and pattern size, the multi-pass cell can adapt to different measurement needs and gas sample characteristics, improving its versatility and flexibility. Attached Figure Description

[0049] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0050] Figure 1 A schematic diagram of light transmission in a multipass pool in a Cartesian coordinate system;

[0051] Figure 2 (a) is a simulation diagram of three-dimensional ray tracing in two parabolic mirrors obtained by the method and Matlab software programming of this application; Figure 2 (b) and Figure 2 (c) and (d) are the light spot diagrams formed by the projection of the intersection points of the light rays and the two mirrors onto the xy plane;

[0052] Figure 3The image shows the light spots formed in the xy plane at the intersection points of the light rays and the two mirrors when the gain factors are 0.5 and 2, respectively. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0054] The following detailed explanation illustrates the specific implementation methods:

[0055] Example:

[0056] This embodiment discloses a design method for a parabolic mirror multi-pass cell for a TDLAS system.

[0057] Design method for multi-pass cell of parabolic mirror for TDLAS system, such as Figure 1 As shown, the multi-pass cell consists of two identical and coaxially opposed parabolic mirrors. The design method includes the following steps:

[0058] S1: Determine the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, and the position (x1, y1, z1) and direction cosine (sx1, sy1, sz1) of the incident light rays entering the multipass cell.

[0059] In this embodiment, the parameter p of the parabolic mirror is given by the parabolic formula y. 2 In 2px, p represents the semi-pivot diameter.

[0060] S2: Calculate the reflected ray parameters of the incident ray each time it passes through the multi-pass mirror using a precise ray tracing method between two parabolic mirrors; the reflected ray parameters include the three-dimensional coordinates of the intersection point of the incident ray and the parabolic mirror and the direction cosine of the reflected ray.

[0061] S3: Project the light spots at all intersections of the light rays with the two parabolic mirrors onto the xy plane to generate a light spot pattern;

[0062] S4: Change the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, the position and direction cosine of the incident light, and the number of reflections n of the light. Repeat steps S2 and S3 until the desired light spot pattern is generated.

[0063] S5: After generating the required light spot pattern, keep the direction cosine and reflection number of the incident light unchanged, and adjust the light spot density and pattern size by adjusting the parameters of the parabolic mirror, the distance L between the centers of the two mirrors, and the position of the incident light to obtain the final multipass cell.

[0064] In this embodiment, the multipass cell composed of two identical and coaxially opposite parabolic mirrors satisfies the self-existence condition, that is, after a cycle with n passes, the incident light can continue to be transmitted and reflected again, and produce the same spot pattern again.

[0065] This invention utilizes two identical, coaxially opposed parabolic mirrors to form a multi-pass cell. Compared to existing multi-pass cells composed of spherical mirrors, this invention offers several advantages: First, parabolic mirrors possess unique focusing characteristics, converging parallel light rays to their focal point, while spherical mirrors exhibit aberrations, particularly at large angles of light reflection. Therefore, the multi-pass cell using parabolic mirrors more effectively focuses incident light and reflects it multiple times within the cell, reducing light divergence and energy loss, and improving the optical path utilization and intensity distribution uniformity. Second, the focusing effect of parabolic mirrors makes the light reflection path within the cell more compact and efficient, allowing for more reflections within the same physical space. This increases the interaction time between light and the analyte gas, enhancing the detection sensitivity of the TDLAS system. Finally, spherical mirrors can cause spot distortion during reflection, affecting the uniformity of the spot pattern and intensity distribution. The parabolic mirrors of this invention effectively reduce this distortion, maintaining a circular or near-circular spot, resulting in a more uniform energy distribution and improving the accuracy and reliability of the multi-pass cell measurement results.

[0066] This invention adjusts the optical path length and volume of a multi-pass cell by changing the parameters of the parabolic mirror, the incident position and direction cosine of the incident light, and the number of reflections. First, by increasing the optical path length of the multi-pass cell, the interaction time between the light and the analyte gas within the cell is prolonged, thereby improving the system's detection sensitivity (especially important for detecting low-concentration gases). Second, by optimizing the parameters of the parabolic mirror and the mirror distance (i.e., the distance between the centers of the two mirrors), the volume of the multi-pass cell can be reduced while increasing the optical path length, making the multi-pass cell structure more compact, which is particularly important for space-constrained applications. The compact structure helps reduce the impact of external factors on system performance (such as vibration, temperature changes, etc.) and also helps reduce production and transportation costs. This patented solution easily yields a small-volume multi-pass cell; a smaller volume also means reduced material usage and potential failure points, improving system stability and reliability.

[0067] Using the method of this invention, the spot density and size of the light spot pattern can be further adjusted by modifying the parameters of the parabolic mirror, the mirror distance, and the incident position of the incident light. Firstly, increasing the spot density means that more light interacts with the gas to be measured per unit volume, thereby improving the system's detection sensitivity. Simultaneously, optimizing the spot pattern ensures that more light paths pass through the gas sample, increasing signal strength. Secondly, adjusting the size and shape of the spot pattern helps optimize the uniformity of gas mixing within the cell, reducing measurement errors caused by uneven gas concentrations (especially when using multi-component gas analysis, a uniform spot pattern ensures that each gas can be effectively detected), thus improving the performance of the multi-pass cell. Finally, different application scenarios may require different spot patterns. By flexibly adjusting the spot density and pattern size, the multi-pass cell can adapt to different measurement needs and gas sample characteristics, improving its versatility and flexibility.

[0068] In the specific implementation process, in the Cartesian coordinate system, the multipass pool is composed of two identical and coaxially opposite parabolic mirrors M1 and M2, and the distance between the centers O1 and O2 of the two mirrors is L;

[0069] The formulas F1(x,y,z) and F2(x,y,z) for two parabolic mirrors are expressed as follows:

[0070] M1:F1(x,y,z)=x 2 +y 2 -2pz = 0;

[0071] M2:F2(x,y,z)=x 2 +y 2 +2p(zL) = 0;

[0072] In the formula: M1 and M2 represent two parabolic mirrors.

[0073] In the specific implementation process, the incident light ray enters from the parabolic mirror M1, and the position and direction cosines of the incident light ray are (x1, y1, z1) and (sx1, sy1, sz1) respectively; the incident light ray is transmitted and reflected in the multi-pass cell, and the position and direction cosines of the nth incident light ray are (x1, y1, z1) and (sx1, sy1, sz1) respectively. n ,y n ,z n ) and (sx n ,sy n ,sz n );

[0074] The formula for the nth incident ray is expressed as:

[0075] x = x n +sx n ·d

[0076] y = yn +sy n ·d;

[0077] z = z n +sz n ·d;

[0078] In the formula: d represents the length of the incident ray.

[0079] In practical implementation, the formula for the reflecting mirror (i.e., the parabolic mirror) of the nth incident ray is expressed as:

[0080]

[0081] In the specific implementation process, the optical path length d of the incident light in the nth transmission is calculated using the following formula. n :

[0082]

[0083] in:

[0084] A n =sx n 2 +sy n 2 ;

[0085] B n =x n ·sx n +y n ·sy n +(-1) n+1 p·sz n ;

[0086]

[0087] In the specific implementation process, after calculating the length of the incident ray, the three-dimensional coordinates (x, y, y) of the intersection point between the nth incident ray and the parabolic mirror are further calculated. n+1 ,y n+1 ,z n+1 The calculation formula is expressed as follows:

[0088] x n+1 =x n +sx n ·d n ;

[0089] y n+1 =y n +sy n ·d n ;

[0090] z n+1 =zn +sz n ·d n .

[0091] In the specific implementation process, according to the vector reflection theorem:

[0092]

[0093] In the formula: and Let represent the direction cosine vectors of the incident and reflected rays of the parabolic mirror, respectively; The normal vector of the reflecting mirror is expressed by the formula:

[0094]

[0095] In practice, the direction cosine vector of the reflected light can be further calculated using the vector formula described above.

[0096]

[0097]

[0098] In the specific implementation process, the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, the position and direction cosine of the incident light, and the number of reflections of the light are adjusted. Based on the existing conditions of the light, the method proposed in this invention is used to perform ray tracing to generate the required light spot pattern.

[0099] In the specific implementation process, after generating the desired light spot pattern, the direction cosine (sx1, sy1, sz1) and reflection number n of the initial incident light rays onto the parabolic mirror M1 are kept constant. The parameters p of the parabolic mirror, the center distance L between the two mirrors, and the position (x1, y1, z1) of the initial incident light rays onto the parabolic mirror M1 are multiplied by the expected gain factor to adjust the size and density of the light spot pattern. Alternatively, the parameters p of the parabolic mirror, the center distance L between the two mirrors, and the incident position (x1, y1) of the initial incident light rays onto the parabolic mirror M1 are all multiplied by the same gain factor to adjust the pattern size of the light spot pattern.

[0100] To better illustrate the advantages of the technical solution of the present invention, the following simulation analysis is disclosed in this embodiment.

[0101] This simulation uses the method proposed in this invention and Matlab software programming to calculate the three-dimensional ray tracing pattern of light in a multipass cell. The double parabolic mirror multipass cell needs to satisfy the inherent condition, that is, after one cycle with n reflections, the incident light can continue to propagate and reflect again, producing the same spot pattern once more.

[0102] During the simulation, the parameters of the parabolic mirror, p = 70 mm, and the direction cosine of the incident ray, are kept constant at (0.1045, 0.1045, 0.9890). The initial position (x1, y1, z1) and the distance L between the centers of the two mirrors are adjusted so that the final ray (x... n+1 ,y n+1 ,z n+1 ), (sx n+1 ,sy n+1 ,sz n+1 The initial rays (x1, y1, z1) and (sx1, sy1, sz1) satisfy the self-presentation condition. When (x1, y1, z1) = (6.00, -6.99, 0.6061) mm, L = 73.38 mm, and n = 490, the parabolic mirror multipass cell satisfies the self-presentation condition. Table 1 shows the ray parameters for multiple iterations.

[0103] Table 1 shows the ray parameters for multiple iterations.

[0104]

[0105] Figure 2 (a) is a three-dimensional ray tracing diagram obtained by programming with the method proposed in this patent and Matlab software, with red lines representing rays. Figure 2 (b) and (c) are the light spot diagrams formed by the projection of the intersection points of the light rays with the parabolic mirrors M1 and M2 onto the xy plane. Figure 2 The light spot pattern in the image is a light spot pattern that has been adjusted and screened, and the corresponding multi-pass cell satisfies the spontaneous occurrence condition.

[0106] Once the desired light spot pattern is obtained, keep the incident ray direction cosine (sx1, sy1, sz1) and reflection number n unchanged, and adjust the light spot density by multiplying the parabolic mirror parameter p, the initial incident beam position (x1, y1) on the parabolic mirror M1, and the center distance L of the two mirrors by the expected gain factor k; or adjust the size of the pattern in the light spot by multiplying the parabolic mirror parameter p, the initial incident beam position (x1, y1) on the parabolic mirror M1, and the center distance L of the two mirrors by the same gain factor k.

[0107] Figure 3 (a) and (b) are the light spot diagrams of the intersection points of the light rays and the mirrors in the xy plane when the gain factors k are 0.5 and 2, respectively, obtained by programming with Matlab software. The blue and green points are the intersection points of the light rays and the mirrors M1 and M2, respectively, and the gray lines represent the projection of the light rays in the xy plane.

[0108] Depend on Figure 3It can be seen that when the gain factor k equals 0.5, the size of the light spot pattern becomes half of its original size; when the gain factor k equals 2, the size of the light spot pattern becomes twice its original size.

[0109] A longer total optical path length can improve the detection sensitivity of a multipass cell, while a smaller multipass cell can not only improve gas exchange rate and shorten response time, but also make the structure more compact. Figure 2 In this model, the distance from the farthest light spot to the origin is chosen as the mirror radius, and the volume V is defined as the product of the mirror area and the distance L between the centers of the two mirrors. The ratio of total optical path length to volume, RLV, can better reflect the spatial utilization of light trajectories in a multipass cell.

[0110] Table 2 lists the simulation results of the multi-pass pool when the gain factor k is equal to 0.5, 1, and 2, respectively.

[0111]

[0112] As shown in Table 2, when the gain factor becomes k times its original value, the total optical path length becomes k times its original value, and the volume becomes k times its original value. 3 The ratio of total optical path length to volume (RLV) becomes 1 / k of its original value. 2 When designing a parabolic multipass cell, the gain factor can be adjusted according to actual needs to obtain the required multipass cell.

[0113] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for designing a multi-pass cell for a parabolic mirror in a TDLAS system, characterized in that, The multi-pass cell consists of two identical and coaxially opposed parabolic mirrors, and the design method includes the following steps: S1: Determine the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, and the position (x1, y1, z1) and direction cosine (sx1, sy1, sz1) of the incident light rays entering the multipass cell. In step S1, in the Cartesian coordinate system, the multipass pool is composed of two identical and coaxially opposite parabolic mirrors M1 and M2, and the distance between the centers O1 and O2 of the two mirrors is L. The formulas F1(x,y,z) and F2(x,y,z) for two parabolic mirrors are expressed as follows: M1:F1(x,y,z)=x 2 +y 2 -2pz=0; M2:F2(x,y,z)=x 2 +y 2 +2p(z-L)=0; In the formula: M1 and M2 represent two parabolic mirrors; S2: Calculate the parameters of the reflected rays of the incident ray each time it passes through the multi-pass mirror using a ray tracing method between two parabolic mirrors; the reflected ray parameters include the three-dimensional coordinates of the intersection point of the incident ray and the parabolic mirror and the direction cosine of the reflected ray. In step S2, the incident light ray enters through the parabolic mirror M1, and the position and direction cosines of the incident light ray are (x1, y1, z1) and (sx1, sy1, sz1), respectively; the incident light ray propagates and reflects in the multi-pass cell, and the position and direction cosines of the nth incident light ray are (x1, y1, z1) and (sx1, sy1, sz1), respectively. n ,y n ,z n ) and (sx n ,sy n ,sz n ); The formula for the nth incident ray is expressed as: x=x n +sx n ·d; y=y n +and n ·d; z=z n +sh n ·d; In the formula: d represents the length of the incident ray; The formula for the reflecting surface of the nth incident ray is expressed as: The optical path length d of the nth incident ray is calculated using the following formula. n : in: A n =sx n 2 +and n 2 ; B n =x n ·sx n +y n ·in n +(-1) n+1 p·sz n 4 S3: Project the light spots at all intersections of the light rays with the two parabolic mirrors onto the xy plane to generate a light spot pattern; S4: Change the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, the position and direction cosine of the incident light, and the number of reflections n of the light. Repeat steps S2 and S3 until the desired light spot pattern is generated. S5: After generating the required light spot pattern, keep the direction cosine and reflection number of the incident light unchanged, and adjust the light spot density and pattern size by adjusting the parameters of the parabolic mirror, the distance L between the centers of the two mirrors, and the position of the incident light to obtain the final multipass cell.

2. The parabolic mirror multi-pass cell design method for TDLAS systems as described in claim 1, characterized in that: In step S2, after calculating the length of the incident ray, the three-dimensional coordinates (x, y, y) of the intersection point between the nth incident ray and the parabolic mirror are further calculated. n+1 ,y n+1 ,z n+1 The calculation formula is expressed as follows: x n+1 =x n +sx n ·d n ; the n+1 =y n +and n ·d n ; With n+1 =z n +sh n ·d n 。 3. The parabolic mirror multi-pass cell design method for a TDLAS system as described in claim 2, characterized in that: In step S2, according to the vector reflection theorem: In the formula: and Let represent the direction cosine vectors of the incident and reflected rays of the parabolic mirror, respectively; The normal vector of the reflecting mirror is expressed by the formula:

4. The parabolic mirror multi-pass cell design method for a TDLAS system as described in claim 3, characterized in that: In step S2, the direction cosine vector of the reflected ray is calculated.

5. The parabolic mirror multi-pass cell design method for a TDLAS system as described in claim 1, characterized in that: In step S4, the parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, the position and direction cosine of the incident light, and the number of reflections of the light are adjusted. Ray tracing is performed according to the existing conditions of the light to generate the required light spot pattern.

6. The parabolic mirror multi-pass cell design method for a TDLAS system as described in claim 1, characterized in that: In step S5, after generating the desired light spot pattern, the direction cosine (sx1, sy1, sz1) and reflection number n of the initial incident light rays on the parabolic mirror M1 are kept unchanged. The parameters p of the parabolic mirror, the distance L between the centers of the two mirrors, and the position (x1, y1, z1) of the initial incident light rays on the parabolic mirror M1 are multiplied by the expected gain factor to adjust the size and density of the light spot pattern.

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