Imaging spectrometer resolution optimization method based on PGP model

Abstract

The invention discloses an imaging spectrometer resolution optimization method based on a PGP model, and the method comprises the steps: respectively calculating a first emergent angle of a maximum incident angle passing through the PGP model and a second emergent angle of a minimum incident angle passing through the PGP model corresponding to a central wavelength spectral line, and determining a bending value of the central wavelength spectral line according to a difference value between the first emergent angle and the second emergent angle, and circularly calculating the angle values of the angle ranges of the first prism and the second prism according to the above steps according to a preset step length to obtain bending values of a plurality of central wavelength spectral lines, and then screening the bending values of the plurality of central wavelength spectral lines to obtain a minimum bending value. And finally, designing and manufacturing a PGP model according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value. According to the method, the condition that the top angles of the two prisms are the same can be calculated, and the condition that the top angles of the two prisms are different can also be calculated, so that the imaging spectrometer can still realize higher spectral resolution in a wider wavelength range.

Description

Technical Field

[0001] The present invention relates to the field of optical imaging technology, and in particular to a method for optimizing the resolution of an imaging spectrometer based on a PGP (Prism-Grating-Prism) model. Background Art

[0002] In the design of imaging spectrometers, spectral resolution is its core indicator. There are many factors that restrict the resolution of spectrometers, but the spectral line bending characteristics that appear after light passes through the dispersion element are an important factor that limits the resolution of spectrometers. Due to the complementary characteristics of spectral line bending of prisms and gratings, some use prism-grating models, but their spectral resolution is relatively low, resulting in poor imaging effects of spectrometers. Summary of the invention

[0003] The present invention aims to solve one of the technical problems in the related art at least to a certain extent. To this end, the first object of the present invention is to propose a method for optimizing the resolution of an imaging spectrometer based on a PGP model.

[0004] To achieve the above-mentioned purpose, the first embodiment of the present invention proposes a method for optimizing the resolution of an imaging spectrometer based on a PGP model, wherein the PGP model includes a first prism, a grating and a second prism, and the first prism, the grating and the second prism are connected in sequence, and the method includes: S1, obtaining an initial value and a maximum value of a vertex angle of the first prism, an initial value and a maximum value of a vertex angle of the second prism, and a spectral range of an incident light; S2, determining a maximum incident angle and a minimum incident angle of the incident light and a central wavelength spectrum of the incident light; S3, respectively calculating a first exit angle and a second exit angle of the maximum incident angle corresponding to the central wavelength spectrum through the PGP model and a minimum incident angle; S4, calculating a first exit angle and a second exit angle of the minimum incident angle according to the first exit angle and the second exit angle; and The bending value of the central wavelength spectrum line is determined by the difference between the incident angles; S5, adjusting the vertex angle value of the second prism according to a preset step size until the vertex angle value of the second prism reaches the maximum vertex angle of the second prism, and repeating the above steps S3 and S4 during the adjustment process to obtain the bending value of the central wavelength spectrum line corresponding to each vertex angle value of the second prism; S6, adjusting the vertex angle value of the first prism according to the preset step size, and repeating the above steps S3-S5 until the vertex angle value of the first prism reaches the maximum vertex angle of the first prism; S7, screening the bending values ​​of the multiple central wavelength spectra to obtain the minimum bending value; S8, designing and manufacturing the PGP model according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value.

[0005] According to the imaging spectrometer resolution optimization method based on the PGP model of the embodiment of the present invention, firstly, the maximum incident angle corresponding to the central wavelength spectrum is calculated through the first exit angle of the PGP model, and the minimum incident angle is calculated through the second exit angle of the PGP model, and the bending value of the central wavelength spectrum is determined according to the difference between the first exit angle and the second exit angle, and the angle values ​​of the angle range of the first prism and the second prism are cyclically calculated according to the preset step length according to the above steps to obtain the bending values ​​of multiple central wavelength spectra, and then the bending values ​​of the multiple central wavelength spectra are screened to obtain the minimum bending value, and finally the PGP model is designed and manufactured according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value. This method can calculate the case where the vertex angles of the two prisms are the same, and can also calculate the case where the vertex angles of the two prisms are different, so that the imaging spectrometer can still achieve higher spectral resolution in a wider wavelength range.

[0006] According to one embodiment of the present invention, the curvature value of the central wavelength spectrum line is determined according to the following formula:

[0007] l i =Δω i *F

[0008] Among them, l i is the bending value of the central wavelength spectrum, Δω i is the difference between the first emergent angle and the second emergent angle, and F is the focal length of the focusing lens.

[0009] According to one embodiment of the present invention, determining the maximum incident angle of the incident light comprises:

[0010] Acquire the length of the slit and the distance between the slit and the first prism;

[0011] The maximum incident angle of the incident light is determined according to the length of the slit and the distance between the slit and the first prism.

[0012] According to one embodiment of the present invention, the maximum incident angle of the incident light is determined according to the following formula:

[0013]

[0014] Wherein, D is half of the length of the slit, and S is the distance from the slit to the first prism.

[0015] According to one embodiment of the present invention, calculating the first output angle of the maximum incident angle corresponding to the central wavelength spectrum line through the PGP model includes: determining the incident angle of the central wavelength spectrum line with the maximum incident angle on the first prism; determining the incident angle of the grating according to the law of refraction; determining the output angle of the grating according to the grating equation; determining the output angle of the second prism according to the law of refraction, the output angle of the second prism being the first output angle.

[0016] According to one embodiment of the present invention, the grating equation is expressed by the following formula:

[0017] d(sinα-sinβ)=mλ

[0018] Among them, d is the grating constant, α represents the incident angle of the light, β represents the exit angle of the light, m ​​represents the diffraction order, and λ represents the wavelength of the light.

[0019] The beneficial effects of the present invention are:

[0020] The prism-grating-prism model has a better effect in suppressing spectral line bending. Since its model has a high utilization rate of light energy, it can still achieve higher spectral resolution within a wider wavelength range. This method can calculate the case where the two prism vertex angles are the same, and it can also calculate the case where the two prism vertex angles are different. It is comprehensive and the results are highly reliable.

[0021] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A flowchart of a method for optimizing the resolution of an imaging spectrometer based on a PGP model according to an embodiment of the present invention;

[0023] Figure 2 Schematic diagram of an imaging spectrometer based on a PGP model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0024] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0025] The following describes a method for optimizing the resolution of an imaging spectrometer based on a PGP model according to an embodiment of the present invention with reference to the accompanying drawings.

[0026] like Figure 2As shown, the imaging spectrometer of the prism-grating-prism (Prism-Grating-Prism, PGP) model is an advanced spectral imaging device that combines the advantages of prisms and gratings. The working principle of the PGP imaging spectrometer is mainly based on the dispersion effect of the prism and the diffraction effect of the grating. When non-monochromatic light is irradiated to the slit, it is converted into parallel light beams through a collimating lens. When these parallel light beams pass through the PGP model, the prism and the grating work together to disperse the light, causing light of different wavelengths to be deflected to different degrees. Subsequently, after passing through a focusing lens, these dispersed light rays are imaged at different positions on the image plane to form a spectral image. The PGP model includes a first prism, a grating and a second prism, and the first prism, the grating and the second prism are connected in sequence. Specifically, the first prism, the grating and the second prism are glued together.

[0027] Figure 1 The figure is a flow chart of a method for optimizing the resolution of an imaging spectrometer based on a PGP model according to an embodiment of the present invention.

[0028] like Figure 1 As shown, the imaging spectrometer resolution optimization method based on the PGP model of an embodiment of the present invention may include the following steps:

[0029] S1, obtaining the initial value and maximum value of the vertex angle of the first prism, the initial value and maximum value of the vertex angle of the second prism, and the spectral range of the incident light.

[0030] For example, the initial value of the vertex angle of the first prism may be 0°, and the maximum value of the vertex angle may be 45°; the initial value of the vertex angle of the second prism may be 0°, and the maximum value of the vertex angle may be 45°; and the spectral range of the incident light may be 750-1050nm.

[0031] S2, determine the maximum incident angle and minimum incident angle of the incident light and the central wavelength spectrum of the incident light.

[0032] The maximum incident angle of the incident light refers to the incident angle corresponding to the edge field of view, and the minimum incident angle of the incident light refers to the incident angle corresponding to the central field of view. The minimum incident angle of the incident light is 0°. When the spectral range of the incident light is 750-1050nm, the wavelength of the central wavelength spectrum is 900nm.

[0033] S3, respectively calculating the first emission angle of the maximum incident angle corresponding to the central wavelength spectrum through the PGP model and the second emission angle of the minimum incident angle through the PGP model.

[0034] S4, determining the curvature value of the central wavelength spectrum line according to the difference between the first emission angle and the second emission angle.

[0035] Specifically, the maximum incident angle corresponding to the center wavelength spectrum line can be calculated through the first output angle of the PGP model and the minimum incident angle through the second output angle of the PGP model according to the prism medium, grating parameters, and the initial value of the vertex angle of the first prism and the initial value of the vertex angle of the second prism. Then, the first output angle is subtracted from the second output angle to obtain the difference, and the corresponding calculation is performed to obtain the curvature value of the center wavelength spectrum line. It should be noted that within the spectral range, the curvature of the center wavelength spectrum line is the smallest, and the smaller the curvature value of the spectrum line, the better.

[0036] According to one embodiment of the present invention, the bending value of the central wavelength spectrum line is determined according to the following formula:

[0037] l i =Δω i *F

[0038] Among them, l i is the bending value of the central wavelength spectrum, Δω i is the difference between the first and second emission angles, and F is the focal length of the focusing lens.

[0039] Substituting the difference between the first and second emission angles and the focal length of the focusing lens (known quantity) into the above formula, the curvature value of the central wavelength spectrum line can be obtained.

[0040] S5, adjusting the vertex angle value of the second prism according to the preset step length until the vertex angle value of the second prism reaches the maximum vertex angle value of the second prism, and repeating the above steps S3 and S4 during the adjustment process to obtain the bending value of the central wavelength spectrum line corresponding to each vertex angle value of the second prism. The preset step length can be calibrated according to actual conditions, for example, the preset step length can be 1°.

[0041] S6, adjusting the vertex angle value of the first prism according to a preset step size, and repeating the above steps S3-S5 until the vertex angle value of the first prism reaches the maximum vertex angle value of the first prism.

[0042] S7, screening the bending values ​​of multiple center wavelength spectral lines to obtain a minimum bending value.

[0043] S8, designing and manufacturing a PGP model according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value.

[0044] For example, first give the initial value of the first prism vertex angle: generally set to 0 degrees; then the vertex angle of the second prism increases from 0 degrees to 45 degrees; the number of grating lines is a constant; that is, (x, y, z), x: the vertex angle of the first prism, y: the number of grating lines, z: the vertex angle of the second prism; the iterative process: (0, 1200, 0) calculates the value of the spectral line bending once, (0, 1200, 1) calculates the value of the spectral line bending once, ... (0, 1200, 45) calculates the value once, and the first group ends; continue to calculate (1, 1200, 0) once, (1, 1200, 1) once, ... (1, 1200, 45) calculates once, and the second group ends; repeat this cycle, and finally (45, 1200, 45) is the last calculation; in this way, all matches between the two prisms at different angles are completed; finally, the minimum value of the spectral line bending of the central wavelength is screened out as the final output result.

[0045] According to the minimum bending value, the corresponding vertex angle value of the first prism and the vertex angle value of the second prism are found, and a PGP model is designed and manufactured according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value. Therefore, the imaging spectrometer using the PGP model has a better suppression effect on spectral line bending. Since the model has a high utilization rate of light energy, a higher spectral resolution can still be achieved within a wider wavelength range.

[0046] It should be understood that the degree of the vertex angle of the prism is the key to the size of the spectral line bending. The prisms in the PGP model are optimized in two cases. When the degrees of the two prisms are the same, that is, the angle range of the two prisms is consistent with the step length, or when the degrees of the two prisms are different, that is, the angle range of the two prisms is different and the step length is the same, the energy is focused for optimization, so this method has high versatility. The PGP model can disperse and focus light more effectively, making the light energy utilization rate higher. The dispersion characteristics of the prism and the grating complement each other, so that the PGP model can achieve higher spectral resolution in a wider wavelength range. Its structure is compact while maintaining high performance. This compactness helps to reduce the size and weight of the spectrometer, making it easy to carry and install.

[0047] According to one embodiment of the present invention, determining the maximum incident angle of the incident light includes: obtaining the length of the slit and the distance between the slit and the first prism; and determining the maximum incident angle of the incident light according to the length of the slit and the distance between the slit and the first prism.

[0048] Further, according to an embodiment of the present invention, the maximum incident angle of the incident light is determined according to the following formula:

[0049]

[0050] Wherein, D is half of the slit length, and S is the distance from the slit to the first prism.

[0051] Specifically, since the length of the slit and the distance between the slit and the first prism are known quantities, the maximum incident angle of the incident light can be obtained by substituting the length of the slit and the distance between the slit and the first prism into the formula for calculation.

[0052] According to one embodiment of the present invention, calculating the first output angle of the maximum incident angle corresponding to the central wavelength spectrum line through the PGP model includes: determining the incident angle of the central wavelength spectrum line with the maximum incident angle on the first prism; determining the incident angle of the grating according to the law of refraction; determining the output angle of the grating according to the grating equation; determining the output angle of the second prism according to the law of refraction, the output angle of the second prism being the first output angle.

[0053] Further, according to one embodiment of the present invention, the grating equation is expressed by the following formula:

[0054] d(sinα-sinβ)=mλ

[0055] Among them, d is the grating constant, α represents the incident angle of the light, β represents the exit angle of the light, m ​​represents the diffraction order, and λ represents the wavelength of the light.

[0056] Specifically, calculating the incident angle of the incident light ray and the exit angle through the PGP model includes the following steps:

[0057] ① Calculate the incident angle of the incident light and the first prism using the following formula:

[0058] Incident vector: Q0(θ s )=Q0(-sinθ s ,0,cosθ s )

[0059] Normal vector: N1(θ t )=N1(0,-sinθ t ,cosθ t )

[0060] Angle of incidence: θ1(θ s ,θ t )=arccos(Q0*N1)

[0061] Among them, θ s is the angle between the projection of the incident wave vector on the sagittal plane (i.e. the incident wave vector) and the optical axis; θ t The angle between the projection of the incident wave vector in the main section and N1, where N1 represents the unit normal vector of each refractive interface.

[0062] ② Calculate the angle of incidence of the incident light after passing through the first surface, which is also the angle of incidence of the grating.

[0063] It can be calculated through the law of refraction (n1sinθ1=n2sinθ2).

[0064] ③ Calculate the angle of incidence of the third surface, that is, the angle of incidence of the light after passing through the grating, which is also the angle of incidence of the fourth surface.

[0065] It can be obtained by calculating the above grating equation.

[0066] ④ Calculate the incidence angle of the fourth surface, which is also the incidence angle of the second prism.

[0067] It can be calculated using the law of refraction.

[0068] Therefore, after the described steps, the first emission angle of the maximum incident angle corresponding to the central wavelength spectrum line through the PGP model and the second emission angle of the minimum incident angle through the PGP model can be calculated respectively.

[0069] In one embodiment of the present invention, the imaging spectrometer resolution optimization method based on the PGP model may include the following steps:

[0070] Step 1. Determine the prism vertex angle range, incident wavelength range, prism refractive index, grating model, input prism vertex angle and incident wavelength according to design requirements, calculate the angle between the projection of the incident wave vector on the sagittal plane and the optical axis, and determine the wave vector through the air through the prism vertex angle and the central field of view and edge field of view of the slit.

[0071] Step 2: Calculate the first surface and use the law of refraction to find the refraction angle of the first surface and the wave vector passing through the first prism.

[0072] Step 3: Calculate the second surface and use the law of refraction to find the incident angle and refraction angle of the second surface and the wave vector passing through the grating.

[0073] Step 4: Calculate the third surface. First, find the azimuth angle of the incident grating, and then use the grating equation to find the exit angle in the grating dispersion direction.

[0074] Step 5: Calculate the fourth surface, use the azimuth angle and the angle of incidence in the grating dispersion direction to express the wave vector in the second prism, and then use its refraction law to calculate the incident angle and refraction angle of the fourth surface.

[0075] Step 6: Calculate the wave vector of the light ray emitted from the fourth plane, and then calculate the angle between its wave vector and the XOZ plane, that is, the pitch angle.

[0076] Step 7, repeat steps 1 to 6, calculate the pitch angle of a wavelength corresponding to different vertex angle prisms passing through the slit, find the value of the spectrum line bending and screen out the minimum value of the spectrum line bending and its corresponding prism vertex angle degree.

[0077] Step 8, repeat steps 1 to 7 to find the values ​​of spectral line bending corresponding to all wavelengths within the input wavelength range, and finally output the minimum value of spectral line bending corresponding to all wavelengths and the degree of prism vertex angle corresponding to the minimum value of spectral line bending.

[0078] In summary, according to the PGP model-based imaging spectrometer resolution optimization method of the embodiment of the present invention, firstly, the maximum incident angle corresponding to the central wavelength spectrum is calculated through the first exit angle of the PGP model, and the minimum incident angle is calculated through the second exit angle of the PGP model, and the bending value of the central wavelength spectrum is determined according to the difference between the first exit angle and the second exit angle, and the angle value of the angle range of the first prism and the second prism is cyclically calculated according to the preset step size according to the above steps to obtain the bending values ​​of multiple central wavelength spectrums, and then the bending values ​​of the multiple central wavelength spectrums are screened to obtain the minimum bending value, and finally the PGP model is designed and manufactured according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value. This method can calculate the case where the vertex angles of the two prisms are the same, and can also calculate the case where the vertex angles of the two prisms are different. It is comprehensive and the result is highly reliable. The optimized PGP model imaging spectrometer has a better suppression effect on the bending of the spectrum and a high utilization rate of light energy, so that the imaging spectrometer can still achieve higher spectral resolution in a wider wavelength range.

[0079] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0080] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0081] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0082] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for optimizing the resolution of an imaging spectrometer based on a PGP model, characterized in that: The PGP model includes a first prism, a grating and a second prism, and the first prism, the grating and the second prism are connected in sequence, and the method includes: S1, obtaining an initial value and a maximum value of the vertex angle of the first prism, an initial value and a maximum value of the vertex angle of the second prism, and a spectral range of the incident light; S2, determining the maximum incident angle and the minimum incident angle of the incident light and the central wavelength spectrum of the incident light; S3, respectively calculating a first emission angle of the maximum incident angle corresponding to the central wavelength spectrum through the PGP model and a second emission angle of the minimum incident angle through the PGP model; S4, determining a curvature value of the central wavelength spectrum line according to a difference between the first emission angle and the second emission angle; S5, adjusting the vertex angle value of the second prism according to a preset step length until the vertex angle value of the second prism reaches the maximum vertex angle value of the second prism, and repeating the above steps S3 and S4 during the adjustment process to obtain the bending value of the central wavelength spectrum line corresponding to each vertex angle value of the second prism; S6, adjusting the vertex angle value of the first prism according to the preset step length, and repeating the above steps S3-S5 until the vertex angle value of the first prism reaches the maximum vertex angle value of the first prism; S7, screening the bending values ​​of the plurality of central wavelength spectra to obtain a minimum bending value; S8, designing and manufacturing the PGP model according to the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value.

2. The imaging spectrometer resolution optimization method based on the PGP model according to claim 1, characterized in that: The bending value of the central wavelength spectrum line is determined according to the following formula: l i =Here i *F Among them, l i is the bending value of the central wavelength spectrum, Δω i is the difference between the first emergent angle and the second emergent angle, and F is the focal length of the focusing lens.

3. The imaging spectrometer resolution optimization method based on the PGP model according to claim 1, characterized in that: Determining the maximum incident angle of the incident light comprises: Acquire the length of the slit and the distance between the slit and the first prism; The maximum incident angle of the incident light is determined according to the length of the slit and the distance between the slit and the first prism.

4. The imaging spectrometer resolution optimization method based on the PGP model according to claim 3, characterized in that: The maximum incident angle of the incident light is determined according to the following formula: Wherein, D is half of the length of the slit, and S is the distance from the slit to the first prism.

5. The imaging spectrometer resolution optimization method based on the PGP model according to claim 1, characterized in that: Calculating the first emission angle of the maximum incident angle corresponding to the central wavelength spectrum line through the PGP model includes: Determine the incident angle of the central wavelength spectrum line of the maximum incident angle at the first prism; determining the incident angle of the grating according to the law of refraction; Determining the exit angle of the grating according to the grating equation; The emergence angle of the second prism is determined according to the law of refraction, and the emergence angle of the second prism is the first emergence angle.

6. The imaging spectrometer resolution optimization method based on the PGP model according to claim 5, characterized in that: The grating equation is expressed by the following formula: d(sinα-sinβ)=mλ Among them, d is the grating constant, α represents the incident angle of the light, β represents the exit angle of the light, m ​​represents the diffraction order, and λ represents the wavelength of the light.

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