A method for optimizing resolution of an imaging spectrometer based on a PGP model

Abstract

The application discloses a kind of based on PGP model's imaging spectrometer resolution optimization method, comprising: respectively calculating the maximum incident angle corresponding to central wavelength spectral line first exit angle of PGP model, minimum incident angle second exit angle of PGP model, and according to the difference between first exit angle and second exit angle determine the bending value of central wavelength spectral line, and according to the angle value of the angle range of first prism and second prism is according to the preset step length is cyclically calculated, obtain the bending value of multiple central wavelength spectral lines, then the bending value of multiple central wavelength spectral lines is screened to obtain minimum bending value, finally according to the apex angle value of first prism and the apex angle value of second prism corresponding to minimum bending value design production PGP model.The method can calculate the same case of two prism apex angle, also can calculate the case that two prism apex angle is not same, so that imaging spectrometer can still realize higher spectral resolution in wider wavelength range.

Description

TECHNICAL FIELD

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

[0002] In the design of an imaging spectrometer, spectral resolution is a core index, and many factors restrict the spectral resolution of the spectrometer, but the spectral line bending characteristics of light after passing through a dispersion element are an important factor limiting the spectral resolution of the spectrometer. Due to the complementary characteristics of prism and grating spectral line bending, some use a prism-grating model, but the spectral resolution is relatively low, resulting in poor imaging effect of the spectrometer. SUMMARY

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

[0004] To achieve the above-mentioned object, the first aspect of the present application proposes an imaging spectrometer resolution optimization method based on a PGP model, the PGP model comprising a first prism, a grating and a second prism, and the first prism, the grating and the second prism being connected in sequence, the method comprising: S1, obtaining an initial value of an apex angle of the first prism, a maximum value of the apex angle, an initial value of an apex angle of the second prism, a maximum value of the apex angle 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 line of the incident light; S3, respectively calculating a first exit angle of the central wavelength spectrum line corresponding to the maximum incident angle through the PGP model and a second exit angle of the central wavelength spectrum line corresponding to the minimum incident angle through the PGP model; S4, determining a bending value of the central wavelength spectrum line according to the difference between the first exit angle and the second exit angle; S5, adjusting the apex angle value of the second prism according to a preset step size until the apex angle value of the second prism reaches the maximum value of the apex angle of the second prism, and repeating the steps S3 and S4 in the adjustment process to obtain the bending value of the central wavelength spectrum line corresponding to each apex angle value of the second prism; S6, adjusting the apex angle value of the first prism according to the preset step size and repeating the steps S3-S5 until the apex angle value of the first prism reaches the maximum value of the apex angle of the first prism; S7, screening the bending values of a plurality of central wavelength spectrum lines to obtain a minimum bending value; S8, designing and manufacturing the PGP model according to the apex angle value of the first prism and the apex angle value of the second prism corresponding to the minimum bending value.

[0005] According to the PGP model-based imaging spectrometer resolution optimization method of the embodiment of the present application, firstly, the first exit angle of the maximum incidence angle of the central wavelength spectrum line and the second exit angle of the minimum incidence angle of the central wavelength spectrum line are calculated respectively through the PGP model, and the bending value of the central wavelength spectrum line is determined according to the difference between the first exit angle and the second exit angle, and the angle values in the angle range of the first prism and the second prism are calculated in a loop according to the preset step length according to the above steps to obtain the bending values of a plurality of central wavelength spectrum lines, then the bending values of the plurality of central wavelength spectrum lines are screened to obtain the minimum bending value, and finally the PGP model is designed and manufactured according to the top angle value of the first prism and the top angle value of the second prism corresponding to the minimum bending value. This method can calculate the case where the top angle of the two prisms is the same, and can also calculate the case where the top angle of the two prisms is not the same, so that the imaging spectrometer can still achieve higher spectral resolution in a wider wavelength range.

[0006] According to an embodiment of the present application, the bending value of the central wavelength spectrum line is determined according to the following formula:

[0007] l i =Δω i *F

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

[0009] According to an embodiment of the present application, the maximum incidence angle of the incident light is determined, comprising:

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

[0011] Determining the maximum incidence angle of the incident light according to the length of the slit and the distance between the slit and the first prism.

[0012] According to an embodiment of the present application, the maximum incidence 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 application, the maximum incident angle corresponding to the center wavelength spectrum line is calculated through the first exit angle of the PGP model, comprising: determining the incident angle of the center wavelength spectrum line of the maximum incident angle at the first prism; determining the incident angle of the grating according to the refraction law; determining the exit angle of the grating according to the grating equation; determining the exit angle of the second prism according to the refraction law, and the exit angle of the second prism is the first exit angle.

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

[0017] d (sin a-sin b) = m l

[0018] Wherein, d is the grating constant, a represents the incident angle of the light, b represents the exit angle of the light, m represents the diffraction order, and l represents the wavelength of the light.

[0019] The present application has the following beneficial effects:

[0020] The prism-grating-prism model has better inhibition effect on spectrum line bending, and since the model has high utilization rate of light energy, higher spectral resolution can still be achieved in a wider wavelength range. The method can calculate the case where the two prisms have the same vertex angle, and can also calculate the case where the two prisms have different vertex angles, and is comprehensive and has high reliability.

[0021] Additional aspects and advantages of the present application will be in part apparent and in part pointed out hereinafter. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 A flowchart of the imaging spectrometer resolution optimization method based on the PGP model according to an embodiment of the present application;

[0023] Figure 2 A schematic diagram of the imaging spectrometer based on the PGP model according to one embodiment of the present application. DETAILED DESCRIPTION

[0024] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference signs represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0025] The imaging spectrometer resolution optimization method based on the PGP model according to the embodiments of the present application is described below with reference to the accompanying drawings.

[0026] As Figure 2As shown, the imaging spectrometer of the Prism-Grating-Prism (PGP) model is an advanced spectral imaging device combining the advantages of prisms and gratings. The working principle of the PGP imaging spectrometer is mainly based on the dispersion of the prism and the diffraction of the grating. When non-monochromatic light is irradiated to the slit, it is converted into parallel light beams by the collimating lens. When these parallel light beams pass through the PGP model, the prism and the grating jointly disperse the light, causing different degrees of deflection of light rays of different wavelengths. Subsequently, after passing through the focusing lens, the dispersed light rays are imaged at different positions on the image plane, forming 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 A flowchart of the PGP model-based imaging spectrometer resolution optimization method according to the embodiment of the present application.

[0028] As shown in Figure 1 The PGP model-based imaging spectrometer resolution optimization method according to the embodiment of the present application can include the following steps:

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

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

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

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

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

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

[0035] Specifically, the maximum incident angle corresponding to the central wavelength spectrum line can be calculated according to the prism medium, the grating parameters, and the initial value of the top angle of the first prism and the initial value of the top angle of the second prism, and the first exit angle of the PGP model and the second exit angle of the PGP model of the minimum incident angle can be calculated. Then, the first exit angle and the second exit angle are subtracted to obtain a difference value, and corresponding calculation can be performed to obtain the bending value of the central wavelength spectrum line. It should be noted that the spectrum line bending of the central wavelength is the smallest in the spectrum range, and the smaller the bending value of the spectrum line is, the better.

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

[0037] l i =Δω i *F

[0038] Wherein, l i is the bending value of the central wavelength spectrum line, Δω i is the difference value between the first exit angle and the second exit angle, and F is the focal length of the focusing lens.

[0039] The difference value between the first exit angle and the second exit angle and the focal length of the focusing lens (a known quantity) are substituted into the above formula to obtain the bending value of the central wavelength spectrum line.

[0040] S5, the top angle value of the second prism is adjusted according to a preset step size until the top angle value of the second prism reaches the maximum top angle value of the second prism, and the steps S3 and S4 are repeated during the adjustment process to obtain the bending value of the central wavelength spectrum line corresponding to each top angle value of the second prism. The preset step size can be calibrated according to actual conditions, for example, the preset step size can be 1°.

[0041] S6, the top angle value of the first prism is adjusted according to a preset step size, and the steps S3-S5 are repeated until the top angle value of the first prism reaches the maximum top angle value of the first prism.

[0042] S7, the bending values of the plurality of central wavelength spectrum lines are screened to obtain the minimum bending value.

[0043] S8, the PGP model is designed and manufactured according to the top angle value of the first prism and the top angle value of the second prism corresponding to the minimum bending value.

[0044] For example, the first prism vertex angle initial value is given first: generally set to 0 degree; then the second prism vertex angle is increased from 0 degree to 45 degrees; the grating ruling number is a fixed value; that is (x, y, z), x: the first prism vertex angle, y: the grating ruling number, z: the second prism vertex angle; the iterative process is: (0, 1200, 0) to calculate the value of the spectral line bending once, (0, 1200, 1) to calculate the value of the spectral line bending once,..., (0, 1200, 45) to calculate the value once, thus the first group ends; continue (1, 1200, 0) to calculate once, (1, 1200, 1) to calculate once,..., (1, 1200, 45) to calculate once, thus the second group ends; the cycle continues, and finally (45, 1200, 45) is the last operation; in this way, all matching between different angles of the two prisms is completed; finally, the minimum value of the central wavelength spectral line bending is screened out as the final output result.

[0045] According to the minimum bending value, the vertex angle value of the first prism and the vertex angle value of the second prism corresponding to the minimum bending value are found, and 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, so that the spectral instrument using the PGP model has better spectral line bending suppression effect, and since the model has high light energy utilization rate, higher spectral resolution can still be realized in a wider wavelength range.

[0046] It should be understood that the prism vertex angle is a key factor affecting the size of the spectral line bending, and the prisms in the PGP model are optimized in two cases, that is, the two prisms have the same prism number, that is, the angle range and step length of the two prisms are consistent, or the two prisms have different prism numbers, that is, the angle range of the two prisms is different and the step length is the same, so that the method has high universality. The PGP model can more effectively disperse and focus light, so that the light energy utilization rate is higher, and the dispersion characteristics of the prisms and the grating are complementary, so that the PGP model can realize higher spectral resolution in a wider wavelength range, and the structure realizes compactness while maintaining high performance. Such compactness helps to reduce the volume and weight of the spectral instrument, facilitating carrying and installation.

[0047] According to an embodiment of the present application, the maximum incidence angle of the incident light is determined by obtaining the length of the slit and the distance from the slit to the first prism, and determining the maximum incidence angle of the incident light according to the length of the slit and the distance from the slit to the first prism.

[0048] Further, according to an embodiment of the present application, the maximum incidence 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 length of the slit and the distance between the slit and the first prism are substituted into the formula for calculation, and the maximum incident angle of the incident light can be obtained.

[0052] According to one embodiment of the present application, the maximum incident angle corresponding to the central wavelength spectrum line is calculated as the first exit angle of the PGP model, comprising: determining 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 refraction law; determining the exit angle of the grating according to the grating equation; determining the exit angle of the second prism according to the refraction law, and the exit angle of the second prism is the first exit angle.

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

[0054] d(sinα-sinβ)=mλ

[0055] Wherein, 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, the calculation of the incident angle of the incident light through the exit angle of the PGP model includes the following steps:

[0057] ① Calculate the incident angle of the incident light and the first prism by 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] Incident angle: θ1(θ s ,θ t )=arccos(Q0*N1)

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

[0062] ② Calculate the exit angle of the incident light through the first surface, which is the incident angle of the grating.

[0063] The calculation can be obtained by the refraction law (n1sinθ1=n2sinθ2).

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

[0065] The calculation can be obtained by the grating equation.

[0066] 4. Calculate the exit angle of the fourth face, that is, the exit angle of the second prism.

[0067] The calculation can be obtained by the refraction law.

[0068] Therefore, by the above steps, the maximum incidence angle corresponding to the central wavelength spectrum line, the first exit angle of the PGP model, and the minimum incidence angle, the second exit angle of the PGP model, can be calculated.

[0069] In an embodiment of the present application, the PGP model-based imaging spectrometer resolution optimization method can include the following steps:

[0070] Step 1. According to the design requirements, the prism vertex angle range, the incidence wavelength range, the prism refractive index, the grating type, the input prism vertex angle, and the incidence wavelength are determined, the projection of the incidence wave vector on the arc vector is calculated, and the wave vector in the air is determined by the prism vertex angle and the central field of view and the edge field of view of the slit.

[0071] Step 2. Calculate the first face, and use the refraction law to calculate the refraction angle of the first face and the wave vector through the first prism.

[0072] Step 3. Calculate the second face, and use the refraction law to calculate the incidence angle and the refraction angle of the second face and the wave vector through the grating.

[0073] Step 4. Calculate the third face, first calculate the azimuth angle of the incident grating, and then use the grating equation to calculate the exit angle of the grating dispersion direction.

[0074] Step 5. Calculate the fourth face, use the azimuth angle and the exit angle of the grating dispersion direction to represent the wave vector in the second prism, and then use the refraction law to calculate the incidence angle and the refraction angle of the fourth face.

[0075] Step 6. Calculate the exit wave vector of the light in the fourth face, and then calculate the angle between the wave vector and the XOZ plane, that is, the pitch angle.

[0076] Step 7. Repeat steps 1 to 6 to calculate the pitch angle of the wavelength corresponding to the different vertex angle prisms through the slit, calculate the spectrum line bending value, and select the minimum value of the spectrum line bending and the prism vertex angle corresponding to the minimum value.

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

[0078] In summary, according to the imaging spectrometer resolution optimization method based on the PGP model, the first exit angle of the PGP model corresponding to the maximum incident angle of the center wavelength spectrum line is calculated, the second exit angle of the PGP model corresponding to the minimum incident angle is calculated, the bending value of the center wavelength spectrum line is determined according to the difference between the first exit angle and the second exit angle, the angle value of the angle range of the first prism and the second prism is calculated according to the preset step length according to the above steps, the bending values of the plurality of center wavelength spectrum lines are obtained, then the bending values of the plurality of center wavelength spectrum lines 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 angle of the two prisms is the same, and can also calculate the case where the vertex angle of the two prisms is not the same. It is comprehensive and the result is highly reliable. The PGP model imaging spectrometer obtained by optimization has better spectral line bending suppression effect and high light energy utilization rate, so that the imaging spectrometer can still achieve higher spectral resolution in a wider wavelength range.

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

[0080] In addition, the terms "first", "second" are only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, the features defined with "first", "second" can explicitly or implicitly include at least one feature. In the description of the present application, the meaning of "a plurality of" is at least two, for example, two, three, etc., unless otherwise specifically limited.

[0081] In this application, unless otherwise clearly indicated and limited, the terms "mounting", "connection", "connecting", "fixing" and the like should be interpreted broadly, for example, can be fixed connection, can also be detachable connection, or integral; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship of two elements, unless otherwise clearly limited. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0082] Although the embodiments of the present application have been shown and described above, it should be understood that the above embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

Claims

1. A method for optimizing the resolution of an imaging spectrometer based on the 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 sequentially. The method includes: S1, obtain the initial value and maximum value of the apex angle of the first prism, the initial value and maximum value of the apex angle of the second prism, and the spectral range of the incident light; S2, determine the maximum and minimum incident angles of the incident light and the center wavelength spectral line of the incident light; S3, calculate the first exit angle of the PGP model with the maximum incident angle corresponding to the center wavelength spectral line and the second exit angle of the PGP model with the minimum incident angle respectively; S4, determine the curvature value of the center wavelength spectral line based on the difference between the first emission angle and the second emission angle; S5, adjust the apex angle value of the second prism according to the preset step size until the apex angle value of the second prism reaches the maximum value of the apex angle of the second prism, and repeat the above steps S3 and S4 during the adjustment process to obtain the bending value of the center wavelength spectral line corresponding to each apex angle value of the second prism. S6, adjust the apex angle value of the first prism according to the preset step size, and repeat the above steps S3-S5 until the apex angle value of the first prism reaches the maximum value of the apex angle of the first prism. S7, the bending values ​​of multiple center wavelength spectral lines are filtered to obtain the minimum bending value; S8, the PGP model is designed and fabricated based on the apex angle values ​​of the first prism and the second prism corresponding to the minimum bending value; wherein, the bending value of the center wavelength spectral line is determined according to the following formula: in, The curvature value of the center wavelength spectral line. The difference between the first emission angle and the second emission angle. The focal length of the focusing lens; The calculation of the first exit angle of the PGP model corresponding to the maximum incident angle of the center wavelength spectral line includes: Determine the center wavelength spectral line at the angle of maximum incident at the first prism; The incident angle of the grating is determined according to the law of refraction; The emission angle of the grating is determined according to the grating equation; The exit angle of the second prism is determined according to the law of refraction, and the exit angle of the second prism is the first exit angle.

2. The method for optimizing the resolution of an imaging spectrometer based on the PGP model according to claim 1, characterized in that, Determining the maximum angle of incidence of the incident ray includes: Obtain 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 based on the length of the slit and the distance between the slit and the first prism.

3. The method for optimizing the resolution of an imaging spectrometer based on the PGP model according to claim 2, characterized in that, The maximum angle of incidence of the incident ray is determined according to the following formula: Where D is half the length of the slit, and S is the distance from the slit to the first prism.

4. The method for optimizing the resolution of an imaging spectrometer based on the PGP model according to claim 1, characterized in that, The grating equation is expressed by the following formula: Where d is the grating constant, α represents the incident angle of the light ray, β represents the exit angle of the light ray, and m represents the diffraction order. Represents the wavelength of light.

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