Spectral data demodulation method

Abstract

The invention relates to the technical field of spectral imaging, in particular to a spectral data demodulation method, which comprises the following steps of: 1, providing an imaging spectrometer, acquiring a plurality of images of the same target point by using the imaging spectrometer, and outputting an electron number expression of a modulation curve corresponding to each image by the imaging spectrometer; step 2, obtaining an optimal solution x0 of a least square problem of an electron number expression by using singular value decomposition; 3, constructing an unconstrained optimization function based on an electron number expression; 4, the optimal solution x0 serves as an initial value of iteration input of the unconstrained optimization function, the minimum solution x of the unconstrained optimization function is obtained through an LM algorithm, and x is spectral data obtained through demodulation. The method is at least beneficial to improving the demodulation precision of the spectral data.

Description

Technical Field

[0001] This invention belongs to the field of spectral imaging technology, and in particular relates to a method for demodulating spectral data. Background Technology

[0002] Spectral imaging technology, a remote sensing technique that emerged in the 1980s, is used to acquire the spectral information of targets, and this technology has experienced rapid development in recent years. When applied to remote sensing, spectral acquisition methods can be mainly divided into two types: dispersive and interferometric. Dispersive imaging can be further divided into grating dispersion and prism dispersion. Both grating dispersion and prism dispersion disperse light containing different wavelengths at different angles and positions to achieve spectral splitting. Interferometric imaging primarily relies on various optical elements to generate optical path differences, using Fourier transform to achieve spectral demodulation.

[0003] A Fabry-Pérot interferometer (FP) is a multi-beam interferometer. Compared to dispersive spectrometers, spectrometers using FP as their dispersive system have higher light energy utilization and extremely high spectral resolution compared to interferometric spectrometers. However, there is a mutual constraint between the spectral resolution and the free spectral range of an FP interferometer. A larger FP spacing (the distance between the two parallel plates in the FP interferometer) results in higher spectral resolution but a smaller free spectral range. If the spectral range exceeds the free spectral range, spectral aliasing occurs, making it impossible to obtain the target's spectral information using intuitive geometric processing methods. Therefore, traditional FP interferometers can only be used in extremely narrow spectral ranges. Related techniques have proposed using singular value decomposition (SVD) to solve for aliased FP interferometric spectral curves; however, this method is sensitive to image noise, which needs to be controlled below 0.2% to reconstruct the spectral curve effectively. This significantly limits the application areas of FP interferometers.

[0004] In summary, for spectrometers that use FP interferometers as their spectroscopic system, optimizing the data demodulation and improving its noise immunity to achieve high-precision spectral detection and applications is a pressing technical problem that needs to be solved in this field. Summary of the Invention

[0005] In view of this, the present invention aims to provide a method for demodulating spectral data, which at least helps to improve the demodulation accuracy of spectral data.

[0006] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0007] This invention provides a method for demodulating spectral data, comprising: Step 1, providing an imaging spectrometer, acquiring multiple images of the same target point using the imaging spectrometer, and outputting an electron number expression for the modulation curve corresponding to each image; Step 2, obtaining the optimal solution x0 of the least squares problem of the electron number expression using singular value decomposition; Step 3, constructing an unconstrained optimization function based on the electron number expression; Step 4, using the optimal solution x0 as the initial value for the iterative input of the unconstrained optimization function, and using the LM algorithm to obtain the minimum solution x of the unconstrained optimization function, where x is the demodulated spectral data.

[0008] Furthermore, the imaging spectrometer includes a front mirror group, an FP module, an imaging mirror, and a detector arranged sequentially. The imaging spectrometer acquires n images of the same target point, and the detector outputs an expression for the number of electrons in the n modulation curves corresponding to the n images. The expression for the number of electrons is as follows: Where i is 1, 2, 3...n, j is 1, 2, 3...n, x(λ) j) λ is the exit pupil radiance of the imaging spectrometer. j Let λ be the wavelength of the different interference rays after the beam is split, h be Planck's constant, C be the speed of light, and I be the wavelength of the interference rays. i For the detector's signal output, T in For the integration time, A d F is the pixel area of ​​the detector. # Let τ0(λ) be the F-number of the imaging spectrometer. j T represents the transmittance of the imaging spectrometer. FP (λ j ,θ i η(λ) is the spectral transmittance function of the FP module. j ) represents the quantum efficiency of the detector, Δλ j For spectral resolution.

[0009] Furthermore, T FP (θ i ,λ j The expression for ) is as follows:

[0010]

[0011] Where θ is the angle at which the beam enters the FP module, R is the specular reflectivity of the FP module, d is the mirror spacing of the FP module, λ is the wavelength, and n is the refractive index of the medium.

[0012] Furthermore, step two also includes: simplifying the electron number expression to Formula 1, as follows: I = Kx; where I is I i The matrix x is x(λ) j A matrix of K, where K is K i The matrix, i is 1, 2, 3...n;

[0013] The optimal solution x0 of the least squares problem in Formula 1 is obtained by using singular value decomposition.

[0014] Furthermore, step three includes: transforming formula 1 into formula 2, as follows:

[0015] F(λ) = I - Kx;

[0016] Based on Equation 2, an unconstrained optimization function is constructed as follows:

[0017]

[0018] Furthermore, the LM algorithm is used to obtain the minimum solution x of the unconstrained optimization function, which includes: selecting initial input parameters β and σ, where β and σ ∈ (0,1), selecting x0 as the initial data point, selecting the allowable error ξ, where the allowable error ξ satisfies 0 ≤ ξ ≤ 1, and determining the small iteration number m and the large iteration number k; obtaining the derivative g(x) of the unconstrained optimization function, where g(x) = ▽f(x); determining whether g(x) satisfies Ⅱg(x)Ⅱ ≤ ξ; if it satisfies Ⅱg(x)Ⅱ ≤ ξ, then stop the calculation and output x; if it does not satisfy Ⅱg(x)Ⅱ ≤ ξ, then solve the system of equations: (J k T J k +u k I0)d=-J k T F k The solution d is obtained. k Where I0 is the identity matrix, F k For x k Substituting into the F(λ) matrix obtained from Formula 2, x k The initial value is x0, J k J is the Jacobian matrix of Formula 2. k T For J k The transpose of u k Given the L2 norm of Formula 2; determine whether f(x) satisfies the condition. k +β m d k )≤f(x k )+σβ m g(x k ) T d k If so, then m = m k If not, then m = 0; based on m, execute α. k :=β m And execute x k +1:=x k+α k d k Determine if m satisfies m < m max If yes, then m = m + 1; otherwise, update u. k u k =||f(x) k )|| 2 Determine if k satisfies k < k max If yes, then k = k + 1; otherwise, output x.

[0019] Compared with existing technologies, the present invention can achieve the following beneficial effects: The spectral data demodulation method provided by the present invention is a data demodulation method for imaging spectrometers based on multi-level aliased FP interferometers. Compared with the method of solving the aliased FP interferometric spectral curves by using singular value decomposition, the present invention constructs an optimization function and uses an optimization iterative algorithm to demodulate the spectral data. Moreover, the initial value of the optimization iterative algorithm is obtained by using singular value decomposition, which can improve the system's anti-noise interference capability and significantly improve the data demodulation accuracy and detection accuracy of the imaging spectrometer. This is conducive to expanding the application scenarios of FP interferometers and has broad engineering application value. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0021] Figure 1 A schematic diagram of the imaging spectrometer described in the embodiments of the present invention;

[0022] Figure 2 A partial flowchart illustrating the spectral data demodulation method described in an embodiment of the present invention.

[0023] Explanation of reference numerals in the attached diagram: 1. Front mirror group; 2. FP module; 3. Imaging mirror; 4. Detector. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0026] In the description of this invention, it should be understood that the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0027] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0028] The spectral data demodulation method provided by this invention includes: Step 1: Providing an imaging spectrometer, acquiring multiple images of the same target point using the imaging spectrometer, and outputting the electron number expression of the modulation curve corresponding to each image; Step 2: Obtaining the optimal solution x0 of the least squares problem of the electron number expression using singular value decomposition; Step 3: Constructing an unconstrained optimization function based on the electron number expression; Step 4: Using the optimal solution x0 as the initial value for the iterative input of the unconstrained optimization function, using the LM (Levenberg-Marquardt method) algorithm as the optimization iterative algorithm to obtain the minimum solution x of the unconstrained optimization function, where x is the demodulated spectral data.

[0029] It should be noted that the spectral data demodulation method provided by this invention is a data demodulation method for imaging spectrometers based on multi-level aliasing FP interferometers. It has stronger anti-noise interference capability, which is beneficial to improving the spectral detection accuracy of imaging spectrometers and has broad engineering application value.

[0030] Further reference Figure 1 The imaging spectrometer includes a front mirror group 1, an FP module 2, an imaging mirror 3, and a detector 4 arranged in sequence. The front mirror group 1 emits parallel light, which is incident on the FP module 2, which is an FP interferometer. The FP module 2 consists of two wedge-shaped prisms and is used to achieve multi-beam interference. The imaging mirror 3 is used to modulate the interference light so that the interference light is imaged on the detector 4, which is used to receive the interference light.

[0031] The spectral data demodulation method provided by this invention includes: acquiring n images of the same target point using an imaging spectrometer; specifically, a pushbroom method can be used to obtain the electron count expression for the same target point at different detector pixels; and the detector outputs the electron count expressions for n modulation curves corresponding to the n images, as follows:

[0032]

[0033] Where i is 1, 2, 3...n, j is 1, 2, 3...n, x(λ)j λ represents the exit pupil radiance of the imaging spectrometer. j Let λ be the wavelength of the different interference rays after the beam is split, h be Planck's constant, C be the speed of light, and I be the wavelength of the interference rays. i For the detector's signal output, T in For the integration time, A d F is the pixel area of ​​the detector. # Let τ0(λ) be the F-number of the imaging spectrometer. j T represents the transmittance of the imaging spectrometer. FP (λ j ,θ i η(λ) is the spectral transmittance function of the FP module. j ) represents the quantum efficiency of the detector, Δλ j For spectral resolution.

[0034] Furthermore, T FP (θ i ,λ j T is related to wavelength and incident angle. FP (θ i ,λ j The expression for ) is as follows:

[0035]

[0036] Where θ is the incident angle of the beam entering the FP module, R is the specular reflectivity of the FP module, d is the mirror spacing of the FP module, λ is the wavelength, and n is the refractive index of the medium.

[0037] Furthermore, step two also includes: simplifying the electron number expression to Formula 1. Specifically, the above electron number expression is a simplified form of the n-electron number expression, which can be as follows:

[0038]

[0039] For n electrons, the expression can be further simplified to:

[0040]

[0041] The above formula can be further simplified to Formula 1, as follows: I = Kx; where I is I i The matrix; x is x(λ) j A matrix of K; K is K i The matrix; K i The expression is as follows:

[0042] Where i is 1, 2, 3...n; the optimal solution x0 of the least squares problem in Formula 1 is obtained by using singular value decomposition.

[0043] Furthermore, step three includes: transforming Equation 1 into Equation 2, as follows: F(λ)=I-Kx; constructing an unconstrained optimization function based on Equation 2, as follows:

[0044] Among them, F(λ)={F1(λ), ​​F2(λ),…, F n (λ)},

[0045] Where i is 1, 2, 3...n.

[0046] Further reference Figure 2 The LM algorithm is used to obtain the minimum solution x of the unconstrained optimization function, specifically including:

[0047] Select initial input parameters β and σ for iteration, where β and σ ∈ (0,1), select x0 as the initial data point, select the allowable error ξ, where the allowable error ξ satisfies 0≤ξ≤1, and determine the small iteration number m and the large iteration number k;

[0048] Obtain the derivative g(x) of the unconstrained optimization function, where g(x) = ▽f(x);

[0049] Determine if g(x) satisfies IIg(x)II≤ξ. If it does, stop the calculation and output x, which is taken as the approximate minimum point. If it does not satisfy IIg(x)II≤ξ, then solve the system of equations.

[0050] The solution d is obtained. k Where I0 is the identity matrix, F k For x k Substituting into the F(λ) matrix obtained from Formula 2, x k The initial value is x0, x k J is the matrix of the exit pupil radiance of the imaging spectrometer when the number of iterations is k. k J is the Jacobian matrix of Formula 2. k T For J k The transpose of u k The L2 norm of Formula 2;

[0051] Determine whether f(x) is satisfied. k +β m d k )≤f(x k )+σβ m g(x k ) T d k If so, then m = m kIf not, then m = 0; based on m, execute α. k :=β m And execute x k+1 :=x k +α k d k Determine if m satisfies m < m max If yes, then m = m + 1; otherwise, update u. k u k =||f(x) k )|| 2 Determine if k satisfies k < k max If yes, then k = k + 1; otherwise, output x.

[0052] Where, f(x) k +β m d k )≤f(x k )+σβ m g(x k ) T d k These are the judgment conditions set based on the Armijo criterion in the optimization iterative algorithm.

[0053] The present invention proposes a data demodulation method for imaging spectrometers. By constructing an optimal function to demodulate the data, the accuracy of the data demodulation results can be greatly increased, and the anti-noise interference capability of the imaging spectrometer system can be improved.

[0054] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0055] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for demodulating spectral data, characterized in that, include: Step 1: Provide an imaging spectrometer, use the imaging spectrometer to acquire multiple images of the same target point, and output the electron number expression of the modulation curve corresponding to each image; Step 2: Obtain the optimal solution x0 of the least squares problem of the electron number expression using singular value decomposition; Step 3: Based on the electron number expression, construct an unconstrained optimization function; Step 4: The optimal solution x0 is used as the initial value of the iterative input of the unconstrained optimization function. The minimum solution x of the unconstrained optimization function is obtained by using the LM algorithm, where x is the demodulated spectral data.

2. The spectral data demodulation method according to claim 1, characterized in that, The imaging spectrometer includes a front mirror group, an FP module, an imaging mirror, and a detector arranged in sequence. The imaging spectrometer acquires n images of the same target point, and the detector outputs an expression for the number of electrons in n modulation curves corresponding to the n images. The expression for the number of electrons is as follows: Where i is 1, 2, 3...n, j is 1, 2, 3...n, x(λ) j) λ is the exit pupil radiance of the imaging spectrometer. j Let λ be the wavelength of the different interference rays after the beam is split, h be Planck's constant, C be the speed of light, and I be the wavelength of the interference rays. i T is the signal output of the detector. in For the integration time, A d F is the pixel area of ​​the detector. # Let τ0(λ) be the F-number of the imaging spectrometer. j T represents the transmittance of the imaging spectrometer. FP (λ j ,θ i ) is the spectral transmittance function of the FP module, η(λ) j Let Δλ be the quantum efficiency of the detector. j For spectral resolution.

3. The spectral data demodulation method according to claim 2, characterized in that, The T FP (θ i ,λ j The expression for ) is as follows: Where θ is the angle at which the light beam enters the FP module, R is the specular reflectivity of the FP module, d is the mirror spacing of the FP module, λ is the wavelength, and n is the refractive index of the medium.

4. The spectral data demodulation method according to claim 2 or 3, characterized in that, Step two further includes: simplifying the electron number expression to Formula 1, which is as follows: I = Kx; where I is I i The matrix x is x(λ) j A matrix of K, where K is K i The matrix, i is 1, 2, 3...n; The optimal solution x0 of the least squares problem in Formula 1 is obtained by using singular value decomposition.

5. The spectral data demodulation method according to claim 4, characterized in that, Step three includes: transforming Formula 1 into Formula 2, as follows: F(λ)=I-Kx; Based on Equation 2, an unconstrained optimization function is constructed as follows:

6. The spectral data demodulation method according to claim 5, characterized in that, The LM algorithm is used to obtain the minimum solution x of the unconstrained optimization function, which includes: Select initial input parameters β and σ for iteration, where β and σ ∈ (0,1), select x0 as the initial data point, select the allowable error ξ, where the allowable error ξ satisfies 0≤ξ≤1, and determine the small iteration number m and the large iteration number k; Obtain the derivative g(x) of the unconstrained optimization function, where g(x) = ▽f(x); Determine whether g(x) satisfies Ⅱg(x)Ⅱ≤ξ; If Ⅱg(x)Ⅱ≤ξ is satisfied, then stop the calculation and output x; If Ⅱg(x)Ⅱ≤ξ is not satisfied, then solve the system of equations: (J k T J k +u k I0)d=-J k T F k The solution d is obtained. k Where I0 is the identity matrix, F k For x k Substituting into the F(λ) matrix obtained from Formula 2, x k The initial value is x0, J k J is the Jacobian matrix of Formula 2. k T For J k The transpose of u k The L2 norm of Formula 2; Determine whether f(x) is satisfied. k +β m d k )≤f(x k )+σβ m g(x k ) T d k ; If so, then m = m k If not, then m = 0; Based on m, execute α k :=β m And execute x k+1 :=x k +α k d k ; Determine if m satisfies m < m max If yes, then m = m + 1; otherwise, update u. k u k =||f(x) k )|| 2 ; Determine if k satisfies k < k max If yes, then k = k + 1; otherwise, output x.

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