A Broadband Spectral Coding Method and Spectral Measurement System Based on the Main Diagonal Dominant Matrix

Abstract

This invention relates to the field of computational spectral measurement technology, and in particular to a broadband spectral coding method and spectral system based on the property of a main diagonally dominant matrix. This invention takes into account the engineering implementation difficulty of spectral filtering devices and the accuracy of reconstructed spectra. Based on matrix condition number theory, it proposes to design spectral transmittance coding according to the strict main diagonally dominant matrix property, which greatly reduces the physical implementation difficulty of spectral coding devices, enhances feasibility, and reduces costs.

Description

Technical Field

[0001] This invention relates to the field of computational spectral measurement technology, and in particular to a broadband spectral coding method and spectral system based on the property of a main diagonally dominant matrix. Background Technology

[0002] Computational spectral measurement based on broadband filtering modulation is a novel spectral measurement technique. Its main characteristic is the use of broadband filtering devices to encode and modulate the incident spectrum along the spectral dimension, and then the true incident spectrum is derived from the inverse transform of the spectral encoding. This technique features high light throughput, compact structure, and ease of miniaturization, making it a hot research topic in the field of spectral measurement and miniaturization of spectral imaging instruments. It also has broad potential applications in consumer electronics and aerospace spectral imaging remote sensing technologies.

[0003] Existing approaches to improving the accuracy of spectral reconstruction can be mainly divided into two categories:

[0004] The first type of method uses a large number of broadband filtering devices with arbitrary spectral transmittance for spectral encoding in order to accurately recover a small number of spectral channels with a high probability from a large amount of measurement data. However, while using a large number of filtering devices with arbitrary spectral transmittance for measurement has certain cost advantages, it will cause a lot of redundancy in other hardware and acquired data, resulting in low spectral observation efficiency. In particular, for applications of spectral imaging, a large amount of spectral encoding and observation will sacrifice more spatial or temporal resolution.

[0005] The second type of method involves specific design for the spectral transmittance of broadband filter devices to improve the performance of the spectral observation matrix, thereby enabling the accurate recovery of an equal or even greater number of spectral channels with fewer broadband spectral filtering measurements. However, given the current manufacturing capabilities of various spectral filter devices (including optical coatings, photonic crystals, surface plasmons, and quantum dot filter devices), accurately achieving a complex spectral transmittance curve of a specific form according to design requirements is extremely difficult and costly. Summary of the Invention

[0006] To address the high implementation difficulty of existing spectral coding schemes, this invention provides a broadband spectral coding scheme based on the property of the main diagonal dominant matrix. This method considers both the engineering implementation difficulty of spectral filtering devices and the accuracy of reconstructed spectra. Based on matrix condition number theory, it proposes designing spectral transmittance coding according to the strictly main diagonal dominant matrix property, significantly reducing the physical implementation difficulty of spectral coding devices, enhancing feasibility, and lowering costs. Furthermore, a broadband spectral coding and measurement system based on the main diagonal dominant matrix property is also provided.

[0007] The broadband spectral coding method proposed in this invention, based on the property of the main diagonal dominant matrix, includes the following steps:

[0008] Step S1: Determine the target measurement spectral range λ0~λ1 of the spectral measurement system, and the number of spectral channels n;

[0009] Step S2: Broadband spectral encoding of the incident spectrum is performed using a band-stop filter array. The performance parameters of the band-stop filter are designed according to the following method: the number of band-stop filters is n, the center wavelength of the band-stop region is uniformly distributed within the measurement spectral range λ0~λ1, the full width at half maximum (FWHM) of the band-stop region is (λ1-λ0) / n, and the actual performance index of the band-stop filter array may deviate from the design value to a certain extent.

[0010] Step S3: Calibrate the spectral radiative response value R(λ) of the actual band-stop filter device, and discretize it using the mean method to obtain R0. i This makes it match the number of spectral channels n;

[0011] Step S4: Based on the discrete spectral response R of the band-stop filter device i and photodetector signal S i The spectral measurement equation is obtained, and elementary transformations are performed on it to transform the spectral measurement matrix into a main diagonally dominant matrix form. Then, the least squares method based on regularization is used to solve for the discrete spectrum E to be measured. i .

[0012] The present invention also proposes a spectral measurement system, comprising:

[0013] Optical systems for harvesting light energy;

[0014] Spectral filtering and encoding devices are used to modulate and encode the spectrum of the target under test;

[0015] An optical signal acquisition system is used to receive the encoded spectrum of the target under test and to complete the photoelectric signal conversion;

[0016] The back-end signal processing system is used to receive the detector signal output by the signal acquisition system and perform spectral reconstruction calculation according to the aforementioned spectral reconstruction calculation method based on adaptive optimization sparse dictionary to obtain the reconstructed spectrum.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] Compared with existing technologies, this invention also uses a group of bandstop filters with the center wavelength of the bandstop band evenly distributed within the measurement target spectral range as a spectral encoding device, which greatly reduces the manufacturing difficulty of spectral filtering devices and expands the application range of this scheme; moreover, while ensuring the accuracy of the reconstructed spectrum, it greatly reduces the physical implementation difficulty of the spectral encoding device, enhances feasibility and reduces costs. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the steps of broadband spectral coding based on the main diagonal dominant matrix property of the present invention.

[0020] Figure 2 This is a schematic diagram illustrating the principle of computational spectral imaging technology based on broadband filter modulation.

[0021] Figure 3 The graph shows the spectral transmittance of a bandstop filter, where... Figure 3 (a) is a typical spectral transmittance curve of a band-blocking filter; Figure 3 (b) is a graph showing the spectral transmittance of the band filter group;

[0022] Figure 4 For the input reference spectrum, where, Figure 4 (a) is the high-resolution original reference spectrum; Figure 4 (b) is a 16-band discrete reference spectrum (with discrete mean values ​​within each band);

[0023] Figure 5 This is a schematic diagram of the simulation process;

[0024] Figure 6 This diagram illustrates the main error types of spectral transmittance, where... Figure 6 (a) is a random error plot for the entire band; Figure 6 (b) is the optical density error diagram of the cutoff band; Figure 6 (c) is the full width at half maximum (FWHM) error plot of the band-stop band; Figure 6 (d) is the center wavelength error diagram of the band-stop band;

[0025] Figure 7 A comparison chart of spectral performance reconstructed from the diagonally dominant matrix with errors is provided, in which... Figure 7 (a) Full-band random errors with standard deviations of 0.01 and 0.001, respectively; Figure 7 (b) Optical density errors at cutoff depths of OD1 and OD2; Figure 7 (c) Random error of full width at half maximum (FWHM), with standard deviation σ FWHM They are 0, 2, 4, and 6 nm, respectively; Figure 7 (d) Random error of the center wavelength, with its standard deviation σ cThey are 1, 3, 5, and 7 nm respectively; Figure 7 (e) The random error σ of the center wavelength obtained by using the adaptive regularization algorithm of generalized cross-validation c Reconstructed spectrum at 5 nm;

[0026] Figure 8 This is a comparison chart showing the accuracy of reconstructed spectra after encoding arbitrary spectral transmittance and encoding with a symmetric tridiagonal spectral observation matrix. Figure 8 (a) Transmittance curves for 16 arbitrary spectra; Figure 8 (b) is a comparison of the accuracy of the reconstructed spectra encoded by the two spectral transmittance methods.

[0027] Figure 9 This is a comparison chart showing the accuracy of reconstructed spectra using a large-scale main diagonal-dominant spectral coding matrix at different band numbers. Figure 9 (a) indicates a band count of 160; Figure 9 (b) has 640 bands; Figure 9 (c) indicates a band number of 1280. Detailed Implementation

[0028] 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 embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0029] Figure 2 The basic principle of broadband filter modulation spectral measurement technology is illustrated below: The total energy received by the detector can be considered as a linear superposition of the light energies of all spectral bands. If the incident light is subjected to multiple broadband filter modulations in the spectral dimension and then combined for measurement, the spectral distribution of the incident light can be obtained by inverse transformation of the spectral modulation code. By performing multiple modulation codes and combined measurements of the incident light in the spectral dimension using multiple broadband filtering devices, and then calculating the spectral information corresponding to each pixel through spectral reconstruction, the spectral information can be obtained. Figure 2 Chinese R t Let λ be the spectral modulation response of the t-th group, and λ be the wavelength. t Let E be the detector measurement signal corresponding to the t-th group of spectral modulation responses. u Let S be the reconstructed spectral intensity corresponding to the u-th band, where u is the total number of spectral bands, and let S be the output signal of the detector, R(λ) i Let ) be the discrete sampling result of R(λ), where λ i Let λ be the nominal center wavelength of the i-th spectral band, λ0 be the lower bound of the system's spectral response, λ1 be the upper bound of the system's spectral response, and E(λ) be the distribution function of the incident spectral intensity with wavelength. i If S is the discrete sampling result of E(λ), then S can be expressed as:

[0030]

[0031] If the spectral response R(λ) is modulated and measured t times, then we can obtain

[0032] S k =R k (λ i )E(λ i (2)

[0033] In the formula: S k Let R represent a column matrix of size t×1, where each element represents the k-th output signal of the detector; k (λ i E(λ) represents a u×t matrix, where the rows represent the modulation response values ​​of a certain group of spectra, and the columns represent the modulation response values ​​of the k-th group of spectra; i ) represents a column matrix of size u×1, where each element represents the incident spectral intensity corresponding to the wavelength of the spectral modulation response.

[0034] The most direct way to change the spectral response of a system is to add filters with different spectral transmittances, let τ k (λ i Let be the discrete spectral transmittance of the k-th filter device. Then, equation (2) can be expressed as:

[0035] S k =τ k (λ i )R(λ i )E(λ i (3)

[0036] Obviously, based on the measured spectral modulation matrix τ k (λ i )R(λ i ) and the actual measurement signal matrix S of the detected target k This means that the discrete incident spectrum can be calculated by inversion, because each set of broadband filter modulations can be understood as a spectral observation; therefore, the spectral modulation matrix τ k (λ i )R(λ i It can also be called a spectral observation matrix.

[0037] In the actual measurement process, τ k (λ i )R(λ i ) and S k All of these are obtained through measurement processes, which inevitably introduce measurement errors. As can be seen from the analysis of equation (3), due to its ill-conditioned nature, it will affect τ during the equation solution process. k (λi )R(λ i ) and S k Measurement errors amplify the accuracy of the reconstructed spectrum, thus reducing its precision. Poor accuracy in spectral reconstruction calculations due to the ill-posedness of the observation system is one of the main problems with this technique, and R(λ) i ) is a constant that remains unchanged, τ k (λ i )R(λ i The main characteristics will be determined by τ k (λ i The characteristics of ) determine that, therefore, for τ k (λ i Special design can greatly improve the system's stability and increase the accuracy of spectral reconstruction.

[0038] In existing research, the coding design of spectral observation systems is mainly based on compressed sensing and deep learning theories. However, for practical engineering applications, these two methods currently face some significant challenges:

[0039] For compressed sensing-based coding designs, universal compressed sensing observation matrices, such as Gaussian random matrices, are difficult to manufacture accurately under current technological conditions. While some spectral observation matrices designed based on the Finite Isometry Property (RIP) (or selecting suitable combinations from a large number of arbitrary filtering devices) have been implemented and verified at the hardware level, they may suffer from inconsistent spectral observation results for different targets. Furthermore, the transmittance of the designed filtering devices remains difficult to manufacture and is very costly. Additionally, compressed sensing spectral reconstruction algorithms have high computational complexity. In contrast, spectral coding methods based on deep learning theory offer relatively better spectral reconstruction results with less computation. However, these methods are data-driven, and their completeness in arbitrary measurement scenarios is difficult to guarantee. Moreover, their design and training processes are very complex, and the problems of accurately achieving the transmittance of the designed broadband spectral filtering devices and high cost persist.

[0040] This invention addresses the problem of the difficulty in accurately physical implementing existing spectral modulation coding matrices. Taking into account both the engineering implementation difficulty of spectral filtering devices and the accuracy of reconstructed spectra, and based on matrix condition number theory, it proposes a scheme for designing spectral transmittance coding based on the strictly diagonally dominant matrix property.

[0041] Please see Figure 1 The broadband spectral coding method based on the property of the main diagonal dominant matrix of the present invention includes the following steps:

[0042] Step S1: Determine the target measurement spectral range λ0~λ1 of the spectral measurement system, and the number of spectral channels n;

[0043] Step S2: Broadband spectral encoding of the incident spectrum is performed using a band-stop filter array. The performance parameters of the band-stop filter are designed according to the following method: the number of band-stop filters is n, the center wavelength of the band-stop region is uniformly distributed within the measurement spectral range λ0~λ1, the full width at half maximum (FWHM) of the band-stop region is (λ1-λ0) / n, and the actual performance index of the band-stop filter array may deviate from the design value to a certain extent.

[0044] Step S3: Calibrate the spectral radiative response value R(λ) of the actual band-stop filter device, and discretize it using the mean method to obtain R0. i This makes it match the number of spectral channels n;

[0045] Step S4: Based on the discrete spectral response R of the band-stop filter device i and photodetector signal S i The spectral measurement equation is obtained, and elementary transformations are performed on it to transform the spectral measurement matrix into a main diagonally dominant matrix form. Then, the least squares method based on regularization is used to solve for the discrete spectrum E to be measured. i .

[0046] Figure 3 (a) is a typical spectral transmittance curve of a band-stop filter. Figure 3 (b) shows the spectral transmittance curves of the bandstop filter group. The center wavelengths of the bandstop bands of each filter are approximately uniformly distributed within the target spectral range. In this case, the general form of the spectral transmittance encoding matrix can be expressed as:

[0047]

[0048] In the formula, m and n ij (i≠j) represents the sampled values ​​of the band-stop and other bands in the spectral transmittance curve of the band-stop filter, with constraints:

[0049] 0≤m<n 12 <n 13 <...≤1, 0≤m≤n 21 <n 31 <...≤1, (5)

[0050] This broadband spectral coding scheme can ensure a low degree of ill-conditioning in the broadband spectral coding matrix and improve the accuracy of the reconstructed spectrum. At the same time, the manufacturing process of band-stop spectral filter devices is relatively simple and mature, with stronger error tolerance and lower cost. Combined with L2 norm optimization algorithms, spectral reconstruction calculations can be quickly realized, making it very suitable for spectral measurement and spectral imaging systems based on this principle.

[0051] Combining the measurement results without broadband spectral filtering devices (i.e., the spectral transmittance of all bands is 1), the spectral observation matrix of equation (4) can be subjected to a simple elementary transformation:

[0052]

[0053] In the formula: (n ij ) is the general expression for the elements of this matrix; a = 1 - m represents the depth of the band-stop region in the spectral transmittance curve of the band-stop filter; b ij =1-n ij , representing the sampled value of the spectral transmittance curve excluding the band-stop region; generally, b ij The value of depends mainly on the position and slope of the "rising edge" and "falling edge" of the band-stop band, while the value at other wavelength positions is basically close to 0.

[0054] If matrix A is a strictly diagonally dominated matrix, then the following constraints apply:

[0055]

[0056] The matrix A satisfying constraint (6) is a strictly diagonally dominated matrix, and its ill-conditioned nature can be estimated using the matrix condition number. According to the matrix condition number theory, the condition number cond(A) of matrix A satisfies:

[0057] cond(A) = ||A|| ∞ ·||A -1 || ∞ (8)

[0058] In the formula ||A|| ∞ Let ||A⁻¹|| denote the infinite norm of matrix A. ∞ Let represent the infinite norm of the inverse matrix A.

[0059] For matrix A, its infinite norm ||A|| ∞ satisfy:

[0060]

[0061] Once the spectral measurement system is determined, matrix A is also determined, and its infinite norm ||A|| ∞ The value of is actually also determined; since matrix A has non-zero values ​​only near the main diagonal and zero in other positions, its infinite norm ||A|| is definite. ∞ ||A|| ∞ It is independent of the order of the matrix and can be considered a constant.

[0062] For the inverse of matrix A, the inverse of a strictly diagonally dominant matrix A has an infinity norm of ||A⁻¹||. ∞ satisfy:

[0063]

[0064] According to equation (9), when matrix A is determined, its elements a and b ij Therefore, the infinity norm ||A⁻¹|| of the inverse matrix of matrix A can be determined. ∞ ||A-1|| ∞ The upper bound of the condition number cond(A) of matrix A; combining equations (7)-(9), it can be seen that the condition number cond(A) of matrix A satisfies:

[0065]

[0066] As can be seen from equation (10), when the spectral observation matrix A satisfies the diagonal dominance constraint, the upper bound of its condition number cond(A) is only related to the values ​​of certain specific elements of matrix A (the diagonal and its vicinity), and is not related to its order. This proves in principle that the ill-conditioning of the spectral measurement system using the diagonal dominance matrix for spectral coding is controllable, and the spectral coding observation using this scheme will have a better measurement effect.

[0067] Combining a and b ij From the physical meaning, simply put, when the cutoff depth of the bandstop region of the bandstop filter is relatively deep, and both the rising and falling edges are relatively steep, the specific quantitative relationship should satisfy the constraint of equation (6); this constraint is relatively weak, and the corresponding spectral transmittance is easily achieved in engineering. Taking a common interference bandstop filter as an example, the cutoff depth of its cutoff region can easily reach 10. -2 The following (a>0.99) requires that the sum of the discrete sample values ​​of the bands corresponding to the "rising edge" and "falling edge" regions only need to be less than a=0.99.

[0068] Compared with the spectral encoding scheme of "symmetric tridiagonal Toeplitz matrix dominated by the main diagonal", this invention also uses a group of bandstop filters with the center wavelength of the bandstop band evenly distributed within the measurement target spectral range as the spectral encoding device. The slopes of the "rising edge" and "falling edge" of the transmittance curve of the spectral filter device required by this invention can be asymmetrically equal, and the corresponding spectral encoding matrix does not have to be a strict "tridiagonal matrix" form, which greatly reduces the manufacturing difficulty of the spectral filter device and expands the application range of this scheme.

[0069] This invention also proposes a spectral measurement system based on main diagonal dominant matrix encoding, comprising:

[0070] Optical systems for harvesting light energy;

[0071] Spectral filtering and encoding devices are used to modulate and encode the spectrum of the target under test;

[0072] An optical signal acquisition system is used to receive the encoded spectrum of the target under test and to complete the photoelectric signal conversion;

[0073] The back-end signal processing system is used to receive the detector signal output by the signal acquisition system and perform spectral reconstruction calculation according to the aforementioned spectral reconstruction calculation method based on adaptive optimization sparse dictionary to obtain the reconstructed spectrum.

[0074] To further explain the specific application methods and effects of this invention, based on the above coding and spectral measurement system scheme, a broadband filtering coding calculation and reconstruction spectral measurement system with a measurement range of 420-740nm and a total of 16 channels was designed and numerically simulated for verification. The specific simulation settings, including simulation parameters, simulation process, and spectral reconstruction calculations, are as follows:

[0075] 1. According to equation (3), the spectral observation device uses a notch filter array based on equation (6), and the standard reference spectrum is as follows: Figure 4 As shown. The spectral band of the simulated target is 420-740nm, the number of bands of the reconstructed target is 16, and the corresponding reconstructed spectral band width FWHM is (740-420) / 16=20nm.

[0076] 2. Basic simulation process as follows Figure 5 As shown, the specific steps are as follows.

[0077] 1) Employing high-resolution (1nm) input parameters to simulate accurate E(λ) and design τ k (λ), and then the simulated S is calculated according to equation (1). k .

[0078] 2) For S k Gaussian random noise (relative value) with a standard deviation of 0.01 is added to simulate the measurement error of the photodetector, and τ is given. k (λ i Different noises are applied to simulate different forms of manufacturing errors, thereby obtaining the simulated actual spectral transmittance τ'. k (λ).

[0079] 3) For E(λ) and τ' k Discrete sampling of (λ) yields the standard E(λ) i ) and the simulated τ' k (λ i ).

[0080] 4) Use S' k and τ' k (λ i By performing spectral reconstruction calculations, the reconstructed discrete spectrum E'(λ) can be obtained. i ), and with the standard E(λ)i The data is compared to verify the spectral observation capability of the encoding. The reconstruction calculation uses the common iterative nonnegative least squares (NNLS) method, which is theoretically mature and will not be described in detail here.

[0081] 3. Various noises are added to the above input parameters to simulate the manufacturing error of the spectral transmittance of the band-stop filter array and the measurement noise of the detector in an actual spectral measurement system. The types of noise and the corresponding errors of the spectral observation matrix are as follows:

[0082] Different noises are applied to the spectral observation matrix to simulate various spectral transmittance manufacturing and calibration errors of spectral modulation devices, such as... Figure 6 As shown. Figure 6 As shown in (a), Gaussian random noise (absolute value) with a standard deviation σ of 0.01 is added to all elements of the observation matrix A. This method can be used to simulate different levels of random transmittance error; Figure 6 As shown in (b), by setting element a in the spectral observation matrix A to 0.999, 0.99, and 0.90, this method can be used to simulate the optical density levels (OD3, OD2, and OD1) in the cutoff regions of different band-stop filters. Figure 6 As shown in (c), setting the full width at half maximum (FWHM) of the band-stop region to different widths can be used to simulate the FWHM error in the band-stop region. From the spectral transmittance curve and the physical meaning of the parameters in A, it can be seen that increasing the width of the band-stop region will affect parameter b in the spectral observation matrix A. ij Increasing the value of and further increasing the bandstop width will severely affect the diagonal dominance of the spectral observation matrix. Therefore, simulation studies should be conducted to address the FWHM error. Figure 6 As shown in (d), the position error of the center wavelength in the band-stop region may affect the values ​​of both parameters a and b, primarily impacting the symmetry of the spectral observation matrix. This bias can be simulated by adding different levels of standard deviation to the center wavelength in the band-stop region.

[0083] 3. The simulation results of the spectral measurement capability of the spectral coding scheme are as follows:

[0084] By adding Gaussian random noise of σ = 0.01 to the accurate signal to simulate measurement error, and adding the various errors described in Section 6.2 to the spectral transmittance encoding, the comparison between the reconstructed spectrum and the standard reference spectrum is as follows: Figure 7 As shown, the types and magnitudes of added errors, the l2 norm condition number C2 of the error-containing spectral encoding matrix, and the root mean square error (RMSE) obtained by comparing the corresponding reconstructed spectrum with the standard reference spectrum are marked. Figure 7 (a) Comparison of the reconstructed spectrum and the reference spectrum after adding full-band Gaussian random noise (noise standard deviation 0.01 and 0.001); Figure 7(b) Comparison of reconstructed spectra with reference spectra at different cutoff depth levels (OD1 and OD2) in the cutoff band; Figure 7 (c) Comparison of reconstructed spectra with reference spectra under different full width at half maximum (FWHM); Figure 7 (d) Comparison of the reconstructed spectrum and the reference spectrum under different center wavelength errors in the band-stop region. From Figure 7 (a) and Figure 7 (b) It can be seen that a certain level of full-band random noise and cutoff depth within the band-stop region have a relatively small impact on the accuracy of spectral reconstruction by the spectral observation system. Figure 7 (c) It can be seen that when the FWHM deviation is small (σ) FWHM When the FWHM bias is 2 nm, the accuracy of the reconstructed spectrum is relatively high; as the FWHM bias gradually increases (σ... FWHM (4nm and 6nm respectively), as the condition number of the spectral observation matrix increases, the accuracy of the reconstructed spectrum decreases. From Figure 7 (d) It can be seen that the accuracy of the reconstructed spectrum decreases with the increase of the center wavelength deviation in the band-stop region; especially when σ c At 7nm, the center wavelength position deviation in the band-stop region is too large, resulting in a significant decrease in the accuracy of the reconstructed spectrum. In summary, to ensure the performance of the diagonally dominant spectral observation matrix, the band-stop width and center wavelength error of the filter device should be carefully constrained.

[0085] It is worth noting that the reconstruction algorithms described above all employ the simplest iterative nonnegative least squares method. However, by using algorithms with better tolerance, even when the condition number of the spectral observation matrix is ​​high, good accuracy in reconstructing the spectrum can still be achieved. Figure 7 (e) For the adaptive regularization algorithm using generalized cross-validation (GCV-based Tikhonov regularization algorithm)... Figure 7 (d) Random error of center wavelength σ c Reconstruction was performed at 5 nm, and the accuracy of the reconstructed spectrum was significantly improved. Simulations were performed using 16 arbitrary broadband spectral filters on the reference spectrum, and the results were compared with the reconstructed spectrum obtained from the main diagonally dominant spectral encoding matrix proposed in this invention. The results are as follows: Figure 8 As shown, the simulation process and Figure 5 same. Figure 8 (a) shows the transmittance curves of 16 arbitrary spectral filters. Figure 8 (b) Comparison of reconstructed spectral accuracy. From Figure 8 It can be seen that the accuracy of the reconstructed spectrum obtained by using the diagonally dominant spectral coding matrix is ​​significantly higher than that of arbitrary transmittance coding.

[0086] Specifically, the impact of the measurement matrix size on the performance of diagonally dominant spectral coding measurements is as follows:

[0087] The performance of the diagonally dominant spectral encoding matrix was simulated under different numbers of reconstructed spectral bands. The simulation process involved adding cutoff depth deviation (OD1), full-band random error (σ = 0.01), and FWHM deviation (σ) to the spectral transmittance curve of a bandstop filter array. FWHM =2nm), center wavelength deviation (σ) c =3nm) to simulate spectral transmittance error; Gaussian random noise of σ=0.01 is added to the simulated measurement signal to simulate detector measurement error. The accuracy of the reconstructed spectrum at different band numbers is as follows: Figure 9 As shown. By Figure 9 It can be seen that when the number of bands in the reconstructed spectrum increases to 1280, the RMSE value of the reconstructed spectrum increases to 0.03, indicating that the accuracy of the reconstructed spectrum is still good. Therefore, under the premise of ensuring the spectral transmittance of the filter device, the spectral observation capability of the main diagonal dominant spectral coding scheme does not decrease with the increase of the matrix order.

[0088] In summary, the simulation results show that the proposed diagonally dominant spectral observation matrix encoding scheme has a significant advantage in system tolerance, enabling the acquisition of reconstructed spectra with higher accuracy. Even when the spectral observation matrix is ​​large and contains a certain level of error, the accuracy of the reconstructed spectrum can still be guaranteed. Furthermore, the manufacturing error requirements for the bandstop filter array in this encoding scheme are relatively lenient, making it easy to implement in engineering.

[0089] It is worth noting that, according to the numerical simulation results of the spectral coding and measurement system, this invention can also be applied when the parameters of the spectral measurement system do not strictly satisfy the general form (6) and the inequality constraint (7). This situation should also be protected by this patent. To clarify the scope of protection of this invention, it should be determined whether the coding scheme used in the actual spectral measurement system belongs to this invention. For the actual spectral coding matrix, the constraint of inequality (7) can be relaxed to the following inequality:

[0090]

[0091] At this point, the coding scheme described in this invention still has good diagonal dominance characteristics. Combined with some advanced optimization algorithms, it can also ensure that the system has good spectral reconstruction measurement accuracy. Therefore, the constraint of equation (12) should be the effective boundary of the spectral coding scheme proposed in this invention. Spectral coding schemes within this boundary should be protected by this patent.

[0092] There are several ways to physically implement this invention:

[0093] 1. For the physical implementation scheme of spectral transmittance modulation coding device, various technical means such as interference optical coating, photonic crystal, surface plasmon polariton, quantum dot filter, etc. can be adopted;

[0094] 2. Spectral coding can also be achieved by directly changing the spectral response of the optical system (or detector, etc.);

[0095] 3. In terms of measurement method, it can be achieved through active illumination coded spectral measurement or passive spectral measurement mode.

[0096] This invention is also suitable for application in spectral imaging systems. Simply replace the optical system with an imaging lens and the detector with an area array detector to achieve spectral imaging. The principles of spectral coding and computational reconstruction are basically the same.

[0097] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A broadband spectral coding and spectral measurement reconstruction method based on the property of a main diagonally dominant matrix, characterized in that, Includes the following steps: Step S1: Determine the target measurement spectral range of the spectral measurement system. λ 0~ λ 1, and the number of spectral channels n ; Step S2: Broadband spectral encoding of the incident spectrum is performed using a band-stop filter array. The performance parameters of the band-stop filter are determined according to the following method: the number of band-stop filter elements is... n The center wavelength of the band-stop region is within the measurement spectral range. λ 0~ λ 1. Uniformly distributed within the band, the full width at half maximum (FWHM) of the band-resistive region is ( λ 1- λ 0) / n The actual performance of the band-stop filter array deviates to some extent from the design value; Step S3: Calibrate the spectral radiative response of the actual band-stop filter device. R ( λ ), and then discretized it using the mean method as ), R i To make it consistent with the number of spectral channels n match; Step S4: Based on the discrete spectral response of the band-stop filter device R i and photodetector signals S i The spectral measurement equation is obtained, and elementary transformations are performed on it to transform the spectral observation matrix into a diagonally dominant matrix form. Then, the least squares method based on regularization is used to solve for the discrete spectrum to be measured. E i ; in: The spectral transmittance matrix of the band-stop filter array is discretely represented as follows: ； m , n ij The sampled values ​​of the band-stop band and other bands in the spectral transmittance curve of the band-stop filter device are represented, and are subject to constraints: , i ≠ j ; In step S4, the spectral observation matrix of the band-stop filter device is subjected to elementary transformations into a matrix. A : a =1- m This indicates the depth of the band-stop region in the spectral transmittance curve of a band-stop filter device. b ij =1- n ij , representing the sampled value of the spectral transmittance curve excluding the band-stop region; Elementary transformations result in strictly diagonally dominant matrices satisfying the following constraints: ， 。 2. The broadband spectral coding and spectral measurement reconstruction method based on the main diagonal dominant matrix property according to claim 1, characterized in that, In step S1, all input parameters of the spectral measurement system are determined, including the target measurement spectral range. λ 0~ λ 1, and the number of spectral channels n .

3. The broadband spectral coding and spectral measurement reconstruction method based on the principal diagonal dominant matrix property according to claim 2, characterized in that, In step S2, the spectral encoding device of the spectral measurement system is an array of band-stop filter devices with the center wavelength evenly distributed within the target spectral range. The full width at half maximum (FWHM) of the band-stop region of each filter device is ( λ 1- λ 0) / n .

4. The broadband spectral coding and spectral measurement reconstruction method based on the main diagonal dominant matrix property according to claim 3, characterized in that, In step S4, various regularization methods, various augmented Lagrange multiplier methods, and non-negative least squares solution methods are used to perform spectral reconstruction calculations.

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