Spectral reconstruction method and spectrometer

Abstract

This invention relates to the field of spectrometer technology and discloses a spectral reconstruction method and a spectrometer. The method involves: acquiring the original broadband Newton's rings image of the broadband light source under test and the reference single-wavelength Newton's rings image of a reference single-wavelength light source, and deriving the single-wavelength Newton's rings pattern set; inputting the original broadband Newton's rings image into a neural network for processing to obtain the first spectral coefficients, which are then weighted and discretely superimposed to obtain the reconstructed broadband Newton's rings pattern; constructing a joint loss function and iteratively updating all optimizable parameters of the neural network to output the second spectral coefficients. This invention solves the technical problem of low contrast in traditional transmission-type Newton's rings patterns affecting reconstruction accuracy, overcomes the shortcomings of pure data-driven methods that rely on large-scale labeled datasets and whose reconstruction results do not conform to physical laws, and achieves high-precision spectral reconstruction over a wide spectral range with a high level of peak resolution.

Description

Technical Field

[0001] This invention relates to the field of spectrometer technology, and in particular to a spectral reconstruction method and a spectrometer. Background Technology

[0002] Spectrometers are widely used in scientific research and industrial testing. Traditional spectrometers achieve high-precision spectral resolution through complex optical path designs containing multiple optical elements such as gratings and mirrors. Their detection principle is based on direct spectral dispersion followed by detector acquisition. Although relying on a complex optical system, the spectral reconstruction process is relatively simple. However, this complex optical path design requires advanced debugging techniques, and the large optical system layout results in a large instrument size, making it difficult to meet the requirements for portability.

[0003] As spectrometers become increasingly miniaturized, the spectral reconstruction problem has shifted towards algorithmic solutions, placing higher demands and challenges on the performance of spectral reconstruction methods. The spectral reconstruction problem in miniature spectrometers is typically modeled as solving a system of linear equations, and the quality of the reconstruction method directly determines the detection accuracy. Traditional least squares methods, limited by their computational principles, struggle to achieve high-resolution spectral reconstruction, leading to the loss of spectral detail. While traditional end-to-end neural network-based spectral reconstruction methods have improved accuracy to some extent, they rely on massive amounts of labeled data, requiring significant time and manpower for dataset collection, labeling, and preprocessing. Furthermore, in some application scenarios, environmental and equipment limitations make it difficult to collect sufficient data for effective training. In addition, the output of these methods often does not conform to physical laws, exhibiting anomalies in spectral intensity, severely restricting their further application in portable devices. Summary of the Invention

[0004] The main objective of this invention is to provide a spectral reconstruction method and spectrometer. This invention solves the technical problem of low contrast of traditional transmission Newton's rings patterns affecting reconstruction accuracy, overcomes the defects of pure data-driven methods that rely on large-scale labeled datasets and whose reconstruction results do not conform to physical laws, and achieves high-precision spectral reconstruction over a wide spectral range with a high level of peak resolution.

[0005] To achieve the above objectives, the present invention provides a spectral reconstruction method, comprising the following steps: Acquire the original broadband Newton's rings image of the broadband light source under test and the reference single-wavelength Newton's rings image of the reference single-wavelength light source, and derive the set of single-wavelength Newton's rings patterns corresponding to the reference single-wavelength Newton's rings image. The original broadband Newton's rings image is input into a neural network for processing to obtain the first spectral coefficient. The first spectral coefficient is then weighted and discretely superimposed with the single-wavelength Newton's rings pattern set to obtain the reconstructed broadband Newton's rings pattern. A joint loss function is constructed based on the reconstructed broad-spectrum Newton's rings pattern, and all optimizable parameters of the neural network are iteratively updated. When the decrease of the joint loss function within a preset number of consecutive iterations is lower than a preset threshold, the iteration stops, and the second spectral coefficient is output.

[0006] Optionally, in a first implementation of the first aspect of the present invention, the step of acquiring the original broadband Newton's rings image of the broadband light source under test and the reference single-wavelength Newton's rings image of the reference single-wavelength light source, and deriving the set of single-wavelength Newton's rings patterns corresponding to the reference single-wavelength Newton's rings image, includes: The first input light of the broadband light source under test and the second input light of the reference single-wavelength light source are respectively injected into the transmission-type coated Newton's rings device for interference modulation to obtain a transmission interference pattern. The transmission interference pattern is recorded by a CCD detector without a lens and in close contact with the transmission-type coated Newton's rings device, resulting in the original broadband Newton's rings image and a reference single-wavelength Newton's rings image. Based on the Newton's rings imaging model, the set of single-wavelength Newton's rings patterns corresponding to each discrete wavelength in the target band of the reference single-wavelength Newton's rings image is derived.

[0007] Optionally, in a second implementation of the first aspect of the present invention, the step of injecting the first input light of the broadband light source under test and the second input light of the reference single-wavelength light source into the transmission-type coated Newton's rings device for interference modulation to obtain a transmission interference pattern includes: The first input light of the broadband light source to be tested and the second input light of the reference single-wavelength light source are respectively injected into the transmissive coated Newton's rings device. A thin air layer is formed between the convex surface of the convex lens of the transmissive coated Newton's rings device and the flat glass. Both the convex surface of the convex lens and the opposite surface of the flat glass are coated with silver film. The silver film on the convex surface of the convex lens and the silver film on the opposite surface of the flat glass are used to transmit and modulate the first input light and the second input light respectively, generating the first transmitted light and the second transmitted light; Based on the thin air layer, the first transmitted light and the second transmitted light are superimposed by interference to obtain a transmission interference pattern.

[0008] Optionally, in a third implementation of the first aspect of the present invention, the step of deriving the set of single-wavelength Newton's ring patterns corresponding to each discrete wavelength in the target band based on the Newton's rings imaging model includes: Based on the Newton's rings imaging model, the spatial scaling factor between the reference single-wavelength Newton's rings image and the Newton's rings pattern at each discrete wavelength point in the target band is derived. The reference single-wavelength Newton's rings image is isotropically scaled according to the spatial scaling factor to obtain a scaled Newton's rings image. Linear interpolation is then performed on the floating-point coordinates of the scaled Newton's rings image to obtain a set of single-wavelength Newton's rings patterns corresponding to each discrete wavelength in the target band.

[0009] Optionally, in a fourth implementation of the first aspect of the present invention, deriving the spatial scaling factor between the reference single-wavelength Newton's rings image and the Newton's rings pattern at each discrete wavelength point within the target band based on the Newton's rings imaging model includes: Based on the physical relationship that the light intensity of the interference pattern in the Newton's rings imaging model is cosine periodically distributed with respect to the ratio of the square of the pixel coordinate to the wavelength, the reference imaging equation of the reference single-wavelength Newton's rings image and the target imaging equation of the Newton's rings pattern at each discrete wavelength point in the target band are established respectively. The pixel coordinates in the target imaging equation are replaced by equivalent substitutions, and the target wavelength in the target imaging equation is merged into the coordinate terms of the reference imaging equation. The spatial scaling factor between the reference single-wavelength Newton's ring image and the Newton's ring pattern of each discrete wavelength point in the target band is derived. The spatial scaling factor is the square root of the ratio of the reference single wavelength to the target discrete wavelength.

[0010] Optionally, in a fifth implementation of the first aspect of the present invention, the step of inputting the original broadband Newton's rings image into a neural network for processing to obtain a first spectral coefficient, and then performing a weighted discrete superposition of the first spectral coefficient with the single-wavelength Newton's rings pattern set to obtain a reconstructed broadband Newton's rings pattern, includes: The original broadband Newton's rings image is input into the residual backbone network of the neural network for multi-scale feature extraction to obtain a multi-scale spectral feature map. The multi-scale spectral feature map is input into the spatial attention module of the neural network. A single-channel attention mask with the same spatial size as the multi-scale spectral feature map is generated through convolution operation. The multi-scale spectral feature map and the single-channel attention mask are multiplied pixel by pixel to obtain a spatially weighted feature map. The spatially weighted feature map is input into the fully connected module of the neural network for calculation to obtain the first spectral coefficient of each discrete wavelength point. The first spectral coefficient is then weighted and discretely superimposed with the single-wavelength Newton's rings pattern set to obtain the reconstructed broadband Newton's rings pattern.

[0011] Optionally, in a sixth implementation of the first aspect of the present invention, the step of inputting the original broadband Newton's rings image into the residual backbone network of the neural network for multi-scale feature extraction to obtain a multi-scale spectral feature map includes: The original broadband Newton's rings image is sequentially input into the first convolutional layer and the max pooling layer in the residual backbone network for downsampling to obtain the initial feature map; The initial feature map is input into the basic residual block in the residual backbone network for shallow feature extraction to obtain a shallow spectral feature map. The shallow spectral feature map is input into the bottleneck residual block in the residual backbone network for deep feature compression and expansion to obtain a multi-scale spectral feature map.

[0012] Optionally, in a seventh implementation of the first aspect of the present invention, the step of constructing a joint loss function based on the reconstructed broad-spectrum Newton's rings pattern and iteratively updating all optimizable parameters of the neural network, stopping the iteration when the decrease in the joint loss function within a consecutive preset number of iterations is lower than a preset threshold, and outputting the second spectral coefficients, includes: The pixel-level L2 norm squared difference between the original broadband Newton's rings image and the reconstructed broadband Newton's rings pattern is used as the physical consistency constraint term; the L2 norm is obtained by successively performing second-order differences on the first spectral coefficients of three adjacent discrete wavelength points as the spectral smoothing regularization term; and the L2 norm of all optimizable parameters in the neural network is used as the weight attenuation term. A joint loss function is constructed based on the physical consistency constraint, the spectral smoothing regularization term, and the weight decay term. The gradient vectors of all optimizable parameters in the neural network are calculated based on the joint loss function, and the all optimizable parameters are iteratively updated. When the decrease of the joint loss function within a preset number of consecutive iterations is lower than a preset threshold, the iteration stops and the second spectral coefficients are output.

[0013] Optionally, in an eighth implementation of the first aspect of the present invention, the step of calculating the gradient vector of all optimizable parameters in the neural network based on the joint loss function, iteratively updating all optimizable parameters, stopping the iteration when the decrease of the joint loss function within a consecutive preset number of iterations is lower than a preset threshold, and outputting the second spectral coefficients, includes: Based on the joint loss function, the gradient vectors of all optimizable parameters in the neural network with respect to the joint loss function are calculated through backpropagation; Based on the gradient vector, the gradient descent algorithm is used to update all the optimizable parameters along the negative gradient direction to obtain the updated optimizable parameters. The updated optimizable parameters are then used to drive the neural network to re-perform forward inference on the original broad-spectrum Newton's rings image to obtain the updated spectral coefficients and the updated broad-spectrum Newton's rings pattern. The loss value of the joint loss function corresponding to the current iteration is calculated based on the updated spectral coefficients and the updated broadband Newton's rings pattern. When the decrease in the loss value of the current iteration compared to the loss value of the previous iteration is less than a preset threshold within a consecutive preset number of iterations, the iteration stops, and the spectral coefficients output by the neural network at the time of stopping the iteration are used as the second spectral coefficients.

[0014] The present invention also provides a spectrometer for implementing the steps of any of the spectral reconstruction methods described herein.

[0015] In summary, this invention uses the close integration of a transmissive coated Newton's rings device and a lensless CCD detector as the basis for image acquisition. Both the convex surface of the convex lens and the opposing surface of the flat glass are coated with silver film, enhancing the fringe contrast of the transmissive interference pattern and solving the technical problem of low contrast in traditional transmissive Newton's rings patterns affecting reconstruction accuracy. In the generation of single-wavelength Newton's rings pattern sets, this invention, based on the physical relationship in the Newton's rings imaging model where the intensity of the interference pattern follows a cosine periodic distribution with respect to the ratio of the square of the pixel coordinates to the wavelength, rigorously derives the square root of the ratio of the reference single wavelength to the target discrete wavelength as a spatial scaling factor. Only a single reference single-wavelength Newton's rings image needs to be isotropically scaled and linearly interpolated to generate a complete set of single-wavelength Newton's rings patterns covering the target band. This completely replaces the cumbersome process of acquiring patterns wavelength by wavelength in traditional methods, significantly shortening calibration time. In the spectral reconstruction stage, this invention cascades a residual backbone network, a spatial attention module, and a fully connected module to form a neural network. Using the original broadband Newton's rings image as the sole input, without any external labeled samples, a loss function is constructed using three constraints: pixel-level physical consistency between the original broadband Newton's rings image and the reconstructed broadband Newton's rings pattern, second-order difference smoothing constraints on the spectral coefficients of adjacent discrete wavelength points, and L2 regularization constraints on the neural network parameters. The network parameters are iteratively optimized using a gradient descent algorithm combined with an early stopping mechanism, ensuring that the reconstructed spectrum converges under the constraints of the physical model. This guarantees the physical interpretability of the reconstruction results and overcomes the shortcomings of purely data-driven methods, such as dependence on large-scale labeled datasets and reconstruction results that do not conform to physical laws. High-precision spectral reconstruction is achieved over a wide spectral range, with a high level of peak resolution. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the steps of the spectral reconstruction method in one embodiment of the present invention; Figure 2 This is a system structure diagram of the miniature spectrometer in an embodiment of the present invention; Figure 3 This is a schematic diagram of the optical path within the transmissive coated Newton's rings air layer in an embodiment of the present invention; Figure 4 This is a diagram of a neural network structure based on physical model constraints in an embodiment of the present invention; Figure 5 This is a schematic diagram of the bottleneck residual block in an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of the basic residual block in an embodiment of the present invention; Figure 7 This is a comparison chart of broadband measurement results in an embodiment of the present invention.

[0017] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] 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.

[0019] Reference Figure 1 This embodiment provides a spectral reconstruction method, including the following steps: S1. Acquire the original broadband Newton's rings image of the broadband light source to be tested and the reference single-wavelength Newton's rings image of the reference single-wavelength light source, and derive the set of single-wavelength Newton's rings patterns corresponding to the reference single-wavelength Newton's rings image. S2, input the original broadband Newton's rings image into the neural network for processing to obtain the first spectral coefficient, and then perform weighted discrete superposition of the first spectral coefficient with the set of single-wavelength Newton's rings patterns to obtain the reconstructed broadband Newton's rings pattern; S3: Construct a joint loss function based on the reconstructed wide-spectrum Newton's rings pattern and iteratively update all optimizable parameters of the neural network. Stop iterating when the decrease of the joint loss function within a preset number of consecutive iterations is lower than a preset threshold, and output the second spectral coefficient.

[0020] Figure 2 This is a schematic diagram of the system structure of the miniature spectrometer of the present invention. The input light enters horizontally from the left as a parallel beam, passing sequentially through two core functional components. Label 1 represents the transmission-type coated Newton's rings device, which consists of a convex lens and a flat glass plate. The convex surface of the convex lens faces the flat glass plate, forming a radially continuously varying thin air layer between them. Both the convex surface of the convex lens and the opposing surface of the flat glass plate are coated with a high-purity silver film, used to modulate the spectral information of the input light into a transmission interference pattern through interference from the thin air layer. Label 2 represents the CCD detector, which has no lens installed at the front end and is directly attached to the transmission-type coated Newton's rings device 1. It is used to directly receive and record the transmission interference pattern modulated by the Newton's rings device, obtaining a broadband Newton's rings image and a reference single-wavelength Newton's rings image, respectively. The two components are integrated tightly, eliminating the need for collimation and focusing optical paths, thus achieving an ultra-thin and miniaturized spectrometer.

[0021] In one example, the original broadband Newton's rings image of the broadband light source under test and the reference single-wavelength Newton's rings image of the reference single-wavelength light source are acquired, and the set of single-wavelength Newton's rings patterns corresponding to the reference single-wavelength Newton's rings image is derived, including: The first input light of the broadband light source under test and the second input light of the reference single-wavelength light source are respectively injected into the transmission-type coated Newton's rings device for interference modulation to obtain a transmission interference pattern. The transmission interference pattern is recorded by a CCD detector without a lens and in close contact with the transmission coated Newton's rings device, and the original broadband Newton's rings image and the reference single-wavelength Newton's rings image are obtained respectively. Based on the Newton's rings imaging model, the set of single-wavelength Newton's rings patterns corresponding to each discrete wavelength in the target band of the reference single-wavelength Newton's rings image is derived.

[0022] In this embodiment, the first input light from the broadband light source under test and the second input light from the reference single-wavelength light source are respectively incident along the same incident path into the transmission-type coated Newton's rings device. Inside the transmission-type coated Newton's rings device, the convex surface of the convex lens faces the flat glass, forming a thin air layer between them. Both the convex surface of the convex lens and the opposing surface of the flat glass are coated with a high-purity silver film to improve the contrast of the transmission interference fringes. The radius of curvature of the convex lens is 6 m, the diameter of the convex lens is 1.5 cm, the diameter of the flat glass is 1.5 cm and the thickness is 2.5 mm, the silver film thickness is 4 nm, and the coating process conditions are a vacuum chamber pressure of 1.0 × 10⁻⁶. -4 The coating speed is approximately 0.2 nm / s, and the coating time is approximately 3 minutes. After the first and second input beams enter the air thin layer, they are transmitted and modulated at the interface between the two coating layers to form two beams of transmitted light participating in interference. Phase difference accumulation occurs within the air thin layer of equal thickness, thus outputting a transmission interference pattern. Because the system adopts a transmission structure, the input light does not need to pass through a complex folding optical path to complete the interference encoding. Therefore, it retains the wavelength-sensitive fringe modulation characteristics of Newton's rings while maintaining the overall ultra-thin integrated structure. In the physical modeling of the interference modulation, the optical path difference between the two transmitted beams within the air thin layer is written as: ; in, is the air refractive index, which is taken as 1 in this embodiment; This represents the thickness of the air layer at the corresponding location; Let be the angle of reflection of the incident light on the flat glass surface. The two transmitted beams interfere at the converging point, and their wave functions are written as: ; ; in, The wave function of the first transmitted light BB' is the wave function of the transmitted light emitted along the direction of point B at point E after the input light is successively transmitted and modulated by the high-purity silver film on the convex surface of the convex lens and the high-purity silver film on the opposite surface of the flat glass. Let represent the wave function of the second transmitted light DD', which is the wave function at point E of the transmitted light emitted along the direction of point D after the input light is successively transmitted and modulated by the high-purity silver film on the convex surface of the convex lens and the high-purity silver film on the opposite surface of the flat glass. The input optical amplitude normalization value is set to 1 in this embodiment; and These are the amplitude reflectances of the convex lens coating interface and the opposite surface coating interface of the flat glass, respectively, both of which are taken as 0.2 in the embodiments. and These represent the phases of the two transmitted beams. From this, we can derive the expression for the interference intensity: ; in, The wavelength is the center wavelength of the monochromatic light source. The above relationship indicates that different wavelengths of input light will form Newton's rings with different spatial periods in the same thin layer of air. Therefore, after broadband light and reference single-wavelength light are incident separately, the original broadband Newton's rings image and the reference single-wavelength Newton's rings image are generated respectively. In the recording stage, the CCD detector is not equipped with a lens and is directly placed in close contact with the transmission-type coated Newton's rings device, so that the transmission interference pattern can fall directly onto the detector surface without passing through an additional imaging lens group, thereby reducing aberration introduction and light energy loss. In actual acquisition, the first input light is incident alone and the broadband transmission interference pattern is recorded to obtain the original broadband Newton's rings image. Then, the second input light is incident separately and the reference transmission interference pattern is recorded to obtain the reference single-wavelength Newton's rings image. Both images can be acquired at a resolution of 1768×1768 pixels, and the image coordinate origin is established with the center of the convex lens. The pixel coordinates of any point are marked as... When deriving the set of single-wavelength Newton's rings patterns for the target band from a reference single-wavelength Newton's rings image, the geometric relationships under the condition of an extremely thin air layer are utilized: ; in, Let be the radial distance from the image point to the central axis of the convex lens. Let be the radius of curvature of the convex lens, taken as 6 m. Substituting the above relationship and the expression for optical path difference into the interference light intensity formula, we obtain the Newton's rings imaging model as follows: ; This equation shows that the spatial distribution of the Newton's rings image is essentially determined by... This control ensures that the spatial scale of the fringes changes synchronously according to a defined ratio when the wavelength changes. Based on this relationship, the reference single-wavelength image and the target discrete-wavelength image are respectively written as: ; ; This results in the target discrete wavelength. The corresponding coordinate terms are merged into the reference wavelength. The corresponding coordinate terms yield the spatial scaling factor as follows: That is, the target single-wavelength Newton's rings pattern can be regarded as the reference single-wavelength Newton's rings image according to... The result after isotropic scaling.

[0023] In one example, the first input light from the broadband light source under test and the second input light from the reference single-wavelength light source are respectively incident into a transmission-type coated Newton's rings device for interference modulation to obtain a transmission interference pattern, including: The first input light of the broadband light source to be tested and the second input light of the reference single-wavelength light source are respectively injected into the transmissive coated Newton's rings device. A thin air layer is formed between the convex surface of the convex lens of the transmissive coated Newton's rings device and the flat glass. Both the convex surface of the convex lens and the opposite surface of the flat glass are coated with silver film. The silver film on the convex surface of the convex lens and the silver film on the opposite surface of the flat glass are used to transmit and modulate the first input light and the second input light respectively, generating the first transmitted light and the second transmitted light. Based on the thin air layer, the first transmitted light and the second transmitted light are interfered and superimposed to obtain a transmission interference pattern.

[0024] In this embodiment, the first input light from the broadband light source under test and the second input light from the reference single-wavelength light source are sequentially introduced into the same transmissive coated Newton's rings device, allowing the two types of input light to complete transmission modulation and interference encoding under consistent structural conditions. The transmissive coated Newton's rings device consists of a convex lens and a flat glass plate, with the convex surface of the convex lens facing the flat glass plate, forming a thin air layer between them. Both the convex surface of the convex lens and the opposite surface of the flat glass plate are coated with silver films, thus forming the dual-interface modulation structure required for transmission interference. After the input light enters the device, it no longer relies on an additional long optical path system, but directly completes wavelength-related modulation within the tiny air layer. When the first and second input lights enter the device respectively, the incident light first reaches the silver film interface corresponding to the convex surface of the convex lens, and forms two main transmission propagation paths between the silver film on the convex surface of the convex lens and the silver film on the opposite surface of the flat glass plate. That is, after the input light is transmitted and modulated by the silver films at the upper and lower interfaces near the incident point of the air layer, two beams of transmitted light propagate along different paths. The two beams of transmitted light then converge again in the corresponding region of the air layer and undergo interference superposition. By controlling the amplitude distribution and propagation path through two coated interfaces, the same incident light is decomposed into two transmitted components with a fixed phase relationship. Since the coating conditions at both interfaces are consistent, and the thickness of the air layer continuously varies radially, comparable transmission interference fringes can be generated under the same geometric boundary regardless of whether broadband or reference single-wavelength input light is present. Furthermore, the air layer plays a role in phase difference accumulation and spatial fringe unfolding. That is, when the two transmitted beams propagate within the air layer, different propagation phase differences arise due to variations in local air layer thickness; when the two transmitted beams coincide in the converging region, this phase difference is transformed into an alternating bright and dark interference intensity distribution. Because the thickness of the air layer gradually changes from the center of the convex lens outwards, the phase difference is not constant but continuously varies with radial position, ultimately causing the transmission interference pattern to exhibit a concentric ring structure expanding outwards from the center. For the second input light, since the second input light is a reference single-wavelength light, the resulting stripes are a standard transmission Newton's rings pattern under single-wavelength conditions; for the first input light, since the first input light contains multiple wavelength components, the result is a composite transmission interference pattern formed by superimposing multiple sets of single-wavelength stripes according to their respective energy weights.

[0025] Figure 3This is a schematic diagram of the optical path within the transmissive coated Newton's rings air layer of the present invention, used to illustrate the interference formation mechanism of the first and second transmitted light in the air layer. The longitudinal central axis is marked O, representing the optical axis of the convex lens; the upper arc is the convex surface curve of the convex lens; the input light at point A is transmitted and modulated by the high-purity silver film at the upper and lower interfaces of the air layer, generating the first and second transmitted light propagating along different paths: the first transmitted light propagates downwards along the path at point C, passes through the flat glass, and exits at point B along the direction B'; the second transmitted light is transmitted through point D and exits along the direction D'. Point E is located near point A within the air layer, where the first transmitted light BB' and the second transmitted light DD' meet and interfere with each other; C' is the virtual image reference point for assisting in the calculation of the optical path difference. Where n0 represents the refractive index of the convex lens glass medium and the flat glass medium, n1 represents the refractive index of the thin air layer formed between the convex surface of the convex lens and the opposite surface of the flat glass, and i0 represents the incident angle of the input light at point A on the convex surface of the convex lens, that is, the angle between the incident ray and the normal of the convex surface of the convex lens at point A. The optical path difference between the two transmitted beams is determined by the thickness of the thin air layer at point A and the refraction angle, and through interference superposition, a transmission interference pattern distributed in concentric rings along the radial direction is formed.

[0026] In one example, based on the Newton's rings imaging model, the set of single-wavelength Newton's ring patterns corresponding to each discrete wavelength in the target band of the reference single-wavelength Newton's rings image is derived, including: Based on the Newton's rings imaging model, the spatial scaling factor between the reference single-wavelength Newton's rings image and the Newton's rings pattern at each discrete wavelength point in the target band is derived. The reference single-wavelength Newton's rings image is isotropically scaled according to the spatial scaling factor to obtain the scaled Newton's rings image. Then, linear interpolation is performed on the floating-point coordinates of the scaled Newton's rings image to obtain the set of single-wavelength Newton's rings patterns corresponding to each discrete wavelength in the target band.

[0027] In this embodiment, since the spatial distribution of the Newton's rings pattern is jointly controlled by the ratio of the squared pixel coordinates to the wavelength, the texture type does not change between the reference single-wavelength Newton's rings image and the Newton's rings pattern corresponding to any discrete wavelength point within the target band. Instead, the fringe radius and ring spacing undergo overall scaling with wavelength variation. Based on this physical relationship, using the reference single-wavelength Newton's rings image as the reference image, imaging representations under the reference wavelength condition and the target discrete wavelength condition are established respectively. Then, the coordinate terms in the imaging representation corresponding to the target discrete wavelength are equivalently replaced, absorbing the target wavelength into the coordinate scale, thereby obtaining the spatial scaling factor between the reference image and the target pattern. The spatial scaling factor is determined by the square root of the ratio of the reference single wavelength to the target discrete wavelength. Therefore, when the target discrete wavelength is greater than the reference single wavelength, the scaling factor is less than 1, corresponding to the overall contraction of the Newton's rings fringes towards the center; when the target discrete wavelength is less than the reference single wavelength, the scaling factor is greater than 1, corresponding to the overall expansion of the Newton's rings fringes outward. When generating a set of single-wavelength Newton's rings patterns, isotropic spatial scaling is performed on the reference single-wavelength Newton's rings image. This means the same scaling factor is applied to both the horizontal and vertical coordinates, ensuring the ring structure remains radially symmetrical before and after scaling, without introducing elliptical distortion. Since the scaled target coordinates generally do not fall exactly at integer pixel positions, and the CCD sampled image itself corresponds to a discrete integer pixel grid, linear interpolation is performed on the floating-point coordinates of the scaled image. This remaps the grayscale values ​​at the floating-point positions to a unified integer pixel coordinate system, allowing single-wavelength Newton's rings patterns generated under different target discrete wavelengths to be precisely aligned within the same spatial coordinate frame. For example, in a broadband measurement scenario, the target wavelength range is 450 nm to 750 nm, and the reference single wavelength is 400 nm. In this case, the spatial scaling factor specifically falls between 0.9428 and 0.7303. That is, as the target discrete wavelength gradually increases from 450 nm to 750 nm, the corresponding Newton's rings pattern will gradually shrink relative to the reference image. In a bimodal spectral measurement scenario, the target wavelength range is 510 nm to 560 nm, and the reference single wavelength is 500 nm. In this case, the spatial scaling factor specifically falls between 0.9901 and 0.9449. This indicates that the scaling amplitude in the bimodal scenario is relatively small and closer to the original scale of the reference image.

[0028] In one example, based on the Newton's rings imaging model, the spatial scaling factor between a reference single-wavelength Newton's rings image and the Newton's rings pattern at discrete wavelengths within the target band is derived, including: Based on the physical relationship that the light intensity of the interference pattern in the Newton's rings imaging model is cosine periodically distributed with respect to the ratio of the square of the pixel coordinate to the wavelength, the reference imaging equation for the reference single-wavelength Newton's rings image and the target imaging equation for the Newton's rings pattern at each discrete wavelength point in the target band are established respectively. By equivalently replacing the pixel coordinates in the target imaging equation and merging the target wavelength in the target imaging equation into the coordinate terms of the reference imaging equation, the spatial scaling factor between the reference single-wavelength Newton's rings image and the Newton's rings pattern at each discrete wavelength point in the target band is derived. The spatial scaling factor is the square root of the ratio of the reference single wavelength to the target discrete wavelength.

[0029] In this embodiment, based on the cosine periodic distribution of the light intensity of the interference pattern with the ratio of the square of the pixel coordinates to the wavelength, the difference between the reference single-wavelength Newton's rings image and the Newton's rings pattern at any discrete wavelength point within the target band does not lie in the change of the fringe generation mechanism, but in the systematic scaling of the spatial scale corresponding to the same cosine periodic structure. Based on this physical relationship, the Newton's rings image under the reference single-wavelength condition is written as a reference imaging equation, and the Newton's rings pattern under the target discrete wavelength condition is written as a target imaging equation, making the two comparable under the same pixel coordinate system. After establishing the two imaging equations, the pixel coordinates in the target imaging equation are equivalently replaced, that is, without directly changing the expression structure of the reference imaging equation, the changes corresponding to the target discrete wavelength are incorporated into the coordinate terms, so that the fringe scale difference caused by the target wavelength is transformed into a coordinate scaling difference. The target imaging equation is rewritten in the same form as the reference imaging equation, but the corresponding horizontal and vertical coordinates need to be multiplied by the same scale factor. Because the Newton's rings pattern itself has radial symmetry, the position of the fringes is affected by the sum of squared coordinates rather than coordinates in a single direction. Therefore, this scaling transformation must maintain consistency in both the horizontal and vertical directions, i.e., isotropic scaling is used. After completing the equivalent replacement, the spatial scaling factor between the reference single-wavelength Newton's rings image and the target discrete-wavelength Newton's rings pattern is obtained. The physical meaning of the spatial scaling factor is to map the distribution of Newton's rings fringes under the target discrete-wavelength condition back to the unified coordinate expression corresponding to the reference single-wavelength condition. The spatial scaling factor is the square root of the ratio of the reference single wavelength to the target discrete wavelength. Therefore, when the target discrete wavelength is greater than the reference single wavelength, the scaling factor is less than 1, and the target pattern shrinks towards the center relative to the reference image; when the target discrete wavelength is closer to the reference single wavelength, the scaling factor is closer to 1, and the fringe shape is closer to the reference image.

[0030] In one example, the original broadband Newton's rings image is input into a neural network for processing to obtain the first spectral coefficients. These first spectral coefficients are then weighted and discretely superimposed with a set of single-wavelength Newton's rings patterns to obtain a reconstructed broadband Newton's rings pattern, including: The original broadband Newton's rings image is input into the residual backbone network of the neural network for multi-scale feature extraction to obtain a multi-scale spectral feature map. The multi-scale spectral feature map is input into the spatial attention module of the neural network. A single-channel attention mask with the same spatial size as the multi-scale spectral feature map is generated through convolution operation. The multi-scale spectral feature map and the single-channel attention mask are multiplied at each pixel position to obtain a spatially weighted feature map. The spatially weighted feature map is input into the fully connected module of the neural network for calculation to obtain the first spectral coefficient of each discrete wavelength point. The first spectral coefficient is then weighted and discretely superimposed with the set of single-wavelength Newton's rings patterns to obtain the reconstructed broadband Newton's rings pattern.

[0031] In this embodiment, the original broadband Newton's rings image is used as the sole input to the neural network. The size of the original broadband Newton's rings image is 1768×1768×1. It is first input into the residual backbone network to complete multi-scale feature extraction. The first layer of the residual backbone network adopts a cascaded downsampling structure of 7×7 convolution and 3×3 max pooling, with a stride of 2 for both. This compresses the input image into an initial feature map of 442×442×64. Then, basic residual blocks and bottleneck residual blocks are alternately stacked in the subsequent backbone. The basic residual blocks are mainly used to preserve details such as shallow stripe edges, ring spacing changes, and local gray-level fluctuations. The bottleneck residual blocks continuously expand the receptive field while controlling the number of parameters through continuous processing of channel compression, spatial feature expansion, and channel recovery. This allows the spatial structure related to wavelength distribution in the Newton's rings pattern to be abstracted layer by layer into deep features. In this process, the spatial resolution of the feature map is halved stepwise from 442 to 221, 111, and 56, while the number of channels is increased stepwise from 64 to 128, 256, and 512. This allows the network to retain fine-grained fringe information near the center while extracting the global ring distribution patterns in large-radius regions, resulting in a multi-scale spectral feature map that can characterize the broadband spectral composition. The multi-scale spectral feature map then enters the spatial attention module. In this module, a single-channel attention mask with the same spatial size as the multi-scale spectral feature map is generated through 3×3 convolution. The single-channel attention mask is then multiplied pixel-wise with the multi-scale spectral feature map to form a spatially weighted feature map. Through the spatial attention module, the key regions in the Newton's rings image that truly carry effective spectral discrimination information are enhanced, while suppressing the influence of background noise, weakly correlated textures, and local random perturbations on coefficient inversion. That is, after spatial weighting, the network concentrates more computational weights on the ring positions that are more sensitive to wavelength distinction, thereby improving the stability and interpretability of the spectral reconstruction. After the spatially weighted feature map is input into the fully connected module, the high-dimensional features are compressed into a global feature vector through global average pooling. Then, two fully connected layers perform dimensionality reduction calculations, reducing the dimensionality from 512 to 256. After activation and sum-normalization using the softplus function, the first spectral coefficients corresponding to each discrete wavelength point within the target band are output. These first spectral coefficients represent the spectral weights of each discrete wavelength point; therefore, each coefficient corresponds to a discrete wavelength pattern in the set of single-wavelength Newton's ring patterns. After obtaining the first spectral coefficients, based on the physical mechanism that a broadband Newton's ring image is formed by superimposing multiple single-wavelength Newton's ring patterns according to their spectral weights, the first spectral coefficients are weighted and discretely superimposed with the set of single-wavelength Newton's ring patterns to obtain the reconstructed broadband Newton's ring pattern. The calculation relationship is as follows: ;in, This represents a reconstruction of the broad-spectrum Newton's rings pattern. Indicates the first The first spectral coefficients corresponding to each discrete wavelength point. Indicates the first The single-wavelength Newton's rings pattern corresponding to each discrete wavelength point. This represents the total number of discrete wavelength points within the target band.

[0032] Figure 4 This is a diagram of the neural network structure based on physical model constraints of the present invention. The overall structure consists of three cascaded parts: a residual backbone network, a spatial attention module, and a fully connected module. The input image (size 1768×1768×1) first enters the residual network: the first layer is a combination of 7×7 convolutions (stride 2) and 3×3 max pooling (stride 2), downsampling the input to 442×442×64; subsequently, bottleneck residual blocks (such as...) are alternately stacked. Figure 5 , Figure 5 This is a schematic diagram of the bottleneck residual block. The bottleneck residual block contains 1×1 convolution with stride 2 + batch normalization, 3×3 convolution, batch normalization + ReLU, 3×3 convolution + batch normalization, and dimension-matching shortcut connections, and the basic residual block (e.g., Figure 6 , Figure 6 The diagram illustrates the structure of the basic residual block. The basic residual block contains 3×3 convolutions + batch normalization + ReLU activation, 3×3 convolutions + batch normalization, and skip connections. The spatial resolution of the feature map is halved step-by-step (442→221→111→56), while the number of channels is increased step-by-step (64→128→256→512), extracting multi-scale spectral feature maps. The multi-scale spectral feature maps enter the spatial attention module, where a single-channel attention mask is generated through 3×3 convolutions. This mask is then multiplied pixel-wise with the backbone network's output feature map to obtain a spatially weighted feature map. The spatially weighted feature map enters the fully connected module, where it is compressed into a global feature vector through global average pooling. This vector is then reduced in dimensionality by two fully connected layers (512→256), activated by softplus, and summed and normalized to output the spectral coefficients (i.e., the reconstructed spectrum) for each discrete wavelength point.

[0033] In one example, the original broadband Newton's rings image is input into the residual backbone network of a neural network for multi-scale feature extraction, resulting in a multi-scale spectral feature map, including: The original broadband Newton's rings image is sequentially input into the first convolutional layer and the max pooling layer in the residual backbone network for downsampling to obtain the initial feature map; The initial feature map is input into the basic residual block in the residual backbone network for shallow feature extraction to obtain a shallow spectral feature map. The shallow spectral feature map is input into the bottleneck residual block in the residual backbone network for deep feature compression and expansion, resulting in a multi-scale spectral feature map.

[0034] In this embodiment, the original broadband Newton's rings image is directly used as the input to the residual backbone network. The residual backbone network first performs uniform downsampling, and then performs hierarchical feature extraction from shallow to deep. The input size of the original broadband Newton's rings image is 1768×1768×1. After entering the residual backbone network, it passes through the first convolutional layer and the max pooling layer in sequence. The first convolutional layer uses a 7×7 convolutional kernel with a stride of 2, and the max pooling uses a 3×3 pooling window with a stride of 2. While preserving the overall radial structure information of Newton's rings, the original image is compressed for the first time, mapping the original high-resolution image to an initial feature map of approximately 442×442×64. The initial feature map is then input into the basic residual block for shallow feature extraction. The basic residual block consists of a 3×3 convolutional layer, batch normalization, and skip connections. Skip connections allow input features to be directly passed to the output, ensuring that the effective low-level information extracted earlier is not excessively weakened by inter-layer transformations as the network deepens, while also mitigating the gradient vanishing problem. Since the shallow information of the Newton's rings image inherently contains significant edge contours, alternating light and dark bands, and a texture rhythm emanating from the center outwards, shallow extraction through the basic residual block results in a more stable shallow spectral feature map. This shallow spectral feature map is then input into the bottleneck residual block for deep feature compression and expansion, yielding a multi-scale spectral feature map. The bottleneck residual block adopts a structure that combines channel compression, spatial convolution, and channel integration. First, 1×1 convolution is used to compress the feature channels to reduce the number of parameters and redundant computation. Then, 3×3 convolution is used to expand the receptive field and capture spatial dependencies over a wider range. After that, subsequent convolutions restore and integrate the channel dimensions. At the same time, shortcut connections with dimension matching are used to maintain the continuity of information transmission. The spatial resolution of the feature map is halved step by step from 442 to 221, 111, and 56, while the number of channels is expanded step by step from 64 to 128, 256, and 512. Therefore, the obtained multi-scale spectral feature map contains both local features of fine stripes in the near-central region and global features of ring distribution and overall energy changes in the large-radius region.

[0035] In one example, a joint loss function is constructed based on the reconstructed broad-spectrum Newton's rings pattern, and all optimizable parameters of the neural network are iteratively updated. Iteration stops when the decrease in the joint loss function within a preset number of consecutive iterations falls below a preset threshold, and the second spectral coefficients are output, including: The pixel-level L2 norm squared difference between the original broadband Newton's rings image and the reconstructed broadband Newton's rings pattern is used as the physical consistency constraint term; the L2 norm is obtained by successively performing second-order differences on the first spectral coefficients of three adjacent discrete wavelength points as the spectral smoothing regularization term; and the L2 norm of all optimizable parameters in the neural network is used as the weight attenuation term. A joint loss function is constructed based on the physical consistency constraint term, the spectral smoothing regularization term, and the weight decay term. The gradient vector of all optimizable parameters in the neural network is calculated based on the joint loss function, and all optimizable parameters are iteratively updated. The iteration stops when the decrease of the joint loss function is lower than a preset threshold within a preset number of consecutive iterations, and the second spectral coefficient is output.

[0036] In this embodiment, the pixel-level deviation between the original broadband Newton's rings image and the reconstructed broadband Newton's rings pattern is used as a physical consistency constraint. This ensures that the reconstructed result, after weighted discrete superposition of the spectral coefficients output by the network with the single-wavelength Newton's rings pattern set, approximates the measured image as closely as possible across the entire pixel range. Furthermore, the first spectral coefficients corresponding to three adjacent discrete wavelength points are sequentially subjected to second-order differences, and the L2 norm squared is calculated on the second-order difference results to form a spectral smoothing regularization term, used to suppress unreasonable and drastic jumps between adjacent wavelength positions. Simultaneously, an L2 norm squared constraint is applied to all optimizable parameters of the neural network, forming a weight decay term, used to limit overfitting and oscillations caused by excessively large overall parameter amplitudes. These three constraints together constitute the joint loss function, the expression of which is: ; in, This represents the original broadband Newton's rings image. This represents the reconstructed broadband Newton's rings pattern obtained by weighted discrete superposition of the first spectral coefficient and the set of single-wavelength Newton's rings patterns. Indicates the first The first spectral coefficients corresponding to each discrete wavelength point. This represents all the optimizable parameters of the neural network. Represents the coefficients of the spectral smoothing regularization term. This represents the coefficient of the weight decay term. This represents the squared L2 norm. Of the three terms above, the first directly embeds the physical formation mechanism of the broadband Newton's rings image into the optimization objective, ensuring the network output returns to the actual imaging result; the second constrains the smooth variation of spectral coefficients along the wavelength axis, maintaining a continuous transition between adjacent wavelength points; the third limits the complexity of network parameters, preventing the network from overfitting local noise when performing self-supervised optimization based on a single measurement image. Iterative updates are performed on all optimizable parameters of the neural network based on the joint loss function. The previous round's parameter state drives the neural network to perform forward inference on the original broadband Newton's rings image, outputting the spectral coefficients corresponding to the current iteration. Then, based on the current spectral coefficients and the single-wavelength Newton's rings pattern set, the reconstructed broadband Newton's rings pattern corresponding to the current iteration is recalculated. The original broadband Newton's rings image, the current reconstructed broadband Newton's rings pattern, the current spectral coefficients, and the current network parameters are all substituted into the joint loss function to obtain the loss value for the current iteration. The gradient vectors of all optimizable parameters with respect to the joint loss function are calculated through backpropagation, and the gradient descent algorithm is used to update all optimizable parameters along the negative gradient direction, resulting in the updated parameter set. After the update, the updated parameters are used to drive the neural network to perform the next round of forward inference, thus forming a closed-loop optimization process: forward inference—loss calculation—backpropagation—parameter update—further forward inference. For the stopping condition, an explicit early stopping mechanism is used to continuously monitor the decrease in the joint loss function. When, within a preset number of iterations, the decrease in the current iteration loss value compared to the previous iteration loss value is consistently lower than a preset threshold, it is determined that further optimization is unlikely to bring effective improvement, and the iteration stops. The spectral coefficients output by the neural network at the time of stopping are then used as the second spectral coefficients output. The preset number of iterations is 250, and the preset threshold is 1×10⁻⁶. 11 When the model fails to achieve a joint loss function value of at least 1×10⁻⁶ within 250 consecutive iterations... 11 When the value decreases, the optimization process automatically ends.

[0037] In one example, the gradient vectors of all optimizable parameters in the neural network are calculated based on the joint loss function, and all optimizable parameters are iteratively updated. Iteration stops when the decrease in the joint loss function within a preset number of consecutive iterations falls below a preset threshold, and the second spectral coefficients are output, including: Based on the joint loss function, the gradient vector of all optimizable parameters in the neural network with respect to the joint loss function is calculated through backpropagation; Based on the gradient vector, the gradient descent algorithm is used to update all optimizable parameters along the negative gradient direction to obtain all updated optimizable parameters. The updated optimizable parameters are then used to drive the neural network to re-perform forward inference on the original broad-spectrum Newton's rings image to obtain the updated spectral coefficients and the updated broad-spectrum Newton's rings pattern. Calculate the loss value of the joint loss function corresponding to the current iteration based on the updated spectral coefficients and the updated broadband Newton's rings pattern; When the decrease in the loss value of the current iteration within a preset number of consecutive iterations is less than a preset threshold, the iteration stops, and the spectral coefficients output by the neural network at the time of stopping the iteration are used as the second spectral coefficients.

[0038] In this embodiment, the neural network is driven by all optimizable parameters of the current iteration to perform forward inference on the original broad-spectrum Newton's rings image, outputting the spectral coefficients corresponding to the current iteration. Then, the current spectral coefficients are re-weighted and discretely superimposed with the single-wavelength Newton's rings pattern set to obtain the broad-spectrum Newton's rings pattern corresponding to the current iteration. The current broad-spectrum Newton's rings pattern and the original broad-spectrum Newton's rings image are substituted into the joint loss function, comprehensively considering physical consistency constraints, spectral smoothing constraints, and parameter regularization constraints to obtain the loss value corresponding to the current iteration. Then, the gradient vector of all optimizable parameters in the neural network with respect to the joint loss function is calculated through backpropagation. After obtaining the gradient vector, the gradient descent algorithm is used to update all optimizable parameters along the negative gradient direction. The updated optimizable parameters are then used to drive the neural network again to perform forward inference on the original broad-spectrum Newton's rings image, obtaining the updated spectral coefficients and the updated broad-spectrum Newton's rings pattern. Based on the updated spectral coefficients and the updated broad-spectrum Newton's rings pattern, the loss value of the joint loss function corresponding to the current iteration is recalculated, serving as the basis for determining whether to continue optimization in the next iteration. Regarding the iteration stopping condition, the rate of loss decrease between two adjacent iterations is continuously monitored. When the rate of decrease of the current iteration loss value compared to the previous iteration loss value is lower than a preset threshold within a preset number of consecutive iterations, the neural network is determined to have entered a stable convergence state and the iteration stops. The preset number of consecutive iterations is 250, and the preset threshold is 1×10⁻⁶. -11 That is, when the model fails to achieve a loss function value of at least 1×10⁻⁶ within 250 consecutive iterations. -11 When the value decreases, the training process automatically stops, and the spectral coefficients output by the neural network at the point of stopping iteration are used as the second spectral coefficients. The reconstructed spectrum corresponding to the second spectral coefficients is quantitatively compared with the spectrum measured by a commercial spectrometer, and the Pearson correlation coefficient (CC) and root mean square error (RMSE) are used as evaluation indicators of reconstruction accuracy. The formula for calculating the Pearson correlation coefficient (CC) is as follows: ; The formula for calculating the root mean square error (RMSE) is: ; in, This indicates that the measurement results of the commercial spectrometer are in the first... Data values ​​at discrete wavelength points This represents the mean of all measurements taken by commercial spectrometers. This indicates that the scheme is in the [number]th [year]. Reconstruction results at discrete wavelength points This represents the mean of all reconstruction results. This represents the total number of discrete wavelength points involved in the evaluation. CC is used to characterize the consistency between the reconstructed spectrum and the spectrum measured by a commercial spectrometer in terms of overall trend. The closer CC is to 1, the stronger the correlation between the two curves. RMSE is used to characterize the average deviation level between the two at each discrete wavelength point. The smaller the RMSE, the closer the reconstructed result is to the measured result.

[0039] Figure 7 This is a comparison chart of broadband spectral measurement results, showing the comparison between the spectral reconstruction method of this invention and the reconstructed spectra of commercial spectrometers within the target wavelength range. The horizontal axis represents wavelength (nm), ranging from 450 to 750 nm; the vertical axis represents normalized intensity (au), ranging from 0 to 1.0. The solid curve represents the spectrum measured by the commercial spectrometer, and the dashed curve represents the reconstructed spectrum of this invention. Both curves show significant peaks at approximately 500 nm and 600 nm, and multiple secondary peaks in the 650–750 nm range, with a high degree of consistency in overall profile. Quantitative evaluation indicators are indicated: Pearson correlation coefficient CC = 0.9919, root mean square error RMSE = 0.0275, demonstrating that this invention achieves high-precision spectral reconstruction results highly consistent with those of commercial spectrometers over a wide spectral range.

[0040] This embodiment provides a spectrometer for implementing the steps of any spectral reconstruction method.

[0041] In this embodiment, the specific implementation of each unit in the above device embodiment is described in the above method embodiment, and will not be repeated here.

[0042] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, apparatus, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, apparatus, article, or method that includes that element.

[0043] The above description is only a preferred 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 spectral reconstruction method, characterized in that, include: Acquire the original broadband Newton's rings image of the broadband light source under test and the reference single-wavelength Newton's rings image of the reference single-wavelength light source, and derive the set of single-wavelength Newton's rings patterns corresponding to the reference single-wavelength Newton's rings image. The original broadband Newton's rings image is input into a neural network for processing to obtain the first spectral coefficient. The first spectral coefficient is then weighted and discretely superimposed with the single-wavelength Newton's rings pattern set to obtain the reconstructed broadband Newton's rings pattern. A joint loss function is constructed based on the reconstructed broad-spectrum Newton's rings pattern, and all optimizable parameters of the neural network are iteratively updated. When the decrease of the joint loss function within a preset number of consecutive iterations is lower than a preset threshold, the iteration stops, and the second spectral coefficient is output.

2. The spectral reconstruction method according to claim 1, characterized in that, The process of acquiring the original broadband Newton's rings image of the broadband light source under test and the reference single-wavelength Newton's rings image of the reference single-wavelength light source, and deriving the set of single-wavelength Newton's rings patterns corresponding to the reference single-wavelength Newton's rings image, includes: The first input light of the broadband light source under test and the second input light of the reference single-wavelength light source are respectively injected into the transmission-type coated Newton's rings device for interference modulation to obtain a transmission interference pattern. The transmission interference pattern is recorded by a CCD detector without a lens and in close contact with the transmission-type coated Newton's rings device, resulting in the original broadband Newton's rings image and a reference single-wavelength Newton's rings image. Based on the Newton's rings imaging model, the set of single-wavelength Newton's rings patterns corresponding to each discrete wavelength in the target band of the reference single-wavelength Newton's rings image is derived.

3. The spectral reconstruction method according to claim 2, characterized in that, The process of injecting the first input light from the broadband light source under test and the second input light from the reference single-wavelength light source into the transmission-type coated Newton's rings device for interference modulation to obtain a transmission interference pattern includes: The first input light of the broadband light source to be tested and the second input light of the reference single-wavelength light source are respectively injected into the transmissive coated Newton's rings device. A thin air layer is formed between the convex surface of the convex lens of the transmissive coated Newton's rings device and the flat glass. Both the convex surface of the convex lens and the opposite surface of the flat glass are coated with silver film. The silver film on the convex surface of the convex lens and the silver film on the opposite surface of the flat glass are used to transmit and modulate the first input light and the second input light respectively, generating the first transmitted light and the second transmitted light; Based on the thin air layer, the first transmitted light and the second transmitted light are superimposed by interference to obtain a transmission interference pattern.

4. The spectral reconstruction method according to claim 3, characterized in that, The method based on the Newton's rings imaging model derives the set of single-wavelength Newton's ring patterns corresponding to each discrete wavelength in the target band of the reference single-wavelength Newton's rings image, including: Based on the Newton's rings imaging model, the spatial scaling factor between the reference single-wavelength Newton's rings image and the Newton's rings pattern at each discrete wavelength point in the target band is derived. The reference single-wavelength Newton's rings image is isotropically scaled according to the spatial scaling factor to obtain a scaled Newton's rings image. Linear interpolation is then performed on the floating-point coordinates of the scaled Newton's rings image to obtain a set of single-wavelength Newton's rings patterns corresponding to each discrete wavelength in the target band.

5. The spectral reconstruction method according to claim 4, characterized in that, The method based on the Newton's rings imaging model derives the spatial scaling factor between the reference single-wavelength Newton's rings image and the Newton's rings pattern at each discrete wavelength point within the target band, including: Based on the physical relationship that the light intensity of the interference pattern in the Newton's rings imaging model is cosine periodically distributed with respect to the ratio of the square of the pixel coordinate to the wavelength, the reference imaging equation of the reference single-wavelength Newton's rings image and the target imaging equation of the Newton's rings pattern at each discrete wavelength point in the target band are established respectively. The pixel coordinates in the target imaging equation are replaced by equivalent substitutions, and the target wavelength in the target imaging equation is merged into the coordinate terms of the reference imaging equation. The spatial scaling factor between the reference single-wavelength Newton's ring image and the Newton's ring pattern of each discrete wavelength point in the target band is derived. The spatial scaling factor is the square root of the ratio of the reference single wavelength to the target discrete wavelength.

6. The spectral reconstruction method according to claim 1, characterized in that, The process of inputting the original broadband Newton's rings image into a neural network for processing to obtain a first spectral coefficient, and then weighted and discretely superimposing the first spectral coefficient with the set of single-wavelength Newton's rings patterns to obtain a reconstructed broadband Newton's rings pattern includes: The original broadband Newton's rings image is input into the residual backbone network of the neural network for multi-scale feature extraction to obtain a multi-scale spectral feature map. The multi-scale spectral feature map is input into the spatial attention module of the neural network. A single-channel attention mask with the same spatial size as the multi-scale spectral feature map is generated through convolution operation. The multi-scale spectral feature map and the single-channel attention mask are multiplied pixel by pixel to obtain a spatially weighted feature map. The spatially weighted feature map is input into the fully connected module of the neural network for calculation to obtain the first spectral coefficient of each discrete wavelength point. The first spectral coefficient is then weighted and discretely superimposed with the single-wavelength Newton's rings pattern set to obtain the reconstructed broadband Newton's rings pattern.

7. The spectral reconstruction method according to claim 6, characterized in that, The step of inputting the original broadband Newton's rings image into the residual backbone network of the neural network for multi-scale feature extraction to obtain a multi-scale spectral feature map includes: The original broadband Newton's rings image is sequentially input into the first convolutional layer and the max pooling layer in the residual backbone network for downsampling to obtain the initial feature map; The initial feature map is input into the basic residual block in the residual backbone network for shallow feature extraction to obtain a shallow spectral feature map. The shallow spectral feature map is input into the bottleneck residual block in the residual backbone network for deep feature compression and expansion to obtain a multi-scale spectral feature map.

8. The spectral reconstruction method according to claim 1, characterized in that, The process involves constructing a joint loss function based on the reconstructed broad-spectrum Newton's rings pattern and iteratively updating all optimizable parameters of the neural network. Iteration stops when the decrease in the joint loss function within a preset number of consecutive iterations falls below a preset threshold, and a second spectral coefficient is output, including: The pixel-level L2 norm squared difference between the original broadband Newton's rings image and the reconstructed broadband Newton's rings pattern is used as the physical consistency constraint term; the L2 norm is obtained by successively performing second-order differences on the first spectral coefficients of three adjacent discrete wavelength points as the spectral smoothing regularization term; and the L2 norm of all optimizable parameters in the neural network is used as the weight attenuation term. A joint loss function is constructed based on the physical consistency constraint, the spectral smoothing regularization term, and the weight decay term. The gradient vectors of all optimizable parameters in the neural network are calculated based on the joint loss function, and the all optimizable parameters are iteratively updated. When the decrease of the joint loss function within a preset number of consecutive iterations is lower than a preset threshold, the iteration stops and the second spectral coefficients are output.

9. The spectral reconstruction method according to claim 8, characterized in that, The process involves calculating the gradient vector of all optimizable parameters in the neural network based on the joint loss function, iteratively updating all optimizable parameters, stopping the iteration when the decrease in the joint loss function is less than a preset threshold within a preset number of consecutive iterations, and outputting the second spectral coefficients, including: Based on the joint loss function, the gradient vectors of all optimizable parameters in the neural network with respect to the joint loss function are calculated through backpropagation; Based on the gradient vector, the gradient descent algorithm is used to update all the optimizable parameters along the negative gradient direction to obtain the updated optimizable parameters. The updated optimizable parameters are then used to drive the neural network to re-perform forward inference on the original broad-spectrum Newton's rings image to obtain the updated spectral coefficients and the updated broad-spectrum Newton's rings pattern. The loss value of the joint loss function corresponding to the current iteration is calculated based on the updated spectral coefficients and the updated broadband Newton's rings pattern. When the decrease in the loss value of the current iteration compared to the loss value of the previous iteration is less than a preset threshold within a consecutive preset number of iterations, the iteration stops, and the spectral coefficients output by the neural network at the time of stopping the iteration are used as the second spectral coefficients.

10. A spectrometer, characterized in that, Steps for implementing the spectral reconstruction method according to any one of claims 1 to 9.

Images