CN110296758B - Spectrograph based on perovskite quantum dot light filtering film and spectral measurement method - Google Patents
Spectrograph based on perovskite quantum dot light filtering film and spectral measurement method Download PDFInfo
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Abstract
The invention relates to a spectrograph based on a perovskite quantum dot light filter film and a spectral measurement method, wherein the method comprises the following steps: s1: attaching a filter membrane with a cut-off edge continuously adjustable in a wave band of 250-850 nm to the photosensitive surface of a CCD camera sensor; s2: constructing a measured value model of a CCD camera of a target spectrum; s3: constructing a gradient function of a target spectrum and an algorithm optimization model of spectrum reconstruction; s4: introducing a Lagrange multiplier into the algorithm optimization model to obtain a Lagrange function of the algorithm optimization model; s5: initializing settings, including: presetting a convergence threshold value, and presetting an initial value, a Lagrange multiplier and a weight parameter of a target spectrum; s6: updating the gradient of the target spectrum, a Lagrange multiplier and a weight parameter according to an ALM iterative reconstruction principle; s7: and outputting the updated target spectrum when the difference value of the target spectrum before and after updating is smaller than the threshold value, otherwise, repeating the steps S6-S7.
Description
Technical Field
The invention relates to the technical field of computational photography, in particular to a spectrograph based on a perovskite quantum dot light filter film and a spectral measurement method.
Background
Spectral imaging has wide applications in the fields of photography, biological and chemical analysis, etc. Currently, the research on spectral imaging is all focused on the development of miniaturization, low cost and easy integration. Spectral imaging generally adopts a filter layer and a detector to realize spectral detection, and the core of the mode is a light splitting element, and more researches are carried out on modes such as plasma filtering, grating arrays, band-pass filters and the like. However, the preparation of the filter element requires processes such as evaporation and ion beam etching, and such systems are complicated and costly. Based on the concept, Jie Bao and Moungi G.Bawendi put forward a quantum dot spectrometer, CdSe and CdS quantum dots are used, a quantum dot/polymer broadband filter film array is manufactured in a printing mode, the principle of multispectral multiplexing is used, the quantum dot/polymer broadband filter film array has the advantages of high light energy utilization rate, high spectral resolution, real-time imaging and the like, and better spectral reconstruction is achieved. The concept of quantum dot spectrometers enables spectral imaging with the advantages of low cost, no angular selectivity, low complexity, small size and light weight.
Because CdSe and CdS quantum dots have the advantage of continuously adjustable band gaps, the CdSe and CdS quantum dots become ideal materials for manufacturing the broadband filter with continuously adjustable cut-off band edges. However, CdSe and CdS quantum dots need to be prepared by a thermal injection method, and have the defects of complex synthesis process, low raw material utilization rate, difficulty in batch control, difficulty in integration, easiness in scattering and unsuitability for batch production. Therefore, Schmidt teaches that the perovskite material has the advantages of adjustable band gap and room-temperature solution preparation, develops a method for preparing the perovskite quantum dot/polymer optical film in situ, has the advantages of simple preparation, low cost and batch production compared with the method for synthesizing the quantum dot by a thermal injection method, and greatly promotes the integrated application of the perovskite quantum material.
Disclosure of Invention
In view of the above, the invention provides a spectrometer based on a perovskite quantum dot filter film and a spectral measurement method based on a method for in-situ preparation of a perovskite quantum dot/polymer optical film, and the spectrometer based on the perovskite quantum dot filter film is prepared by firstly utilizing the characteristic that the cut-off edge of a perovskite material is continuously adjustable and combining a CCD camera sensor, and then performing spectral reconstruction on data acquired by the spectrometer by utilizing a data reconstruction algorithm based on compressed sensing.
According to one aspect of the invention, a spectral measurement method based on a perovskite quantum dot filter film is provided, and comprises the following steps:
step S1: attaching a filter film formed by perovskite nanocrystals or polymers to the photosensitive surface of a CCD camera sensor, wherein the cut-off edge of the filter film is continuously adjustable within the wavelength range of 250 nm-850 nm;
step S2: constructing a measured value model of a CCD camera of a target spectrum;
step S3: constructing a gradient function of a target spectrum, and constructing an algorithm optimization model of spectrum reconstruction according to the measured value model and the gradient function;
step S4: introducing a Lagrange multiplier into the algorithm optimization model to obtain a Lagrange function of the algorithm optimization model;
step S5: initializing settings, including: presetting a convergence threshold value, and presetting an initial value, a Lagrange multiplier and a weight parameter of the target spectrum in the Lagrange function;
step S6: according to the iterative reconstruction principle of the augmented Lagrange method, the gradient of the target spectrum, the Lagrange multiplier and the weight parameter are updated in sequence; and
step S7: outputting the updated target spectrum when the difference between the updated target spectrum and the target spectrum before updating is less than the convergence threshold, otherwise repeating steps S6-S7 with the updated target spectrum, the Lagrangian multiplier and the weight parameters.
Preferably, in step S1, the filter film is obtained by forming a plurality of perovskite nanocrystal or polymer composite thin film array dots on the surface of a quartz substrate using an in-situ method.
Preferably, in step S2:
sampling a target spectrum, a spectrum of each composite film and a spectrum of a CCD camera by adopting the same frequency to obtain a discretized target spectrum, a discretized spectrum of each composite film and a discretized spectrum of the CCD camera;
establishing a sampling matrix A according to the discretized spectrum of each composite film and the discretized spectrum of the CCD camera; and
the measured value model of the CCD camera of the target spectrum is constructed as Ax ═ b, wherein,
Preferably, in step S3, the gradient function of the target spectrum is configured as g ═ Gx; and
the spectral reconstruction algorithm optimization model is constructed as follows:
wherein g represents the gradient of the target spectrum; g represents a gradient calculation matrix;
representing a total variation of the target spectrum;
an equality constraint representing the total variation of the target spectrum.
Preferably, in step S4, the equation constraint in step S3 is incorporated into the total variation of the target spectrum by introducing a lagrangian multiplier to obtain a lagrangian function of the algorithm optimization model for spectrum reconstruction, which is expressed as follows:
wherein, y1And y2Is a lagrange multiplier; mu.s1And mu2Is a weight parameter.
Preferably, in step S5, the lagrangian function is preset with: gradient computation matrix G, Lagrange multiplier y10 and y20, weight parameter mu11 and μ21 is ═ 1; and
in step S6, the gradient of the target spectrum is updated according to the following expression:
wherein the content of the first and second substances,
for threshold operation, the expression is as follows:
wherein g' represents the updated gradient of the target spectrum.
Preferably, in step S5, the lagrangian function is preset with: the sampling matrix A and a measurement value matrix b of the CCD camera; and
in step S6, the target spectrum is updated according to the following expression:
wherein x' represents the updated target spectrum.
Preferably, in step S5, algorithm parameters ρ, μ are preset1 maxAnd mu2 max(ii) a And
in step S6, the lagrangian multiplier and weight parameters are updated according to the following expressions:
wherein, ρ, μ1 maxAnd mu2 maxFor adjusting the maximum values of the growth rate and the weight parameters; y is1' and y2' represents the updated Lagrangian multiplier; mu.s1' and mu2' represents the updated weight parameter.
According to another aspect of the present invention, there is provided a perovskite quantum dot filter film based spectrometer comprising:
a CCD camera sensor;
the light filter film is formed by perovskite nanocrystals or polymers and attached to the photosensitive surface of the CCD camera sensor, wherein the cut-off edge of the light filter film is continuously adjustable within the wavelength range of 250-850 nm; and
a processing unit for receiving data from the CCD camera sensor and performing the following operations:
operation S11: constructing a measured value model of a CCD camera of a target spectrum;
operation S12: constructing a gradient function of a target spectrum, and constructing an algorithm optimization model of spectrum reconstruction according to the measured value model and the gradient function;
operation S13: introducing a Lagrange multiplier into the algorithm optimization model to obtain a Lagrange function of the algorithm optimization model;
operation S14: initializing settings, including: presetting a convergence threshold value, and presetting an initial value, a Lagrange multiplier and a weight parameter of the target spectrum in the Lagrange function;
operation S15: according to the iterative reconstruction principle of the augmented Lagrange method, the gradient of the target spectrum, the Lagrange multiplier and the weight parameter are updated in sequence; and
operation S16: outputting the updated target spectrum when a difference between the updated target spectrum and the target spectrum before updating is less than the convergence threshold, otherwise repeating operations S15-S16 with the updated target spectrum, the Lagrangian multiplier, and the weight parameters.
Preferably, the filter film is obtained by forming a plurality of perovskite nanocrystal or polymer composite thin film array dots on the surface of a quartz substrate by an in-situ method.
Compared with the prior art, one or more embodiments in the above scheme can have the following advantages or beneficial effects:
compared with the existing quantum dot spectrometer or spectral measurement method, the invention firstly utilizes the characteristic that the cut-off edge of a perovskite material is continuously adjustable and combines a CCD camera sensor to prepare the spectrometer based on the perovskite quantum dot filter film, and then utilizes a data reconstruction algorithm based on compressed sensing to carry out spectral reconstruction on the data acquired by the spectrometer, thereby overcoming the technical problems of complex process, high cost, difficult batch control and low reconstruction spectral resolution of the existing spectral measurement method, realizing spectral measurement with high resolution, and simultaneously promoting the application of the low-cost quantum dot spectrometer.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
Fig. 1 is a schematic diagram of a spectrometer based on a perovskite quantum dot filter film for collecting spectral information according to an embodiment of the present invention.
Fig. 2 is a flowchart of a spectral measurement method based on a perovskite quantum dot filter film according to an embodiment of the present invention.
FIG. 3 schematically shows an array of filter films according to an embodiment of the invention.
FIG. 4 is a spectrum diagram of ambient light after passing through a portion of the composite film in the filter array according to an embodiment of the invention.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented. It should be noted that, as long as there is no conflict, the embodiments and the features of the embodiments of the present invention may be combined with each other, and the technical solutions formed are within the scope of the present invention.
In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the embodiments of the invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced without some of these specific details or with other methods described herein.
In order to solve the technical problems of complex preparation or measurement process, high cost, difficulty in batch control and low reconstruction spectral resolution of the conventional quantum dot spectrometer and spectral measurement method, an embodiment of the invention firstly provides a spectrometer based on a perovskite quantum dot filter film and a spectral measurement method.
The following will comprehensively describe the spectrometer and the spectral measurement method based on the perovskite quantum dot filter film provided by the invention with reference to the attached drawings and an embodiment.
Fig. 1 is a schematic diagram of a spectrometer based on a perovskite quantum dot filter film for collecting spectral information according to an embodiment of the present invention. As shown in fig. 1, the spectrometer based on the perovskite quantum dot filter film (hereinafter referred to as perovskite quantum dot spectrometer) includes: a filter 101 and a CCD camera sensor 102. In addition, the perovskite quantum dot spectrometer further comprises a processing unit (not shown in fig. 1) connected to the CCD camera sensor 102 for receiving data from the CCD camera sensor 102 and performing an operation of target spectrum reconstruction.
As shown in fig. 1, after the target spectrum 100 reaches the filter 101, the filter 101 performs corresponding modulation filtering on the target spectrum 100, and then the CCD camera sensor 102 collects the target spectrum 100 after passing through the filter 101 to obtain a measured value of the target spectrum after passing through the filter 101, and sends the measured value of the target spectrum to the processing unit.
Fig. 2 is a flowchart of a spectral measurement method based on a perovskite quantum dot filter film according to an embodiment of the present invention. FIG. 3 schematically illustrates a filter according to an embodiment of the invention. As shown in fig. 2 and 3, one embodiment of the present invention takes advantage of the ease of preparation and continuously adjustable cutoff edge of perovskite materials. In step S1, a plurality of composite thin films formed by perovskite nanocrystals or polymers are formed on the surface of the quartz substrate by in-situ preparation method, and the composite thin films together form the filter according to an embodiment of the present invention. It should be noted that other types of substrates can be used to prepare the filter, and the invention is not limited thereto. In addition, the size of the substrate and the number of the composite films may be adjusted according to the actual situation, and the present invention is not limited thereto. For example, the size of the quartz substrate in one embodiment of the present invention is preferably 5.5cm × 5.5cm, and the number of composite films is preferably 196.
In one embodiment of the invention, the cut-off edge of each composite film is different, and the cut-off edge of each composite film is continuously adjustable within the wavelength range of 250nm to 850 nm.
For example, taking a composite film as an example of the filter film, the cut-off edge of the composite film is adjusted to 300nm by utilizing the characteristic that the cut-off edge of the perovskite material is continuously adjustable. At this time, the composite film has a strong inhibiting effect on the external light with a wavelength less than the cut-off edge (300nm), i.e., the external light with a wavelength less than 300nm is prevented from transmitting. In contrast, the transmittance of the composite film is greater than 90% for external light having a wavelength greater than its cut-off edge (300 nm). Therefore, by adjusting the cut-off edge of each composite film in the filter film, each composite film can selectively transmit light rays with different wave bands, and then different spatial positions of the filter film have different filtering effects on the light rays.
FIG. 4 is a spectrum diagram of ambient light after passing through a portion of the composite film in the filter according to an embodiment of the invention. In an embodiment of the invention, different composite films in the filter film have different cut-off edges, and the cut-off edges are all within the range of visible light. As shown in fig. 4, it can be clearly seen that the composite film in the filter film has a filtering effect on the external light, and the transmittance of the external light is very low in the wavelength band smaller than the cut-off edge of the composite film, and the transmittance of the external light is very high in the wavelength band larger than the cut-off edge of the composite film.
Referring back to fig. 2, the flow of the spectral measurement method based on the perovskite quantum dot filter film according to an embodiment of the present invention is described in detail below.
First, in step S1, 196, for example, composite thin films capable of covering a wavelength range of 400nm to 700nm are formed on the surface of a quartz substrate of, for example, 5.5cm × 5.5cm by the in-situ preparation method, and constitute a filter array.
In step S1, the prepared filter is then integrated into the interior of the CCD camera and attached to the light sensing surface of the CCD camera sensor.
After step S1 is completed, the spectrum of the CCD camera is measured and the spectrum of each composite film in the filter is measured for reconstruction of the target spectrum in the subsequent steps.
Next, step S2 is executed: a model of the measured values of the CCD camera of the target spectrum is constructed. The method specifically comprises the following steps: firstly, a target spectrum is set as r (lambda), and according to the camera imaging principle, the measured value of the target spectrum acquired by the CCD camera is the result of integration of a target spectrum curve, a spectrum curve of each composite film and a spectrum curve of the camera.
Therefore, a measurement value model of the CCD camera is constructed for the target spectrum transmitted through any one composite film in the filter film array, and the expression of the measurement value model is as follows:
zi＝∫λdi(λ)r(λ)c(λ)dλ，
wherein i is 1,2, …, n, i is the serial number of the composite film in the filter film array, di(lambda) is the spectrum of the ith composite film in the filter film array; c (λ) is the spectrum of the camera; z is a radical ofiIs a CCD camera pairAnd (4) measuring the target spectrum after the ith composite film in the filter film array is transmitted.
To facilitate the reconstruction of the spectrum, next, the spectrum d of each composite film is separately calculated for the target spectrum r (λ)i(λ) and the spectrum c (λ) of the camera. Specifically, the same frequency is adopted for the target spectrum r (lambda) and the spectrum d of each composite filmiAnd (lambda) sampling the spectrum c (lambda) of the CCD camera to obtain a discretized target spectrum, a discretized spectrum of each composite film and a discretized spectrum of the CCD camera.
Constructing a measurement value model of the discretized CCD camera for the discretized target spectrum which penetrates through any one composite film in the filter film array, wherein the expression is as follows:
wherein k is 1,2, …, m is the total number of elements, di(k) Is the k element in the spectrum of the discretized i composite film; r (k) is the kth element in the discretized target spectrum; c (k) is the kth element in the spectrum of the discretized camera; z is a radical ofi' is the measured value of the discretized target spectrum after the CCD camera transmits the ith composite film in the filter film array.
Next, a sampling matrix a is established from the spectrum of each of the discretized composite films and the spectrum of the discretized CCD camera, the expression of which is as follows:
wherein d isn(m) represents an m-th element in the spectrum of the discretized n-th composite film, and c (m) represents an m-th element in the spectrum of the discretized CCD camera.
Since the measurement value of the CCD camera is a set of measurement values of the discretized target spectrum after passing through all the composite films in the filter array, the measurement value matrix of the CCD camera can be set as:
b＝[z1'z2'...zn']T∈Rn×1，
on the basis of this, the measured value model of the CCD camera of the target spectrum is constructed as Ax ═ b, where x denotes the discretized target spectrum and x ═ r (1), r (2),.., r (m).
Next, step S3 is executed: and constructing a gradient function of a target spectrum, and constructing an algorithm optimization model for spectrum reconstruction according to a measured value model of the CCD camera of the target spectrum and the gradient function of the target spectrum.
The method specifically comprises the following steps: in step S3, an embodiment of the present invention employs a Compressed Sensing (CS) based ensemble variational (TV) algorithm for spectral reconstruction. The compressed sensing aims at reconstructing a real signal from an underdetermined linear system by utilizing the prior information of the signal, and the gradient integral of the spectrum in nature is lower as can be known from statistical analysis. Based on the prior information that the gradient integral of the spectrum is low in nature, the gradient function of the target spectrum is constructed as g ═ Gx for any one target spectrum. Where G denotes the gradient of the target spectrum and G denotes the gradient calculation matrix.
In step S3, an algorithm optimization model for spectrum reconstruction is then constructed from the model of the measured value of the CCD camera of the target spectrum and the gradient function of the target spectrum. The method specifically comprises the following steps: and expressing the total variation of the target spectrum by using a first-order norm of the gradient g of the target spectrum, and using a gradient function of the target spectrum and a measurement value model of a CCD camera of the target spectrum as an equality constraint of the total variation of the target spectrum to construct an algorithm optimization model of spectrum reconstruction.
The spectral reconstruction algorithm optimization model is constructed as follows:
wherein g represents the gradient of the target spectrum;
representing the total variation of the target spectrum;
an equality constraint representing the total variation of the target spectrum.
Next, step S4 is executed: and introducing a Lagrange multiplier into the spectral reconstruction algorithm optimization model to obtain a Lagrange function of the spectral reconstruction algorithm optimization model. The method specifically comprises the following steps: incorporating the equation constraint in step S3 into the total variation of the target spectrum by introducing a lagrangian multiplier to obtain a lagrangian function of the algorithm optimization model of the spectral reconstruction, which is expressed as follows:
wherein the content of the first and second substances,<·>is the inner product sign; y is1And y2Is a lagrange multiplier; mu.s1And mu2Is a weight parameter.
Further, through inner product and norm conversion, the above function expression can be written as:
next, step S5 is executed: initializing settings, including: presetting convergence threshold value and algorithm parameters rho and mu1 maxAnd mu2 maxPresetting the following lagrange function: initial value of target spectrum, gradient calculation matrix G, sampling matrix A, measurement value matrix b of CCD camera and Lagrange multiplier y10 and y20 and a weight parameter mu11 and μ2＝1。
It should be noted that, in step S5, the sampling matrix a is not randomly preset, but is obtained by measuring the spectrum of the actual CCD camera and measuring the spectrum of each composite film in the actual filter array. Likewise, the measurement value matrix b of the CCD camera is not randomly preset, but is an actual measurement result measured by the CCD camera. In addition, other parameters in step S5 may be randomly set according to the actual situation, for example, the lagrangian multiplier and the weighting parameter may be preset to other reasonable values, which is not limited by the present invention.
Next, step S6 is executed: and according to the iterative reconstruction principle of the augmented Lagrangian method, sequentially updating the gradient of the target spectrum, the Lagrangian multiplier and the weight parameter in the Lagrangian function.
The method specifically comprises the following steps: according to the iterative reconstruction principle of the Augmented Lagrangian Method (ALM), the updating principle of each variable is to minimize the Lagrangian function while keeping other variables unchanged. The update process is as follows:
first, the gradient of the target spectrum is updated:
(1) removing variables that are independent of g, the lagrange function is:
(2) in order to distinguish the gradients of the target spectrum before and after the update, the gradient of the target spectrum after the update is not indicated by g'.
According to the derivation of the augmented Lagrange method, the expression for updating the gradient of the target spectrum is as follows:
wherein the content of the first and second substances,
for threshold operation, the expression is as follows:
next, the target spectrum is updated with the updated g':
(1) removing variables that are independent of x, the lagrange function is:
(2) calculate the gradient of the function L (x) over x:
(3) in order to distinguish the target spectra before and after the update, the target spectrum after the update is not represented by x'.
Order to
The expression for updating the target spectrum is as follows:
next, the lagrangian multiplier and the weight parameter are updated by using the updated g 'and x', and the expression is as follows:
where ρ, μ1 max,μ2 maxThe algorithm parameters are used for adjusting the maximum values of the growth speed and the weight parameters; y is1' and y2' represents the updated Lagrangian multiplier; mu.s1' and mu2' denotes the updated weight parameter.
Next, step S7 is executed: outputting the updated target spectrum when the difference between the updated target spectrum and the target spectrum before updating is less than the convergence threshold, otherwise repeating steps S6-S7 with the updated target spectrum, the updated Lagrangian multiplier and the updated weight parameter.
The method specifically comprises the following steps: judging whether the difference between the target spectrum updated in the step S6 and the target spectrum before updating is smaller than a convergence threshold, outputting an updated target spectrum x' when the difference between the updated target spectrum and the target spectrum before updating is smaller than the convergence threshold, otherwise, updating by the iteration at this timeNew target spectrum x', lagrange multiplier y1' and y2' and a weight parameter mu1' and mu2' As input for the next iteration, steps S6-S7 are repeated.
It is to be understood that the above steps S2 to S7 may be performed by a processing unit of a perovskite quantum dot spectrometer according to an embodiment of the present invention for reconstruction of a target spectrum.
In summary, the invention provides a spectrometer based on a perovskite quantum dot filter film and a spectral measurement method, compared with the existing quantum dot spectrometer or spectral measurement method, the invention firstly utilizes the characteristic that the cut-off edge of a perovskite material is continuously adjustable and combines a CCD camera sensor to prepare the perovskite quantum dot spectrometer, and then utilizes a data reconstruction algorithm based on compressed sensing to carry out spectral reconstruction on data acquired by the perovskite quantum dot spectrometer, thereby overcoming the technical problems of complex process, high cost, difficulty in batch control and low reconstruction spectral resolution of the existing spectral measurement method, realizing spectral measurement with high resolution, and simultaneously promoting the application of the low-cost quantum dot spectrometer.
It is to be understood that the disclosed embodiments of the invention are not limited to the particular process steps or materials disclosed herein, but rather, are extended to equivalents thereof as would be understood by those of ordinary skill in the relevant art. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
Reference in the specification to "an embodiment" means that a particular feature, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Thus, the appearances of the phrase or "an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment.
Furthermore, the described features or characteristics may be combined in any other suitable manner in one or more embodiments. In the above description, certain specific details are provided, such as thicknesses, amounts, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth.
While the above examples are illustrative of the principles of the present invention in one or more applications, it will be apparent to those of ordinary skill in the art that various changes in form, usage and details of implementation can be made without departing from the principles and concepts of the invention. Accordingly, the invention is defined by the appended claims.
Claims (8)
1. A spectral measurement method based on a perovskite quantum dot light filter film comprises the following steps:
step S1: attaching a filter film formed by perovskite nanocrystals or polymers to the photosensitive surface of a CCD camera sensor, wherein the cut-off edge of the filter film is continuously adjustable within the wavelength range of 250 nm-850 nm;
step S2: constructing a measured value model of a CCD camera of a target spectrum;
step S3: constructing a gradient function of a target spectrum, and constructing an algorithm optimization model of spectrum reconstruction according to the measured value model and the gradient function;
step S4: introducing a Lagrange multiplier into the algorithm optimization model to obtain a Lagrange function of the algorithm optimization model;
step S5: initializing settings, including: presetting a convergence threshold value, and presetting an initial value, a Lagrange multiplier and a weight parameter of the target spectrum in the Lagrange function;
step S6: according to the iterative reconstruction principle of the augmented Lagrange method, the gradient of the target spectrum, the Lagrange multiplier and the weight parameter are updated in sequence; and
step S7: outputting the updated target spectrum when the difference between the updated target spectrum and the target spectrum before updating is less than the convergence threshold, otherwise repeating steps S6-S7 with the updated target spectrum, the updated Lagrangian multiplier and the updated weight parameter,
wherein, in step S2:
sampling a target spectrum, a spectrum of each composite film and a spectrum of a CCD camera by adopting the same frequency to obtain a discretized target spectrum, a discretized spectrum of each composite film and a discretized spectrum of the CCD camera;
establishing a sampling matrix A according to the discretized spectrum of each composite film and the discretized spectrum of the CCD camera; and
the measured value model of the CCD camera of the target spectrum is constructed as Ax ═ b, wherein,
wherein, in step S3:
constructing a gradient function of the target spectrum as g ═ Gx; and
the spectral reconstruction algorithm optimization model is constructed as follows:
s.t.Gx＝g
Ax＝b
wherein g represents the gradient of the target spectrum; g represents a gradient calculation matrix;
representing a total variation of the target spectrum;
an equality constraint representing the total variation of the target spectrum.
2. The spectral measurement method according to claim 1, wherein the filter film is obtained by forming a plurality of perovskite nanocrystal or polymer composite thin film array dots on the surface of a quartz substrate using an in-situ method in step S1.
3. The method for spectral measurement according to claim 1, wherein in step S4, the equation constraint in step S3 is incorporated into the total variation of the target spectrum by introducing a lagrangian multiplier to obtain the lagrangian function of the algorithm optimization model for spectral reconstruction, which is expressed as follows:
wherein, y1And y2Is a lagrange multiplier; mu.s1And mu2Is a weight parameter.
4. The spectral measurement method according to claim 3,
in step S5, of the lagrangian functions: gradient computation matrix G, Lagrange multiplier y10 and y20, weight parameter mu11 and μ21 is ═ 1; and
in step S6, the gradient of the target spectrum is updated according to the following expression:
wherein the content of the first and second substances,
for threshold operation, the expression is as follows:
wherein g' represents the updated gradient of the target spectrum.
5. The spectral measurement method according to claim 4,
in step S5, of the lagrangian functions: the sampling matrix A and a measurement value matrix b of the CCD camera; and
in step S6, the target spectrum is updated according to the following expression:
wherein x' represents the updated target spectrum.
6. The spectral measurement method according to claim 5,
in step S5, algorithm parameters ρ, μ are preset1maxAnd mu2max(ii) a And
in step S6, the lagrangian multiplier and weight parameters are updated according to the following expressions:
wherein, ρ, μ1maxAnd mu2maxFor adjusting the maximum values of the growth rate and the weight parameters; y is1' and y2' represents the updated Lagrangian multiplier; mu.s1' and mu2' represents the updated weight parameter.
7. A perovskite quantum dot filter film based spectrometer comprising:
a CCD camera sensor;
the light filter film is formed by perovskite nanocrystals or polymers and attached to the photosensitive surface of the CCD camera sensor, wherein the cut-off edge of the light filter film is continuously adjustable within the wavelength range of 250-850 nm; and
a processing unit for receiving data from the CCD camera sensor and performing the following operations:
operation S11: constructing a measured value model of a CCD camera of a target spectrum;
operation S12: constructing a gradient function of a target spectrum, and constructing an algorithm optimization model of spectrum reconstruction according to the measured value model and the gradient function;
operation S13: introducing a Lagrange multiplier into the algorithm optimization model to obtain a Lagrange function of the algorithm optimization model;
operation S14: initializing settings, including: presetting a convergence threshold value, and presetting an initial value, a Lagrange multiplier and a weight parameter of the target spectrum in the Lagrange function;
operation S15: according to the iterative reconstruction principle of the augmented Lagrange method, the gradient of the target spectrum, the Lagrange multiplier and the weight parameter are updated in sequence; and
operation S16: outputting the updated target spectrum when a difference between the updated target spectrum and the target spectrum before updating is less than the convergence threshold, otherwise repeating operations S15-S16 with the updated target spectrum, the updated Lagrangian multiplier, and the updated weight parameters,
wherein, in step S11:
sampling a target spectrum, a spectrum of each composite film and a spectrum of a CCD camera by adopting the same frequency to obtain a discretized target spectrum, a discretized spectrum of each composite film and a discretized spectrum of the CCD camera;
establishing a sampling matrix A according to the discretized spectrum of each composite film and the discretized spectrum of the CCD camera; and
the measured value model of the CCD camera of the target spectrum is constructed as Ax ═ b, wherein,
wherein, in step S12:
constructing a gradient function of the target spectrum as g ═ Gx; and
the spectral reconstruction algorithm optimization model is constructed as follows:
s.t.Gx＝g
Ax＝b
wherein g represents the gradient of the target spectrum; g represents a gradient calculation matrix;
representing a total variation of the target spectrum;
an equality constraint representing the total variation of the target spectrum.
8. The spectrometer of claim 7, wherein the filter film is obtained by forming a plurality of perovskite nanocrystal or polymer composite thin film array dots on the surface of a quartz substrate using an in-situ method.
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