Spectral reconstruction method based on full-system polarization calibration and data demodulation

Abstract

The application discloses a kind of spectral reconstruction methods based on full system polarization calibration and data demodulation, comprising:1. using wide-band light source, calibration linear polarizer, calibration achromatic quarter-wave plate to the channel type polarized spectrometer full system to be calibrated is polarized calibration;2. by the channel type polarized spectrometer full system after calibration measurement spectral power distribution, and the polarization effect of system is calculated to create Mueller matrix;3. using sparse dictionary to sparse representation of stokes parameter, and construct target equation;4. using least square method to solve target equation, complete spectral reconstruction.The application improves the traditional channel type polarized spectral calibration method, and the polarization calibration is carried out to the full system, and the polarization effect of system can be more accurately obtained, so that more accurate reconstruction result is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optical device calibration, in particular to a polarization effect calibration method for a channel type polarimetric spectrometer whole system and a reconstruction method for a measured spectrum in combination with compressed sensing. BACKGROUND

[0002] In recent years, as an advanced polarimetric spectral measurement technology, channel polarimetric spectral measurement technology can make snapshot, static and full Stokes parameter measurement on a target to be measured in a wide waveband, and is therefore widely applied in the fields of atmospheric aerosol characterization, target identification and remote sensing detection. The channel type polarimetric spectrometer system as a whole comprises a polarimetric spectral intensity modulation module (PSIM) composed of two multi-stage wave plates and a linear polarizer A, a spectrometer and a computer.

[0003] Most of the existing calibration technologies are based on modeling of the polarimetric spectral intensity modulation module, and in fact, sine and cosine signals are regarded as modulation coefficients of the intensity modulation module, so a linear polarized light with a specific azimuth angle of 22.5° is needed to calibrate the polarimetric spectral intensity modulation module. These precise angle conditions are all relative to the reference direction of the intensity modulation module. However, in addition to the fast and slow axis directions and phase factors of the multi-stage wave plates in the polarimetric spectral intensity modulation module which can significantly affect the measurement results, the polarization effects of other optical systems in the channel type polarimetric spectrometer whole system can also introduce measurement errors, resulting in a deviation of the real measured spectral power distribution.

[0004] Accurate reconstruction of Stokes spectral parameters is crucial in this snapshot technology. The traditional reconstruction method is based on Fourier transform. Specifically, the measured spectrum is subjected to Fourier transform to obtain an autocorrelation function, which is then cut by a window function and subjected to inverse Fourier transform. However, this method is sensitive to noise and channel crosstalk, and also limits the form of the physical model of the channel type polarimetric spectrometer whole system and the polarization calibration process. When discussing the influence of polarization effects on the system model, if other polarization effects are included, the physical model will no longer be limited to the form only modulated by sine and cosine functions as shown in the polarimetric spectral intensity modulation module, which makes the traditional Fourier transform and its inverse transform no longer applicable when reconstructing the spectrum. SUMMARY

[0005] The present application is to solve the above-mentioned problems of the prior art. The present application proposes a spectral reconstruction method based on whole system polarization calibration and data demodulation, so as to calibrate all possible polarization effects in the whole system, obtain more accurate polarization effects of the system, and thus obtain more accurate reconstruction results.

[0006] To achieve the above object, the present application provides the following technical solutions.

[0007] The spectral reconstruction method based on full-system polarization calibration and data demodulation has the characteristics of being applied to a channel type polarization spectrum full system, the calibration light source of the channel type polarization spectrometer full system is a wide-band light source, and the channel type polarization spectrometer full system comprises a multi-stage wave plate R1, a multi-stage wave plate R2 and a linear polarizer A, wherein the fast axis direction of the multi-stage wave plate R1 is 0 degrees relative to the horizontal direction, the fast axis direction of the multi-stage wave plate R2 is 45 degrees relative to the horizontal direction, and the transmission axis direction of the linear polarizer A is 0 degrees, and the spectral reconstruction method comprises the following steps.

[0008] Step 1, polarization calibration is performed on the channel type polarization spectrometer full system to obtain a Mueller matrix The first row element in the Mueller matrix is obtained, so that the modulation spectrum of the full system is obtained ;

[0009] Step 2, sparse dictionary is used to perform sparse representation on Stokes parameters, so as to obtain a sparse representation modulation spectrum , so as to construct a target equation together with . Wherein, represents the sparse coefficient corresponding to the four Stokes parameters;

[0010] Step 3, the target equation is solved to obtain the optimal sparse coefficient of the first Stokes parameter , so as to obtain the first optimal Stokes parameter by using formula (12) , for reconstructing the spectrum.

[0011] (12).

[0012] The spectral reconstruction method based on full-system polarization calibration and data demodulation has the characteristics that the step 1 comprises:

[0013] Step 1.2, a linear polarizer is added behind the calibration light source , and the transmission axis of the linear polarizer is rotated in turn in the 0-degree polarized light direction, the 45-degree polarized light direction and the 90-degree polarized light direction, so that the channel type polarization spectrometer full system is used for measurement to obtain the optical power spectrum distribution corresponding to three linear polarization states of the full system, and the optical power spectrum distribution is recorded as , , .

[0014] Step 1.3, online polarizer Add a wideband achromatic quarter-wave plate behind it ,make The transmission axis is at a 45-degree angle relative to the horizontal direction. With the fast axis at 0 degrees, the optical power spectrum distribution under a calibrated light source is obtained using the entire system of the channel-type polarization spectrometer, denoted as […]. ;

[0015] Step 1.4: Using equation (1), obtain the polarization transmittance of the entire system for the 0-degree polarized light direction, the 45-degree polarized light direction, the 90-degree polarized light direction, and the left-handed circularly polarized light direction. , , , ;

[0016] (1)

[0017] Step 1.5: Calculate the Mueller matrix of the entire channel-type polarization spectrometer system using equation (2). The first polarization response in the first row The second polarization response in the first row The third polarization response in the first row The fourth polarization response in the first row :

[0018] (2)

[0019] Step 1.6, let Any element other than the first row Line number The elements of a column are denoted as , , Then, the Mueller matrix is ​​obtained from equation (3). :

[0020] (3)

[0021] The modulation spectrum of the entire system is obtained using equation (4). :

[0022] (4)

[0023] In equation (4), , , , These are the four Stokes parameters of the input light.

[0024] Furthermore, step 2 includes:

[0025] Step 2.1, Construct a sparse dictionary :

[0026] Step 2.1.1: Obtain the discrete cosine transform basis using equation (5). The expression:

[0027] (5)

[0028] In equation (5), Represents the basis matrix of the discrete cosine transform The element in the m-th row and n-th column of the denominator, where m represents the row number of the discrete cosine transform basis and n represents the column number of the discrete cosine transform basis. This represents the number of sampling points;

[0029] Step 2.1.2: Obtain the Legendre polynomial using equation (6). The expression is used to obtain the nth Legendre polynomial vector composed of Legendre polynomials using equation (7). The expression;

[0030] (6)

[0031] (7)

[0032] In equations (6) and (7), n represents the index of the nth Legendre polynomial vector. , x represents the set of uniformly sampled points in the range (-1,1), and a is the number of cyclic summations in the Legendre polynomial; This represents the sampled value of the k-th uniform sampling point. Indicates the number of uniform sampling points;

[0033] Step 2.1.3: Obtain the sparse dictionary using equation (8). ;

[0034] (8)

[0035] Step 2.1.4, using equation (9) to process the first... Stokes parameters Perform sparse representation. :

[0036] (9)

[0037] In equation (9), Indicates the first The sparsity coefficients corresponding to each Stokes parameter;

[0038] Step 2.1.5, constructing the modulated spectrum by sparse representation of formula (10)

[0039] (10)

[0040] Step 2.2, constructing the target equation by formula (10)

[0041] (11)

[0042] In formula (11), denotes a regularization term, denotes sparse coefficients corresponding to 4 stokes parameters, denotes a regularization coefficient, denotes the spectrum received by the whole system in actual measurement.

[0043] The electronic device of the present application comprises a memory and a processor, and the memory is used to store a program supporting the processor to execute any of the spectrum reconstruction methods, and the processor is configured to execute the program stored in the memory.

[0044] The computer readable storage medium of the present application stores a computer program, and the computer program is executed by the processor to perform the steps of any of the spectrum reconstruction methods.

[0045] Compared with the prior art, the present application has the following advantages:

[0046] 1. The present application adopts full-system polarization calibration, which contains all possible polarization effects of the optical elements in the whole system of the channel-type polarization spectrometer, making the calibration model more accurate compared with the method of calibrating only the direction angle and phase factor of the polarization spectrum intensity modulation module.

[0047] 2. The present application adopts the sampling method of compressive sensing (CS), which reduces the encoding complexity by linear projection and simultaneous sampling and compression, and restores the original complete signal from a small amount of compressed signal through a series of processes such as constructing a sparse dictionary for sparse representation of stokes parameters, constructing a target equation and solving it. The advantage of this method is that it does not need to preset that the stokes parameter component must be modulated by a sine signal, and it can be adapted to the calibration model established by the full-system polarization calibration method in the present application, and the accurate reconstruction of the full stokes parameter spectrum is realized by solving the target equation. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 ​​The system flow chart of the channel type polarization spectrometer full system polarization calibration and data demodulation method is shown in the figure.

[0049] Figure 2 The calibration structure diagram of the channel type polarization spectrometer (CSP) full system is shown in the figure.

[0050] Figure 3 The real spectrum data of the LED light source is shown in the figure. The Stokes parameters of the LED light source are shown in the figure, wherein The spectral lines of the Stokes parameters are shown in the figure. The spectral lines of the Stokes parameters are substantially overlapped.

[0051] Figure 4 The spectral results reconstructed by the channel type polarization spectrometer full system polarization calibration and the compression sensing algorithm are shown in the figure. The reconstructed Stokes parameters are shown in the figure. DETAILED DESCRIPTION

[0052] In the embodiment, as shown in the figure, Figure 1 A spectrum reconstruction method based on full system polarization calibration and data demodulation includes the following steps:

[0053] Step 1, the polarization calibration of the channel type polarization spectrometer full system, the optical path required for the polarization calibration is shown in the figure. Figure 2

[0054] Step 1.1, using a wide-band light source as the calibration light source of the channel type polarization spectrometer system, and building the channel type polarization spectrometer system. The channel type polarization spectrometer includes: multi-stage wave plate R1, multi-stage wave plate R2, and linear polarizer A. The fast axis direction of R1 is 0 degrees relative to the horizontal direction, the fast axis direction of R2 is 45 degrees relative to the horizontal direction, and the transmission axis direction of A is 0 degrees.

[0055] Step 1.2, the calibration light source is a commercial wide-band light source, the wavelength range used in the calibration process is 400-700 nm, the light power spectrum distribution of the system under the illumination of the calibration light source is recorded by the channel type polarization spectrometer system, and is recorded as .

[0056] Step 1.3, in the full system polarization calibration process, a linear polarizer is added behind the calibration light source for the calibration process of the linear polarization effect, the transmission axis of the linear polarizer is rotated to 0 degrees, 45 degrees and 90 degrees in turn, and the channel type polarization spectrometer is used to record, respectively, to obtain the transmission power spectrum of the full system corresponding to the three linear polarization states, recorded as , , .

[0057] ​Step 1.4, the polarized transmittance of the channel-type polarized spectrometer system to 0 degree, 45 degree and 90 degree linearly polarized light is obtained according to formula (1) :

[0058] (1)

[0059] Step 1.5, the linear polarizer A broadband achromatic quarter-wave plate is added behind The optical elements are adjusted so that the transmission axis of the quarter-wave plate is 45 degrees relative to the horizontal direction, the fast axis of the linear polarizer is 0 degree, and the transmittance spectrum of the system under illumination of the standard light source is recorded as Thus, the polarized transmittance of the whole system to left-handed circularly polarized light is obtained from formula (2) .

[0060] (2)

[0061] Step 1.6, the polarized transmittance of the whole system to four kinds of polarized light under illumination of the same light source can be obtained by the above method of making a ratio. The optical path structure required for the above polarization calibration of the whole system is shown in Figure 2 The polarization effect of the system can be obtained by using the four kinds of polarized transmittance, i.e. the polarized response of the whole system of the channel-type polarized spectrometer is obtained by calculating the obtained 0 degree, 45 degree, 90 degree and left-handed circularly polarized transmittance according to formula (3) :

[0062] (3)

[0063] In formula (3), is the Mueller matrix created by the polarization calibration of the whole system, represents the elements of the Mueller matrix except the first row.

[0064] Step 1.7, the Stokes parameters of the input light of the whole system are as follows: wherein, represents the wavelength of light; the output of the input light after passing through the optical system can be expressed as formula (5):

[0065] (5)

[0066] Since the CCD records the light intensity information in work, i.e. only the first row of the optical system output , the can not be additionally calibrated.

[0067] ​​Step 1.8: The modulation spectrum of the entire system can be represented by equation (6):

[0068] (6)

[0069] In equation (4), , , , These are the four Stokes vectors of the input light.

[0070] Step 2: Use a sparse dictionary to sparsely represent the Stokes parameters and construct the objective equation:

[0071] Step 2.1: Construct a sparse dictionary The sparse dictionary consists of discrete cosine transform basis and Legendre polynomial vectors;

[0072] Step 2.2: Construct the discrete cosine transform basis. The expression for is shown in equation (7):

[0073] (7)

[0074] In equation (7), Let m represent any element in the discrete cosine transform basis matrix, where m represents the m-th row of the discrete cosine transform basis and n represents the n-th column of the discrete cosine transform basis. This represents the number of sampling points.

[0075] Step 2.3: Construct the Legendre polynomial The expression is shown in equation (8):

[0076] (8)

[0077] Construct the first polynomial consisting of Legendre polynomials Legendre polynomial vectors The expression for is shown in equation (9);

[0078] (9)

[0079] In equations (8) and (9), Uniform sampling is performed in (-1,1). Let represent the specific value of the k-th sampling point of the uniform sampling number on (-1,1), and a be the number of cyclic summations in the Legendre polynomial. This refers to the number of samples. Indicates the first Legendre polynomial vectors The index of the vector. .

[0080] Step 2.4, Construction Sparse dictionary The expression of the sparse dictionary is formula (10);

[0081] (10)

[0082] Step 2.5, sparse representation of the Stokes parameters , using formula (11);

[0083] (11)

[0084] In formula (11), represents the sparse coefficients of the Stokes parameters.

[0085] Step 2.6, substituting the sparse representation of the Stokes parameters into formula (6) to construct the sparse representation of the modulation spectrum :

[0086] (12)

[0087] Step 2.7, construction of the objective equation :

[0088] (13)

[0089] In formula (13), represents the regularization term, represents the sparse coefficients of the 4 Stokes parameters, represents the regularization coefficient, represents the spectrum received by the whole system in actual measurement.

[0090] Step 3, optimization solution of the objective equation The purpose of solving formula (13) is to obtain the optimal sparse coefficient of the i-th Stokes parameter by continuously optimizing the sparse coefficient , and to obtain the i-th reconstructed Stokes parameter , by using formula (14), which is used to reconstruct the spectrum.

[0091] (14)

[0092] In this embodiment, the spectral line diagram of the spectrum is as shown in Figure 3 and Figure 4 . Figure 3 is the true spectrum of the LED spectrum, wherein the spectral lines coincide;Figure 4 After the whole system polarization calibration of the above-mentioned channel type polarization spectrometer, the spectral results reconstructed by the compressed sensing algorithm are compared, and it can be seen that the spectral reconstruction method of the whole system polarization calibration and data demodulation proposed in this embodiment has good reconstruction effect.

[0093] In this embodiment, an electronic device includes a memory for storing a program supporting a processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0094] In this embodiment, a computer readable storage medium has a computer program stored thereon, and the computer program is run by a processor to execute the steps of the above method.

Claims

1. A spectral reconstruction method based on whole-system polarization calibration and data demodulation, characterized in that, This method is applied to a complete channel-type polarization spectroscopy system. The calibration light source of the complete channel-type polarization spectrometer system is a broadband light source. The complete channel-type polarization spectrometer system includes: multi-level waveplates R1 and R2, and a linear polarizer A. The fast axis of the multi-level waveplate R1 is 0 degrees relative to the horizontal direction, the fast axis of the multi-level waveplate R2 is 45 degrees relative to the horizontal direction, and the transmission axis of the linear polarizer A is 0 degrees. The spectral reconstruction method includes the following steps: Step 1: Perform polarization calibration on the entire channel-type polarization spectrometer system to obtain the Mueller matrix. The first row of elements is used to obtain the modulation spectrum of the entire system. ; Step 1.1: Add a linear polarizer behind the calibration light source. The linear polarizer is rotated sequentially according to the 0-degree polarization direction, the 45-degree polarization direction, and the 90-degree polarization direction. The transmission axis is determined, and the entire system of the channel-type polarization spectrometer is measured to obtain the optical power spectrum distribution corresponding to the three linear polarization states of the entire system, which are denoted as follows: , , ; Step 1.2, online polarizer Add a wideband achromatic quarter-wave plate behind it ,make The transmission axis is at a 45-degree angle relative to the horizontal direction. With the fast axis at 0 degrees, the optical power spectrum distribution under a calibrated light source is obtained using the entire system of the channel-type polarization spectrometer, denoted as […]. ; Step 1.3: Using equation (1), obtain the polarization transmittance of the entire system for the 0-degree polarized light direction, the 45-degree polarized light direction, the 90-degree polarized light direction, and the left-handed circularly polarized light direction. , , , ; (1) Step 1.4: Calculate the Mueller matrix of the entire channel-type polarization spectrometer system using equation (2). The first polarization response in the first row The second polarization response in the first row The third polarization response in the first row The fourth polarization response in the first row : (2) Step 1.5, let Any element other than the first row Line number The elements of a column are denoted as , , Then, the Mueller matrix is ​​obtained from equation (3). : (3) Step 1.6: Use equation (4) to obtain the modulation spectrum of the entire system. : (4) In equation (4), , , , These are the four Stokes parameters of the input light; Step 2, using a sparse dictionary Sparse representation of the Stokes parameters is used to obtain the sparsely represented modulation spectrum. Thus with Jointly construct the objective equation ,in, This represents the sparsity coefficients corresponding to the four Stokes parameters; Step 3, for the objective equation Solving for the first... Optimal sparsity coefficients for each Stokes parameter Thus, the first equation can be obtained using equation (12). Optimal Stokes parameters , Used to reconstruct the spectrum; (12)。 2. The spectral reconstruction method based on whole-system polarization calibration and data demodulation according to claim 1, characterized in that, Step 2 includes: Step 2.1, Construct a sparse dictionary : Step 2.1.1: Obtain the discrete cosine transform basis using equation (5). The expression: (5) In equation (5), Represents the basis matrix of the discrete cosine transform The element in the m-th row and n-th column of the denominator, where m represents the row number of the discrete cosine transform basis and n represents the column number of the discrete cosine transform basis. This represents the number of sampling points; Step 2.1.2: Obtain the Legendre polynomial using equation (6). The expression is used to obtain the nth Legendre polynomial vector composed of Legendre polynomials using equation (7). The expression; (6) (7) In equations (6) and (7), n represents the index of the nth Legendre polynomial vector. , x represents the set of uniformly sampled points in the range (-1,1), and a is the number of cyclic summations in the Legendre polynomial; This represents the sampled value of the k-th uniform sampling point. Indicates the number of uniform sampling points; Step 2.1.3: Obtain the sparse dictionary using equation (8). ; (8) Step 2.1.4, using equation (9) to process the first... Stokes parameters Perform sparse representation. : (9) In equation (9), Indicates the first The sparsity coefficients corresponding to each Stokes parameter; Step 2.1.5: Constructing formula (10) yields the modulation spectrum after sparse representation. ; (10) Step 2.2, construct the objective equation using equation (10). : (11) In equation (11), Represents the regularization term, This represents the sparsity coefficients corresponding to the four Stokes parameters. Represents the regularization coefficient. This represents the spectrum received by the entire system during actual measurements.

3. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing any of the spectral reconstruction methods of claims 1-2, and the processor is configured to execute the program stored in the memory.

4. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of any of the spectral reconstruction methods described in claims 1-2.

Images