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

Abstract

The invention discloses a spectrum reconstruction method based on full-system polarization calibration and data demodulation. The method comprises the following steps: 1, carrying out polarization calibration on a full system of a channel type polarization spectrometer to be calibrated by utilizing a broadband light source, a calibration line polaroid and a calibration broadband achromatic quarter-wave plate; 2, measuring spectral power distribution by the whole system of the calibrated channel type polarization spectrometer, and calculating to obtain a polarization effect of the system so as to create a Mueller matrix; 3, performing sparse representation on the Stokes parameters by using the sparse dictionary, and constructing a target equation; and 4, solving the target equation by using a least square method to complete spectrum reconstruction. A traditional channel type polarization spectrum calibration method is improved, polarization calibration is carried out on the whole system, the polarization effect of the system can be obtained more accurately, and therefore a more accurate reconstruction result is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of optical device calibration, and in particular to a polarization effect calibration method for a channel-type polarization spectrometer system, and a method for reconstructing a measured spectrum in combination with compressed sensing. Background Art

[0002] In recent years, channel polarization spectroscopy measurement technology, as an advanced polarization spectroscopy measurement technology, can perform snapshot, static, full-Stokes parameter measurements on the target in a wide band, and is therefore widely used in atmospheric aerosol characterization, target identification, and remote sensing detection. The channel polarization spectrometer system as a whole includes: a polarization spectral intensity modulation module (PSIM) consisting 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 the modeling of polarization intensity modulation modules. In fact, the sine and cosine signals are regarded as the modulation coefficients of the intensity modulation module. Therefore, it is necessary to use linear polarized light with a specific azimuth angle of 22.5° to calibrate the polarization spectrum intensity modulation module. These precise angle conditions are 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-level wave plates in the polarization spectrum intensity modulation module, which will significantly affect the measurement results, the polarization effects of other optical systems in the channel-type polarization spectrometer system will also introduce measurement errors, resulting in deviations in the actual measured spectral power distribution.

[0004] The accurate reconstruction of Stokes spectrum parameters is crucial in this snapshot technology, and the traditional reconstruction method is based on Fourier transform. The specific method is to perform Fourier transform on the measured spectrum to obtain the autocorrelation function, which is intercepted by the window function and then inverse Fourier transform is performed. However, in addition to being very sensitive to noise and channel crosstalk, this method also limits the form of the physical model of the entire system of the channel-type polarization spectrometer and the polarization calibration process. When discussing the impact of polarization effects on the system model, if other polarization effects are included, the physical model will no longer be limited to the form of modulation only by sine and cosine functions shown by the polarization spectrum intensity modulation module, which makes the traditional Fourier transform and its inverse transform no longer applicable when reconstructing the spectrum. Summary of the invention

[0005] The present invention aims to solve the deficiencies of the above-mentioned prior art. The present invention proposes a spectral reconstruction method based on full-system polarization calibration and data demodulation, in order to perform polarization calibration on all polarization effects that may exist in the whole system, so as to more accurately obtain the polarization effect of the system, thereby obtaining a more accurate reconstruction result.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The spectrum reconstruction method based on full-system polarization calibration and data demodulation of the present invention is characterized in that it is 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. The spectrum reconstruction method comprises the following steps:

[0008] Step 1: perform polarization calibration on the entire channel polarization spectrometer system to obtain the Mueller matrix The first row of elements in the system can be used to obtain the modulation spectrum of the whole system. ;

[0009] Step 2: Using sparse dictionary The Stokes parameters are sparsely represented to obtain the modulation spectrum of the sparse representation , thus with Jointly construct the target equation ,in, Represents the sparse coefficients corresponding to the four Stokes parameters;

[0010] Step 3: For the target equation Solve and get The optimal sparse coefficients of Stokes parameters , and then use formula (12) to get the Optimal Stokes parameters , , used to reconstruct the spectrum.

[0011] (12).

[0012] The spectral reconstruction method based on full system polarization calibration and data demodulation described in the present invention is also characterized in that step 1 comprises:

[0013] Step 1.2: Add a linear polarizer behind the calibration light source , and rotate the linear polarizer in the direction of 0 degree polarization, 45 degree polarization, and 90 degree polarization in sequence The transmission axis of the channel-type polarization spectrometer is used to measure the optical power spectrum distribution of the whole system corresponding to the three linear polarization states, which is recorded as , , ;

[0014] Step 1.3, Online Polarizer A wideband achromatic quarter wave plate is added behind ,make The transmission axis is 45 degrees relative to the horizontal direction. The fast axis is 0 degrees, so the optical power spectrum distribution under the calibration light source is obtained by using the channel type polarization spectrometer system, which is recorded as ;

[0015] Step 1.4, use formula (1) to obtain the polarization transmittance of the whole system for 0 degree polarization direction, 45 degree polarization direction, 90 degree polarization direction and left circular polarization direction , , , ;

[0016] (1)

[0017] Step 1.5, calculate the Mueller matrix of the whole system of the channel type polarization spectrometer by formula (2): The first polarization response of the first row in , the second polarization response of the first row , the third polarization response of the first row , the fourth polarization response of the first row :

[0018] (2)

[0019] Step 1.6, let Any element except the first row Line The elements of the column are recorded as , , , then the Mueller matrix is ​​obtained from formula (3): :

[0020] (3)

[0021] Using formula (4) we can get the modulation spectrum of the whole system: :

[0022] (4)

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

[0024] Furthermore, the step 2 comprises:

[0025] Step 2.1, build a sparse dictionary :

[0026] Step 2.1.1: Use equation (5) to get the discrete cosine transform basis The expression is:

[0027] (5)

[0028] In formula (5), Represents the discrete cosine transform basis matrix The mth row and nth column element in , m represents the row number of the discrete cosine transform basis, n represents the column number of the discrete cosine transform basis, is the number of sampling points;

[0029] Step 2.1.2: Use equation (6) to obtain the Legendre polynomial The expression of , using equation (7) to obtain the nth Legendre polynomial vector composed of Legendre polynomials Expression of

[0030] (6)

[0031] (7)

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

[0033] Step 2.1.3: Use formula (8) to get the sparse dictionary ;

[0034] (8)

[0035] Step 2.1.4: Use formula (9) to calculate Stokes parameters For sparse representation, :

[0036] (9)

[0037] In formula (9), Indicates The sparse coefficients corresponding to the Stokes parameters;

[0038] Step 2.1.5: Construct equation (10) to obtain the modulation spectrum after sparse representation ;

[0039] (10)

[0040] Step 2.2: Use equation (10) to construct the target equation :

[0041] (11)

[0042] In formula (11), represents the regularization term, Represents the sparse coefficients corresponding to the four Stokes parameters, represents the regularization coefficient, Represents the spectrum received by the entire system in actual measurement.

[0043] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute any of the spectral reconstruction methods, and the processor is configured to execute the program stored in the memory.

[0044] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes any step of the spectrum reconstruction method when executed by a processor.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. The present invention adopts full-system polarization calibration. Compared with the method of only performing directional angle, phase factor and other calibration on the polarization spectrum intensity modulation module, the full-system polarization calibration includes all possible polarization effects of the optical components of each part of the channel-type polarization spectrometer system, making the calibration model more accurate.

[0047] 2. The present invention adopts the sampling method of Compressive Sensing (CS), reduces the coding complexity by sampling and compressing simultaneously through linear projection, sparsely represents the Stokes parameters by constructing a sparse dictionary, constructs the target equation and solves it, and a series of processes, and the original complete signal can be restored with a small amount of compressed signal. The advantage of this method is that it does not need to preset that the Stokes parameter components must be modulated by sine and cosine signals, and can be adapted to the calibration model established by the full system polarization calibration method in the present invention, and by solving the target equation, the accurate reconstruction of the full Stokes parameters of the spectrum is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1It is a system flow chart of the polarization calibration and data demodulation method of the whole system of the channel type polarization spectrometer of the present invention.

[0049] Figure 2 It is a calibration structure diagram of the whole system of the channel type polarization spectrometer (CSP) of the present invention.

[0050] Figure 3 is the real spectrum data of LED light source, represents the Stokes parameter of the LED light source, where The spectrum and The spectral lines basically overlap.

[0051] Figure 4 After the full system polarization calibration of the channel-type polarization spectrometer, the spectrum results reconstructed by the compressed sensing algorithm are: represents the reconstructed Stokes parameters. DETAILED DESCRIPTION

[0052] In this implementation example, Figure 1 As shown, a spectrum reconstruction method based on full system polarization calibration and data demodulation includes the following steps:

[0053] Step 1: perform polarization calibration on the entire channel type polarization spectrometer system. The optical path required for polarization calibration is shown in the figure below: Figure 2 As shown:

[0054] Step 1.1, use a wide-band light source as the calibration light source of the channel-type polarization spectrometer system, and build 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 broadband light source. The wavelength range used in the calibration process is 400-700 nm. The channel-type polarization spectrometer system performs the initial measurement and records the optical power spectrum distribution of the system under the illumination of the calibration light source, which is recorded as .

[0056] Step 1.3: During the full system polarization calibration process, the calibration process for the linear polarization effect requires adding a linear polarizer after the calibration light source. , the transmission axis of the rotating linear polarizer is set to 0, 45, and 90 degrees in turn, and the transmission power spectra of the whole system corresponding to the three linear polarization states are recorded respectively by a channel-type polarization spectrometer, and recorded as , , .

[0057] Step 1.4: According to formula (1), the polarization transmittance of the channel-type polarization spectrometer system for three linear polarization states of light at 0 degrees, 45 degrees, and 90 degrees is obtained: :

[0058] (1)

[0059] Step 1.5: In-line polarizer A wideband achromatic quarter wave plate is added at the rear , adjust the optical components so that The transmission axis is 45 degrees relative to the horizontal direction. The fast axis is 0 degrees, and the transmission power spectrum of the system under the illumination of the calibration light source is recorded as , and thus the polarization transmittance of the whole system for left-handed circularly polarized light is obtained from formula (2): .

[0060] (2)

[0061] Step 1.6: By using the ratio method mentioned above, the polarization transmittance of the whole system to four polarized lights under the same light source can be obtained. The optical path structure required to achieve the above-mentioned full system polarization calibration is as follows: Figure 2 As shown in the figure, the polarization effect of the system can be obtained by using the four polarization transmittances, that is, the transmittances of the four polarization states of 0 degree, 45 degree, 90 degree and left-handed circular polarization are calculated by formula (3) to obtain the polarization response of the whole system of the channel type polarization spectrometer. :

[0062] (3)

[0063] In formula (3), The Mueller matrix created for the full system polarization effect using polarization calibration, represents the Mueller matrix All elements except the first row.

[0064] Step 1.7: Let the Stokes parameter of the input light of the whole system be: ,in, represents the wavelength of light; then the output of the Stokes parameter of the input light after passing through the optical system can be expressed as formula (5):

[0065] (5)

[0066] Since CCD records light intensity information during operation, it only records the output of the optical system. The first line of No additional calibration work is required.

[0067] Step 1.8: The modulation spectrum of the whole system can be expressed by equation (6):

[0068] (6)

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

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

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

[0072] Step 2.2: Construct discrete cosine transform basis The expression of is shown in formula (7):

[0073] (7)

[0074] In formula (7), represents any element in the discrete cosine transform basis matrix, m represents the mth row of the discrete cosine transform basis, n represents the nth column of the discrete cosine transform basis, is the number of sampling points.

[0075] Step 2.3: Construct Legendre polynomials The expression of is shown in formula (8):

[0076] (8)

[0077] Construct the first Legendre polynomial vector The expression of is shown in formula (9);

[0078] (9)

[0079] In formula (8) and formula (9), It is uniformly sampled at (-1,1). represents the specific value of the kth sampling point of the uniform sampling number on (-1,1), a is the number of cyclic additions in the Legendre polynomial, is the number of samples; Indicates A vector of Legendre polynomials, is the sequence number of the vector, .

[0080] Step 2.4: Build Sparse dictionary The expression of is formula (10);

[0081] (10)

[0082] Step 2.5: Use formula (11) to calculate the Stokes parameter , Perform sparse representation;

[0083] (11)

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

[0085] Step 2.6: Stokes parameters to be sparsely represented Substituting into equation (6), we can construct the sparsely represented modulation spectrum: :

[0086] (12)

[0087] Step 2.7: Construct the target equation :

[0088] (13)

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

[0090] Step 3: For the target equation The purpose of solving equation (13) is to continuously optimize the sparse coefficient , get the optimal sparse coefficient of the i-th Stokes parameter , using formula (14) to obtain the i-th reconstructed Stokes parameter , , used to reconstruct the spectrum.

[0091] (14)

[0092] In this embodiment, the spectrum line diagram of the spectrum is as follows Figure 3 and Figure 4 shown. Figure 3 is the real spectrum of LED spectrum, where The spectral lines overlap; Figure 4 This is the spectrum result reconstructed by the compressed sensing algorithm after the full-system polarization calibration of the channel-type polarization spectrometer. By comparison, it can be seen that the spectrum reconstruction method of full-system polarization calibration and data demodulation proposed in this embodiment has a good reconstruction effect.

[0093] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the 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 stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A spectrum reconstruction method based on full system polarization calibration and data demodulation, characterized in that: The invention is applied to a channel-type polarization spectrum system, wherein the calibration light source of the channel-type polarization spectrometer system is a wide-band light source, and the channel-type polarization spectrometer 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. The spectrum reconstruction method comprises the following steps: Step 1: perform polarization calibration on the entire channel polarization spectrometer system to obtain the Mueller matrix The first row of elements in the system can be used to obtain the modulation spectrum of the whole system. ; Step 2: Using sparse dictionary The Stokes parameters are sparsely represented to obtain the modulation spectrum of the sparse representation , thus with Jointly construct the target equation ,in, Represents the sparse coefficients corresponding to the four Stokes parameters; Step 3: For the target equation Solve and get The optimal sparse coefficients of Stokes parameters , and then use formula (12) to get the Optimal Stokes parameters , , used to reconstruct the spectrum; (12)。 2. The spectrum reconstruction method based on full system polarization calibration and data demodulation according to claim 1, characterized in that: The step 1 comprises: Step 1.2: Add a linear polarizer behind the calibration light source , and rotate the linear polarizer in the direction of 0 degree polarization, 45 degree polarization, and 90 degree polarization in sequence The transmission axis of the channel-type polarization spectrometer is used to measure the optical power spectrum distribution of the whole system corresponding to the three linear polarization states, which is recorded as , , ; Step 1.3, Online Polarizer A broadband achromatic quarter wave plate is added behind ,make The transmission axis is 45 degrees relative to the horizontal direction. The fast axis is 0 degrees, so the optical power spectrum distribution under the calibration light source is obtained by using the channel type polarization spectrometer system, which is recorded as ; Step 1.4, use formula (1) to obtain the polarization transmittance of the whole system for 0 degree polarization direction, 45 degree polarization direction, 90 degree polarization direction and left circular polarization direction , , , ; (1) Step 1.5, calculate the Mueller matrix of the whole system of the channel type polarization spectrometer by formula (2): The first polarization response of the first row in , the second polarization response of the first row , the third polarization response of the first row , the fourth polarization response of the first row : (2) Step 1.6, let Any element except the first row Line The elements of the column are recorded as , , , then the Mueller matrix is ​​obtained from formula (3): : (3) Using formula (4) we can get the modulation spectrum of the whole system: : (4) In formula (4), , , , are the four Stokes parameters of the input light.

3. The spectrum reconstruction method based on full system polarization calibration and data demodulation according to claim 2, characterized in that: The step 2 comprises: Step 2.1, build a sparse dictionary : Step 2.1.1: Use equation (5) to get the discrete cosine transform basis The expression is: (5) In formula (5), Represents the discrete cosine transform basis matrix The mth row and nth column element in , m represents the row number of the discrete cosine transform basis, n represents the column number of the discrete cosine transform basis, is the number of sampling points; Step 2.1.2: Use equation (6) to obtain the Legendre polynomial The expression of , using equation (7) to obtain the nth Legendre polynomial vector composed of Legendre polynomials Expression of (6) (7) In equations (6) and (7), n represents the serial number of the nth Legendre polynomial vector. , x represents a set of uniformly sampled points in the range (-1,1), and a is the number of cyclic additions in the Legendre polynomial; represents the sampling value of the kth uniform sampling point, represents the number of uniform sampling points; Step 2.1.3: Use formula (8) to get the sparse dictionary ; (8) Step 2.1.4: Use formula (9) to calculate Stokes parameters For sparse representation, : (9) In formula (9), Indicates The sparse coefficients corresponding to the Stokes parameters; Step 2.1.5: Construct equation (10) to obtain the modulation spectrum after sparse representation ; (10) Step 2.2: Use equation (10) to construct the target equation : (11) In formula (11), represents the regularization term, Represents the sparse coefficients corresponding to the four Stokes parameters, represents the regularization coefficient, Represents the spectrum received by the entire system in actual measurement.

4. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports a processor to execute the spectrum reconstruction method according to any one of claims 1 to 3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the spectrum reconstruction method according to any one of claims 1 to 3 are executed.

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