Spectroscopic polarization measurement system and method

Abstract

The present application provides a kind of spectral polarization measurement system and method, including spectrometer, first polarizer and second polarizer are placed before spectrometer, the light to be measured sequentially after rotating first polarizer and second polarizer enters spectrometer, signal is exported from spectrometer, after arranging series data, Fourier series is obtained using Powell algorithm, batch gradient descent algorithm, and linear polarization state of the light to be measured is obtained according to the corresponding formula of Fourier series and stokes parameter.The present application provides a kind of spectral polarization measurement system and method to obtain high-precision spectral polarization information measurement system on wide spectral range, in the field of spectral and polarization state of measurement beam, polarization characteristics of optical element on spectrum, absorption and polarization characteristics of biological sample on spectrum, etc.

Description

Technical Field

[0001] This invention relates to linear polarization measurement technology, and more particularly to a spectral polarization measurement system and method. Background Technology

[0002] In the field of aerospace optical remote sensing, polarization and spectroscopy are optical properties that require attention due to the wealth of information they carry. For polarization information, a common approach is a time-division polarization measurement system, such as one that mounts three polarizers on a rotating disk. However, the accuracy of this system is significantly affected by the positioning accuracy of the polarizer's transmission axis and by the stability of the detector and light source, making high-precision measurements difficult. Another approach is an amplitude-division polarization measurement system using a Wollaston prism to separate p- and s-beams. This system forms two identical optical paths after the Wollaston prism splits the light, resulting in a complex system composition and a measurement accuracy highly dependent on the direction of the Wollaston prism's transmission axis, leading to high cost and difficult assembly. A focal plane polarization measurement system using a new type of detector is also an option, but due to manufacturing limitations, the focal plane cannot achieve a high extinction ratio, resulting in large measurement errors. Finally, a full Stokes parametric measurement system using a rotating waveplate is another option. While this system uses a waveplate, it provides accurate phase delay over a very narrow spectral range but exhibits significant errors over a wide spectral range, making it impossible to obtain polarization information across a broad spectrum in a single measurement.

[0003] Therefore, how to achieve simultaneous measurement of spectral and polarization information and improve measurement accuracy and spectral range is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] The first objective of this invention is to provide a spectral polarization measurement method that addresses the problems in the prior art, such as the significant impact of polarization sensitivity on measurement accuracy in grating spectrometers, stability errors in spectrometer detectors, and extinction ratio errors in polarization elements.

[0005] Therefore, the above-mentioned objectives of the present invention are achieved through the following technical solutions:

[0006] A method for measuring the polarization state of light in a spectral polarization measurement system includes the following steps:

[0007] Step one: The light being measured passes through the first polarizer and the second polarizer before entering the spectrometer. The first polarizer is driven to rotate continuously. The modulation of the incident light is described using the Stokes vector and the Mueller matrix as follows:

[0008]

[0009] Where S in Let be the Stokes vector of the incident light, and s0 to s2 be the components of the Stokes vector of the incident light; S outM1(β) is the Stokes vector at the point of arrival at the detector; M2 is the Mueller matrix of the first polarizer; M3 is the Mueller matrix of the second polarizer; and M4 is the Mueller matrix of the grating spectrometer's own polarization. 11 ~m 33 is its matrix element; β is the polarization azimuth angle of the first polarizer (1), and τ is the extinction ratio of the polarizer;

[0010] Step two: By continuously rotating the first polarizer and sampling multiple times at equal intervals, the output values ​​of the spectrometer are assembled into a series of data I = {I1, I2, I3, ..., I...} N Establish the polarization state of the incident beam (S0, S1, S2). T and a n b n The relationship between the Fourier series of the signal and the Stokes parameters of the beam is obtained by performing Fourier analysis on the series of data using the Powell algorithm and the batch gradient descent algorithm to obtain a0, a2, a4, b2, b4.

[0011] I=a0+a2cos(2β)+a4cos(4β)+b2sin(2β)+b4sin(4β)

[0012] in:

[0013]

[0014]

[0015]

[0016]

[0017] Where a0, a2, a4, b2, and b4 are Fourier series of orders 0, 2, and 4, respectively;

[0018] Step 3: Calculate the Stokes parameter of the incident light using the following formula to obtain the polarization state:

[0019]

[0020]

[0021]

[0022] Step 4: Obtain all polarization information of the incident light by using the polarization angle Ψ and the degree of linear polarization DoLP.

[0023]

[0024]

[0025] The second objective of this invention is to provide a spectral polarization measurement system to address the shortcomings of existing technologies.

[0026] Therefore, the above-mentioned objectives of the present invention are achieved through the following technical solutions:

[0027] A spectral polarization measurement system is characterized by comprising a spectrometer, a first polarizer and a second polarizer placed in front of the spectrometer, the light to be measured sequentially passing through the first polarizer and the second polarizer before entering the spectrometer, the spectrometer outputting a signal, and after processing a series of data, using the Powell algorithm and the batch gradient descent algorithm to obtain a Fourier series, and obtaining the linear polarization state of the light to be measured according to the corresponding formula of the Fourier series and the Stokes parameter.

[0028] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:

[0029] As a preferred technical solution of the present invention: the first polarizer and the second polarizer are broadband linear grating polarizers with an extinction ratio greater than 1000:1 in the 450-2400nm band; the direction of the transmission axis of the second polarizer is fixed and fixed at the angle when the spectrometer output is at its maximum; the first polarizer, which is away from the spectrometer, can rotate 360° around the optical axis of the system.

[0030] As a preferred technical solution of the present invention: the first polarizer is installed on an electrically controlled turntable, and continuous rotation is achieved by the electrically controlled turntable.

[0031] As a preferred technical solution of the present invention: the spectrometer is a grating spectrometer, covering the 450-2400nm band, with a spectral resolution of 3nm in the 450-1000nm band, 8nm in the 1500nm band, and 6nm in the 2100nm band.

[0032] This invention provides a spectral polarization measurement system and method. Based on the verification that a grating spectrometer has high polarization sensitivity, a broadband linear grating polarizer with a fixed angle is used as the second polarizer to suppress its polarization sensitivity, thus improving measurement accuracy. Combined with a time-division polarization measurement technique using a rotating first polarizer, multiple measurements are taken at different points during a single rotation, independent of the polarizer's transmission axis direction. Simultaneously, multi-point measurements reduce the impact of detector and light source stability errors on the measurement. With the aid of a matching control program and Fourier analysis data processing algorithm, simultaneous measurement of spectral and polarization information is achieved in the 450–2400 nm spectral range. The advantages of this invention are its wide applicability to a wide spectral range, high spectral resolution, high precision, and simple structure that is easy to assemble and adjust. The spectral polarization measurement system provided by this invention is a high-precision spectral polarization information measurement system that acquires information over a wide spectral range (450–2400 nm). It has broad application prospects in measuring the spectrum and polarization state of light beams, the polarization characteristics of optical elements in the spectrum, and the absorption and polarization characteristics of biological samples in the spectrum. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of a spectral polarization measurement system provided by the present invention;

[0034] In the attached diagram, 1 is the first polarizer; 2 is the second polarizer; and 3 is the spectrometer.

[0035] Figure 2 A schematic diagram of the optical path for using a spectral polarization measurement system provided by the present invention to measure the polarization characteristics of a depolarizer in a wide-swath hyperspectral greenhouse gas monitor;

[0036] In the attached diagram, 4 represents the spectral polarization analysis section; 5 represents the integrating sphere; 6 represents the third polarizer; 7 represents the polarization source section; and 8 represents the depolarizer.

[0037] Figure 3 This is a diagram illustrating the distribution of the degree of linear polarization of fully linearly polarized light in the spectrum, obtained by measuring the spectral polarization degree of a spectral polarization measurement system and method provided by the present invention. Detailed Implementation

[0038] The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

[0039] like Figure 1 As shown, a spectral polarization measurement system of the present invention includes two polarizers and a spectrometer. Two polarizers, namely a first polarizer 1 and a second polarizer 2, are placed in front of the spectrometer 3. The light to be measured sequentially passes through the rotated first polarizer 1 and second polarizer 2 before entering the spectrometer. The spectrometer 3 outputs a signal, and after data processing to organize the series of data, a Fourier series is obtained using the Powell algorithm and batch gradient descent algorithm. The linear polarization state of the light to be measured is obtained according to the corresponding formula between the Fourier series and the Stokes parameter.

[0040] The first polarizer 1 and the second polarizer 2 are broadband linear grating polarizers with an extinction ratio greater than 1000 in the 450-2400nm band; the second polarizer 2, which is closer to the spectrometer 3, is fixed; the first polarizer 1, which is farther away from the spectrometer 3, can rotate 360° around the optical axis of the system.

[0041] Spectrometer 3 is a grating spectrometer covering the 450–2400 nm band, with spectral resolutions of 3 nm in the 450–1000 nm band, 8 nm in the 1500 nm band, and 6 nm in the 2100 nm band.

[0042] Grating spectrometers, through grating dispersion, can acquire spectral information in the 450–2400 nm wavelength range with spectral resolutions of 3 nm@450–1000 nm, 8 nm@1500 nm, and 6 nm@2100 nm. Their structure uses a cross-type CT structure, comprising two mirrors and a grating. Gratings generally possess high polarization sensitivity, meaning they have different diffraction efficiencies for light with different polarization directions, as do mirrors; therefore, grating spectrometers inherently possess a certain polarization sensitivity. Polarization sensitivity is defined as follows: when a beam of completely linearly polarized light is incident on an optical system, during a 180-degree rotation of the polarization direction of the incident linearly polarized light, let the maximum and minimum values ​​of the emitted light intensity be I0 and I1, respectively. max and I min The mathematical expression for linear polarization sensitivity is: Measurements showed that the polarization sensitivity of the grating spectrometer varied with wavelength, exceeding 20% ​​at its maximum. Because of its polarization sensitivity and the difficulty in obtaining its Mueller matrix, directly measuring the beam using it would introduce significant errors, contradicting the original intent of this invention.

[0043] To eliminate the adverse effects of the polarization sensitivity of the grating spectrometer on measurement accuracy, a second polarizer 2 is introduced, with its transmission axis fixed. This ensures that light of any polarization direction, when passing through the second polarizer 2 and entering the spectrometer 3, maintains the same polarization direction, unaffected by the polarization sensitivity of the grating spectrometer. The first polarizer 1 is driven to rotate one revolution by a precision electronically controlled turntable, thus modulating the intensity of the incident beam.

[0044] The light first passes through the first polarizer 1, then the second polarizer 2, and finally enters the spectrometer 3. After modulation and dispersion by the spectrometer, its polarization state can be calculated from the system's Mueller matrix:

[0045]

[0046]

[0047] Where S in S is the Stokes vector of the incident light, and s0 to s2 are its components; outM1(β) is the Stokes vector when the light reaches the detector; M2 is the Mueller matrix of the first polarizer 1; M3 is the Mueller matrix of the second polarizer 2; and M4 is the Mueller matrix of the self-polarization of the grating spectrometer 3. 11 ~m 33 Let be the matrix element; β be the polarization azimuth angle of the first polarizer, and τ be the extinction ratio of the polarizer. The detector is only sensitive to light intensity, and the extinction ratio of the selected polarizer is greater than 1000. Treating it as an ideal polarizer, the detection equation of the measurement system is:

[0048]

[0049] Because the polarization characteristics of the spectrometer itself are a fixed gain parameter in the detection equation of the measurement system, the detection equation can be rewritten as follows:

[0050]

[0051] It can be seen that it is a periodic function of β, and can be expressed in the form of a Fourier series:

[0052] I=a0+a2cos(2β)+a4cos(4β)+b2sin(2β)+b4sin(4β)

[0053] This establishes the polarization state of the incident beam (s0(λ), s1(λ), ​​s2(λ)). T and a n b n Based on this relationship, Fourier analysis can be performed on the series of data output by the system to deduce the Stokes vector.

[0054] In reality, across a wide spectral range, the extinction ratio of a polarizer can only reach 1000:1 or higher; treating it as an ideal polarizer would introduce errors. To improve accuracy, the polarizer's extinction ratio is taken into account during data processing. The Mueller matrix of the system after considering the extinction ratio is as follows:

[0055]

[0056] The light intensity obtained on the detector is:

[0057]

[0058] This can be expressed as I = a0 + a2Cos[2β] + a4Cos[4β] + b2Sin[2β] + b4Sin[4β]. This establishes the relationship between the Fourier series a0 to b4 of the acquired signal and the Stokes parameters s0 to s2 of the beam.

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] It can be seen that a0~b4 is a function of s0~s2 and extinction ratio τ. In the inverse solution process, it is necessary to consider the error caused by the calibration error of the polarizer extinction ratio τ to s0~s2. We can take the partial derivative of τ with respect to the linear combination of a0~b4 and select the combination with the smallest error.

[0065] The final inversion formula from a0 to b4 to s0 to s2 is determined as follows:

[0066]

[0067]

[0068]

[0069] The polarization angle Ψ and linear polarization degree DoLP of the incident light can be calculated using the following formulas, thus obtaining all the polarization information of the incident light:

[0070]

[0071]

[0072] The spectral polarization measurement system and method of this invention mainly have two errors: the stability error of the spectrometer detector and the extinction ratio error of the polarization element. Regarding the stability error, this system samples multiple times during the rotation of the first polarizer 1. Let the number of samplings be N, and the spectrometer detector drift Δ1 be 1%. Based on the Fourier series relationship between a0~b4 and s0~s2, and with appropriate scaling, the system error δ1 caused by stability is less than... The extinction ratio error of a polarizing element refers to the deviation between the extinction ratio obtained during the calibration of the polarizer's extinction ratio and the true value. This error varies depending on the calibration method used by the polarizer manufacturer. Numerical simulation based on the inversion formula from a0 to b4 to s2 to s2 shows that the system δ2 caused by the extinction ratio error of the polarization element is less than 0.12%, therefore the total system error is...

[0073] This invention provides a spectral polarization measurement system and method that uses dual polarizers and a spectrometer to simultaneously measure the polarization and spectral characteristics of a light beam, covering a spectral range of 450–2400 nm. Its structure is simple and easy to assemble and adjust. A precision electrically controlled turntable drives the first polarizer 1 to modulate the intensity of the incident light beam. Multi-point measurements during polarizer rotation make the system independent of the polarizer's transmission axis direction. Multi-point measurements also reduce the impact of detector and light source stability errors on the measurement. A second polarizer 2 with a fixed transmission axis is introduced, ensuring that light of any polarization direction remains consistent when passing through the second polarizer 2 and entering the spectrometer 3. This eliminates the influence of the polarization sensitivity of the grating spectrometer, improving the system's measurement accuracy. The spectral polarization measurement method provided by this invention utilizes Fourier analysis and data processing methods incorporating the specific extinction ratio τ of the polarizer to achieve high-precision spectral polarization information measurement.

[0074] like Figure 3 As shown, the present invention provides a spectral polarization measurement system and method that measures the distribution of the degree of linear polarization of a fully linearly polarized light in the spectrum, with the visible error controlled within 0.5%.

[0075] 1) First, place the light source to be tested, the second polarizer 2, and the spectrometer 3 in the optical path, and use the theodolite as an auxiliary tool for alignment.

[0076] 2) Control the first polarizer 2 to rotate 180°, find the angle with the maximum output of the spectrometer, and fix it at this angle.

[0077] 3) Place the first polarizer 1 into the optical path and align it using a theodolite.

[0078] 4) Use a precision electronically controlled turntable to rotate the first polarizer 1 one revolution. Simultaneously, set the spectrometer 3 to scan at 6-second intervals and record 100 sets of data.

[0079] 5) Data processing:

[0080] ① Read 100 data points from each group and save them as .npy files;

[0081] ② The 0th, 2nd, and 4th harmonic coefficients a0 to b4 of the Fourier series were initially fitted using the Powell algorithm;

[0082] ③Then, the batch gradient descent algorithm is used to train the data to obtain a more accurate Fourier series a0~b4;

[0083] ④ The Stokes parameters s0, s1, and s2 can be calculated using the Fourier series a0 to b4, and the polarization angle and degree of polarization can be further calculated.

[0084] Example 1

[0085] 1. This system has been used to measure the polarization characteristics of the depolarizer, a key optical component of the wide-swath hyperspectral greenhouse gas monitor, a main payload of the XX-2 satellite. The specific optical path diagram is shown below. Figure 2 As shown. The measurement process is as follows:

[0086] 1) Adjust the optical path of the polarization light source 7, turn on the integrating sphere 5 light source, and wait for the light source to stabilize.

[0087] 2) Adjust the optical path of polarization spectral analysis section 4.

[0088] 3) Install the depolarizer 8 on the sample stage so that the depolarizer 8 is in the parallel optical path of the system.

[0089] 4) Rotate polarizer 6 and collect a set of data every 10° interval; rotate polarizer 6 180° to complete the data collection, and a total of 18 sets of data will be obtained.

[0090] Then the debiasing degree D of debiasing device 8 is DOLP 输出 -DOLP 光源 Among the 18 sets of data, the minimum depolarization degree was selected to characterize the depolarization performance of the depolarizer.

[0091] 2. Before measurement, the system accuracy was verified using a fully linearly polarized light source. The results are as follows: Figure 3 As shown, the accuracy is better than 0.5%.

[0092] This invention discloses a spectral polarization measurement system and method. A spectrometer is used as the detector, capable of detecting spectral radiance with a maximum spectral resolution of 3 nm. A second polarizer, positioned close to the spectrometer, fixes the transmission axis to eliminate the spectrometer's polarization sensitivity. A first polarizer, positioned away from the spectrometer, is mounted on a precision turntable to modulate the intensity of the incident light. After the first polarizer rotates once, multiple measurements are taken, and Fourier analysis is performed on the series of data to obtain the Stokes parameters of the light beam in the spectrum. This system can simultaneously measure the linear polarization state of light beams in the 450-2400 nm wavelength range and the polarization sensitivity of optical elements.

[0093] The above specific embodiments are used to explain and illustrate the present invention, and are only preferred embodiments of the present invention, not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for measuring the polarization state of light in a spectral polarization measurement system, comprising the following steps: Step one: The light being measured sequentially passes through the first polarizer and the second polarizer before entering the spectrometer. The transmission axis of the second polarizer is fixed, and fixed at the angle when the spectrometer output is at its maximum. This ensures that light of any polarization direction has the same polarization direction when it passes through the second polarizer and re-enters the spectrometer. Fixing the second polarizer degenerates the spectrometer's polarization Mueller matrix into a fixed gain parameter, effectively suppressing the spectrometer's polarization sensitivity. The first polarizer is driven to rotate continuously, and both the first and second polarizers are treated as non-ideal polarizers with an extinction ratio of τ. The modulation of the incident light is described using the Stokes vector and the Mueller matrix as follows: ， in Let Stokes be the incident light vector. It is a component of the Stokes vector of the incident light; The Stokes vector at the time of arrival at the detector; Here is the Mueller matrix of the first polarizer; The Mueller matrix of the second polarizer; The Mueller matrix represents the polarization of the grating spectrometer itself. Its matrix elements; The polarization azimuth angle of the first polarizer (1) is... The extinction ratio of the polarizer; Step two: By continuously rotating the first polarizer and sampling multiple times at equal intervals, the influence of detector and light source stability errors on the measurement is reduced. The systematic error δ1 caused by stability is less than (28 / N)×Δ1, where Δ1 is the spectrometer detector drift. The output values ​​of the spectrometer are then grouped into a series of data I={I1, I2, I3, ..., I... N Establish the polarization state of the incident beam (S0, S1, S2). T and , The relationship between the Fourier series of the signal and the Stokes parameters of the beam was obtained by performing Fourier analysis on the series of data using the Powell algorithm and the batch gradient descent algorithm to obtain a0, a2, a4, b2, b4. in: ， Where a0, a2, a4, b2, and b4 are Fourier series of orders 0, 2, and 4, respectively; Step 3: Since a0~b4 is a function of s0~s2 and the extinction ratio τ, calculate the partial derivative of τ with respect to the linear combination of a0~b4. Select the combination that minimizes the error of s0~s2 caused by the calibration error of the extinction ratio τ. Based on this, determine and calculate the Stokes parameters of the incident light using the following formula to obtain the polarization state: ， To suppress the measurement error δ2 caused by the polarizer extinction ratio calibration error to below 0.12%, Step four, through the polarization angle of the incident light By combining the linear polarization degree DoLP, we obtain all the polarization information of the incident light: ， The total measurement error in the 450~2400nm wide spectrum is ≤0.304%, and the linear polarization error of the measured fully linearly polarized light is controlled within 0.5%.

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