Dual-pem polarization state analysis accurate correction device and method

Abstract

This invention belongs to the technical field of precise correction methods for polarization state analysis, specifically relating to a dual-PEM polarization state analysis precise correction device and method. It includes a test light, a first elastic modulator, a second elastic modulator, an analyzer, a detector, an elastic drive control and multi-channel digital lock-in amplifier circuit, and a computer. The first elastic modulator, second elastic modulator, analyzer, and detector are sequentially arranged along the optical path of the test light. The first elastic modulator, second elastic modulator, and detector are electrically connected to the elastic drive control and multi-channel digital lock-in amplifier circuit, which is electrically connected to the computer. This invention uses two elastic modulators combined with lock-in amplification to obtain multiple signals with different difference frequencies and harmonic frequencies. Combined with theoretical calculations, it corrects the static phase delay and modulation phase amplitude instability caused by the inherent effects of the two elastic modulators and environmental influences.

Description

Technical Field

[0001] This invention belongs to the technical field of precise correction methods for polarization state analysis, specifically relating to a dual PEM polarization state analysis precise correction device and method. Background Technology

[0002] Stokes parameters have been widely used in the study of polarization variations of vector beams and can describe all polarization states and light intensities of the beam. Therefore, by measuring the Stokes parameters of all four elements, the polarization state analysis of different beams can be determined. Methods for measuring Stokes parameters fall into two categories: one is the amplitude division method, which uses four photodetectors to simultaneously detect the beam split into four beams, thus measuring each Stokes parameter; the other is the polarization modulation method, which involves adding a phase retarder and a polarizer to the modulation optical path. By rotating these components around the optical axis at multiple angles, different modulation results are obtained at different angles, which can satisfy the measurement of most polarized light.

[0003] Photoelastic modulators (PEMs) are polarization modulation devices that operate at resonant frequencies. A PEM is a high-speed phase modulation device based on the photoelastic effect of optical birefringent crystal materials. Due to its advantages such as no mechanical vibration, large incident angle, high modulation frequency, low loss, and wide wavelength range (from vacuum ultraviolet to far-infrared), it has played a positive role in optical polarization analysis, biophysics, and physical chemistry. However, traditional photoelastic modulation polarization measurement methods are based on low-frequency measurements and are not suitable for high-speed polarization state measurement and analysis. Therefore, Wang Zhibin's research group proposed a dual-photoelastic polarization analysis method, "Photoelastic Modulation Polarization Stokes Parameter Measurement and Error Analysis [J]. Laser Technology, 2014, 38(2):5," which can be used for high-speed polarization measurement without rotating the experimental setup. However, due to the influence of ambient temperature and residual stress birefringence during long-term operation, the phase delay amplitude of the photoelastic modulation cannot be accurately corrected over a long period, leading to a decrease in polarization measurement accuracy. Summary of the Invention

[0004] To address the technical problem mentioned above regarding the inability to accurately correct the phase delay amplitude of existing photoelectro-optical modulation (PEM) polarization state analysis over long periods, which leads to a decrease in polarization measurement accuracy, this invention provides a dual PEM polarization state analysis accurate correction device and method. This method employs two PEMs combined with a phase-locked loop to accurately measure the full Stokes parameters of different frequency signals, thereby obtaining the phase delay amplitude of the two PEMs in real time. This enables real-time tracking of the phase delay amplitude of the dual PEMs, and thus accurately obtains the four elements of the full Stokes parameters of the measured light.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A precise correction device for dual PEM polarization state analysis includes a test light, a first elastic modulator, a second elastic modulator, an analyzer, a detector, an elastic drive control and multi-channel digital lock-in amplifier circuit, and a computer. The first elastic modulator, the second elastic modulator, the analyzer, and the detector are arranged sequentially along the optical path of the test light. The first elastic modulator, the second elastic modulator, and the detector are electrically connected to the elastic drive control and multi-channel digital lock-in amplifier circuit, which is electrically connected to the computer.

[0007] The first elastic modulator is a 45° elastic modulator, the second elastic modulator is a 0° elastic modulator, and the analyzer is a 45° analyzer.

[0008] A correction method for a precise correction device for dual PEM polarization state analysis includes the following steps:

[0009] S1. The light to be measured passes through the first spring-loaded optical modulator, the second spring-loaded optical modulator, the analyzer, and the detector in sequence to form the measurement optical path;

[0010] S2. Based on the dual PEM frequency signals provided by the photodynamic drive control and multi-channel digital lock-in amplifier circuit, the digital lock-in amplifier performs phase-locked amplification on the modulation signal obtained by the detector.

[0011] S3. The phase delay amplitude of the first and second light-sensitive modulators is obtained in real time through computer data processing, thereby accurately obtaining the four elements of the Stokes parameter of the measured light.

[0012] The method in S3 for obtaining the phase delay amplitude of the first and second optical modulators in real time through computer data processing is as follows:

[0013] S3.1 Calculate the Stokes parameter S of the measured light. out ;

[0014] S3.2 Calculate the Miller matrix corresponding to the elastic-optical modulator, the second elastic-optical modulator, and the analyzer;

[0015] S3.3 Calculate the Bessel function for the intensity of the detected light by the detector;

[0016] S3.4 Calculate the modulation phase delay amplitude of the first and second optical modulators at any time.

[0017] The Stokes parameter S of the light being measured in S3.1 in Stokes parameter S after modulation of the entire measurement optical path out for:

[0018] S out =M P M PEM2 M PEM1 S in (1)

[0019] Among them, S in =[I in Q in U in V in ] T ,S out =[I out Q out U out V out ] T ;

[0020] The Miller matrices corresponding to the first optical modulator, the second optical modulator, and the analyzer in S3.1 are M, respectively. PEM1 M PEM2 and M P :

[0021]

[0022] Where, δ1=δ 01 +δ 10 sin(2πf1t),δ2=δ 02 +δ 20 sin(2πf2t);

[0023] Wherein, δ1 and δ2 are the modulation phases of the first and second photoelectric modulators, respectively, δ 01 and δ 02 The static birefringence or residual stress birefringence phase delays of the first and second elastic modulators are respectively, δ 10 and δ 20 f1 and f2 are the modulation phase delay amplitudes of the first and second optical modulators, respectively, and the modulation drive frequencies of the first and second optical modulators, respectively.

[0024] The method for calculating the Bessel function of the detector's light intensity in S3.3 is as follows:

[0025] Since the detector can only obtain the Stokes parameter S out I in out Therefore, the Bessel function expansion of the light intensity detected by the detector is:

[0026]

[0027] Where m is an odd number, n is an even number, and J x (y) is the x-th Bessel function corresponding to y.

[0028] The method for calculating the modulation phase delay amplitude of the first and second optical modulators at any time in S3.4 is as follows:

[0029] Based on the Bessel function expansion formula for the detector's light intensity, and combined with lock-in amplification, the amplitudes of signals at different frequencies can be obtained as follows:

[0030]

[0031] Among them, I dc , The detectors, after phase-locked amplification, obtain signal amplitudes with frequencies of DC, nf2, mf2, n1f1±n2f2, nf1±mf2, mf1±nf2, and m1f1±m2f2, respectively.

[0032] Taking a few specific frequencies, we get:

[0033]

[0034] According to the above formula, the modulation phase delay amplitude δ of the first and second optical modulators at any time is obtained. 10 and δ 20 :

[0035]

[0036] in, for The inverse function of .

[0037] The method for obtaining the four elements of the Stokes parameter of the measured light in S3 is as follows:

[0038] Substituting equations (6-1) and (6-2) into equation (4), we get:

[0039]

[0040] Based on the simultaneous equations of (6) and (7), we obtain: I in Q in U in V in δ 01 δ 02 δ 10 δ 20 .

[0041] Compared with the prior art, the beneficial effects of this invention are:

[0042] 1. This invention uses two elastic-optical modulators and lock-in amplification to obtain multiple signals with different difference frequencies and harmonic frequencies. It also uses theoretical calculations to correct the static phase delay and modulation phase amplitude instability caused by the influence of the two elastic-optical modulators themselves and the environment.

[0043] 2. This invention can obtain the static phase delay δ of the first and second elastic optical modulators at every moment. 01 δ 02 And the amplitude δ of the modulation phase delay of the first and second optical modulators at any time. 10 δ 20 This improves the accuracy of polarization measurements. Attached Figure Description

[0044] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0045] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0046] Figure 1 This is a schematic diagram of the structure of the present invention.

[0047] Wherein: 1 is the light being measured, 2 is the first light-sensitive modulator, 3 is the second light-sensitive modulator, 4 is the analyzer, 5 is the detector, 6 is the light-sensitive drive control and multi-channel digital lock-in amplifier circuit, and 7 is the computer. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. These descriptions are only for further illustrating the features and advantages of the present invention, and not for limiting the claims of the present invention. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0049] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0050] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0051] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0052] In this embodiment, as Figure 1 As shown, the test system consists of the light under test 1, a first photoelectric modulator 2, a second photoelectric modulator 3, an analyzer 4, a detector 5, a photoelectric drive control and multi-channel digital lock-in amplifier circuit 6, and a computer 7. The light under test 1 passes sequentially through the first photoelectric modulator 2, the second photoelectric modulator 3, the analyzer 4, and the detector 5 to form the measurement optical path. Based on the dual PEM frequency signal provided by the photoelectric drive control and multi-channel digital lock-in amplifier circuit 6, the digital lock-in amplifier amplifies the modulation signal obtained by the detector 5. Finally, the computer 7 processes the data to obtain the phase delay amplitude of the two photoelectric modulators in real time, thereby accurately obtaining the four elements of the Stokes parameters of the light under test. The x-axis is used as the reference 0° direction.

[0053] Furthermore, the modulation frequencies of the first optical modulator 2 and the second optical modulator 3 are f1 = 50 kHz and f2 = 42 kHz, respectively. The modulation frequencies of the first optical modulator 2 and the second optical modulator 3 can be reasonably selected according to the detector response speed and actual requirements.

[0054] Using the x-axis as a reference for the 0° direction, the specific scheme is as follows:

[0055] Stokes parameter S of the measured light 1 in Stokes parameter S after modulation of the entire measurement optical path out for:

[0056] S out =M P M PEM2M PEM1 S in (1)

[0057] Among them, S in =[I in Q in U in V in ] T ,S out =[I out Q out U out V out ] T M PEM1 M PEM2 and M P The Miller matrices corresponding to the first optical modulator 2, the second optical modulator 3, and the analyzer 4 are as follows:

[0058]

[0059] Where, δ1=δ 01 +δ 10 sin(2πf1t),δ2=δ 02 +δ 20 sin(2πf²t)

[0060] Wherein, δ1 and δ2 are the modulation phases of the first photoelectric modulator 2 and the second photoelectric modulator 3, respectively, δ 01 and δ 02 The static birefringence or residual stress birefringence phase delays of the first elastic modulator 2 and the second elastic modulator 3 are respectively, δ 10 and δ 20 f1 and f2 are the modulation phase delay amplitudes of the first optical modulator 2 and the second optical modulator 3, respectively, and the modulation drive frequencies of the first optical modulator 2 and the second optical modulator 3, respectively.

[0061] Since the detector can only obtain the Stokes parameter S out I in out Therefore, detector 5 detects the light intensity and expands it using the Bessel function as follows:

[0062]

[0063] Where m is an odd number and n is an even number, J x (y) is the x-th Bessel function corresponding to y.

[0064] Traditional methods neglect the static birefringence or residual stress birefringence phase delay (i.e., δ) of the first elastic modulator 2 and the second elastic modulator 3. 01 =δ 02=0), and it is assumed that the modulation phase delay amplitude δ of the first optical modulator 2 and the second optical modulator 3 is 0). 10 and δ 20 Constant; however, in practical applications, due to the fixed materials or installation, the first elastic modulator 2 and the second elastic modulator 3 exhibit static birefringence (δ). 01 ≠0, δ 02 ≠0), and due to issues such as ambient temperature and resonant frequency drift caused by prolonged operation of the elastic adjuster, the modulation phase delay amplitude δ of PEM1 and PEM2 is reduced. 10 and δ 20 Unstable.

[0065] To accurately obtain the polarization state S of the measured light in =[I in Q in U in V in ,] T Of the four elements, static birefringence (δ) of PEM1 and PEM2 must be considered. 01 ≠0, δ 02 ≠0) and modulation phase delay amplitude δ 10 and δ 20 Factors such as instability, which means that δ needs to be obtained at all times. 01 δ 02 δ 10 δ 20 That is, formula (3) has a total of I in Q in U in V in δ 01 δ 02 δ 10 δ 20 Eight signals to be measured, according to formula (3), combined with lock-in amplification, can be obtained as follows:

[0066]

[0067] Among them, I dc , The detectors, after phase-locked amplification, obtain signal amplitudes with frequencies of DC, nf2, mf2, n1f1±n2f2, nf1±mf2, mf1±nf2, and m1f1±m2f2, respectively.

[0068] By taking a few specific frequencies, we can obtain:

[0069]

[0070] According to the above formula, the modulation phase delay amplitude δ of the first optical modulator 2 and the second optical modulator 3 at any time can be obtained.10 and δ 20 :

[0071]

[0072] Substituting equations (9-1) and (9-2) into equation (8), we get:

[0073]

[0074] By solving the system of equations (9) and (10), we can obtain: I in Q in U in V in δ 01 δ 02 δ 10 δ 20 .

[0075] Based on the above derivation, it can be seen that as long as the amplitudes of the detector signals with frequencies of DC, 8kHz, 16kHz, 24kHz, 42kHz, 52kHz, 58kHz, 74kHz, 84kHz, 92kHz, 100Hz, 108kHz, 126kHz, 148kHz, 150kHz, 158kHz, 168kHz, 184kHz, and 200kHz are obtained, the Stokes parameter S of the measured light can be obtained. in =[I in Q in U in V in ] T The static phase delay and δ of the first optical modulator 2 and the second optical modulator 3 01 δ 02 The amplitude δ of the modulation phase delay at any time is denoted by the first optical modulator 2 and the second optical modulator 3. 10 δ 20 This will solve the problem of decreased polarization measurement caused by environmental influences and the inherent effects of the elastic-optical modulator itself, which lead to static phase delay and unstable modulation phase amplitude.

[0076] The above description only illustrates the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention, and all such changes should be included within the protection scope of the present invention.

Claims

1. A method for correcting a dual-PEM polarization state analysis precision correction device, characterized in that: Includes the following steps: S1. The light to be measured passes through the first spring-loaded optical modulator, the second spring-loaded optical modulator, the analyzer, and the detector in sequence to form the measurement optical path; S2. Based on the dual PEM frequency signals provided by the photodynamic drive control and multi-channel digital lock-in amplifier circuit, the digital lock-in amplifier performs phase-locked amplification on the modulation signal obtained by the detector. S3. The modulation phase delay amplitude of the first and second light-sensitive modulators is obtained in real time through computer data processing, thereby accurately obtaining the four elements of the Stokes parameter of the measured light. S3.1, calculating the Stokes parameters S of the measured light out ; S3.2 Calculate the Miller matrix corresponding to the first optical modulator, the second optical modulator, and the analyzer; S3.3 Calculate the Bessel function for the intensity of the detected light by the detector; S3.4 Calculate the modulation phase delay amplitude of the first and second elastic optical modulators at any time; Based on the Bessel function expansion formula for the detector's light intensity, and combined with lock-in amplification, the amplitudes of signals at different frequencies can be obtained as follows: in, After phase-locked amplification, the detector obtains signal amplitudes with frequencies of DC, nf2, mf2, n1f1±n2f2, nf1±mf2, mf1±nf2, and m1f1±m2f2, respectively. Taking a few specific frequencies, we get: Where, δ 01 and δ 02 The static birefringence or residual stress birefringence phase delays of the first and second elastic modulators are respectively, δ 10 and δ 20 f1 and f2 are the modulation phase delay amplitudes of the first and second optical modulators, respectively, and the modulation drive frequencies of the first and second optical modulators, respectively. According to the above formula, the modulation phase delay amplitude δ of the first and second electro-optic modulators at any instant of time is obtained 10 and δ 20 : wherein is the inverse function of Substituting equations (6-1) and (6-2) into equations (4-1) to (4-7), we get: By solving the system of equations (6-1), (6-2), and (7-1) to (7-9), we obtain: I in Q in U in V in δ 01 δ 02 δ 10 δ 20 .

2. The method of claim 1, wherein the method is characterized by: The Stokes parameter S of the light measured in S3.1 in The Stokes parameter S modulated through the entire measurement light path out is: (1) Among them, S in =[I in , Q in , In in , V in ] T , S out =[I out , Q out , In out , V out ] T 。 3. The method of claim 1, wherein the method is characterized by: The Miller matrices corresponding to the first and second polarization modulators and the polarizer in S3.1 are M PEM1 , M PEM2 , and M P , respectively. , , (2) wherein ; Wherein, δ1 and δ2 are the modulation phases of the first and second photoelectric modulators, respectively.

4. The method of claim 1, wherein the method is characterized by: The method for calculating the Bessel function of the detector's light intensity in S3.3 is as follows: Since the detector can only obtain the Stokes parameter S out , I out , the Bessel function expansion of the light intensity detected by the detector is: (3) where m is an odd number, n is an even number, J x (y) is the xth order Bessel function of argument y.

5. A device for accurate correction of polarization state analysis of a dual PEM according to the method of any one of claims 1-4, characterized in that: The device includes a light under test (1), a first light-sensitive modulator (2), a second light-sensitive modulator (3), an analyzer (4), a detector (5), a light-sensitive drive control and multi-channel digital lock-in amplifier circuit (6), and a computer (7). The light under test (1) is provided with the first light-sensitive modulator (2), the second light-sensitive modulator (3), the analyzer (4), and the detector (5) in sequence along the optical path. The first light-sensitive modulator (2), the second light-sensitive modulator (3), and the detector (5) are electrically connected to the light-sensitive drive control and multi-channel digital lock-in amplifier circuit (6), which is electrically connected to the computer (7).

6. The precise correction device for dual PEM polarization state analysis according to claim 5, characterized in that: The first elastic modulator (2) is a 45° elastic modulator, the second elastic modulator (3) is a 0° elastic modulator, and the analyzer (4) is a 45° analyzer.

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