Method for calculating additional birefringence of quarter-wave plate of optical voltage transformer based on linear demodulation mode

Abstract

The invention relates to an optical voltage transformer quarter-wave plate additional birefringence calculation method based on a linear demodulation mode, and belongs to the technical field of high voltage measurement and optical voltage transformers. Linear demodulation of phase delay is realized based on an S-wave plate, specifically, light emitted by a light source forms linearly polarized light through a polarizer, electro-optical phase delay is generated through an electro-optical crystal modulated by an electric field, the linearly polarized light is synthesized under the action of a quarter-wave plate, and additional birefringence generated by the quarter-wave plate due to temperature drift is considered. Electro-optic phase delay and additional birefringence (collectively referred to as phase delay variation) are both converted into rotation of a linearly polarized light polarization plane, after the linearly polarized light passes through the S wave plate and the polarization analyzer, the rotation angle of the polarization plane is converted into linear translation of a strip-shaped light spot, and the rotation angle and the linear translation meet a linear relation. Therefore, the displacement of the light spot is determined by positioning the light spot, and the rotation angle of the polarization plane can be measured. And the additional birefringence introduced by the quarter-wave plate can be calculated by modulating the alternating-current voltage to be measured.

Description

Technical Field

[0001] The invention relates to a method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode. Background Art

[0002] Optical Voltage Transducer (OVT) is based on the principle of Pockels electro-optical effect. It has high measurement sensitivity, large measurement range, no risk of open circuit and combustion and explosion, and uses optical fiber to transmit signals to achieve high voltage optical isolation. It has excellent insulation performance and is green and environmentally friendly. Therefore, OVT is the development direction of the new generation of voltage transformers.

[0003] The quarter-wave plate is an indispensable optical device in OVT. Its function is to produce a 90° phase delay and convert the phase delay generated in the crystal into the rotation of the polarization plane of linearly polarized light. However, temperature changes affect the refractive index of the quarter-wave plate, outputting a non-ideal phase delay (i.e. ≠90°). The additional birefringence introduced is coupled with the electro-optical phase delay of the OVT in a nonlinear relationship, affecting the measurement accuracy of the OVT. Since the existing OVT is mostly based on the light intensity demodulation mode, that is, the phase delay is converted into a change in light intensity in an approximately linear relationship, and the phase delay is measured by detecting the light intensity. In the approximate linear measurement mode, the change in the output light intensity and the phase delay do not satisfy a linear relationship, resulting in the difficulty in separating the additional birefringence introduced by the quarter-wave plate from the electro-optical phase delay. This problem has been difficult to solve. Summary of the invention

[0004] The purpose of the present invention is to address the defects and shortcomings of the prior art and provide a method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode. The method utilizes the linear demodulation mode of the optical voltage transformer to directly measure the rotation angle of the polarization plane of linear polarized light, and calculates the additional birefringence introduced by the quarter-wave plate by modulating the electro-optical phase delay.

[0005] To achieve the above object, the technical solution of the present invention is: a method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode, and realizing linear demodulation of phase delay based on an S-wave plate.

[0006] In one embodiment of the present invention, after linear demodulation of the phase delay, the electro-optic phase delay and the additional birefringence introduced by the quarter-wave plate (collectively referred to as the phase delay variation) are converted into a linear translation of the fixed spot image, and the phase delay variation and the spot translation satisfy a linear relationship.

[0007] In one embodiment of the present invention, by modulating the AC voltage to be measured, the electro-optical phase delay is a known quantity, and the additional birefringence introduced by the quarter-wave plate can be calculated based on the light spot translation.

[0008] In one embodiment of the present invention, the method is specifically implemented as follows:

[0009] The light emitted by the light source passes through the polarizer to form linearly polarized light. Under the action of electric field modulation, the linearly polarized light passes through the electro-optical crystal to produce electro-optical phase delay. Then the output light is synthesized into linearly polarized light under the action of a quarter-wave plate. At the same time, considering the additional birefringence caused by the temperature drift of the quarter-wave plate, the electro-optical phase delay and the additional birefringence (collectively referred to as the phase delay variation) are converted into the rotation of the polarization plane of the linear polarized light. After passing through the S-wave plate and the analyzer, the rotation angle of the polarization plane is converted into the linear translation of the strip light spot, and the phase delay variation and the light spot translation satisfy a linear relationship.

[0010] In one embodiment of the present invention, after the linear polarized light enters the electro-optical crystal, it is decomposed into two linear polarized lights, o light and e light, with orthogonal polarization directions. Due to the different refractive indices of the two polarization directions, the o light and the e light generate an electro-optical phase delay after propagating a predetermined distance in the crystal. Subsequently, the o-light and the e-light are synthesized into linearly polarized light under the action of the quarter-wave plate. At the same time, considering the additional birefringence caused by the temperature drift of the quarter-wave plate, the electro-optical phase delay and the additional birefringence (collectively referred to as the phase delay change) are converted into the rotation of the polarization plane of the linear polarized light, and the angle is θ1; after passing through the S-wave plate and the analyzer, the rotation angle of the polarization plane is converted into the linear translation of the strip spot, and the phase delay change and the spot translation satisfy a linear relationship.

[0011] In one embodiment of the present invention, the direction of the polarizer is parallel to the x-axis, and the incident light is linearly polarized after passing through the polarizer. Assuming that the light intensity amplitude is A, the Jones vector of the linearly polarized light is expressed as:

[0012]

[0013] When modulated by the electric field to be measured, the phase delay of linearly polarized light in the electro-optical crystal is The Jones matrix of the crystal is:

[0014]

[0015] Then the Jones matrix of linearly polarized light after passing through the electro-optical crystal is:

[0016]

[0017] Ideally, the Jones matrix of the quarter wave plate is:

[0018]

[0019] At the same time, the additional birefringence of the quarter-wave plate due to temperature drift is considered but:

[0020]

[0021] Linear polarized light passes through a quarter wave plate and is obtained as follows:

[0022]

[0023] According to formula (6), the light vectors of the outgoing light on the x-axis and y-axis can be expressed as:

[0024]

[0025] Where ω represents angular velocity and t represents time;

[0026] Let E 0x and E 0y They are the amplitudes of the emitted light in the coordinate axis directions:

[0027]

[0028] when When , the rotation angle θ of the polarization plane of the outgoing polarized light is:

[0029]

[0030] when When , the outgoing polarized light becomes elliptically polarized light; but considering is small, the elliptically polarized light can be considered as a linear polarized light, and the rotation angle θ1 of its polarization plane is the angle between the major axis of the elliptically polarized light and the x-axis;

[0031] According to formula (7), by eliminating ωt, we can obtain:

[0032]

[0033] The oblique ellipse in formula (10) is transformed into a standard ellipse by coordinate transformation, and the coordinate rotation angle is θ1. The coordinate rotation equation is as follows:

[0034]

[0035] Among them, x1 and y1 represent the coordinate axes after the coordinates change;

[0036] Substituting equation (11) into equation (10), we obtain:

[0037]

[0038] After simplification, we get:

[0039]

[0040] Further simplification yields:

[0041]

[0042] visible, The additional polarization rotation angle introduced is coupled to θ in a nonlinear relationship, where θ1-θ is Additional birefringence introduced;

[0043] The Jones vector of the S waveplate is expressed as:

[0044]

[0045] Where, l is the length of the S wave plate;

[0046] After the incident light emitted from the 1 / 4 wave plate passes through the S wave plate, the Jones vector E4 of the emitted light is:

[0047]

[0048] After passing through the analyzer, the Jones vector of the outgoing light is obtained as:

[0049]

[0050] Then the intensity distribution I of the emitted light is:

[0051]

[0052] Among them, θ1 and the abscissa x are limited by the length of the S wave plate:

[0053]

[0054] Combining equations (18) and (19), the output light intensity is minimal when the following conditions are met:

[0055]

[0056] It can be seen that when the light spot is extremely small, that is, the center position of the dark pattern of the light spot will change linearly with the change of θ1, that is, θ1 and the displacement of the light spot satisfy a linear change relationship. Therefore, by detecting the displacement of the dark pattern of the light spot, direct and linear measurement of θ1 can be achieved.

[0057] According to the Pockels effect, the phase delay of electro-optical crystal The voltage U to be measured satisfies:

[0058]

[0059] Among them, Uπ is the half-wave voltage of the crystal, which is related to the parameters of the crystal and is a known quantity;

[0060] When the measured AC voltage modulation is a known quantity, the additional birefringence introduced by the quarter-wave plate can be calculated according to equations (14) and (20). π / 4, that is, U=π / 4, according to formula (21), we know Under this condition, the displacement of the positioning spot △x can be obtained by substituting it into formula (20): because Substituting into equation (14), we can get the additional birefringence introduced by the quarter-wave plate:

[0061]

[0062] Therefore, the additional birefringence introduced by the quarter-wave plate is calculated according to formula (22) to complete the error compensation.

[0063] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0064] Compared with the prior art, the present invention has the following beneficial effects: the present invention utilizes the linear demodulation mode of the optical voltage transformer to directly measure the rotation angle of the polarization plane of linearly polarized light, that is, to obtain the relationship between the electro-optical phase delay and the additional birefringence introduced by the quarter-wave plate; by modulating the voltage to be measured, the electro-optical phase delay and the additional birefringence of the quarter-wave plate can be separated, thereby calculating the additional birefringence. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Schematic diagram of the measurement principle of an embodiment of the present invention.

[0066] Figure 2 It is a schematic diagram of the linear relationship between the rotation angle of the polarization plane of linearly polarized light and the displacement of the exit light spot according to an embodiment of the present invention.

[0067] Figure 3 Schematic diagram of the detection principle of an embodiment of the present invention. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0069] The present invention provides a method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode, and realizes linear demodulation of electro-optical phase delay based on an S-wave plate. Figure 1As shown. The light emitted by the light source passes through the polarizer to form linear polarized light, and then passes through the electro-optical crystal. Under the action of electric field modulation, the linear polarized light enters the crystal and is decomposed into two linear polarized lights, o light and e light, with orthogonal polarization directions. Due to the different refractive indices of the two polarization directions, the o light and the e light produce electro-optical phase delay after propagating a certain distance in the crystal. Then, the o-light and the e-light are synthesized into linearly polarized light under the action of the quarter-wave plate, and the additional birefringence caused by the temperature drift of the quarter-wave plate is taken into account. The electro-optical phase delay and the additional birefringence (collectively referred to as the phase delay variation) are both converted into the rotation of the polarization plane of the linearly polarized light, with an angle of θ1. After passing through the S-wave plate and the analyzer, the rotation angle of the polarization plane of the linearly polarized light is converted into a linear translation △x of the light spot, where When the AC voltage to be measured is modulated to a known value, that is, If we know

[0070] The specific mathematical model is as follows:

[0071] According to the attached Figure 1 , the direction of the polarizer is parallel to the x-axis, and the incident light is linearly polarized after passing through the polarizer. Assuming its light intensity amplitude is A, the Jones vector of the linearly polarized light can be expressed as:

[0072]

[0073] When modulated by the electric field to be measured, the phase delay of linearly polarized light in the electro-optical crystal is The Jones matrix of the crystal is:

[0074]

[0075] Then the Jones matrix of linearly polarized light after passing through the electro-optical crystal is:

[0076]

[0077] Ideally, the Jones matrix of the quarter wave plate is:

[0078]

[0079] At the same time, the additional birefringence of the quarter-wave plate due to temperature drift is considered but:

[0080]

[0081] Linear polarized light passes through a quarter wave plate and is obtained as follows:

[0082]

[0083] According to formula (6), the light vectors of the outgoing light on the x-axis and y-axis can be expressed as:

[0084]

[0085] Where ω represents angular velocity and t represents time;

[0086] Let E 0x and E 0y They are the amplitudes of the emitted light in the coordinate axis directions:

[0087]

[0088] when When , the rotation angle θ of the polarization plane of the outgoing polarized light is:

[0089]

[0090] when When , the outgoing polarized light becomes elliptically polarized light; but considering is small, the elliptically polarized light can be considered as a linear polarized light, and the rotation angle θ1 of its polarization plane is the angle between the major axis of the elliptically polarized light and the x-axis;

[0091] According to formula (7), by eliminating ωt, we can obtain:

[0092]

[0093] The oblique ellipse in formula (10) is transformed into a standard ellipse by coordinate transformation, and the coordinate rotation angle is θ1. The coordinate rotation equation is as follows:

[0094]

[0095] Among them, x1 and y1 represent the coordinate axes after the coordinates change;

[0096] Substituting equation (11) into equation (10), we obtain:

[0097]

[0098] After simplification, we get:

[0099]

[0100] Further simplification yields:

[0101]

[0102] visible, The additional polarization rotation angle introduced is coupled to θ in a nonlinear relationship, where θ1-θ is Additional birefringence introduced;

[0103] The Jones vector of the S waveplate is expressed as:

[0104]

[0105] Where, l is the length of the S wave plate;

[0106] After the incident light emitted from the 1 / 4 wave plate passes through the S wave plate, the Jones vector E4 of the emitted light is:

[0107]

[0108] After passing through the analyzer, the Jones vector of the outgoing light is obtained as:

[0109]

[0110] Then the intensity distribution I of the emitted light is:

[0111]

[0112] Among them, θ1 and the abscissa x are limited by the length of the S wave plate:

[0113]

[0114] Combining equations (18) and (19), the output light intensity is minimal when the following conditions are met:

[0115]

[0116] It can be seen that when the light spot is extremely small, that is, the center position of the dark pattern of the light spot will change linearly with the change of θ1, that is, θ1 and the displacement of the light spot satisfy a linear change relationship. Therefore, by detecting the displacement of the dark pattern of the light spot, direct and linear measurement of θ1 can be achieved.

[0117] According to the Pockels effect, the phase delay of electro-optical crystal The voltage U to be measured satisfies:

[0118]

[0119] Among them, U π is the half-wave voltage of the crystal, which is related to the parameters of the crystal and is a known quantity;

[0120] When the measured AC voltage modulation is a known quantity, the additional birefringence introduced by the quarter-wave plate can be calculated according to equations (14) and (20). π / 4, that is, U=π / 4, according to formula (21), we know Under this condition, the displacement of the positioning spot △x can be obtained by substituting it into formula (20): because Substituting into equation (14), we can get the additional birefringence introduced by the quarter-wave plate:

[0121]

[0122] Therefore, the additional birefringence introduced by the quarter-wave plate is calculated according to formula (22) to complete the error compensation.

[0123] Attached Figure 3 Further explain the detection principle of the present invention. When θ1=0, the dark pattern of the light spot is in the middle. And affected by temperature drift, the quarter wave plate introduces additional phase delay At this time, according to the light spot dark pattern displacement △x, substitute θ1 can be calculated, and combined with formula (14), it can be calculated as

[0124] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0125] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode, characterized in that: Linear demodulation of phase delay is achieved based on S-wave plate.

2. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 1, characterized in that: After linear demodulation of the phase delay, the phase delay variation is converted into a linear translation of the fixed spot image, and the phase delay variation and the spot translation satisfy a linear relationship.

3. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 2, characterized in that: When the additional birefringence introduced by the temperature drift of the quarter-wave plate is considered, the phase delay variation is the sum of the electro-optic phase delay and the additional birefringence.

4. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 3, characterized in that: When the AC voltage to be measured is zero, the electro-optical phase delay is also zero. At this time, the measured light spot shift corresponds to the error caused by the additional birefringence introduced by the quarter-wave plate.

5. A method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to any one of claims 1 to 4, characterized in that: The specific implementation of this method is as follows: The light emitted by the light source passes through the polarizer to form linearly polarized light. Under the action of electric field modulation, the linearly polarized light passes through the electro-optical crystal, generating electro-optical phase delay. Then the outgoing light is synthesized into linearly polarized light under the action of a quarter-wave plate, and the phase delay change is converted into the rotation of the polarization plane of the linear polarized light. After passing through the S-wave plate and the analyzer, the rotation angle of the polarization plane is converted into the linear translation of the strip light spot, and the phase delay change and the light spot translation satisfy a linear relationship.

6. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 5, characterized in that: After the linear polarized light enters the electro-optical crystal, it is decomposed into two linear polarized lights, o light and e light, with orthogonal polarization directions. Due to the different refractive indices of the two polarization directions, the o light and the e light produce an electro-optical phase delay after propagating a predetermined distance in the electro-optical crystal. Then, the o-light and the e-light are synthesized into linearly polarized light under the action of the quarter-wave plate, and the additional birefringence caused by the temperature drift of the quarter-wave plate is taken into account. Both the electro-optic phase delay and the additional birefringence are converted into the rotation of the polarization plane of the linearly polarized light, with an angle of θ1; after passing through the S-wave plate and the analyzer, the rotation angle of the polarization plane is converted into the linear translation of the strip spot, and the phase delay change and the spot translation satisfy a linear relationship.

7. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 5, characterized in that: The direction of the polarizer is parallel to the x-axis. After the incident light passes through the polarizer, it becomes linearly polarized light. Assuming its light intensity amplitude is A, the Jones vector of the linearly polarized light is expressed as: When modulated by the electric field to be measured, the phase delay of linearly polarized light in the electro-optical crystal is The Jones matrix of the crystal is: Then the Jones matrix of linearly polarized light after passing through the electro-optical crystal is: Ideally, the Jones matrix of a quarter wave plate is: At the same time, the additional birefringence of the quarter-wave plate due to temperature drift is considered but: Linear polarized light passes through a quarter wave plate and is obtained as follows: According to formula (6), the light vectors of the outgoing light on the x-axis and y-axis can be expressed as: Where ω represents angular velocity and t represents time; Let E 0x and E 0y They are the amplitudes of the emitted light in the coordinate axis directions: when When , the rotation angle θ of the polarization plane of the outgoing polarized light is: when When , the outgoing polarized light becomes elliptically polarized light; but considering is small, the elliptically polarized light can be considered as a linear polarized light, and the rotation angle θ1 of its polarization plane is the angle between the major axis of the elliptically polarized light and the x-axis; According to formula (7), by eliminating ωt, we can obtain: The oblique ellipse in formula (10) is transformed into a standard ellipse by coordinate transformation, and the coordinate rotation angle is θ1. The coordinate rotation equation is as follows: Among them, x1 and y1 represent the coordinate axes after the coordinates change; Substituting equation (11) into equation (10), we obtain: After simplification, we get: Further simplification yields: visible, The additional polarization rotation angle introduced is coupled to θ in a nonlinear relationship, where θ1-θ is Additional birefringence introduced; The Jones vector of the S waveplate is expressed as: Where, l is the length of the S wave plate; After the incident light emitted from the 1 / 4 wave plate passes through the S wave plate, the Jones vector E4 of the emitted light is: After passing through the analyzer, the Jones vector of the outgoing light is obtained as: Then the intensity distribution I of the emitted light is: Among them, θ1 and the abscissa x are limited by the length of the S wave plate: Combining equations (18) and (19), the output light intensity is minimal when the following conditions are met: It can be seen that when the light spot is extremely small, that is, the center position of the dark pattern of the light spot will change linearly with the change of θ1, that is, θ1 and the displacement of the light spot satisfy a linear change relationship. Therefore, by detecting the displacement of the dark pattern of the light spot, direct and linear measurement of θ1 can be achieved.

8. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 7, characterized in that: Electro-optical crystal phase delay The AC voltage U to be measured satisfies: Among them, U π is the half-wave voltage of the crystal, which is related to the parameters of the crystal and is a known quantity; When the AC voltage modulation U to be measured is a known quantity, the additional birefringence introduced by the quarter-wave plate can be calculated according to equations (14) and (20) to complete the error compensation.

9. The method for calculating the additional birefringence of a quarter-wave plate of an optical voltage transformer based on a linear demodulation mode according to claim 8, characterized in that: Assume that the AC voltage modulation to be measured is U π / 4, according to formula (21) we can know Under this condition, the positioning spot translation △x can be substituted into formula (20) to obtain because Substituting into equation (14), we can get the additional birefringence introduced by the quarter-wave plate: Therefore, the additional birefringence introduced by the quarter-wave plate is calculated according to formula (22).

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