Method and system for calibrating a polarimeter

Abstract

The present application relates to the technical field of optical equipment, and discloses a calibration method and system of a polarization measuring instrument to improve calibration accuracy. The method comprises the following steps: determining an iteration step for adjusting the included angle between a polarizing polarizer and an analyzing polarizer; in each iteration process, obtaining a light intensity variation curve corresponding to one rotation of a wave plate from the acquisition of a detector, performing fast Fourier transform on the light intensity variation curve to obtain a group of coefficients, and calculating the R value corresponding to the included angle between the polarizing polarizer and the analyzing polarizer in each iteration process according to the group of coefficients; drawing a curve of the included angle between the polarizing polarizer and the analyzing polarizer and the R value, finding two included angles that are 90 degrees apart and have the closest R value difference of 0 in the curve, and determining that the included angle corresponding to the two included angles between the polarizing polarizer and the analyzing polarizer is a ±45 degree relationship; and rotating the analyzing polarizer to be parallel to the polarizing polarizer serving as a reference based on the included angle between the polarizing polarizer and the analyzing polarizer being a ±45 degree relationship.

Description

Technical Field

[0001] This invention relates to the field of optical equipment technology, and in particular to a calibration method and system for a polarization measuring instrument. Background Technology

[0002] The polarization angle of the polarization measuring instrument is referenced to the angle of the built-in polarizer.

[0003] After the polarization measuring instrument is assembled and before leaving the factory, it needs to be calibrated based on the calibration fixture. During this process, the polarization angle of the built-in analyzer of the polarization measuring instrument needs to be measured with an external polarizer to ensure that the polarization angle is parallel to the analysis angle and the error does not exceed ±0.05°.

[0004] However, in polarization measuring instruments, if a waveplate is placed before the built-in polarizer, the noise interference from the fixture platform and the built-in detector of the polarization measuring instrument makes it difficult to accurately collect calibration parameters and achieve calibration.

[0005] According to the principle of polarization measuring instruments, if the incident light is linearly polarized, the PD detector will obtain a sine curve after the waveplate rotates one revolution. The trough position is the theoretical value of 0 only when the polarization angle is perpendicular to the analyzer angle and the fast axis of the waveplate rotates to be parallel or perpendicular to the polarization angle. Therefore, when the polarization angle is slowly rotated to the lowest point of the curve trough, the polarization angle will be perpendicular to the analyzer angle. This is the extinction method for finding the polarization angle.

[0006] The extinction method measures the extreme point of the Malus curve trough, where the slope is 0. Due to the low stability of the incident laser and the polarization detector (PD), high-precision angle identification is impossible in actual measurements. This means that the polarization angle between the polarization initiation and analysis is closer to the extreme point of the trough than 0° at a trough (e.g., -0.1°, 0.15°). Therefore, using the extinction method to find the polarization angle, under normal circumstances, it is difficult to achieve an accuracy of ±0.1°. Furthermore, to ensure that the incident light intensity is as unaffected as possible by the polarization initiation angle, it is also necessary to ensure that the incident light is perfectly circularly polarized or completely unpolarized, posing an extremely stringent challenge to the calibration environment setup. Summary of the Invention

[0007] The purpose of this invention is to disclose a calibration method and system for a polarization measuring instrument to improve calibration accuracy.

[0008] To achieve the above objectives, in the method disclosed in this invention, the polarization measuring instrument includes a rotatable waveplate located in front of the incident beam of the polarizer and a detector located behind the polarizer. The method of this invention includes:

[0009] Step S1: Determine the iteration step size used to adjust the angle between the polarizing filter and the analyzing polarizing filter;

[0010] Step S2: In each iteration, obtain the light intensity change curve corresponding to one rotation of the waveplate acquired by the detector, and perform a fast Fourier transform on the light intensity change curve to obtain the following 5 coefficients:

[0011] A0=0.5*S0-0.25*(cos(delta)+1)*S1;

[0012] A2=0.5*S3*sin(delta)*sin(2*fai0);

[0013] B2=0.5*S3*sin(delta)*cos(2*fai0);

[0014] A4=0.25*(cos(delta)-1)*S2*sin(4*fai0)+0.25*(cos(delta)-1)*S1*cos(4*fai0);

[0015] B4=0.25*(cos(delta)-1)*S2*cos(4*fai0)-0.25*(cos(delta)-1)*S1*sin(4*fai0);

[0016] Where [S0 S1 S2 S3] is the Stokes vector of the incident beam from the polarizer to the waveplate, delta and fai0 are the phase delay and initial fast axis angle of the rotating waveplate, respectively, and fai is the actual angle of the waveplate; and the light intensity I0 is a function of fai, which can be expressed as a function in Fourier series expansion:

[0017] I0=A0+A2*cos(2*fai)+B2*sin(2*fai)+A4*cos(4*fai)+B4*sin(4*fai);

[0018] Step S3: Calculate the R value corresponding to the angle between the polarizer and the analyzer in each iteration process. The calculation formula is:

[0019]

[0020] Step S4: Plot the curve of the angle between the polarizing filter and the analyzer versus the R value. In this curve, find the two angles that are 90° apart and whose R values ​​are closest to 0. Determine that the angle between the polarizing filter and the analyzer corresponding to these two angles is ±45°.

[0021] Step S5: Using the angle between the polarizing filter and the analyzing polarizing filter as a reference of ±45°, rotate the analyzing polarizing filter to make it parallel to the polarizing filter used as a reference.

[0022] Preferably, the accuracy of each motor of the rotating waveplate and the polarizer is 0.02°.

[0023] Preferably, a circular polarizer is deployed in front of the polarizing plate.

[0024] To achieve the above objectives, the present invention also discloses a calibration system for a polarization measuring instrument, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0025] The present invention has the following beneficial effects:

[0026] Based on the ±45° angle between the polarizer and analyzer determined by this invention, which is significantly different from other similar points, it is easy to distinguish. Therefore, on the calibration fixture platform, this invention can adjust the angle between the polarizer and analyzer within ±0.1° based on the reference ±45° relationship, thereby establishing an extremely stringent calibration environment and significantly improving calibration accuracy.

[0027] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0028] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0029] Figure 1 This is an optical path architecture diagram of the calibration system of the polarization measuring instrument disclosed in the embodiments of the present invention.

[0030] Figure 2 This is a schematic flowchart of the calibration method for the polarization measuring instrument disclosed in an embodiment of the present invention.

[0031] Figure 3 This is a schematic diagram showing the relationship between the R value and the angle between the starting and detecting biases, as disclosed in an embodiment of the present invention.

[0032] Figure 4 Based on Figure 3 Find a diagram showing two included angles that are 90° apart and whose R values ​​are closest to 0, where the included angle between two points connected by the same dashed line in the diagram is 90° apart. Detailed Implementation

[0033] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0034] Example 1

[0035] This embodiment discloses a calibration method for a polarization measuring instrument, applicable to, for example... Figure 1 The polarization measurement instrument calibration system shown is designed to improve calibration accuracy.

[0036] exist Figure 1 In this device, the polarization measuring instrument includes a rotatable waveplate located in front of the incident beam of the polarizer and a detector (PD) located behind the polarizer; the tooling platform for calibrating the polarization measuring instrument also includes a polarizing plate and a circular polarizer outside the polarization measuring instrument.

[0037] like Figure 2 As shown, the method in this embodiment includes the following steps:

[0038] Step S1: Determine the iteration step size used to adjust the angle between the polarizer and the analyzer.

[0039] Step S2: In each iteration, obtain the light intensity change curve corresponding to one rotation of the waveplate collected by the detector, and obtain a set of coefficients by performing a fast Fourier transform on the light intensity change curve.

[0040] In this step, let fai be the actual angle of the waveplate, then the light intensity I0 is a function of fai, and its Fourier series expansion is as follows:

[0041] I0=A0+A2*cos(2*fai)+B2*sin(2*fai)+A4*cos(4*fai)+B4*sin(4*fai).

[0042] in:

[0043] A0=0.5*S0-0.25*(cos(delta)+1)*S1;

[0044] A2=0.5*S3*sin(delta)*sin(2*fai0);

[0045] B2=0.5*S3*sin(delta)*cos(2*fai0);

[0046] A4=0.25*(cos(delta)-1)*S2*sin(4*fai0)+0.25*(cos(delta)-1)*S1*cos(4*fai0);

[0047] B4=0.25*(cos(delta)-1)*S2*cos(4*fai0)-0.25*(cos(delta)-1)*S1*sin(4*fai0);

[0048] In the above calculation formula, [S0, S1, S2, S3] is the Stokes vector of the incident beam from the polarizer to the waveplate (known alternative expressions include, but are not limited to, [I, Q, U, V], etc.), and delta and fai0 are the phase delay and initial fast axis angle of the rotating waveplate, respectively.

[0049] In this step, the coefficients of each group are obtained by FFT of the data sampled by the instrument for one cycle, which has excellent stability and accuracy.

[0050] Step S3: Calculate the R value corresponding to the angle between the polarizing filter and the analyzing polarizing filter in each iteration process.

[0051] In this step, the calculation formula is:

[0052]

[0053] In this step, R is the ratio of two numbers, which is linearly related to light intensity and can eliminate the influence of light intensity changes on the measurement results.

[0054] Step S4: Plot the curve of the angle between the polarizing filter and the analyzer versus the R value. In this curve, find the two angles that are 90° apart and whose R values ​​are closest to 0. Determine that the angle between the polarizing filter and the analyzer corresponding to these two angles is ±45°.

[0055] In this step, the curve of the angle between the polarizing filter and the analyzing polarizing filter versus the R value is as follows: Figure 3 As shown, it is obvious that the R value and the angle between the starting and detecting biases exhibit a regular change.

[0056] exist Figure 3 In the process, due to the influence of laser power fluctuations and PD noise, it is still difficult to accurately locate the extreme point in the neighborhood of the extreme point. The curve is symmetrical about the extreme point; therefore, in order to find the extreme point more accurately, we can find two points at 90° intervals on the curve. The center point of the x-coordinate of these two points is the corresponding extreme point if and only if the ordinates of these two points are the same.

[0057] exist Figure 3 In the curve, the position of the peak is symmetrical. This means that the values ​​at two points within ±45° of the peak are equal. Therefore, the curve can be further processed as follows:

[0058] Subtracting the value at each point from the value 90° away and taking the absolute value yields a new curve. The point closest to 0 on this new curve is the point within ±45°, i.e.,... Figure 4 The intersection of the dashed line parallel to the horizontal axis and the R-value curve shown above, and the other adjacent points, all have significant differences from the aforementioned value closest to 0.

[0059] Step S5: Using the angle between the polarizing filter and the analyzing polarizing filter as a reference of ±45°, rotate the analyzing polarizing filter to make it parallel to the polarizing filter used as a reference.

[0060] Preferably, the accuracy of each motor of the rotating waveplate and the polarizer is 0.02°. Therefore, the iterative compensation determined in step S1 is also 0.02°, and thus, based on this embodiment, the polarization angle between the polarizer and the polarizer can be well controlled within the range of ±0.1°.

[0061] Example 2

[0062] This embodiment discloses a calibration system for a polarization measuring instrument, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method described above.

[0063] In summary, the methods and systems disclosed in the above embodiments of the present invention determine an angle of ±45° between the polarizing filter and the analyzing polarizing filter, which is significantly different from other similar points and easy to distinguish. Therefore, on the calibration fixture platform, the present invention can adjust the angle between the polarizing filter and the analyzing polarizing filter to within ±0.1° based on the reference ±45° relationship, thereby establishing an extremely stringent calibration environment and significantly improving calibration accuracy.

[0064] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A calibration method for a polarization measuring instrument, the polarization measuring instrument comprising a rotatable waveplate located in front of an incident beam from a polarizer and a detector located behind the polarizer, characterized in that, include: Step S1: Determine the iteration step size used to adjust the angle between the polarizing filter and the analyzing polarizing filter; Step S2: In each iteration, obtain the light intensity change curve corresponding to one rotation of the waveplate acquired by the detector, and perform a fast Fourier transform on the light intensity change curve to obtain the following 5 coefficients: A0=0.5*S0-0.25*(cos(delta)+1)*S1; A2=0.5*S3*sin(delta)*sin(2*fai0); B2=0.5*S3*sin(delta)*cos(2*fai0); A4=0.25*(cos(delta)-1)*S2*sin(4*fai0)+0.25*(cos(delta)-1)*S1*cos(4*fai0); B4=0.25*(cos(delta)-1)*S2*cos(4*fai0)-0.25*(cos(delta)-1)*S1*sin(4*fai0); Where [S0 S1 S2 S3] is the Stokes vector of the incident beam from the polarizer to the waveplate, delta and fai0 are the phase delay and initial fast axis angle of the rotating waveplate, respectively, and fai is the actual angle of the waveplate; and the light intensity I0 is a function of fai, which can be expressed as a function in Fourier series expansion: I0=A0+A2*cos(2*fai)+B2*sin(2*fai)+A4*cos(4*fai)+B4*sin(4*fai); Step S3: Calculate the R value corresponding to the angle between the polarizer and the analyzer in each iteration process. The calculation formula is: Step S4: Plot the curve of the angle between the polarizing filter and the analyzer versus the R value. In this curve, find the two angles that are 90° apart and whose R values ​​are closest to 0. Determine that the angle between the polarizing filter and the analyzer corresponding to these two angles is ±45°. Step S5: Using the angle between the polarizing filter and the analyzing polarizing filter as a reference of ±45°, rotate the analyzing polarizing filter to make it parallel to the polarizing filter used as a reference.

2. The method according to claim 1, characterized in that, The accuracy of the motor for rotating the waveplate is 0.02°.

3. The method according to claim 1, characterized in that, The accuracy of the motor that rotates the polarizer is 0.02°.

4. The method according to any one of claims 1 to 3, characterized in that, A circular polarizer is deployed in front of the polarizing plate.

5. A calibration system for a polarization measuring instrument, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method described in any one of claims 1 to 4.

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