A multi-degree of freedom telescope testing system

Abstract

The application discloses a multi-degree-of-freedom telescope testing system, which comprises a laser, an acousto-optic modulator, a beam splitter, a transverse beam splitter, a plane mirror, a half-wave plate, a quarter-wave plate, a corner cube reflector, a half mirror, a photodetector, a four-quadrant detector and a digital phase meter; by means of heterodyne interferometric measurement, the heterodyne interference signal, the differential wavefront phase detection signal and the differential power detection signal are combined to provide multi-degree-of-freedom high-precision measurement, and the change of the structure of a sample to be measured in each degree of freedom is obtained. The interferometer structure adopted by the method is compact, has high precision and high efficiency, and effectively guarantees the high-precision requirement of the telescope structure stability test in multiple degrees of freedom.

Description

Technical Field

[0001] This invention relates to a multi-degree-of-freedom telescope testing system, which can efficiently and accurately measure the structural changes of a sample under test in multiple degrees of freedom. Background Technology

[0002] To successfully complete space measurement missions, spaceborne optical components, such as telescopes, need to possess characteristics such as high stability, lightweight design, and resistance to deformation to withstand external influences such as temperature changes and vibrations, ensuring measurement accuracy. Therefore, pre-testing the structural stability of spaceborne optical components is particularly important. Optical interferometers, with their high precision and high signal-to-noise ratio, are often the first choice for testing the structural stability of telescopes. Currently used test optical paths are either limited to measurements in a single degree of freedom or constrained by measurement accuracy. Therefore, it is necessary to research a compact, efficient, high-precision, and multi-degree-of-freedom testing method.

[0003] Therefore, this high-precision, multi-degree-of-freedom testing method is proposed. By utilizing a transverse beam splitter, the reference and measurement beams are made to travel along the same path as much as possible, thereby minimizing common-mode noise. Combining differential wavefront phase detection signals, differential power detection signals, and phase information, the changes in the structure of the sample under test in each degree of freedom can be measured simultaneously, exhibiting high efficiency. Furthermore, by combining a retroreflector, a quarter-wave plate, and a semi-reflective mirror, the changes in the telescope's roll degree of freedom can be effectively measured while maintaining a compact optical path structure. Therefore, this testing system can well meet the requirements for testing the structural stability of spaceborne optical devices, ensuring efficient and accurate testing. Summary of the Invention

[0004] The technical problem solved by this invention is to address the issues of insufficient accuracy and limitation to a single degree of freedom in common structural stability testing methods in the existing technology. This invention optimizes existing solutions and proposes a high-precision and efficient multi-degree-of-freedom telescope testing method.

[0005] The present invention solves the above-mentioned technical problem through the following technical solution:

[0006] A multi-degree-of-freedom telescope testing system includes a first laser, a second laser, a first acousto-optic modulator, a second acousto-optic modulator, a first beam splitter, a second beam splitter, a third beam splitter, a first lateral beam splitter, a second lateral beam splitter, a third lateral beam splitter, a first plane mirror, a second plane mirror, a third plane mirror, a half-wave plate, a quarter-wave plate, a pyramidal retroreflector, a semi-reflective mirror, a first photodetector, a second photodetector, a first quadrant detector, a second quadrant detector, and a digital phase meter.

[0007] The first laser and the second laser each output a laser beam with a wavelength of 1064nm. After passing through the first acousto-optic modulator and the second acousto-optic modulator respectively, a reference beam with a frequency of f1 and a measurement beam with a frequency of f2 are obtained. Then, both beams enter the interferometer.

[0008] The reference light, output from the first laser and frequency f1 after frequency shifting by the first acousto-optic modulator, first enters the first beam splitter. After being split by the beam splitter, it is divided into a reflection component and a transmission component. The transmission component enters the first transverse beam splitter, and after transmission and reflection by the first transverse beam splitter, the output light is two parallel beams. The two beams are transmitted through the second beam splitter and reflected by the second plane mirror, and then enter the second beam splitter again. After that, the two beams are reflected by the second beam splitter to the second transverse beam splitter, and after two more reflections, they are received by the first four-quadrant detector and the first photodetector, respectively. The reflection component passes through the half-wave plate and enters the first plane mirror, and then is reflected by the third transverse beam splitter to the third beam splitter. After passing through the third beam splitter, the transmission component of this beam is received by the second four-quadrant detector, and its reflection component is received by the second photodetector.

[0009] The measurement light, output from the second laser and then frequency-shifted to f2 by the second acousto-optic modulator, first passes through the first transverse beam splitter and is reflected to form two parallel components. After both beams pass through the second beam splitter, the component reflected from the first transverse beam splitter to the second beam splitter is reflected by the third plane mirror and then re-enters the second beam splitter. It is then reflected by the second beam splitter to the second transverse beam splitter, transmitted through the second transverse beam splitter, and received by the first photodetector. The component transmitted from the first transverse beam splitter to the second beam splitter first passes through a semi-reflecting mirror, then a portion of the beam is reflected back to the second beam splitter by the semi-reflecting mirror, reflected again by the second beam splitter to the second transverse beam splitter, and then transmitted through the second transverse beam splitter to the first four-image beam splitter. The beam is received by the first photodetector; another part passes through the semi-reflecting mirror to the retroreflector; the beam component incident on the retroreflector, after being reflected by the retroreflector, will pass through the quarter-wave plate and be incident on the second beam splitter again, and then reflected by the beam splitter to the third beam splitter; after passing through the third beam splitter, the transmitted component of the beam will be received by the second photodetector, and the reflected component will be received by the second fourth-quadrant detector; the beams incident on the first photodetector and the first fourth-quadrant detector will interfere to form optical beats, and then be received by the first photodetector and the first fourth-quadrant detector respectively; the beams incident on the second photodetector and the second fourth-quadrant detector will interfere to form optical beats, and then be received by the second photodetector and the second fourth-quadrant detector respectively.

[0010] The signals output from the first photodetector, the second photodetector, the first quadrant detector, and the second quadrant detector are converted from analog to digital and then input into the digital phase meter. After processing, phase information, differential wavefront phase detection signal, and differential power detection signal can be obtained.

[0011] The obtained differential wavefront phase detection signal is processed to obtain the variation θ of the sample in the azimuth direction. y and the change in pitch direction θ x By processing the differential power detection signal, the sample's variation along the x-axis (Δx) and y-axis (Δy) are obtained; by processing the output phase result, the sample's variation along the axial direction (Δz) and the variation in rolling degree of freedom (θ) are obtained. z Therefore, the deformation and displacement of the sample under test are detected in three translational degrees of freedom and three rotational degrees of freedom, so as to achieve the purpose of multi-degree-of-freedom structural stability measurement.

[0012] The frequency difference Δf between the reference light and the measurement light is f1 - f2 = 1 MHz.

[0013] Both the beam splitter and the transverse beam splitter used are non-polarizing beam splitters, and the transmission-to-reflection ratio is 50:50.

[0014] The surface of the retroreflector is respectively attached with a semi-reflecting mirror and a quarter-wave plate, each occupying half of the area.

[0015] The third plane mirror and the retroreflector are fixed at both ends of the sample to be tested, thereby allowing measurement of the size of the sample along each degree of freedom.

[0016] The processed phase information, differential wavefront phase detection signal, and differential power detection signal include:

[0017] The optical beat signals received by the four detector pixels on the surface of the first four-quadrant detector are processed by a digital phase meter to obtain four phase results, denoted as Φ. A Φ B Φ C and Φ D Overall phase results of the first four-quadrant detector It can be defined as:

[0018]

[0019] Calculate the differential wavefront phase probe signal; the differential wavefront phase probe signal is used to measure the wavefront deviation angle of two beams, and can be divided into the horizontal signal DWS. h and vertical signal DWS v The calculation method is as follows:

[0020]

[0021]

[0022] By performing area integration on the received light intensity, the average optical power received in each quadrant of the second four-quadrant detector is obtained.

[0023]

[0024] Where Z is the dielectric impedance; E R E is the reference photoelectric field component; M To measure the photoelectric field components, the average power in each quadrant is denoted as... DPS signals can be divided into horizontal and vertical signals, denoted as DPS respectively. h and DPS v Defined as:

[0025]

[0026]

[0027] The change θ of the sample in the azimuth direction y and the change in pitch direction θ x The sample's x-axis variation Δx and y-axis variation Δy are obtained by processing the differential wavefront phase detection signal; the sample's axial variation Δz and θ-axis variation are obtained by processing the differential wavefront phase detection signal. z The phase is obtained by processing the output phase result. The specific calculation steps are as follows:

[0028] The axial variation Δz is the phase signal obtained from the first photodetector and the first four-quadrant detector. and Find:

[0029]

[0030] Δx and Δy are obtained from the differential power detection signal. Because a retroreflector is used to reflect the beam, when the sample structure changes in the horizontal or vertical direction, the retroreflector position changes accordingly. This causes the position of the measurement beam on the surface of the second quadrant detector to shift, thus altering the DPS signal. For small-range changes, we have:

[0031] Δx=C1·DPS h

[0032] Δy=C2·DPS v

[0033] Where C1 and C2 are proportionality coefficients;

[0034] θ y θ x Obtained from the differential wavefront phase detection signal; for a small range of offset, the DWS signal is proportional to the corresponding offset angle, from which we can obtain:

[0035] θ y ∝DWS h

[0036] θ x ∝DWS v

[0037] The differential wavefront phase detection signal can be calibrated in advance to find the relationship between the differential wavefront phase detection signal and the change θ, so that the change can be calculated in subsequent measurements.

[0038] θ z The calculation is as follows: When the sample to be tested changes along the rolling direction, the retroreflector will rotate accordingly, which in turn will cause the quarter-wave plate on the surface of the retroreflector to rotate; therefore, the angle between the fast axis of the quarter-wave plate and the horizontal direction will change; if the laser incident on the quarter-wave plate is linearly polarized light, when the polarization direction of the incident linearly polarized light makes a certain angle α with the fast axis of the quarter-wave plate, and At this time, the outgoing light is elliptically polarized; rotating the quarter-wave plate will change the ellipticity of the outgoing elliptically polarized light; for small angular changes, the deflection angle and ellipticity have an approximately linear relationship, from which we can conclude:

[0039]

[0040] k is a scaling factor, a is the major semi-axis of the ellipsoidal beam, and b is the minor semi-axis of the ellipsoidal beam. The reference light reflected by beam splitter 1 is linearly polarized. Rotating the half-wave plate makes the polarization direction of the reference light form a 45° angle with the major axis of the ellipsoidal beam. The polarization direction can be obtained by a polarization measuring instrument. At this time, the phase signal change obtained by the second photodetector can be written as:

[0041]

[0042] Where a is the major semi-axis of the ellipsoidal light; b is the minor semi-axis of the ellipsoidal light; γ is the angle between the polarization direction of the reference light and the major axis of the ellipsoidal light. This refers to the common-mode portion; when the initial included angle is 45°, the phase change caused by polarization includes:

[0043]

[0044] That is, the phase change is equivalent to the ellipticity change; and because the angle change is small, it can be considered that during the measurement process, the phase change is equivalent to the ellipticity change; therefore, we can conclude that:

[0045]

[0046] in Obtained from the first photodetector, minus Noise introduced by the acousto-optic modulator can be removed, thereby obtaining Then we get θ z .

[0047] The advantages of this invention compared to the prior art are:

[0048] (1) The present invention provides a method for testing the structural stability of a multi-degree-of-freedom telescope. By using heterodyne interferometry, combined with phase information, differential wavefront phase probe (DWS) signal and differential power probe (DPS) signal, the structural changes of the sample under test in three translational degrees of freedom and three rotational degrees of freedom are measured. It has the characteristics of high precision and high efficiency.

[0049] (2) This invention combines a retroreflector, a semi-reflective mirror, and a quarter-wave plate, which makes the optical path design more compact and reduces the volume occupied while meeting measurement requirements, thereby obtaining a more stable optical path structure. This effectively improves the stability of the measurement system and its ability to cope with environmental changes. Attached Figure Description

[0050] Figure 1 This is a flowchart of the present invention;

[0051] Figure 2 This is a schematic diagram of the optical path of the present invention;

[0052] Figure 3 This is a top view of the optical path diagram of the present invention; Specific implementation methods

[0053] This invention discloses a multi-degree-of-freedom telescope testing system, comprising a first laser, a second laser, a first acousto-optic modulator, a second acousto-optic modulator, a first beam splitter, a second beam splitter, a third beam splitter, a first lateral beam splitter, a second lateral beam splitter, a third lateral beam splitter, a first plane mirror, a second plane mirror, a third plane mirror, a half-wave plate, a quarter-wave plate, a pyramidal retroreflector, a semi-reflective mirror, a first photodetector, a second photodetector, a first quadrant detector, a second quadrant detector, and a digital phase meter;

[0054] First, the retroreflector RR and the plane mirror M3 are fixed at both ends of the sample to be tested. Then, the reference light and the measurement light are introduced by lasers 1 and 2, respectively. The reference light and the measurement light pass through an acousto-optic modulator, thereby obtaining a frequency difference of 1 MHz.

[0055] The reference light first enters beam splitter BS1, where it is split into a reflected component and a transmitted component. The transmitted component enters transverse beam splitter LBS1, and after transmission and reflection, emerges as two parallel beams. These two beams are transmitted through beam splitter BS2, reflected by plane mirror M2, and then re-enter beam splitter BS2. Subsequently, the two beams are reflected by beam splitter BS2 back to transverse beam splitter LBS2, and after two more reflections, are received by quadrant detector QPD1 and photodetector PD1, respectively. The reflected component of the reference light, after passing through beam splitter BS1, passes through half-wave plate HWP and enters plane mirror M1, then is reflected by transverse beam splitter LBS3 back to beam splitter BS3. After passing through beam splitter BS3, the transmitted component of this beam is received by quadrant detector QPD2, and the reflected component is received by photodetector PD2.

[0056] The measurement light first passes through the transverse beam splitter LBS1, where it is transmitted and reflected to form two parallel components. After passing through beam splitter BS2, the component reflected from LBS1 to BS2 is reflected by plane mirror M3 and then re-enters beam splitter BS2. It is then reflected back to LBS2, transmitted through BS2, and received by photodetector PD1. The component transmitted from LBS1 to BS2 first passes through a semi-reflecting mirror SRM. A portion of the beam is then reflected back to beam splitter BS2, reflected again by BS2, and then transmitted through LBS2 to be received by four-quadrant detector QPD1. Another portion passes through a semi-reflecting mirror to retroreflector RR. The beam component incident on the retroreflector is reflected by the retroreflector and then passes through a quarter-wave plate QWP before re-entering beam splitter BS2. It is then reflected back to beam splitter BS3. After passing through beam splitter BS3, the transmitted component of the beam will be received by photodetector PD2; the reflected component will be received by quadrant detector QPD2.

[0057] The beams incident on photodetector PD1 and quadrant detector QPD1 will interfere to form optical beats, which will then be received by photodetector PD1 and quadrant detector QPD1 respectively; the beams incident on photodetector PD2 and quadrant detector QPD2 will interfere to form optical beats, which will then be received by photodetector PD2 and quadrant detector QPD2 respectively.

[0058] After processing by the phase meter, phase information, differential wavefront phase detection (DWS) signal, and differential power detection (DPS) signal can be obtained. The differential wavefront phase detection signal is used to measure the wavefront deviation angle of the two beams and can be divided into horizontal signal DWS. h and vertical signal DWS v The calculation method is as follows:

[0059]

[0060]

[0061] The differential power sensing (DPS) signal is divided into horizontal and vertical signals, denoted as DPS respectively. h and DPS v Defined as:

[0062]

[0063]

[0064] Δz can be obtained from the phase signal of photodetector PD1 and quadrant detector QPD1. and Find:

[0065]

[0066] θ y θ x It can be obtained from the differential wavefront phase detection (DWS) signal. For a small range of offset, the DWS signal is proportional to the corresponding offset angle, from which we can obtain:

[0067] θ y ∝DWS h

[0068] θ x ∝DWS v

[0069] The differential wavefront phase detection signal can be pre-calibrated to find the relationship between the differential wavefront phase detection signal and the change θ, thereby allowing the change to be calculated in subsequent measurements; Δx and Δy can be obtained from the differential power detection (DPS) signal. For small-range changes, we have:

[0070] Δx=C1·DPS h

[0071] Δy=C2·DPS v

[0072] C1 and C2 are proportionality coefficients; when the sample to be tested changes along the rolling direction, for a small range of angular changes, the deflection angle and ellipticity have an approximately linear relationship, from which we can obtain:

[0073]

[0074] k is a scaling factor, a is the major semi-axis of the ellipsoidally polarized light, and b is the minor semi-axis of the ellipsoidally polarized light. The reference light reflected by the beam splitter BS1 is linearly polarized. Rotating the half-wave plate makes the polarization direction of the reference light form a 45° angle with the major axis of the ellipsoidally polarized light. The polarization direction can be obtained by a polarization measuring instrument. At this time, the phase signal change obtained by the detector PD2 can be written as:

[0075]

[0076] Where a is the major semi-axis of the ellipsoidal light; b is the minor semi-axis of the ellipsoidal light; γ is the angle between the polarization direction of the reference light and the major axis of the ellipsoidal light. This is the common-mode portion. When the initial included angle is 45°, the phase change caused by polarization includes:

[0077]

[0078] That is, the phase change is equivalent to the ellipticity change; and because the angle change is small, it can be considered that during the measurement process, the phase change is equivalent to the ellipticity change. Therefore, we can conclude:

[0079]

[0080] It can be obtained from detector PD1, minus Noise introduced by the acousto-optic modulator can be removed, thereby obtaining Then we get θ z .

[0081] From this, we can obtain the variations of the sample under test in the x, y, and z directions (Δx, Δy, Δz); and the variations in azimuth, pitch, and roll directions (θ). y θ x θ z .

Claims

1. A multi-degree-of-freedom telescope testing system, characterized in that, It includes a first laser, a second laser, a first acousto-optic modulator, a second acousto-optic modulator, a first beam splitter, a second beam splitter, a third beam splitter, a first lateral beam splitter, a second lateral beam splitter, a third lateral beam splitter, a first plane mirror, a second plane mirror, a third plane mirror, a half-wave plate, a quarter-wave plate, a pyramidal retroreflector, a semi-reflective mirror, a first photodetector, a second photodetector, a first four-quadrant detector, a second four-quadrant detector, and a digital phase meter; The first laser and the second laser each output a laser beam, which then passes through the first acousto-optic modulator and the second acousto-optic modulator, respectively, to obtain a frequency of... The reference light and frequency are The measuring light, and then both beams enter the interferometer; The output from the first laser, after frequency shifting by the first acousto-optic modulator, is: The reference light first enters the first beam splitter, and after being split by the beam splitter, it is divided into a reflection component and a transmission component. The transmission component enters the first transverse beam splitter, and after being transmitted and reflected by the first transverse beam splitter, the outgoing light is two parallel beams. The two beams are transmitted through the second beam splitter, and then reflected by the second plane mirror, and will enter the second beam splitter again. After that, the two beams are reflected by the second beam splitter to the second transverse beam splitter, and after being reflected twice more, they are received by the first four-quadrant detector and the first photodetector, respectively. The reflection component will pass through the half-wave plate and enter the first plane mirror, and then be reflected by the third transverse beam splitter to the third beam splitter. After passing through the third beam splitter, the transmission component of this beam is received by the second four-quadrant detector, and its reflection component is received by the second photodetector. The output is from the second laser, and then the frequency is shifted by the second acousto-optic modulator. The measuring light first passes through a first transverse beam splitter, where it is transmitted and reflected to form two parallel components. After both beams pass through a second beam splitter, the component reflected from the first transverse beam splitter to the second beam splitter is reflected by a third plane mirror and then re-enters the second beam splitter. It is then reflected by the second beam splitter back to the second transverse beam splitter, transmitted through the second transverse beam splitter, and received by a first photodetector. The component transmitted from the first transverse beam splitter to the second beam splitter first passes through a semi-reflecting mirror. A portion of this beam is then reflected back to the second beam splitter by the semi-reflecting mirror, reflected again by the second beam splitter to the second transverse beam splitter, and then transmitted through the second transverse beam splitter to be received by a first four-quadrant detector. The remaining component... The beam passes through a semi-reflecting mirror to a retroreflector; the beam component incident on the retroreflector, after being reflected by the retroreflector, will pass through a quarter-wave plate and re-enter the second beam splitter, and then be reflected by the beam splitter to the third beam splitter; after passing through the third beam splitter, the transmitted component of the beam will be received by the second photodetector, and the reflected component will be received by the second quadrant detector; the beams incident on the first photodetector and the first quadrant detector will interfere to form optical beats, and then be received by the first photodetector and the first quadrant detector respectively; the beams incident on the second photodetector and the second quadrant detector will interfere to form optical beats, and then be received by the second photodetector and the second quadrant detector respectively. The signals output from the first photodetector, the second photodetector, the first quadrant detector, and the second quadrant detector are converted from analog to digital and then input into the digital phase meter. After processing, phase information, differential wavefront phase detection signal, and differential power detection signal can be obtained. The obtained differential wavefront phase detection signal is processed to obtain the change of the sample in the azimuth direction. and changes in pitch direction By processing the differential power detection signal, the sample's variation along the x-axis (Δx) and y-axis (Δy) are obtained; by processing the output phase result, the sample's variation along the axial direction (Δz) and its variation in the rolling degree of freedom are obtained. ; Therefore, the deformation and displacement of the sample under test are detected in three translational degrees of freedom and three rotational degrees of freedom, so as to achieve the purpose of multi-degree-of-freedom structural stability measurement. The surface of the retroreflector is respectively attached with a semi-reflecting mirror and a quarter-wave plate, each occupying half of the area.

2. The multi-degree-of-freedom telescope testing system according to claim 1, characterized in that: The frequency difference between the reference light and the measurement light .

3. The multi-degree-of-freedom telescope testing system according to claim 1, characterized in that: Both the beam splitter and the transverse beam splitter used are non-polarizing beam splitters, and the transmission-to-reflection ratio is 50:

50.

4. The multi-degree-of-freedom telescope testing system according to claim 1, characterized in that: The third plane mirror and the retroreflector are fixed at both ends of the sample to be tested, thereby allowing measurement of the size of the sample along each degree of freedom.

5. The multi-degree-of-freedom telescope testing system according to claim 1, characterized in that: The processed phase information, differential wavefront phase detection signal, and differential power detection signal include: The optical beat signals received by the four detector pixels on the surface of the first four-quadrant detector are processed by a digital phase meter to obtain four phase results, which are denoted as follows: , , and Overall phase results of the first four-quadrant detector It can be defined as: Calculate the differential wavefront phase probe signal; the differential wavefront phase probe signal is used to measure the wavefront deviation angle of two beams, and can be divided into horizontal signals. and vertical signal The calculation method is as follows: ； By performing area integration on the received light intensity, the average optical power received in each quadrant of the second four-quadrant detector is obtained. : Where Z is the dielectric impedance; ; For reference photoelectric field components; To measure the photoelectric field components, the average power in each quadrant is denoted as... , , , DPS signals can be divided into horizontal and vertical signals, denoted as follows: and Defined as: 。 6. The multi-degree-of-freedom telescope testing system according to claim 5, characterized in that: The change of the sample in the orientation direction and changes in pitch direction This is obtained by processing the differential wavefront phase detection signal; The sample's variation along the x-axis (Δx) and y-axis (Δy) is obtained using differential power detection signals; the sample's variation along the axial direction (Δz) and its variation in the rolling degree of freedom are also obtained. The phase is obtained by processing the output phase result. The specific calculation steps are as follows: The axial variation Δz is the phase signal obtained from the first photodetector and the first four-quadrant detector. and Find: Δx and Δy are obtained from the differential power detection signal. Because a retroreflector is used to reflect the beam, when the sample structure changes in the horizontal or vertical direction, the retroreflector position changes accordingly. This causes the position of the measurement beam on the surface of the second quadrant detector to shift, thus altering the DPS signal. For small-range changes, we have: , This is the proportionality coefficient; , Obtained from the differential wavefront phase detection signal; for a small range of offset, the DWS signal is proportional to the corresponding offset angle, from which we can obtain: The differential wavefront phase detection signal can be pre-calibrated to find the relationship between the differential wavefront phase detection signal and the change. The relationship can be used to calculate the change in subsequent measurements; The calculation is as follows: When the sample to be tested changes along the rolling direction, the retroreflector will rotate accordingly, which in turn will cause the quarter-wave plate on the surface of the retroreflector to rotate; therefore, the angle between the fast axis of the quarter-wave plate and the horizontal direction will change; if the laser incident on the quarter-wave plate is linearly polarized light, when the polarization direction of the incident linearly polarized light makes a certain angle α with the fast axis of the quarter-wave plate, and At this time, the outgoing light is elliptically polarized; rotating the quarter-wave plate will change the ellipticity of the outgoing elliptically polarized light; for small angular changes, the deflection angle and ellipticity have an approximately linear relationship, from which we can conclude: k is a scaling factor, a is the major semi-axis of the ellipsoidal beam, and b is the minor semi-axis of the ellipsoidal beam. The reference light reflected by beam splitter 1 is linearly polarized. Rotating the half-wave plate makes the polarization direction of the reference light form a 45° angle with the major axis of the ellipsoidal beam. The polarization direction can be obtained by a polarization measuring instrument. At this time, the phase signal change obtained by the second photodetector can be written as: Where a is the major semi-axis of the ellipsoid; b is the minor semi-axis of the ellipsoid. The angle between the reference light polarization direction and the major axis of the elliptically polarized light; This refers to the common-mode portion; when the initial included angle is 45°, the phase change caused by polarization includes: That is, the phase change is equivalent to the ellipticity change; and because the angle change is small, it can be considered that during the measurement process, the phase change is equivalent to the ellipticity change; therefore, we can conclude that: in Obtained from the first photodetector, minus Noise introduced by the acousto-optic modulator can be removed, thereby obtaining And thus obtain .

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