Phase control based weak value amplification beam deflection measurement system and method

Abstract

The application discloses a weak value amplification light beam deflection measurement system and method based on phase control, and belongs to the technical field of precise optical measurement. The system comprises a laser light source, a polarization state preparation module, a Sagnac interferometer and a detection module. The phase control unit built in the interferometer adopts a specific wave plate combination scheme to introduce a geometric phase, and has the advantages of simple structure, convenient debugging, no need for complex matching control equipment, utilization of the linear relationship between the wave plate rotation angle and the system phase difference, realization of accurate phase control. Meanwhile, by utilizing the common mode rejection characteristic of the Sagnac interferometer, the phase drift problem caused by path separation of the traditional double optical path interferometer is solved from the physical structure. The application can realize high-sensitivity and high-signal-to-noise-ratio precise measurement of micro-radian level light beam deflection, and is suitable for the precise detection demand of the light beam deflection quantity in the precise optical field.

Description

Technical Field

[0001] This application belongs to the field of precision optical measurement technology, specifically relating to a weak-value amplified beam deflection measurement system and method based on phase modulation. Background Technology

[0002] The statements in this section are merely to provide background information in relation to this application to aid in understanding it, and such background information does not necessarily constitute prior art.

[0003] The Sagnac interferometer, a classic common-path interferometer, possesses the core advantage of sharing identical optical path components between two beams of light propagating clockwise and counterclockwise. This common-mode characteristic endows it with a natural ability to suppress external interference noise such as environmental vibrations and temperature drift, effectively ensuring the stability of the measurement process and the reliability of the measurement results. Based on this advantage, the Sagnac interferometry principle is widely used in high-precision inertial navigation equipment such as fiber optic gyroscopes (FOGs), serving as the technical support for detecting the rotational angular velocity of the system. With the rapid iteration of quantum precision measurement technology, weak value amplification (WVA) technology based on the Aharonov-Albert-Vaidman (AAV) effect has emerged, providing a new technical path to break through the accuracy limits of Sagnac interferometers in non-rotational quantity measurements. This technology, through the synergistic control of pre-selection, weak interaction, and near-orthogonal post-selection, can amplify minute physical quantity signals by several orders of magnitude, significantly improving the detection sensitivity and resolution of weak signals.

[0004] However, in the practical construction and engineering application of the Sagnac weak measurement system, the precise introduction and accurate calibration of phase are bottlenecks restricting further improvement in the system's measurement accuracy. Currently, most mainstream phase control schemes employ the Soleil-Babinet Compensator (SBC), which achieves phase control based on the translational motion of the wedge angle of a birefringent crystal. This operation requires driving the crystal through a mechanical differential or micrometer head to complete micrometer-level translation. This manual adjustment method easily introduces additional vibration interference, leading to beam drift and affecting the accuracy of phase control. Furthermore, the phase difference of the SBC is non-linearly related to its differential or micrometer head readings and is significantly affected by changes in ambient temperature. Real-time calibration is required to maintain its measurement accuracy, which increases the complexity and operating cost of system debugging and limits the long-term stable operation performance of the system. Summary of the Invention

[0005] To solve the aforementioned technical problems, this application relies on the Sagnac common-path architecture and waveplate combination phase modulation unit, utilizing a 45° QWP- The HWP-45°QWP incorporates a combination of waveplates to introduce geometric phase. By leveraging the linear relationship between the half-wave plate rotation angle and the system phase difference, precise phase control is achieved. Simultaneously, combined with Sagnac common-mode suppression characteristics, environmental noise interference is effectively suppressed, improving measurement stability and accuracy, and enabling highly sensitive and precise measurement of micro-radian beam deflection.

[0006] To achieve the above objectives, the technical solution adopted in this application is as follows:

[0007] According to the first aspect of this application, this application provides a weak-value amplified beam deflection measurement system based on phase modulation, comprising: an input light source, a polarization state preparation module, a Sagnac interferometer, and a detection module arranged sequentially along the beam propagation path. The Sagnac interferometer includes a first beam splitter, a third mirror, a piezoelectric screw-driven mirror, a fourth mirror, a phase modulation unit, and a second half-wave plate. The first beam splitter, third mirror, piezoelectric screw-driven mirror, and fourth mirror are arranged sequentially in a clockwise direction, forming a rectangular closed optical path. The second half-wave plate is disposed between the third mirror and the piezoelectric screw-driven mirror, and the phase modulation unit is disposed between the piezoelectric screw-driven mirror and the fourth mirror. The clockwise and counterclockwise beams output by the first beam splitter return to the first beam splitter along the rectangular closed optical path and interfere destructively, then are combined to output interference light. The phase adjustment unit consists of a second quarter-wave plate, a third half-wave plate, and a third quarter-wave plate arranged sequentially along the beam propagation path. The fast axis angles of the second quarter-wave plate and the third quarter-wave plate are both fixed at 45 degrees. By adjusting the rotation angle of the third half-wave plate, a phase difference is generated between the clockwise and counterclockwise beams output by the first beam splitter.

[0008] Preferably, the phase difference rotation angle with the third half-wave plate The relationship is .

[0009] Preferably, the Sagnac interferometer further includes a second beam splitter, which is disposed on the transmission optical path of the interference light output by the first beam splitter and is used to separate the main interference light signal from the stray light signal; wherein the second beam splitter and the first beam splitter are parallel at the same height on the same transmission optical path.

[0010] Preferably, the detection module includes an optical power meter and a beam quality analyzer; wherein, the optical power meter is disposed on the reflected light path output by the second beam splitter for monitoring light intensity, and the beam quality analyzer is disposed on the transmitted light path output by the second beam splitter for measuring the lateral offset of the centroid position of the light spot.

[0011] Preferably, the polarization state preparation module is used to ensure that the light beam incident on the Sagnac interferometer is horizontally polarized. It includes a first quarter-wave plate, a first half-wave plate, and a polarizing beam splitter arranged sequentially along the beam propagation path. The first quarter-wave plate is used to restore the elliptically polarized light emitted from the input light source to linearly polarized light; the first half-wave plate is used to change the angle between its incident light polarization direction and the horizontal optical axis of the polarizing beam splitter to adjust the light intensity entering the Sagnac interferometer; and the polarizing beam splitter is used to allow only the horizontally polarized light calibrated by the first half-wave plate to transmit into the Sagnac interferometer.

[0012] Preferably, a lens assembly is also provided between the polarization state preparation module and the Sagnac interferometer. The lens assembly consists of a first lens and a second lens arranged sequentially along the beam propagation path. The lens assembly is used to magnify the spot diameter of the incident light and reduce the spread of the spot during subsequent propagation.

[0013] Preferably, the fast axis angle of the second half-wave plate is 45 degrees, which is used to symmetrically flip the polarization state of the light beam incident on the second half-wave plate with respect to the fast axis of the second half-wave plate.

[0014] Preferably, a collimation module is further provided between the input light source and the polarization state preparation module. This module consists of a first reflecting mirror, a second reflecting mirror, and an aperture arranged sequentially along the beam propagation path. It is used to collimate the beam from the input light source so that the beam incident on the Sagnac interferometer is a collimated parallel beam.

[0015] According to a second aspect of this application, a weak-value amplification beam deflection measurement method based on phase modulation is provided, implemented using the measurement system of the first aspect, comprising: activating an input light source to make the incident beam received by the Sagnac interferometer horizontally polarized; adjusting the Sagnac interferometer so that the clockwise and counterclockwise beams return along the rectangular closed loop to the first beam splitter and interfere destructively thereon; adjusting the rotation angle of the third half-wave plate in the phase modulation unit to a preset angle to introduce a phase difference between the clockwise and counterclockwise beams; adjusting the piezoelectric screw-driven reflector to deflect it to apply a perturbation signal to the system; measuring the lateral offset of the spot centroid position after the perturbation signal is applied using the detection module, and calculating the deflection angle of the piezoelectric screw-driven reflector based on the rotation angle of the third half-wave plate and the lateral offset of the spot centroid position using the weak-value amplification principle.

[0016] Preferably, the method further includes removing the first beam splitter and measuring the unmagnified reference offset, wherein the ratio of the lateral offset of the spot centroid position to the reference offset is the magnification factor.

[0017] Compared with the prior art, the main advantages of this application are:

[0018] This application, based on the Sagnac common-path architecture and geometric phase control principle, uses a waveplate combination to replace the traditional SBC. Precise phase control can be achieved simply by rotating the half-wave plate, offering convenient operation without the need for complex real-time calibration. It avoids the problems of vibration and nonlinear phase response introduced by the SBC, reducing the difficulty of device debugging and use. Furthermore, this application features a simple structure, requiring no additional complex optical components, resulting in a compact size and high stability, making it suitable for practical applications in precision optical measurement. In addition, the waveplate combination uses highly stable materials, minimizing the impact of ambient temperature and eliminating the need for complex temperature compensation and related control equipment, further enhancing the practicality and convenience of the device and facilitating the application of weak amplification technology in precision beam deflection measurement. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0020] Figure 1 This is a schematic diagram of the optical path of a phase-modulated weak-value amplified beam deflection measurement system according to an embodiment of this application;

[0021] Figure 2 This is a schematic flowchart of a phase-modulated weak-value amplified beam deflection measurement method according to an embodiment of this application;

[0022] Figure 3 This is a flowchart illustrating a phase-modulated weak-value amplified beam deflection measurement method according to another embodiment of this application.

[0023] Figure label:

[0024] 1-Input light source, 2-First reflecting mirror, 3-Second reflecting mirror, 4-Aperture, 5-First quarter-wave plate, 6-First half-wave plate, 7-Polarizing beam splitter, 8-First lens, 9-Second lens, 10-First beam splitter, 11-Third reflecting mirror, 12-Fourth reflecting mirror, 13-Piezoelectric screw driven reflecting mirror, 14-Second half-wave plate, 15-Second quarter-wave plate, 16-Third half-wave plate, 17-Third quarter-wave plate, 18-Second beam splitter, 19-Optical power meter, 20-Beam quality analyzer. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided through specific embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0026] The present application will be further described below with reference to the accompanying drawings and specific embodiments.

[0027] As mentioned in the background section, phase control of the Sagnac weak measurement system using the SBC (Single Beam Balance) suffers from prominent problems such as vibration interference, nonlinear correlation, temperature sensitivity, and complex debugging. To address these issues, the inventors, through long-term experimental exploration and technical optimization, discovered that specific waveplate combinations offer significant advantages over SBC in phase control. Compared to the SBC's mechanical translation-based control method, waveplate combinations do not require complex mechanical drive structures, effectively avoiding vibration interference caused by manual adjustment, reducing beam drift at the source, and ensuring the stability of phase control. The phase control process relies on its own optical properties, eliminating the need for cumbersome real-time calibration, significantly reducing system debugging difficulty and operating costs. Furthermore, it is unaffected by significant changes in ambient temperature, maintaining stable control accuracy over long periods. More importantly, a reasonable waveplate combination can achieve a linear correlation between phase and control parameters, facilitating precise and continuous phase control, providing a new technical path for improving the measurement accuracy of the Sagnac weak measurement system.

[0028] Figure 1 This is a schematic diagram of the optical path of a phase-modulated weak-value amplified beam deflection measurement system according to an embodiment of this application. Figure 1As shown, the system mainly includes: an input light source 1, a polarization state preparation module, a Sagnac interferometer, and a detection module arranged sequentially along the beam propagation path. The beam emitted from the input light source 1 passes sequentially through the polarization state preparation module and the Sagnac interferometer before being transmitted to the detection module, enabling the acquisition and analysis of beam deflection signals. The Sagnac interferometer includes a first beam splitter 10, a third reflector 11, a piezoelectric screw-driven reflector 13, a fourth reflector 12, a phase adjustment unit, and a second half-wave plate 14. The first beam splitter 10, the third reflector 11, the piezoelectric screw-driven reflector 13, and the fourth reflector 12 are arranged sequentially in a clockwise direction, forming a rectangular closed optical path. The second half-wave plate 14 is positioned between the third reflector 11 and the piezoelectric screw-driven reflector 13, and the phase adjustment unit is positioned between the piezoelectric screw-driven reflector 13 and the fourth reflector 12. The clockwise and counterclockwise beams output from the first beam splitter 10 return to the first beam splitter 10 along the rectangular closed optical path and undergo destructive interference, resulting in a combined output interference beam. The phase adjustment unit consists of a second quarter-wave plate 15, a third half-wave plate 16, and a third quarter-wave plate 17 arranged sequentially along the beam propagation path. The fast axis angles of the second quarter-wave plate 15 and the third quarter-wave plate 17 are both fixed at 45 degrees. By adjusting the rotation angle of the third half-wave plate 16, a phase difference is generated between the clockwise and counterclockwise beams output by the first beam splitter 10.

[0029] The embodiments of this application feature a simple and efficient structural design, eliminating the need for additional complex optical adjustment devices. Built upon the Sagnac common-path architecture and waveplate combination phase control unit, the overall assembly is convenient and the operation process is simple, significantly reducing the difficulty of equipment debugging and daily maintenance, and improving the efficiency of measurement work. For phase control, a specific waveplate combination of 45°QWP (quarter-wave plate) - βHWP (variable angle half-wave plate) - 45°QWP is used. The fast axis of the 45°QWP forms a 45° angle with the polarization direction of the linearly polarized light output from the polarization state preparation module. The HWP can rotate around the optical axis without complex driving equipment. Geometric phase can be precisely introduced simply by rotating the half-wave plate. Utilizing the linear correspondence between the half-wave plate rotation angle and the system phase difference, continuous and precise phase control can be achieved, providing technical support for high-sensitivity measurements. Simultaneously, the waveplate combination is less affected by temperature, eliminating the need for complex temperature compensation devices, further enhancing the ease of control and stability. Furthermore, leveraging the inherent common-mode suppression characteristics of the Sagnac common-path architecture, the influence of external environmental noise, temperature fluctuations, vibrations, and other interference factors on the measurement system can be effectively offset, significantly improving the stability of the measurement process and the accuracy of the measurement results. The piezoelectric screw-driven reflector employs a high-precision micro-displacement driving structure, with fine-tuning accuracy down to the micro-radian level. This enables the embodiments of this application to achieve high-sensitivity precision measurement of micro-radian-level beam deflection, overcoming the shortcomings of traditional measurements in weak deflection measurements. It can be widely applied in optical detection, precision instruments, quantum sensing, and other fields, providing a reliable measurement solution for technological upgrades in related fields.

[0030] In some embodiments, the input light source 1 is a laser with a stable output wavelength to ensure the repeatability of the measurement, and the wavelength of the output beam is 795nm.

[0031] In some embodiments, the fast axis angle of the second half-wave plate 14 is 45 degrees, which is used to symmetrically flip the polarization state of the light beam incident on the second half-wave plate 14 with respect to the fast axis of the second half-wave plate 14.

[0032] Continue to refer to Figure 1 In some embodiments, the Sagnac interferometer further includes a second beam splitter 18, which is disposed on the transmission optical path of the interference light output by the first beam splitter 10, and is used to separate the main interference signal from the stray light signal. The embodiments of this application can effectively strip away scattered reflections in the optical path, thereby achieving high-sensitivity, high-signal-to-noise ratio precision measurement of micro-radian beam deflection without the need for complex phase-locked loops.

[0033] Continue to refer to Figure 1 In some embodiments, the detection module includes an optical power meter 19 and a beam quality analyzer 20. The optical power meter 19 is positioned on the reflected light path output from the second beam splitter 18 to monitor light intensity, while the beam quality analyzer 20 is positioned on the transmitted light path output from the second beam splitter 18 to measure the lateral offset of the beam's centroid position. The optical power meter 19 acquires the beam intensity signal, and the beam quality analyzer 20 detects the lateral offset of the beam's centroid position; together, they enable accurate calculation of the beam deflection.

[0034] Continue to refer to Figure 1In some embodiments, a polarization state preparation module is used to ensure that the beam incident on the Sagnac interferometer is horizontally polarized. This module includes a first quarter-wave plate 5, a first half-wave plate 6, and a polarization beam splitter 7 arranged sequentially along the beam propagation path. The first quarter-wave plate 5 is used to restore the elliptically polarized light emitted from the input light source 1 to linearly polarized light, eliminating the influence of polarization ellipticity. The first half-wave plate 6 is used to change the angle between its incident light polarization direction and the horizontal optical axis of the polarization beam splitter 7, thereby adjusting the light intensity entering the Sagnac interferometer. The polarization beam splitter 7 is used to allow only the horizontally polarized light calibrated by the first half-wave plate 6 to transmit into the Sagnac interferometer, reflecting and filtering out vertically polarized light to obtain high-purity horizontally polarized light as the incident light of the Sagnac interferometer, providing the required polarization state for the pre-selection process.

[0035] Continue to refer to Figure 1 In some embodiments, a lens assembly is also provided between the polarization state preparation module and the Sagnac interferometer. The lens assembly consists of a first lens 8 and a second lens 9 arranged sequentially along the beam propagation path. The lens assembly is used to magnify the spot diameter of the incident light and reduce the diffusion of the spot during subsequent propagation.

[0036] Continue to refer to Figure 1 In some embodiments, a collimation module is also provided between the input light source 1 and the polarization state preparation module. The collimation module consists of a first reflecting mirror 2, a second reflecting mirror 3 and an aperture 4 arranged sequentially along the beam propagation path. It is used to collimate the beam from the input light source 1 so that the beam incident on the Sagnac interferometer is a collimated parallel beam.

[0037] According to one embodiment of this application, the optical path of the measurement system is as follows: The light beam emitted by the input light source 1 is collimated by the first reflecting mirror 2, the second reflecting mirror 3, and the aperture 4. After being amplified by a lens combination, it enters the polarization state preparation module composed of the first quarter-wave plate 5, the first half-wave plate 6, and the polarization beam splitter 7. At this time, the incident light is prepared into a pure horizontal polarization state. Then, it is split into two beams by the first beam splitter 10, and the two beams propagate in clockwise and counterclockwise directions, respectively. Among them, the clockwise beam is reflected by the third reflecting mirror 11 and then converted into a vertical polarization state by the second half-wave plate 14. After that, it is reflected by the piezoelectric screw-driven reflecting mirror 13 into the phase adjustment unit, and then reflected back to the first beam splitter 10 by the fourth reflecting mirror 12. After being reflected by the fourth mirror 12, the counterclockwise beam enters the phase adjustment unit. At this time, the horizontally polarized light remains horizontally polarized after passing through the phase adjustment unit. It is then reflected by the piezoelectric screw driven by the mirror 13 to the second half-wave plate 14, which flips the horizontally polarized light to a vertically polarized state. Finally, it is reflected by the third mirror 11 back to the first beam splitter 10.

[0038] The clockwise and counterclockwise beams are represented at different stages as follows:

[0039] When the light beam is split and reflected once by each of the mirrors, but does not pass through any other devices, this can be expressed as formula (1):

[0040] (1)

[0041] in, Indicates the initial input state. Indicates the horizontal polarization state. Indicates the clockwise path state of light. This represents the counterclockwise path of light.

[0042] When the clockwise beam passes through the second half-wave plate 14 and the counterclockwise beam passes through the phase adjustment unit, it can be expressed as formula (2):

[0043] (2)

[0044] in, This indicates a vertically polarized state. A clockwise beam becomes vertically polarized after passing through the second half-wave plate 14. The counterclockwise beam remains horizontally polarized after passing through the phase adjustment unit. .

[0045] The state of the two beams of light, rotating clockwise and counterclockwise, at the exit of the Sagnac interferometer (where the first beam splitter 10 interferes), which is the pre-selected state, is given by formula (3):

[0046] (3)

[0047] in, Indicates the pre-selection state. This indicates that the first beam splitter 10 applies a force to the reflected light. / 2 phase shift, It represents the relative phase difference between clockwise and counterclockwise light.

[0048] When a small perturbation is applied to the piezoelectric screw driving the reflector 13, the joint state of the positional degree of freedom and the path degree of freedom is given by formula (4):

[0049] (4)

[0050] in, This represents the total state after the positional degrees of freedom and path degrees of freedom become entangled. Indicates the lateral position state. For position wave function, To apply the disturbance momentum, A is the system operator, expressed as formula (5):

[0051] (5)

[0052] in, Indicates the conjugate state of a clockwise path. This represents the conjugate state of a counterclockwise path.

[0053] Post-selection state Represented as formula (6):

[0054] (6)

[0055] Projecting the selected state onto the post-selected state yields formula (7):

[0056] (7)

[0057] in, This represents the unnormalized pointer state obtained after post-selection projection. Indicates the left arrow selected afterward.

[0058] Evolution Operator Expanded using the first-order approximation (satisfying) ,in , Let be the initial transverse root-mean-square radius of the beam, which is the initial width of the Gaussian beam in position space (transverse) before the light is incident on the Sagnac interferometer; The second moment (variance) represents the position of the centroid of the light spot. It is the square root of the variance, describing the initial spatial broadening of the beam.

[0059] (8)

[0060] Substituting formula (8) into formula (7) yields formula (9):

[0061] (9)

[0062] in, This represents the inner product of the first and last selections. This indicates the position of the centroid of the beam detected by the beam quality analyzer 20.

[0063] Weakness It can be defined as formula (10):

[0064] (10)

[0065] Formula (11) can be obtained through calculation:

[0066] (11)

[0067] Take a smaller angle as an approximation. ( ),so:

[0068] (12)

[0069] Regarding the phase adjustment unit, embodiments of this application can use a combination of waveplates with geometrical phase as the phase adjustment unit to achieve phase difference control. Besides employing a 45° QWP- The waveplate combination structure of HWP-45°QWP, and also 45°QWP- The waveplate combination structure of HWP-135°QWP is presented here. Detailed calculations and analyses of the phase introduced by the two waveplate combination structures are performed to verify the effectiveness of using 45°QWP- The combined structure of HWP-45°QWP is used to introduce a phase difference. The specific calculation and analysis process is as follows:

[0070] General form of waveplate Jones matrix:

[0071] ;

[0072] in, This represents the general form of the waveplate Jones matrix. Indicates the phase delay. Indicates the fast axis angle.

[0073] (1) Combination 1: 45°QWP- HWP-45°QWP

[0074] Total matrix ;

[0075] in, This represents the Jones matrix of a quarter-wave plate with a fast axis angle of 45°, and the phase delay. , .

[0076] Indicates the fast axis angle as The half-waveplate Jones matrix, phase delay fast axis angle .

[0077] Calculation yields .

[0078] Linearly polarized light with pure horizontal polarization After waveplate combination, the output is As can be seen, it still maintains a horizontal polarization state.

[0079] The theoretical derivation is as follows:

[0080] ①Derivation of the Jones matrix for clockwise path (CW)

[0081] Optical sequence: 45°HWP → 45°QWP → HWP → 45°QWP;

[0082] Jones matrix of clockwise path :

[0083] ;

[0084] in, Indicates the fast axis angle as The half-waveplate Jones matrix, phase delay ; This represents the Jones matrix of a half-waveplate with a fast axis angle of 45°, and the phase delay. , .

[0085] The simplified result is: .

[0086] The clockwise optical path output is:

[0087] ;

[0088] in, Represents the polarization state of the emitted light along a clockwise path. This represents the polarization state of the incident light.

[0089] The output polarization state of the emitted light along the clockwise path is vertically polarized, with a phase of... .

[0090] ② Derivation of the Jones matrix for the counterclockwise path (CCW)

[0091] Optical sequence: 45° QWP → HWP → 45°QWP → 45°HWP;

[0092] Jones matrix of counterclockwise path ;

[0093] Because light enters the waveplate assembly in the opposite direction along the counter-clockwise path, the sign of the angle is reversed. Among these, This represents the Jones matrix of a half-waveplate with a fast axis angle of 45° in a counterclockwise optical path. . This represents the Jones matrix of a quarter-wave plate with a fast axis angle of 45° in a counterclockwise optical path. . The angle of the fast axis in the counterclockwise optical path is... The Jones matrix of half-wave plate.

[0094] The simplified result is: .

[0095] The counter-clockwise optical path output is:

[0096] ;

[0097] in, This represents the polarization state of the emitted light following a counterclockwise path.

[0098] The output polarization state of the light emitted from the counterclockwise path is vertically polarized, with a phase of... .

[0099] Phase difference .

[0100] (2) Combination 2: 45°QWP- HWP-135°QWP

[0101] Overall matrix: ;

[0102] in, This represents the Jones matrix of a quarter-wave plate with a fast axis angle of 135°, and the phase delay. , .

[0103] Calculation yields .

[0104] Linearly polarized light with pure horizontal polarization After waveplate combination, the output is We can see that it has been converted to a vertical polarization state.

[0105] The theoretical derivation is as follows:

[0106] ①Derivation of the Jones matrix for clockwise path (CW)

[0107] Optical sequence: 45°HWP → 45°QWP → HWP → 135° QWP;

[0108] matrix: ;

[0109] After simplification, we get:

[0110] .

[0111] ② Derivation of the Jones matrix for the counterclockwise path (CCW)

[0112] Optical sequence: 135° QWP → HWP → 45°QWP → 45°HWP;

[0113] matrix: ;

[0114] After complete simplification:

[0115] .

[0116] The results show that No phase difference was introduced.

[0117] The above analysis shows that using combination 1: 45°QWP- The HWP-45°QWP waveplate combination scheme utilizes a 16° rotation of the middle third half-waveplate. It can linearly control the system phase difference without changing the linear polarization characteristics of the emitted light.

[0118] This application embodiment can also use the SBC as a phase adjustment unit to achieve phase difference control. Clockwise and counterclockwise beams pass through the SBC with orthogonal polarization states (H state and V state), respectively. Adjusting the differential (or micrometer) head of the SBC can change the effective thickness difference of the passing beams, thereby introducing a phase difference between the two beams. .

[0119] Figure 2 This is a schematic flowchart illustrating a phase-modulated weak-value amplified beam deflection measurement method according to an embodiment of this application. Figure 2 As shown, the measurement method is implemented using the measurement system in the aforementioned embodiment, including: Step S201: Activating the input light source 1 to make the incident beam received by the Sagnac interferometer horizontally polarized. Step S202: Adjusting the Sagnac interferometer so that the clockwise and counterclockwise beams return to the first beam splitter 10 along a rectangular closed loop and interfere destructively there. Step S203: Adjusting the rotation angle of the third half-wave plate 16 in the phase adjustment unit to a preset angle to introduce a phase difference between the clockwise and counterclockwise beams. Step S204: Adjusting the piezoelectric screw driving the reflector 13 to deflect it to apply a disturbance signal to the system. Step S205: Measuring the lateral offset of the spot centroid position after the disturbance signal is applied using the detection module, and calculating the deflection angle of the piezoelectric screw driving the reflector 13 based on the rotation angle of the third half-wave plate 16 and the lateral offset of the spot centroid position using the weak value amplification principle.

[0120] Figure 3 This is a flowchart illustrating a phase-modulated weak-value amplified beam deflection measurement method according to another embodiment of this application.

[0121] like Figure 3As shown, in step S301: the beam emitted by the 795nm laser is collimated. The collimated light is then polarized by the first quarter-wave plate (QWP) 5, the first half-wave plate (HWP) 6, and the polarization beam splitter (PBS) 7 to ensure that the light entering the Sagnac interferometer is in a pure horizontal polarization state, thus avoiding impure polarization state from affecting the interference effect and subsequent beam intensity distribution.

[0122] Step S302: Construct the Sagnac interferometer. After initial construction, alternating bright and dark fringes will be observed on the beam quality analyzer. This indicates an angular deviation between the clockwise and counterclockwise propagating beams, preventing them from aligning. Slightly adjust the angle of the third mirror 11 or the fourth mirror 12 to widen the fringes until they disappear, becoming a uniform dark spot. At this point, the Sagnac interferometer is considered properly configured, and the transmitted light after beam combining by the first beam splitter 10 is at the dark port. Place the second beam splitter 18 on the transmission path of the first beam splitter 10. Due to the thickness of the glass substrate, the first beam splitter 10 will produce non-interfering back surface reflections. The function of the second beam splitter 18 is to separate the main interference signal from stray light signals. It is crucial to ensure that the second beam splitter 18 and the first beam splitter 10 are on the same transmission path and parallel at the same height.

[0123] Step S303: The polarization state is changed by placing a 45-degree second half-wave plate 14 between the third reflecting mirror 11 and the piezoelectric screw-driven reflecting mirror 13; the phase adjustment unit placed between the fourth reflecting mirror 12 and the piezoelectric screw-driven reflecting mirror 13 is adjusted to introduce a preset phase difference into the clockwise and counterclockwise beams. For example, the rotation angle of the third half-wave plate 16 in the wave plate assembly can be adjusted to a preset angle.

[0124] Step S304: Activate the piezoelectric screw to drive the reflector 13 to deflect it. The piezoelectric screw to drive the reflector 13 is not used to adjust the system phase, but as a signal source to apply a controllable small angle deflection to the system. For example, the small perturbation applied to the mirror each time is set to 3.5 urad to simulate the weak physical perturbations that may occur in actual application scenarios.

[0125] Step S305: The optical power meter 19 on the reflected optical path of the second beam splitter 18 detects and collects power changes in real time, and the beam quality analyzer 20 on the transmitted optical path of the second beam splitter 18 measures and collects the lateral offset of the spot centroid position. By processing and comparing the collected information, the lateral offset of the spot centroid position after applying a disturbance to the system using the piezoelectric screw-driven reflector 13 can be obtained. The approximate value can be expressed as follows: (13)

[0126] (13)

[0127] The value of the disturbance applied to the system can be obtained by inversion using formula (13). This allows us to obtain the actual deflection angle of the beam.

[0128] Refer to Figure 3 In some embodiments, the method may further include: removing the first beam splitter 10, measuring the unamplified reference offset, and the ratio of the lateral offset to the reference offset being the amplification factor. The amplification factor confirms the system's ability to amplify weak signals, ensuring that weak signals below the detector resolution can be detected.

[0129] This application utilizes the linear relationship between the rotation angle of the half-wave plate and the system phase difference in a waveplate assembly to introduce a preset phase difference between clockwise and counterclockwise beams. The entire adjustment process requires no complex driving equipment or real-time calibration; precise phase control can be achieved simply by rotating the half-wave plate. This is convenient and allows for accurate resetting. If the measurement accuracy needs adjustment or the measurement conditions need to be changed, only the angle of the half-wave plate needs to be rotated again; no disassembly or adjustment of other optical components is required. This simplifies operation and significantly improves measurement efficiency and practicality. A piezoelectric screw drives a reflector to apply a small angular deflection to the system. This small angular deflection represents the weak interaction being measured, simulating the small deflection of the beam in actual measurements, ensuring the precise controllability of the weak interaction process.

[0130] References to "various embodiments," "some embodiments," "one embodiment," or "embodiment," etc., in this specification refer to a specific feature, structure, or property described in connection with an embodiment that is included in at least one embodiment. Therefore, the appearance of the phrases "in various embodiments," "in some embodiments," "in one embodiment," or "in an embodiment," etc., throughout this specification does not necessarily refer to the same embodiment. Furthermore, specific features, structures, or properties can be combined in any suitable manner in one or more embodiments. Therefore, a specific feature, structure, or property shown or described in connection with one embodiment can be combined, in whole or in part, with features, structures, or properties of one or more other embodiments without limitation, provided that such combination is not illogical or inoperable.

[0131] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments or implementation methods. Similar or identical parts between the various embodiments of this application can be referred to mutually. The implementation principles and technical effects of the inventive concept can be mutually referenced, and will not be repeated here. Where there is no conflict, the various embodiments or implementation methods in this application can be combined with each other.

[0132] It should be noted that although the steps are described in a specific order above, it does not mean that the steps must be executed in the above specific order. In fact, some of these steps can be executed concurrently or even in a different order, as long as the required function can be achieved.

[0133] The embodiments of this application have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used in the embodiments of this application is chosen to best explain the principles, practical applications, or technological improvements in the market, or to enable other those skilled in the art to understand the embodiments disclosed in this application.

Claims

1. A weak-value amplified beam deflection measurement system based on phase modulation, characterized in that, include: The input light source (1), polarization state preparation module, Sagnac interferometer and detection module are arranged sequentially along the beam propagation path; The Sagnac interferometer includes a first beam splitter (10), a third mirror (11), a piezoelectric screw-driven mirror (13), a fourth mirror (12), a phase adjustment unit, and a second half-wave plate (14). The first beam splitter (10), the third mirror (11), the piezoelectric screw-driven mirror (13), and the fourth mirror (12) are arranged in a clockwise direction to form a rectangular closed optical path. The second half-wave plate (14) is located between the third mirror (11) and the piezoelectric screw-driven mirror (13), and the phase adjustment unit is located between the piezoelectric screw-driven mirror (13) and the fourth mirror (12). The clockwise beam and the counterclockwise beam output by the first beam splitter (10) return to the first beam splitter (10) along the rectangular closed optical path and interfere with each other, resulting in destructive interference. The beam is then combined and output as interference light. The phase adjustment unit consists of a second quarter-wave plate (15), a third half-wave plate (16), and a third quarter-wave plate (17) arranged sequentially along the beam propagation path. The fast axis angles of the second quarter-wave plate (15) and the third quarter-wave plate (17) are both fixed at 45 degrees. By adjusting the rotation angle of the third half-wave plate (16), a phase difference is generated between the clockwise and counterclockwise beams output by the first beam splitter (10).

2. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 1, characterized in that, Phase difference rotation angle with the third half-wave plate (16) The relationship is .

3. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 1, characterized in that, The Sagnac interferometer also includes a second beam splitter (18), which is disposed on the transmission path of the interference light output by the first beam splitter (10) and is used to separate the main interference light signal from the stray light signal; wherein the second beam splitter (18) and the first beam splitter (10) are parallel at the same height on the same transmission path.

4. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 3, characterized in that, The detection module includes an optical power meter (19) and a beam quality analyzer (20); wherein, the optical power meter (19) is set on the reflected light path output by the second beam splitter (18) for monitoring light intensity, and the beam quality analyzer (20) is set on the transmitted light path output by the second beam splitter (18) for measuring the lateral offset of the centroid position of the light spot.

5. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 1, characterized in that, The polarization state preparation module is used to make the beam incident on the Sagnac interferometer horizontally polarized. It includes a first quarter-wave plate (5), a first half-wave plate (6), and a polarization beam splitter (7) arranged sequentially along the beam propagation path. The first quarter-wave plate (5) is used to restore the elliptically polarized light emitted from the input light source (1) to linearly polarized light; the first half-wave plate (6) is used to change the angle between the polarization direction of its incident light and the horizontal optical axis of the polarization beam splitter (7) to adjust the light intensity entering the Sagnac interferometer; the polarization beam splitter (7) is used to allow only the horizontally polarized light calibrated by the first half-wave plate (6) to be transmitted into the Sagnac interferometer.

6. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 5, characterized in that, A lens assembly is also provided between the polarization state preparation module and the Sagnac interferometer. It consists of a first lens (8) and a second lens (9) arranged sequentially along the beam propagation path. The lens assembly is used to amplify the beam diameter of the incident light and reduce the spread of the beam in the subsequent propagation process.

7. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 1, characterized in that, The fast axis angle of the second half-wave plate (14) is 45 degrees, which is used to symmetrically flip the polarization state of the light beam incident on the second half-wave plate (14) with respect to the fast axis of the second half-wave plate (14).

8. The weak-value amplified beam deflection measurement system based on phase modulation according to claim 1, characterized in that, A collimation module is also provided between the input light source (1) and the polarization state preparation module. It consists of a first reflector (2), a second reflector (3), and an aperture (4) arranged sequentially along the beam propagation path. It is used to collimate the beam from the input light source (1) so that the beam incident on the Sagnac interferometer is a collimated parallel beam.

9. A method for measuring the deflection of a weakly amplified beam based on phase modulation, implemented using the measurement system described in any one of claims 1-8, characterized in that, include: Start the input light source (1) to make the incident beam received by the Sagnac interferometer horizontally polarized; Adjust the Sagnac interferometer so that the clockwise beam and the counterclockwise beam return along the rectangular closed loop to the first beam splitter (10) and therein interference cancellation occurs; The rotation angle of the third half-wave plate (16) in the phase adjustment unit is adjusted to a preset angle to introduce a phase difference between the clockwise beam and the counterclockwise beam; Adjust the piezoelectric screw to drive the reflector (13) to deflect it, thereby applying a disturbance signal to the system; The detection module is used to measure the lateral offset of the center of mass of the light spot after the disturbance signal is applied, and the deflection angle of the piezoelectric screw-driven reflector (13) is calculated based on the rotation angle of the third half-wave plate (16) and the lateral offset of the center of mass of the light spot using the weak value amplification principle.

10. The method according to claim 9, characterized in that, Also includes: Remove the first beam splitter (10) and measure the unmagnified reference offset. The ratio of the lateral offset of the spot centroid position to the reference offset is the magnification factor.

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