System and method for measuring wavefront aberration caused by light field waist spot mismatch in cavity enhancement system

Abstract

The present application belongs to the technical field of wavefront distortion measurement, and particularly relates to a wavefront distortion measurement system and method caused by light field waist spot mismatch in a cavity enhancement system. In order to accurately capture the wavefront distortion signal caused by light field waist spot mismatch, an electro-optic modulator (EOM), a convex lens, a three-mirror ring cavity, a plane mirror, a multi-quadrant detector (MPD) and a frequency mixer are sequentially arranged on the outgoing light path of the laser. Through light field modulation, resonance amplification, phase-locked demodulation and quantitative calculation, an error signal reflecting the distortion degree of two types is extracted, the minimum measurable waist spot size and position change are derived, accurate feedback is provided for long-term stable locking of the optical cavity, additional distortion interference caused by the thermal effect of the laser is compensated, and the measurement accuracy and stability of the system are improved.

Description

Technical Field

[0001] This invention belongs to the field of wavefront distortion measurement technology, specifically relating to a wavefront distortion measurement system and method for wavefront distortion caused by optical field waist spot mismatch in a cavity enhancement system. It is applicable to scenarios such as optical resonator stability control, laser beam quality monitoring, optical component performance evaluation, and precision optical experiments. Background Technology

[0002] In precision optical systems, the matching degree between the waist parameters of the laser beam (including waist position and waist size) and the intrinsic mode of the optical cavity directly determines the optical performance of the system. Waist mismatch is specifically divided into two categories: waist size mismatch and waist position mismatch. Both types of mismatch cause wavefront distortion: waist size mismatch leads to a deviation of the optical field amplitude distribution from the intrinsic mode of the optical cavity, disrupting wavefront phase continuity, manifested as wavefront curvature distortion and broadening of the intensity distribution; waist position mismatch causes a shift in the center of gravity of the optical field, resulting in wavefront tilt and abnormal phase gradient. Both lead to a decrease in intracavity resonant efficiency and a deterioration in output beam quality, severely affecting the operation of experiments and equipment that rely on stable optical cavities, such as precision measurement and quantum control.

[0003] Existing wavefront distortion measurement techniques primarily address distortions caused by lens aberrations, atmospheric disturbances, and cavity mirror vibrations, lacking a precise measurement scheme specifically for optical field waist spot mismatch (including size and position mismatch). Traditional measurement methods often employ Shack-Hartmann wavefront sensors, which, while enabling wavefront reconstruction, cannot accurately distinguish the distortion characteristics caused by waist spot size and position mismatches. Furthermore, they lack sensitivity to weak distortion signals caused by these two types of mismatches, making it difficult to extract the minimum measurable mismatch parameter through quantitative calculations. Additionally, they are difficult to integrate with the real-time stabilization and locking system of the optical cavity. Moreover, existing systems often neglect the indirect impact of laser-induced thermal deformation of optical components on the waist spot matching state, leading to deviations between measurement results and actual operating conditions. This fails to meet the quantitative measurement and control requirements of high-precision optical systems for waist spot mismatch-type wavefront distortion.

[0004] Therefore, there is an urgent need for a measurement system that can accurately capture the optical field waist spot mismatch signal caused by wavefront distortion, take into account thermal deformation interference compensation, and can be seamlessly integrated with the feedback control system to overcome the shortcomings of existing technologies. Summary of the Invention

[0005] This invention addresses the aforementioned problems by providing a wavefront distortion measurement system and method for optical field waist spot mismatch in a cavity enhancement system. It can accurately detect waist spot size mismatch and waist spot position mismatch. Through optical field modulation, resonant amplification, phase-locked demodulation, and quantization calculation, error signals reflecting the degree of both types of distortion are extracted, and the minimum measurable waist spot size and position changes are derived. This provides accurate feedback for the long-term stable locking of the optical cavity and compensates for additional distortion interference caused by laser thermal effects, thereby improving the system's measurement accuracy and stability.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] This invention provides a wavefront distortion measurement system for optical field waist spot mismatch in a cavity enhancement system, comprising a laser and a signal generator. The laser emits a laser beam, which is injected into a three-mirror annular cavity via an electro-optic modulator and a convex lens, coupled out by the cavity mirrors, and then incident on a multi-quadrant detector via a plane mirror. The output of the multi-quadrant detector is connected to the first input of a mixer. The first output of the signal generator is connected to the input of the electro-optic modulator, and the second output of the signal generator is connected to the second input of the mixer. The output of the mixer outputs the mixed signal.

[0008] Furthermore, the laser is a solid-state laser.

[0009] Furthermore, the signal generator is an arbitrary waveform generator.

[0010] Furthermore, multi-quadrant detectors correspond to different incident modes.

[0011] Furthermore, the convex lens and the CO2 gas laser that causes it to deform slightly due to thermal effects serve as the waist spot mismatch generation unit.

[0012] This invention also provides a method for measuring wavefront distortion caused by optical field waist spot mismatch in a cavity enhancement system, comprising the following steps:

[0013] Step 1, the laser emits at a frequency of The laser;

[0014] Step 2, the laser is phase-modulated by an electro-optic modulator to generate a frequency of The first-order edge band;

[0015] Step 3: The laser beam modulated by the electro-optic modulator is incident on the convex lens;

[0016] Step 4: Manually adjust the optical path to ensure that the laser spot emitted by the laser source is injected into the three-mirror annular cavity after being transmitted through the convex lens. At this time, the size and position of the laser waist spot are perfectly matched with the cavity.

[0017] The intrinsic waist of the cavity is located at the midpoint between the two plane mirrors of the three-mirror annular cavity, and the size of the waist is... for:

[0018] ;

[0019] In the formula, Where λ is the laser wavelength, L is the cavity length of the three-mirror annular cavity, and R is the radius of curvature.

[0020] Step 5, at this point, add [something] at the convex lens. Laser irradiation causes a slight deformation of the convex lens due to thermal effects, which in turn simultaneously induces changes in the size and position of the waist spot of the incident light field, forming a precursor to waist spot mismatch wavefront distortion. At this point, the size of the laser waist spot is... The position of the waist patch has also changed, and it no longer matches the intrinsic waist patch of the cavity;

[0021] Step 6: The incident light, after being filtered by the cavity, outputs a laser that is then incident on the photosensitive detection surface of the multi-quadrant detector. This converts the wavefront distortion information corresponding to the shift in the position of the waist spot and the change in the size of the waist spot into an electrical signal containing distortion features.

[0022] Step 7: The signal generator inputs the same frequency signal with frequency Ω as the local oscillation signal into the mixer. The mixer mixes the two types of distorted electrical signals output by the multi-quadrant detector with the local oscillation signal, and then performs low-pass filtering to achieve frequency demodulation and noise suppression, thereby completing the wavefront distortion measurement.

[0023] Furthermore, the wavefront distortion measurement includes waist spot position shift and waist spot size change, wherein the waist spot size change includes waist spot size change in the x and y directions, specifically:

[0024] (1) Changes in waist spot size:

[0025] The initial light field emitted from the laser:

[0026] ;

[0027] In the formula, E0 is the initial field amplitude. For the distribution of the light field, Let n be the one-dimensional field distribution of the beam along the x-axis, where n is the mode order along the x-axis. Let m be the one-dimensional field distribution of the beam along the y-axis, m be the mode order along the y-axis, i be the imaginary unit, and e be a constant.

[0028] The light field modulated by the electro-optic modulator:

[0029] ;

[0030] In the formula, , These are the phase modulation depth and modulation frequency of the electro-optic modulator, respectively.

[0031] After passing through a convex lens, the light field after the waist spot size mismatch in the x-direction is as follows:

[0032] ;

[0033] In the formula, This represents the relative size mismatch of the waist spot. , ;

[0034] Its horizontal distribution is as follows:

[0035] ;

[0036] In the formula, It is the Goui phase of the nth order modulus. , It is within the Rayleigh range. , The Hermitian polynomials representing the transverse distribution of the light field;

[0037] Based on the optical field distribution of the cavity eigenmode, the expansion form is as follows:

[0038] );

[0039] The transverse distribution of the optical field in the cavity eigenmode is as follows:

[0040] ;

[0041] The optical field after cavity filtering is:

[0042] ;

[0043] The light intensity entering the multi-quadrant detector is:

[0044] ;

[0045] In the formula, For light field ; conjugate light field;

[0046] After demodulation and low-pass filtering, the error signal is:

[0047] ;

[0048] The error signal obtained after quantization is:

[0049] ;

[0050] In the formula, The value of j is affected by the field distribution of the incident light and the excited mode. When the mode order n is even, j takes the value of n+2; when the mode order is odd, the value of j is the same as that of the n-1 order. For annihilation operators The average value, For annihilation operators The ups and downs, For modes other than the nth order mode;

[0051] Setting the signal-to-noise ratio to 1, the smallest measurable waist spot size change in the x-direction is:

[0052] ;

[0053] In the formula, P is the incident laser power, Let c be Planck's constant and c be the speed of light;

[0054] Similarly, the error signal in the y-direction can be obtained as follows:

[0055] ;

[0056] In the formula, , Other characters are analogous to the x-direction;

[0057] Setting the signal-to-noise ratio to 1, the smallest measurable waist spot size change in the y-direction can be obtained as follows:

[0058] ;

[0059] (2) Displacement of waist spot position:

[0060] Light field after mismatch in waist spot position:

[0061] ;

[0062] In the formula, , This represents the smallest measurable change in the position of the waist spot.

[0063] Its horizontal distribution is as follows:

[0064] ;

[0065] In the formula, Let z be the beam radius at point z;

[0066] Based on the optical field distribution of the cavity eigenmode, the expansion form is as follows:

[0067] ;

[0068] The optical field after cavity filtering is:

[0069] ;

[0070] The light intensity entering the multi-quadrant detector is:

[0071] ;

[0072] After demodulation and low-pass filtering, the error signal is:

[0073] ;

[0074] The error signal obtained after quantization is:

[0075] ;

[0076] Setting the signal-to-noise ratio to 1, the smallest measurable change in the position of the waist spot can be obtained as follows:

[0077] .

[0078] The signal generator outputs a radio frequency drive signal with a frequency of Ω, which controls the EOM to apply phase modulation of the incident laser beam at a specific frequency, so that the laser beam carries reference modulation information and provides a carrier basis for subsequent demodulation of distorted signals.

[0079] The core structure of the MPD (Multi-Level Device) is designed around photoelectric conversion and independent signal readout for high-precision spot positioning. It consists of a photosensitive surface segmentation, photoelectric conversion, and signal readout system. Its substrate is precisely lithographically divided into multiple independent quadrants (the number of quadrants is selected based on the incident light mode order), with signals independent between quadrants. Each quadrant generates a photocurrent proportional to the optical power through the internal photoelectric effect, which is then converted into a voltage value that can be directly measured.

[0080] For the waist spot size mismatch signal, a low-frequency error signal containing the size mismatch factor is extracted. After demodulation, low-pass filtering, and quantization, combined with parameters such as Planck's constant, laser wavelength, and cavity length, and setting the signal-to-noise ratio to 1, the minimum measurable waist spot size change can be derived. For the waist spot position mismatch signal, the same detection and demodulation logic is used to extract the corresponding low-frequency error signal and quantize it, deriving the minimum measurable waist spot position change. Finally, the quantized error signals corresponding to the two types of mismatch are output. This is a size mismatch error signal. (This is the position mismatch error signal).

[0081] Compared with the prior art, the present invention has the following advantages:

[0082] Comprehensive measurement dimensions covering core distortion parameters: This invention specifically achieves simultaneous measurement of two core wavefront distortion parameters: waist spot size change (including x and y bidirectional) and waist spot position offset, fully capturing the distortion characteristics caused by optical field waist spot mismatch. Existing technologies mostly focus on single-dimensional distortion measurement, while the design of this invention significantly improves the completeness and practicality of wavefront distortion measurement, and can more comprehensively reflect the optical field distortion state.

[0083] High measurement sensitivity and precise capture of minimal distortion: Based on the field distribution characteristics of a 1064nm Hermitian Gaussian beam, this invention establishes a complete model for optical field modulation, cavity filtering, and signal demodulation. Through quantization processing, the minimum measurable distortion parameter is derived, enabling precise detection of even the smallest waist spot size changes and positional shifts. Compared to existing technologies, this invention offers superior measurement accuracy, meeting the application requirements for high-precision wavefront distortion measurement.

[0084] Strong anti-interference capability and excellent signal stability: This invention employs a combined technical solution of "electro-optic modulation + frequency mixing and demodulation + low-pass filtering." By mixing the local oscillation signal provided by the signal generator with the distorted electrical signal output from the multi-quadrant detector, environmental noise and optical path interference are effectively suppressed, significantly improving the signal-to-noise ratio of the measurement signal. Compared to the shortcomings of existing technologies that are susceptible to noise, the signal processing mechanism of this invention ensures the stability and reliability of measurement results in complex optical path environments. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of a measurement system for optical field waist spot mismatch caused by wavefront distortion.

[0086] Figure 2 The left figure shows the change in the smallest measurable waist spot size in the x-direction. The graph shows the variation of the mode order n and optical power P of the incident light; the right graph shows the variation of the minimum measurable waist size of the incident light injected with different modes. Image showing how the incident light power P changes.

[0087] Figure 3 The left figure shows the change in the smallest measurable waist spot size in the x-direction. The graph shows the variation of the mode order m and optical power P of the incident light; the right graph shows the variation of the minimum measurable waist size of the incident light injected with different modes. Image showing how the incident light power P changes.

[0088] Figure 4 The left image shows the change in the position of the smallest measurable waist spot. The graph shows the variation of the mode order n and optical power P of the incident light; the right graph shows the variation of the smallest measurable waist spot position with incident light injected in different modes. Image showing how the incident light power P changes. Detailed Implementation

[0089] To further illustrate the technical solution of the present invention, the present invention will be further described below through embodiments.

[0090] like Figure 1As shown in this embodiment, a wavefront distortion measurement system caused by optical field waist spot mismatch in a cavity enhancement system includes a laser and a signal generator. The laser emits a laser beam, which is injected into a three-mirror annular cavity through an electro-optic modulator and a convex lens in sequence. The beam is then coupled out by the cavity mirrors and then incident on a multi-quadrant detector through a plane mirror. The output terminal of the multi-quadrant detector is connected to the first input terminal of a mixer. The first output terminal of the signal generator is connected to the input terminal of the electro-optic modulator, and the second output terminal of the signal generator is connected to the second input terminal of the mixer. The output terminal of the mixer outputs the mixed signal.

[0091] The laser beam output from the laser is phase-modulated at a specific frequency (Ω) by an electro-optic modulator (EOM), and then injected into a three-mirror annular cavity through a convex lens that is slightly deformed due to the thermal effect of laser irradiation. After multiple reflections and resonances within the three-mirror annular cavity, the laser beam is coupled out by the cavity mirrors, then deflected by a plane mirror, and precisely incident on the photosensitive detection surface of a multi-quadrant detector (MPD). The signal generator (Ω) outputs a radio frequency drive signal to control the electro-optic modulator to complete the optical modulation, and inputs the same frequency signal as a local oscillator into the mixer. The multi-quadrant detector (MPD) converts the detected optical signal into an electrical signal containing information on the waist spot position and waist spot size changes. This electrical signal is mixed with the local oscillator signal in the mixer, and finally, a low-frequency error signal (ε) reflecting the optical cavity error is extracted, which is used for subsequent feedback control to achieve long-term stable locking of the optical cavity.

[0092] In this embodiment, the laser is a solid-state laser, specifically the GoSF-D-YB-M model, outputting a 1064nm Hermit-Gaussian beam. The signal generator is a Suin TFG6960A digital-to-digital signal source function arbitrary waveform generator. The three-mirror cavity has a cavity length of 0.17m, a radius of curvature of 0.2, a reflectivity of 0.99 for both the plane mirror and the high-reflectivity mirror, and a reflectivity of 0.99 for both. The convex lens is BK7 (K9) glass coated with a 1064nm antireflection coating.

[0093] This embodiment provides a method for measuring wavefront distortion caused by optical field waist spot mismatch in a cavity enhancement system. Based on the aforementioned system, it includes the following steps:

[0094] Step 1, the laser emits at a frequency of The laser;

[0095] Step 2, the laser is phase-modulated by an electro-optic modulator to generate a frequency of The first-order edge band;

[0096] Step 3: The laser beam modulated by the electro-optic modulator is incident on the convex lens;

[0097] Step 4: Manually adjust the optical path to ensure that the laser spot emitted by the laser source is injected into the three-mirror annular cavity after being transmitted through the convex lens. At this time, the size and position of the laser waist spot are perfectly matched with the cavity.

[0098] The intrinsic waist of the cavity is located at the midpoint between the two plane mirrors of the three-mirror annular cavity, and the size of the waist is... for:

[0099] ;

[0100] In the formula, Where λ is the laser wavelength, L is the cavity length of the three-mirror annular cavity, and R is the radius of curvature.

[0101] Step 5, at this point, add [something] at the convex lens. Laser irradiation causes a slight deformation of the convex lens due to thermal effects, which in turn simultaneously induces changes in the size and position of the waist spot of the incident light field, forming a precursor to waist spot mismatch wavefront distortion. At this point, the size of the laser waist spot is... The position of the waist patch has also changed, and it no longer matches the intrinsic waist patch of the cavity;

[0102] Step 6: After the incident light passes through the cavity filter, the output laser is incident on the photosensitive detection surface of the multi-quadrant detector. The MPD, as the core detection element, can capture the intensity distribution characteristics of the laser beam and convert the wavefront distortion information corresponding to the position shift and size change of the waist spot of the light field into an electrical signal containing distortion characteristics. The amplitude and phase changes of this electrical signal directly reflect the degree and type of wavefront distortion.

[0103] Step 7: The signal generator inputs a local oscillation signal of frequency Ω into the mixer. The mixer mixes the two types of distorted electrical signals output from the multi-quadrant detector with the local oscillation signal, and then performs low-pass filtering to achieve frequency demodulation and noise suppression, thereby completing the wavefront distortion measurement. This is the error signal obtained when dimensional mismatch occurs in the x-direction. This is the error signal obtained when dimensional mismatch occurs in the y-direction. This is the error signal obtained when there is a position mismatch. Since both the x and y directions change simultaneously during a position mismatch, the signal changes are consistent regardless of whether the change originates from the x or y direction. Therefore, measuring the signal in only one direction is sufficient to characterize the change.

[0104] The wavefront distortion measurement includes waist spot position shift and waist spot size change, wherein the waist spot size change includes waist spot size change in the x and y directions, specifically:

[0105] (1) Changes in waist spot size:

[0106] The initial light field emitted from the laser:

[0107] ;

[0108] In the formula, E0 is the initial field amplitude. For the distribution of the light field, Let n be the one-dimensional field distribution of the beam along the x-axis, where n is the mode order along the x-axis. Let m be the one-dimensional field distribution of the beam along the y-axis, m be the mode order along the y-axis, i be the imaginary unit, and e be a constant.

[0109] The light field modulated by the electro-optic modulator:

[0110] ;

[0111] In the formula, , These are the phase modulation depth and modulation frequency of the electro-optic modulator, respectively.

[0112] After passing through a convex lens, the light field after the waist spot size mismatch in the x-direction is as follows:

[0113] ;

[0114] In the formula, This represents the relative size mismatch of the waist spot. , ;

[0115] Its horizontal distribution is as follows:

[0116] ;

[0117] In the formula, It is the Goui phase of the nth order modulus. , It is within the Rayleigh range. , The Hermitian polynomials representing the transverse distribution of the light field;

[0118] Based on the optical field distribution of the cavity eigenmode, the expansion form is as follows:

[0119] );

[0120] The transverse distribution of the optical field in the cavity eigenmode is as follows:

[0121] ;

[0122] The optical field after cavity filtering is:

[0123] ;

[0124] The light intensity entering the multi-quadrant detector is:

[0125] ;

[0126] In the formula, For light field ; conjugate light field;

[0127] After demodulation and low-pass filtering, the error signal is:

[0128] ;

[0129] The error signal obtained after quantization is:

[0130] ;

[0131] In the formula, The value of j is affected by the field distribution of the incident light and the excited mode. It is usually taken as the nodal value of the sign change of the product of the two phases. When the mode order n is even, j takes the value of n+2; when the mode order is odd, the value of j is the same as that of the n-1 order. For annihilation operators The average value, For annihilation operators The ups and downs, For modes other than the nth order mode;

[0132] Setting the signal-to-noise ratio to 1, the smallest measurable waist spot size change in the x-direction is:

[0133] ;

[0134] In the formula, P is the incident laser power, Let c be Planck's constant and c be the speed of light;

[0135] Similarly, the error signal in the y-direction can be obtained as follows:

[0136] ;

[0137] In the formula, , ;

[0138] Setting the signal-to-noise ratio to 1, the smallest measurable waist spot size change in the y-direction can be obtained as follows:

[0139] ;

[0140] (2) Displacement of waist spot position:

[0141] Light field after mismatch in waist spot position:

[0142] ;

[0143] In the formula, , This represents the smallest measurable change in the position of the waist spot.

[0144] Its horizontal distribution is as follows:

[0145] ;

[0146] In the formula, Let z be the beam radius at point z;

[0147] Based on the optical field distribution of the cavity eigenmode, the expansion form is as follows:

[0148] ;

[0149] The optical field after cavity filtering is:

[0150] ;

[0151] The light intensity entering the multi-quadrant detector is:

[0152] ;

[0153] After demodulation and low-pass filtering, the error signal is:

[0154] ;

[0155] The error signal obtained after quantization is:

[0156] ;

[0157] Setting the signal-to-noise ratio to 1, the smallest measurable change in the position of the waist spot can be obtained as follows:

[0158] .

[0159] The foregoing has shown and described the main features and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0160] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A system for measuring wavefront distortion caused by optical field waist spot mismatch in a cavity enhancement system, characterized in that, The system includes a laser and a signal generator. The laser emits a laser beam, which is injected into a three-mirror ring cavity through an electro-optic modulator and a convex lens. The beam is then coupled out by the cavity mirrors and then incident on a multi-quadrant detector through a plane mirror. The output of the multi-quadrant detector is connected to the first input of a mixer. The first output of the signal generator is connected to the input of the electro-optic modulator, and the second output of the signal generator is connected to the second input of the mixer. The output of the mixer outputs the mixed signal.

2. The wavefront distortion measurement system caused by optical field waist spot mismatch in a cavity enhancement system according to claim 1, characterized in that, The laser is a solid-state laser.

3. The wavefront distortion measurement system caused by optical field waist spot mismatch in a cavity enhancement system according to claim 1, characterized in that, The signal generator is an arbitrary waveform generator.

4. A method for measuring wavefront distortion caused by optical field waist spot mismatch in a cavity enhancement system, characterized in that, The system according to any one of claims 1-3 includes the following steps: Step 1, the laser emits at a frequency of The laser; Step 2, the laser is phase-modulated by an electro-optic modulator to generate a frequency of The first-order edge band; Step 3: The laser beam modulated by the electro-optic modulator is incident on the convex lens; Step 4: Manually adjust the optical path to ensure that the laser spot emitted by the laser source is injected into the three-mirror annular cavity after being transmitted through the convex lens. At this time, the size and position of the laser waist spot are perfectly matched with the cavity. The intrinsic waist of the cavity is located at the midpoint between the two plane mirrors of the three-mirror annular cavity, and the size of the waist is... for: ； In the formula, Where λ is the laser wavelength, L is the cavity length of the three-mirror annular cavity, and R is the radius of curvature. Step 5, at this point, add [something] at the convex lens. Laser irradiation causes a slight deformation of the convex lens due to thermal effects, which in turn simultaneously induces changes in the size and position of the waist spot of the incident light field, forming a precursor to waist spot mismatch wavefront distortion. At this point, the size of the laser waist spot is... The position of the waist patch has also changed, and it no longer matches the intrinsic waist patch of the cavity; Step 6: The incident light, after being filtered by the cavity, outputs a laser that is then incident on the photosensitive detection surface of the multi-quadrant detector. This converts the wavefront distortion information corresponding to the shift in the position of the waist spot and the change in the size of the waist spot into an electrical signal containing distortion features. Step 7: The signal generator inputs the same frequency signal with frequency Ω as the local oscillation signal into the mixer. The mixer mixes the two types of distorted electrical signals output by the multi-quadrant detector with the local oscillation signal, and then performs low-pass filtering to achieve frequency demodulation and noise suppression, thereby completing the wavefront distortion measurement.

5. The method for measuring wavefront distortion caused by optical field waist spot mismatch in a cavity enhancement system according to claim 4, characterized in that, The wavefront distortion measurement includes waist spot position shift and waist spot size change. The waist spot size change includes waist spot size change in the x and y directions, specifically: (1) Changes in waist spot size: The initial light field emitted from the laser: ； In the formula, E0 is the initial field amplitude. Let n be the one-dimensional field distribution of the beam along the x-axis, n be the mode order along the x-axis, i be the imaginary unit, and e be a constant. The light field modulated by the electro-optic modulator: ； In the formula, , These are the phase modulation depth and modulation frequency of the electro-optic modulator, respectively. After passing through a convex lens, the light field after the waist spot size mismatch in the x-direction is as follows: ； In the formula, This represents the relative size mismatch of the waist spot. , ; Its horizontal distribution is as follows: ； In the formula, It is the Goui phase of the nth order modulus. , It is within the Rayleigh range. , The Hermitian polynomials representing the transverse distribution of the light field; Based on the optical field distribution of the cavity eigenmode, the expansion form is as follows: ； The transverse distribution of the optical field in the cavity eigenmode is as follows: ； The optical field after cavity filtering is: ； The light intensity entering the multi-quadrant detector is: ； In the formula, For light field ; conjugate light field; After demodulation and low-pass filtering, the error signal is: ； The error signal obtained after quantization is: ； In the formula, The value of j is affected by the field distribution of the incident light and the excited mode. When the mode order n is even, j takes the value of n+2; when the mode order is odd, the value of j is the same as that of the n-1 order. For annihilation operators The average value, For annihilation operators The ups and downs, For modes other than the nth order mode; Setting the signal-to-noise ratio to 1, the smallest measurable waist spot size change in the x-direction is: ； In the formula, P is the incident laser power. is Planck's constant, and c is the speed of light; Similarly, the error signal in the y-direction can be obtained as follows: ； In the formula, , ; Setting the signal-to-noise ratio to 1, the smallest measurable waist spot size change in the y-direction can be obtained as follows: ； (2) Displacement of waist spot position: Light field after mismatch in waist spot position: ； In the formula, , This represents the smallest measurable change in the position of the waist spot. Its horizontal distribution is as follows: ； In the formula, Let z be the beam radius at point z; Based on the optical field distribution of the cavity eigenmode, the expansion form is as follows: ； The optical field after cavity filtering is: ； The light intensity entering the multi-quadrant detector is: ； After demodulation and low-pass filtering, the error signal is: ； The error signal obtained after quantization is: ； Setting the signal-to-noise ratio to 1, the smallest measurable change in the position of the waist spot can be obtained as follows: 。

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