A method for nonlinear suppression in sinusoidal frequency modulation

Abstract

This application discloses a nonlinear suppression method in sinusoidal frequency modulation, belonging to the field of frequency modulation technology. The method includes: acquiring two original interference voltage signals corresponding to an initial sinusoidal modulation signal and performing correction processing to obtain two target correction signals; performing phase calculation based on the two target correction signals to generate phase information associated with the sinusoidal frequency modulation process of a laser, and obtaining a nonlinear evaluation result based on the phase information, which characterizes the degree of nonlinear modulation of the sinusoidal frequency corresponding to the laser; generating a compensation signal based on the nonlinear evaluation result; and adjusting the initial sinusoidal modulation signal based on the compensation signal to generate a target modulation signal and drive the laser. According to the embodiments of this application, dynamic evaluation and active suppression of the degree of nonlinearity in the high-frequency sinusoidal frequency modulation process can be achieved.

Description

Technical Field

[0001] This application belongs to the field of frequency modulation technology, and particularly relates to a nonlinear suppression method in sinusoidal frequency modulation. Background Technology

[0002] Sinusoidal frequency modulation interferometers are widely used in ultra-precision measurement, but tunable lasers generally exhibit modulation nonlinearity. Even with an ideal sinusoidal input signal, the actual output laser frequency deviates from the ideal sinusoidal law, introducing high-order harmonic components and directly degrading measurement accuracy. Existing nonlinearity assessment methods mainly rely on static DC testing, performing polynomial fitting by measuring the steady-state output wavelength under different drive currents. This can only reflect low-frequency or quasi-static nonlinearity and cannot characterize the dynamic nonlinear distortion in the high-frequency sinusoidal modulation process. Furthermore, existing suppression strategies are mostly based on static models to construct pre-distortion compensation, which is difficult to adapt to high-frequency dynamic response characteristics and results in low compensation accuracy.

[0003] Therefore, there is an urgent need for a method that can dynamically assess the degree of nonlinearity and actively suppress it during high-frequency sinusoidal frequency modulation. Summary of the Invention

[0004] This application provides a nonlinearity suppression method in sinusoidal frequency modulation, which can dynamically evaluate and actively suppress the degree of nonlinearity in the high-frequency sinusoidal frequency modulation process.

[0005] In a first aspect, embodiments of this application provide a method for suppressing nonlinearity in sinusoidal frequency modulation, including: Two original interference voltage signals corresponding to the initial sinusoidal modulation signal are obtained, and the two original interference voltage signals are corrected to obtain two target correction signals. The two original interference voltage signals are the signals obtained by optical mixing of the laser corresponding to the initial sinusoidal modulation signal after unequal arm length processing. Phase calculation is performed based on two target correction signals to generate phase information associated with the sinusoidal frequency modulation process of the laser. Based on the phase information, the corresponding nonlinear evaluation results are obtained. The nonlinear evaluation results are used to characterize the degree of nonlinear modulation of the sinusoidal frequency corresponding to the laser. Based on the nonlinear evaluation results, a compensation signal is generated to suppress nonlinear distortion. The initial sinusoidal modulation signal of the laser is adjusted based on the compensation signal to generate the target modulation signal, and the laser is driven based on the target modulation signal.

[0006] In one implementation, acquiring the two original interference voltage signals corresponding to the initial sinusoidal modulation signal includes: The laser corresponding to the initial sinusoidal modulation signal is injected into two optical paths with unequal arm lengths to obtain two beams with a fixed time delay difference. Two beams are input into an optical mixer for coherent coupling to generate multiple interference optical signals. Based on the multi-channel interference optical signal, the multi-channel interference optical signal is converted into two original interference voltage signals.

[0007] In one implementation, the two original interference voltage signals are corrected to obtain two target correction signals, including: The extreme values ​​of the two original interference voltage signals within the complete signal period are obtained, and the DC bias parameters and AC amplitudes of the two original interference voltage signals are determined based on the extreme values. Based on the DC bias parameters and AC amplitude of the two original interference voltage signals, the two original interference voltage signals are preprocessed using an ellipse fitting algorithm to generate two target correction signals.

[0008] In one implementation, based on the DC bias parameters and AC amplitudes of the two original interference voltage signals, an ellipse fitting algorithm is used to preprocess the two original interference voltage signals to generate two target correction signals, including: Based on the DC bias parameters and AC amplitude, the two original interference voltage signals are center-shifted and amplitude-normalized to obtain two first-stage correction signals after eliminating DC bias differences. The two first-stage correction signals are orthogonally linearly transformed to generate two second-stage correction signals. Amplitude correction is performed on the two second-stage correction signals to generate two target correction signals. The two target correction signals have equal amplitudes and a phase difference of 90 degrees.

[0009] In one implementation, phase calculation is performed based on two target correction signals to generate phase information associated with the sinusoidal frequency modulation process of the laser, including: Perform arctangent calculation on the two target correction signals to generate initial phase information; The initial phase information is unwrapped to generate phase information.

[0010] In one implementation, the corresponding nonlinear evaluation result is obtained based on phase information, including: Perform a fast Fourier transform on the phase information to obtain the spectral information of the phase information in the frequency domain; Based on the spectral information, the first amplitude parameter corresponding to the fundamental frequency of the initial sinusoidal modulation signal and the second amplitude parameter corresponding to at least one higher-order harmonic component in the initial sinusoidal modulation signal are extracted. The second amplitude parameter includes at least the amplitude of the second-order harmonic component. Based on the first amplitude parameter and the second amplitude parameter, a nonlinear evaluation result is generated.

[0011] In one implementation, a compensation signal for suppressing nonlinear distortion is generated based on the nonlinear evaluation results, including: Based on the nonlinear evaluation results, the amplitude and phase of the higher-order harmonic components are determined; Based on the amplitude and phase of the higher-order harmonic components, determine the amplitude coefficient and phase offset; A compensation signal is generated based on the amplitude coefficient and phase offset.

[0012] In one implementation, the amplitude coefficient is positively correlated with the amplitude of the higher-order harmonic components, and the phase offset is 180 degrees out of phase with the higher-order harmonic components.

[0013] In one implementation, the target modulation signal is determined according to a first formula, which is: in, The target modulation signal corresponding to the current time t. For the first The amplitude coefficients corresponding to the first harmonic components, For the first Phase corresponding to the first harmonic component The amplitude corresponding to the initial sinusoidal modulation signal. This is the modulation angular frequency corresponding to the initial sinusoidal modulation signal.

[0014] In one implementation, after adjusting the initial sinusoidal modulation signal of the laser based on the compensation signal to generate a target modulation signal, and driving the laser based on the target modulation signal, the method further includes: The target modulation signal is updated to the initial sinusoidal modulation signal, and the process jumps to obtain the two original interference voltage signals corresponding to the initial sinusoidal modulation signal, and performs correction processing on the two original interference voltage signals to obtain the two target correction signals, until the updated nonlinear evaluation result is obtained. If the updated nonlinear evaluation result is greater than the preset threshold, an updated compensation signal is generated based on the updated nonlinear evaluation result. Based on the updated compensation signal and the initial sinusoidal modulation signal of the laser, an updated target modulation signal is generated, and the laser is driven based on the updated target modulation signal. Then, the process jumps to the step of updating the target modulation signal to the initial sinusoidal modulation signal until the updated nonlinear evaluation result is less than a preset threshold.

[0015] Secondly, embodiments of this application provide a nonlinear suppression device for sinusoidal frequency modulation, comprising: The signal output unit is used to generate an initial sinusoidal modulation signal and to superimpose the initial sinusoidal modulation signal with the feedback compensation signal to generate the target modulation signal. A tunable laser, connected to a signal output unit, is used to output laser light under the drive of an initial sinusoidal modulation signal or a target modulation signal; An unequal arm length optical path is connected to a tunable laser to receive laser light and split the laser light into two beams with a fixed time delay difference. An optical mixer, connected to an optical path of unequal arm length, is used to receive two beams and coherently couple them to generate multiple interference optical signals. The photoelectric detection module, connected to the optical mixer, is used to receive multiple interference optical signals and convert them into two original interference voltage signals. The signal acquisition module, connected to the photoelectric detection module, is used to acquire the two original interference voltage signals; The signal processing and analysis module, connected to the signal acquisition module and the signal output unit respectively, is used to correct the two original interference voltage signals to obtain two target correction signals; based on the two target correction signals, phase calculation is performed to generate phase information associated with the sinusoidal frequency modulation process of the laser, and nonlinear evaluation results are obtained based on the phase information. The nonlinear evaluation results are used to characterize the degree of nonlinear modulation of the laser; and based on the nonlinear evaluation results, a compensation signal for suppressing nonlinear distortion is generated and fed back to the signal output unit.

[0016] Thirdly, embodiments of this application provide an electronic device, the device comprising: Processor and memory storing programs or instructions; The processor can implement the nonlinear suppression method in sinusoidal frequency modulation described above when executing programs or instructions.

[0017] Fourthly, embodiments of this application provide a computer-readable storage medium storing a program or instructions, which, when executed by a processor, implement the aforementioned nonlinear suppression method in sinusoidal frequency modulation.

[0018] Fifthly, embodiments of this application provide a computer program product in which instructions, when executed by a processor of an electronic device, cause the electronic device to perform the aforementioned nonlinear suppression method in sinusoidal frequency modulation.

[0019] This application provides a method for suppressing nonlinearity in sinusoidal frequency modulation. It acquires and corrects two original interference voltage signals, which are obtained by optical mixing of the laser corresponding to the sinusoidal modulation signal after unequal arm length processing. The correction process eliminates or reduces systematic errors such as DC bias differences, amplitude inconsistencies, and orthogonality deviations, resulting in two high-fidelity target correction signals. Phase calculation is then performed based on these target correction signals to generate phase information associated with the sinusoidal frequency modulation process of the laser. Nonlinearity evaluation results are obtained based on this phase information. The phase calculation ensures that the extracted phase information accurately reflects the dynamic nonlinearity of the laser under high-frequency sinusoidal modulation, overcoming the limitation of traditional static testing in characterizing dynamic nonlinearity. Furthermore, a compensation signal is generated based on the nonlinearity evaluation results and superimposed on the initial sinusoidal modulation signal to generate a target modulation signal to drive the laser, thus achieving dynamic evaluation and active suppression of nonlinearity in the high-frequency sinusoidal frequency modulation process. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating a nonlinear suppression method in sinusoidal frequency modulation provided in an embodiment of this application; Figure 2 This is a system structure diagram of a nonlinear suppression device in sinusoidal frequency modulation provided in an embodiment of this application; Figure 3 This is a schematic diagram of the system structure for generating two original interference voltage signals in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 4 This is a schematic diagram of an optical mixer in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 5 This is a schematic diagram of the process for obtaining two original interference voltage signals in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 6 This is a schematic diagram of the process for generating two target correction signals in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 7 This is a schematic diagram of the process for generating phase information in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 8This is a schematic diagram of the process for obtaining nonlinear evaluation results in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 9 This is a schematic diagram of the process of generating a compensation signal in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 10 This is a schematic diagram of the process of generating a target modulation signal in a nonlinear suppression method for sinusoidal frequency modulation provided in an embodiment of this application; Figure 11 This is a flowchart illustrating another nonlinear suppression method in sinusoidal frequency modulation provided in an embodiment of this application; Figure 12 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0022] In the attached diagram: 1. Signal output unit; 2. Adjustable laser; 3. Unequal arm length optical path; 4. Optical mixer; 5. Photoelectric detection module; 6. Signal acquisition module; 7. Signal processing and analysis module; 8. Beam; 9. Interference optical signal; 10. Original interference voltage signal. Detailed Implementation

[0023] The features and exemplary embodiments of various aspects of this application will be described in detail below. To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain this application and not to limit it. For those skilled in the art, this application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of this application by illustrating examples.

[0024] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0025] It should be noted that the acquisition, storage, use, and processing of data in this application embodiment all comply with the relevant provisions of national laws and regulations.

[0026] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0027] In the field of sinusoidal frequency modulation interferometry, the linearity of laser frequency modulation is one of the key factors determining the accuracy of interferometry. Ideally, the frequency modulation response of a tunable laser is linear. When an ideal sinusoidal modulation signal is input, the output optical frequency of the laser should change sinusoidally. After unequal arm length interference and optical mixing, the phase information associated with the modulation process can be accurately extracted from the interference signal.

[0028] However, in practical applications, tunable lasers generally suffer from modulation nonlinearity. Even with an ideal sinusoidal modulation signal, the actual output laser frequency deviates from the ideal sinusoidal law, introducing higher-order harmonic components of the modulation frequency. This modulation nonlinearity is directly coupled to the interferometric measurement link, transforming into a systematic measurement nonlinearity error, significantly degrading measurement accuracy and making it difficult to meet the stringent requirements of ultra-high precision applications such as workpiece stage positioning in lithography machines.

[0029] While some nonlinearity assessment and suppression methods based on static DC testing exist, these methods measure the static output wavelength of the laser under different drive currents and then characterize the modulation nonlinearity through polynomial fitting. Essentially, these are DC static tests, which can only reflect nonlinear characteristics under low-frequency or quasi-static conditions and cannot directly assess dynamic nonlinearity in high-frequency sinusoidal modulation. Regarding nonlinearity suppression, existing methods typically perform polynomial fitting based on the measured static response and then use an ideal sinusoidal drive to inversely deduce the pre-distortion excitation signal. However, their correction model is still based on the static response and is insufficient to effectively suppress dynamic nonlinear distortion under high-frequency sinusoidal modulation.

[0030] In view of the above, in order to solve the aforementioned technical problems, the embodiments of this application provide, as follows: Figure 1 This paper illustrates a nonlinear suppression method in sinusoidal frequency modulation. To facilitate understanding of the technical solution of this application, it is first discussed in conjunction with the appendix. Figure 2 This application describes a nonlinear suppression device in sinusoidal frequency modulation upon which the embodiments are based. Figure 2 As shown, Figure 2The diagram illustrates the system structure of a nonlinear suppression device in sinusoidal frequency modulation according to an embodiment of this application. The system includes a signal output unit 1, a tunable laser 2, an unequal arm length optical path 3, an optical mixer 4, a photoelectric detection module 5, a signal acquisition module 6, and a signal processing and analysis module 7. The nonlinear suppression device provided in this embodiment has a simple structure and low hardware complexity. It does not require additional configuration of a highly complex calibration optical path. It can achieve nonlinear distortion characterization and active suppression in the high-frequency sinusoidal modulation process by relying solely on unequal arm length interference, optical mixing, and digital signal processing, effectively reducing the difficulty of system debugging and hardware costs.

[0031] The signal output unit 1 outputs a preset initial sinusoidal modulation signal to the tunable laser 2 and dynamically adjusts the output waveform parameters based on the compensation signal fed back by the signal processing and analysis module 7. It actively suppresses nonlinear distortion in the sinusoidal frequency modulation of the laser by injecting a target modulation signal. The signal output unit 1 can employ any circuit or instrument capable of generating and dynamically adjusting the electrically driven signal, including but not limited to arbitrary waveform generators, programmable signal sources, or digital signal generation modules; no specific limitations are imposed here.

[0032] The tunable laser 2 is connected to the signal output unit 1 and is used to receive the modulation drive signal output by the signal output unit 1. The output optical frequency of the tunable laser 2 changes dynamically with the modulation signal, and outputs a laser beam with frequency modulation characteristics. The type of tunable laser 2 is not limited here, and includes, but is not limited to, distributed feedback lasers, distributed Bragg reflector lasers, external cavity tunable lasers, and other light source devices with frequency modulation capabilities.

[0033] The unequal-arm-length optical path 3 is connected to the tunable laser 2 and is used to receive the laser output from the tunable laser 2, splitting it into two beams. The splitting ratio is not limited, and the two beams propagate along different optical paths, forming a fixed time delay difference. The implementation form of the unequal-arm-length optical path 3 is not limited here, and includes, but is not limited to, fiber optic optical paths, spatial optical optical paths, or optical paths combining fiber optics and spatial optics.

[0034] Optical mixer 4 is connected to unequal-arm-length optical path 3 and is used to receive two beams with time delay difference output from unequal-arm-length optical path 3. After coherent coupling, it outputs an interference optical signal for subsequent effective extraction of interference phase information. The type and structure of optical mixer 4 are not limited here, and include, but are not limited to, fiber optic couplers, spatial optical beam splitters and combiners, or integrated optical coherent coupling devices.

[0035] The photoelectric detection module 5 is connected to the optical mixer 4 and is used to receive the interference light signal output by the optical mixer 4 and convert the light intensity signal into an electrical signal. The type, response band, and packaging of the photoelectric detection module 5 are not limited here, and include, but are not limited to, photoelectric conversion devices such as photodiodes, phototransistors, avalanche photodiodes, or photomultiplier tubes.

[0036] The signal acquisition module 6 is connected to the photoelectric detection module 5 and is used to condition, amplify, and perform analog-to-digital conversion on the analog electrical signal output by the photoelectric detection module 5, converting the analog signal into a digital signal and transmitting it to the signal processing and analysis module 7. The acquisition rate, accuracy, and number of channels of the signal acquisition module 6 can be flexibly configured according to measurement requirements, and the specific implementation form is not limited, including but not limited to high-speed data acquisition cards, integrated analog-to-digital conversion modules, or multi-channel synchronous acquisition systems.

[0037] The signal processing and analysis module 7 is connected to both the signal acquisition module 6 and the signal output unit 1. It receives the electrical signal output from the signal acquisition module 6 and corrects for DC bias differences, amplitude inconsistency errors, and the non-ideal 90-degree phase deviation of the optical mixer 4 introduced by the photoelectric detection module 5 using an elliptic fitting algorithm. This eliminates the influence of system errors on phase calculation, ensuring high fidelity between the demodulated phase and the actual frequency modulation process of the laser. Simultaneously, it performs spectral analysis on the corrected target signal to quantitatively assess the nonlinearity of the sinusoidal frequency modulation. Based on the nonlinearity assessment results, it feeds back a compensation signal to the signal output unit 1, achieving closed-loop suppression of modulation nonlinearity. This signal processing and analysis module 7 can utilize any hardware platform with digital signal processing capabilities, including but not limited to field-programmable gate arrays, digital signal processors, or industrial control computers.

[0038] Based on the system architecture of the above-described device, the specific steps of a nonlinear suppression method in sinusoidal frequency modulation provided in this application embodiment will be described in detail below. Figure 1 As shown, Figure 1 The diagram illustrates a flowchart of a nonlinear suppression method in sinusoidal frequency modulation according to an embodiment of this application. This nonlinear suppression method is applicable to the modulation of sinusoidal frequency modulation interferometers or sinusoidal phase modulation interferometers. Figure 1 As shown, the nonlinear suppression method in this sinusoidal frequency modulation includes the following steps: S110. Obtain the two original interference voltage signals corresponding to the initial sinusoidal modulation signal, and perform correction processing on the two original interference voltage signals to obtain two target correction signals. The two original interference voltage signals are the signals obtained by optical mixing after the laser corresponding to the initial sinusoidal modulation signal is processed by unequal arm length. S120. Based on the two target correction signals, perform phase calculation to generate phase information associated with the sinusoidal frequency modulation process of the laser, and obtain nonlinear evaluation results based on the phase information. The nonlinear evaluation results are used to characterize the degree of nonlinear modulation of the sinusoidal frequency corresponding to the laser. S130. Based on the nonlinear evaluation results, generate a compensation signal to suppress nonlinear distortion; S140. Adjust the initial sinusoidal modulation signal of the laser based on the compensation signal to generate the target modulation signal, and drive the laser based on the target modulation signal.

[0039] As described above, the nonlinear suppression method in sinusoidal frequency modulation of this application involves obtaining two original interference voltage signals corresponding to the initial sinusoidal modulation signal through optical mixing, then acquiring and correcting these two original interference voltage signals to obtain two target correction signals. This overcomes the inherent defect of traditional static DC testing in failing to reflect high-frequency dynamic nonlinear distortion, while eliminating the interference of systematic errors such as DC bias differences, amplitude inconsistencies, and orthogonality deviations in the photoelectric detection link on phase extraction. This ensures that the phase information obtained from subsequent phase calculations is highly correlated with the actual sinusoidal frequency modulation process of the laser. Based on this, spectral analysis is performed using this phase information to obtain nonlinear evaluation results. Then, a compensation signal is generated based on the nonlinear evaluation results and superimposed with the initial sinusoidal modulation signal to form a target modulation signal to drive the laser. This achieves the suppression of nonlinear distortion in the sinusoidal frequency modulation process of the laser, thereby realizing the active suppression of nonlinear distortion in the high-frequency sinusoidal modulation process.

[0040] The specific implementation methods of steps 110 to 140 above will be described in detail below.

[0041] In S110, as an example, the initial sinusoidal modulation signal can be expressed as shown in equation (1): (1) in, The amplitude of the initial sinusoidal modulation signal. The modulation angular frequency of the initial sinusoidal modulation signal. , The modulation frequency of the initial sinusoidal modulation signal. For time variables, is the initial phase constant.

[0042] The aforementioned laser can refer to a tunable laser with frequency modulation capability. Under the drive of an initial sinusoidal modulation signal, the laser output frequency dynamically changes with the modulation signal. The specific type of laser is not limited here; for example, it can be a distributed feedback laser, a distributed Bragg reflector laser, an external cavity tunable laser, or other light source devices with frequency modulation capability.

[0043] It should be added that, ideally, the frequency modulation response of a laser is linear, and when an ideal sinusoidal modulation signal is input, the laser frequency should change sinusoidally. However, in practice, tunable lasers generally exhibit modulation nonlinearity, and even when an ideal sinusoidal modulation signal is input, the actual output laser frequency will deviate from the ideal sinusoidal law. To facilitate quantitative analysis of modulation nonlinearity, in some examples, the laser's frequency response, i.e., the voltage-frequency conversion relationship, can be modeled as a quadratic polynomial, as shown in equation (2) below: (2) in, The instantaneous frequency of the laser. These are second-order nonlinear coefficients. The coefficients are first-order linear coefficients. This is a constant term. The initial sinusoidal modulation signal... Substituting into equation (2) above, we can obtain the instantaneous frequency of the laser as shown in equation (3) below: (3) make , We can obtain the following formula (4): (4) As can be seen from the above equation, due to the second-order nonlinear coefficients The presence of this component means that the actual output frequency of the laser includes not only the expected fundamental sinusoidal component. In addition, a second harmonic cosine component also appeared. This introduces the second-order harmonic component of the modulation frequency, which is the mathematical manifestation of modulation nonlinearity. It's understandable that the above explanation only uses second-order nonlinearity as an example; actual lasers may also exhibit third-order and higher-order nonlinearities, in which case higher-order harmonic components will appear in the frequency expression.

[0044] The phase of the optical field is the integral of frequency over time. Therefore, the phase of the optical field of the initial sinusoidally modulated laser can be expressed as shown in equation (5): (5) in, For the instantaneous phase of the light field, The initial phase constant is... For the fundamental frequency modulation depth, The second harmonic modulation depth, These are second-order nonlinear coefficients. The coefficients are first-order linear coefficients. The modulation frequency of the initial sinusoidal modulation signal. The modulation angular frequency of the initial sinusoidal modulation signal.

[0045] Based on the above, after acquiring the two original interference voltage signals, they need to be corrected to obtain two target corrected signals. The correction process aims to eliminate or reduce the impact of systematic errors such as DC bias differences, amplitude inconsistencies, and orthogonality deviations on phase extraction. As an example, the correction process can be implemented based on an ellipse fitting algorithm. The basic principle of this ellipse fitting algorithm is that, ideally, the Lissajous trajectory formed by the two orthogonal interference voltage signals on the plane is a standard circle centered at the origin with a radius of 1. However, in actual systems, due to errors, the Lissajous trajectory formed by the two non-ideal signals on the plane often deviates from the standard circle, presenting as an ellipse with an offset center, unequal major and minor axes, and rotation angles. By fitting the parameters of this ellipse trajectory, systematic error parameters such as DC bias, amplitude ratio, and orthogonality deviation can be derived. These parameters can then be used to perform corresponding error correction processes on the original signals, such as center shifting, amplitude normalization, and orthogonality compensation.

[0046] The two target correction signals mentioned above can refer to a pair of signals that, after the above correction processing, satisfy the conditions of equal amplitude and phase difference of approximately 90 degrees, i.e., orthogonality. They can serve as reliable inputs for subsequent phase calculation, so that the phase information calculated from the target correction signals maintains a high degree of fidelity correlation with the actual frequency modulation process of the laser.

[0047] In S120, based on the two target correction signals obtained in S110, phase calculation is performed to generate phase information associated with the frequency modulation process of the laser, and the corresponding nonlinear evaluation result is obtained based on this phase information. The aforementioned phase calculation can refer to the process of using the amplitude ratio relationship between the two target correction signals to inversely calculate the corresponding phase angle through arctangent operation, and obtaining continuous phase information in the time domain through phase continuity recovery processing.

[0048] After obtaining the aforementioned phase information, the corresponding nonlinear evaluation result is obtained based on this phase information. The aforementioned nonlinear evaluation result can refer to one or more index quantities that can quantitatively reflect the severity of nonlinear distortion in the sinusoidal frequency modulation process of the laser, and are used to characterize the degree of nonlinear modulation of the corresponding sinusoidal frequency of the laser.

[0049] In S130, based on the nonlinear evaluation results obtained in S120, a compensation signal for suppressing nonlinear distortion is generated. This compensation signal can refer to a compensation drive signal superimposed on the initial sinusoidal modulation signal. Its function is to suppress harmonic distortion caused by inherent nonlinearity during the laser modulation response by introducing a compensation component at the drive end that matches the inherent nonlinear distortion characteristics of the laser in advance.

[0050] It should be added that in the above S130, the process of generating a compensation signal to suppress nonlinear distortion based on the obtained nonlinear evaluation result is an iterative process. That is, in the initial process of the method, a nonlinear evaluation result is first obtained to characterize the degree of nonlinearity of the laser under the current modulation signal. That is, the degree of nonlinearity of the laser under the current modulation signal can be determined from the result. Then, the compensation signal is initialized based on the nonlinear evaluation result. The initialization setting is to pre-set the adjustable parameters corresponding to the compensation signal, namely the amplitude and phase offset, while the fixed parameters corresponding to the compensation signal, namely the waveform and frequency, are determined by the modulation signal corresponding to the laser. If the modulation signal corresponding to the laser remains unchanged, the fixed parameters corresponding to the compensation signal will not change.

[0051] The initial amplitude of the aforementioned compensation signal can be determined by multiplying the nonlinear evaluation result obtained in the first round with the amplitude of the modulation signal corresponding to the laser, while the phase can be any value between 0 and 360°. Subsequently, after adjusting the initial compensation signal and the initial sinusoidal modulation signal corresponding to the laser, a target modulation signal is generated. The laser is then driven based on the initialized target modulation signal to obtain the nonlinear evaluation result corresponding to the initialized compensation signal. The adjustable parameters of the compensation signal are then iteratively updated based on the nonlinear evaluation result until the updated nonlinear evaluation result is less than a preset threshold.

[0052] In S140, a target modulation signal is generated based on the compensation signal and the initial sinusoidal modulation signal generated in S130, and the laser is driven based on the target modulation signal. The aforementioned target modulation signal can refer to a composite modulation signal generated by superimposing the compensation signal and the initial sinusoidal modulation signal, which is used to finally drive the laser. It contains both the desired fundamental frequency sinusoidal modulation component and a compensation component to compensate for the modulation nonlinearity of the laser.

[0053] After generating the target modulation signal, the target modulation signal is applied to the modulation input terminal of the laser to drive the laser to operate. The aforementioned modulation input terminal can refer to the electrical signal input interface on the laser used to receive external electrical drive signals to modulate its output optical frequency. For different types of tunable lasers, the specific form of the modulation input terminal may vary. For example, it can be an injection current drive port or a control voltage input port of the cavity tuning element, etc., which is not limited here.

[0054] During the application process, the compensation component embedded in the target modulation signal and the inherent nonlinear response of the laser produce the following cancellation effect: the nonlinear frequency response of the laser generates a nonlinear mapping on all frequency components of the driving signal. Taking second-order nonlinearity as an example, when the fundamental frequency component in the target modulation signal... After mapping with a second-order nonlinear term, second-order harmonic distortion is generated. Simultaneously, the compensation component, after being mapped through the laser's linear response and some nonlinearity, also generates corresponding additional frequency components. By appropriately setting the amplitude (amplitude coefficient) and phase (phase offset) of the compensation component, the harmonic distortion of the fundamental frequency component caused by the laser's nonlinear response can be precisely weakened or canceled by the additional harmonics generated by the compensation component after modulation. This effectively suppresses the nonlinear harmonic components in the actual output frequency of the laser, making the output frequency approach the ideal sinusoidal modulation law. Therefore, in the laser output frequency driven by the target modulation signal, the fundamental frequency component is preserved, while all nonlinear harmonic components are significantly suppressed, effectively improving the linearity of frequency modulation.

[0055] It should be added that the superposition of the aforementioned compensation signal and the initial sinusoidal modulation signal, as well as the laser driving process, can be combined with... Figure 2 The system structure diagram shown illustrates this process. Signal output unit 1 adjusts the output waveform parameters based on the nonlinear evaluation results fed back from signal processing and analysis module 7, embedding the compensation component into the initial sinusoidal modulation signal to generate the target modulation signal, which is then output to the modulation input of tunable laser 2. Driven by the target modulation signal, tunable laser 2 outputs a nonlinearly compensated sinusoidal modulated laser. This laser then enters the unequal arm length optical path 3, and after passing through optical mixer 4 and photoelectric detection module 5, it is converted back into an interference voltage signal. This signal then passes through signal acquisition module 6 and enters signal processing and analysis module 7, thus forming a complete closed loop from nonlinear sensing and quantization evaluation to active suppression.

[0056] Optionally, according to some embodiments of this application, in conjunction with Figure 5 As shown, obtaining the two original interference voltage signals corresponding to the initial sinusoidal modulation signal in S110 may include: S111, the laser corresponding to the initial sinusoidal modulation signal is injected into two optical paths with unequal arm lengths to obtain two beams with a fixed time delay difference. S112 inputs two beams into an optical mixer for coherent coupling to generate multi-channel interference optical signals; S113 converts multiple interference optical signals into two original interference voltage signals based on multiple interference optical signals.

[0057] In S111, the aforementioned unequal arm length optical paths can refer to two transmission paths with different optical path lengths, used to split and transmit the same laser beam, resulting in a definite time delay between the two beams when they reach the subsequent beam-combining point. The aforementioned fixed time delay difference can refer to the propagation time difference caused by the difference in optical path length between the two arms, which remains constant during measurement, and is related to the optical path difference between the two arms. and the speed of light in a medium The relationship between them can be represented as In an optical fiber path, the speed of light... ,in The speed of light in a vacuum is the refractive index of the fiber core.

[0058] As an example, Figure 3 The system structure diagram of the two-channel original interference voltage signal generation process in an embodiment of this application is shown, wherein, as Figure 3 As shown, the laser output from the tunable laser 2 is input into the unequal-arm-length optical path 3 via an optical fiber, generating two beams 8. The two beams 8 have a definite phase relationship in the time domain, and the phase difference between them is... This information contains dynamic changes during the sinusoidal frequency modulation process of the laser, providing a physical basis for subsequently extracting modulation nonlinear features from the interference signal. The phase of the optical field after transmission through the short arm. The phase of the light field after transmission via the long arm is shown. Subsequently, the two beams 8 are coherently coupled by the optical mixer 4 and output a multi-channel interference light signal 9 with a specific phase relationship. Then, the multi-channel interference light signal 9 is split into two channels and the light intensity signal is converted into a corresponding voltage signal by the photoelectric detection module, finally obtaining two original interference voltage signals 10.

[0059] The specific implementation of the aforementioned optical paths with unequal arm lengths is not limited here. Depending on the needs of the actual application scenario, it can be a fiber optic path, a space optic path, or a combination of fiber optic and space optics. The beam splitting ratio of the optical path can also be flexibly set according to actual needs. For example, a 1:1 equal beam splitting ratio can be used, or other beam splitting ratios can be used according to the optical power distribution requirements.

[0060] In S112, coherent coupling can refer to the process in which two or more beams that meet certain conditions are superimposed in space, resulting in a redistribution of light intensity due to interference effects.

[0061] As an example, combined Figure 4 The illustrated ideal model of an optical mixer, which may include two input ports, such as... Figure 4 The first input port 23 and the second input port 24, as well as the four output ports shown, are as follows: Figure 4 The first output port 25, the second output port 26, the third output port 27, and the fourth output port 28 are shown.

[0062] As an example, combined Figure 3 As shown, the modulated laser output from the tunable laser is split by an optical fiber input fiber coupler, resulting in two separate optical paths. These paths are transmitted through two optical fibers of different lengths. One fiber is connected to a delay fiber to introduce a fixed time delay difference, thus forming an optical path with unequal arm lengths. The phases of the two optical fields can be represented by equations (6) and (7), respectively: (6) (7) in, The phase of the optical field after transmission through the short arm. The phase of the optical field after long-arm transmission. The fixed time delay between the two arms is caused by the delay fiber. The modulation angular frequency of the initial sinusoidal modulation signal. , The modulation frequency of the initial sinusoidal modulation signal. For time variables, The initial phase constant is... The second harmonic modulation depth, These are second-order nonlinear coefficients. The coefficients are first-order linear coefficients. This represents the fundamental frequency modulation depth.

[0063] Two beams 8 with a fixed time delay difference are input into an optical mixer for coherent coupling to generate multiple interferometric optical signals 9. The type and structure of the optical mixer are not limited here; for example, it can be an optical fiber coupler, a spatial beam splitter and combiner, or an integrated optical coherent coupling device.

[0064] Combination Figure 4 As shown, an ideal model of an optical mixer can include two input ports and four output ports. Let the complex amplitudes of the two input optical fields be respectively... and After the optical mixer is coherently coupled, the four output optical fields can be expressed as shown in equations (8) and (9) below: ， (8) ， (9) Specifically, the first output port 25 and the second output port 26 form a pair of complementary output ports, and the third output port 27 and the fourth output port 28 form another pair of complementary output ports. The ideal phase difference between the two pairs of output ports is 90 degrees. , , , is the complex amplitude of the interference optical field at the four output ports of the optical mixer, and A and B are the coupling coefficients at the two input ports of the optical mixer, respectively. , These are the phases of the two input light fields, respectively.

[0065] In S113, the aforementioned conversion can refer to the process of converting a light intensity signal into a corresponding voltage signal using a photodetector. The two original interference voltage signals carry information about the phase change during the sinusoidal frequency modulation of the laser, serving as the original input data for subsequent correction processing and phase calculation.

[0066] In practical implementation, as an example, the complementary relationship between the output ports of an optical mixer can be utilized, connecting the complementary output ports to the differential inputs of a balanced photodetector. Combined with... Figure 3 As shown, the four interference light signals are input into the photodetector module, which converts the light intensity signals into electrical signals. The type, response band, and packaging of the photodetector module are not limited here; it can be a photodiode, phototransistor, avalanche photodiode, or photomultiplier tube, or other photoelectric conversion device.

[0067] As a specific example, the first output port 25 and the second output port 26 are respectively connected to the two differential input terminals of a balanced photodetector, which outputs differential electrical signals. As shown in equation (10): (10) Similarly, by connecting the third output port 27 and the fourth output port 28 to the two differential input terminals of another balanced photodetector, the differential electrical signal output will be... As shown in equation (11): (11) Will , Substituting the values, we can obtain the output of the two photodetectors under ideal conditions as shown in equation (12): , (12) in, Let B be the phase difference between the two arms, and let B be the signal amplitude related to the incident light power and photoelectric conversion efficiency. The two signals mentioned above... and Ideally, this would form a pair of orthogonal interference voltage signals with equal amplitude and a 90-degree phase difference.

[0068] However, in practical applications, due to factors such as the non-ideal orthogonality of the optical mixer, the difference in DC bias of the photodetector, the inconsistency in amplitude, and the quantization error of the signal acquisition module, the two original interference voltage signals actually acquired are usually not ideal orthogonal signals, but can be expressed as shown in the following equation (13): , (13) in, and These are the DC biases for the two original interference voltage signals, respectively. and These represent the AC amplitudes of the two original interference voltage signals, respectively. The orthogonal deviation angle is the angle that deviates from the ideal orthogonality. The phase of the optical field after transmission through the short arm. This represents the phase of the optical field after long-arm transmission. Directly calculating the phase of the non-ideal signal containing systematic errors will introduce additional nonlinear measurement errors, leading to distortion of subsequent nonlinear evaluation results.

[0069] The aforementioned balanced photodetector refers to a photoelectric detection device with a differential input structure. Internally, it contains two matched photodiodes and a differential amplifier circuit. It converts two complementary input optical signals into photocurrents, which are then differentially amplified, resulting in a voltage signal at the output reflecting the difference between the two optical signals. By employing a balanced detection method, common-mode noise components in the two optical signals can be effectively suppressed, while the differential-mode signal components are amplified, thereby helping to improve the signal-to-noise ratio of the output signal.

[0070] As a concrete example, assuming the power of each of the two input optical signals is approximately 1mW, the responsivity of the photodetector is approximately 0.8A / W, and the transimpedance gain is approximately 10kV / A, then the amplitude of the AC component in the two original interference voltage signals is... It is approximately on the order of 8V. In practical applications, this amplitude can fluctuate due to factors such as optical path loss, fiber coupling efficiency, differences in detector quantum efficiency, and amplifier gain deviation. When the phase difference... As time changes, the two original interference voltage signals oscillate according to cosine and sine laws, respectively, which fully records the phase dynamic changes during the laser frequency modulation process, thus providing the original data basis for subsequent correction processing and phase calculation.

[0071] As described above, the embodiments of this application inject laser light into optical paths of unequal arm lengths composed of time-delay fibers, thereby generating a fixed time delay difference between the two beams corresponding to the optical path difference. Then, the two beams are coherently coupled using an optical mixer, and the cosine component of the phase difference is extracted from the intensity difference between the complementary output ports. Sine component Information; finally, the interference light signals of the complementary port pair are differentially converted into two original interference voltage signals, one containing cosine components and the other containing sine components, by a balanced photodetector. Thus, this scheme completely and faithfully maps the phase change information during the laser's sinusoidal frequency modulation process to the electrical signal domain, and the balanced detection method effectively suppresses common-mode interference such as laser relative intensity noise, providing a high-quality orthogonal interference voltage signal source for subsequent correction processing and phase calculation.

[0072] Optionally, according to some embodiments of this application, in S110, the two original interference voltage signals are corrected to obtain two target correction signals, including: The extreme values ​​of the two original interference voltage signals within the complete signal period are obtained, and the DC bias parameters and AC amplitudes of the two original interference voltage signals are determined based on the extreme values. Based on the DC bias parameters and AC amplitude of the two original interference voltage signals, the two original interference voltage signals are preprocessed using an ellipse fitting algorithm to generate two target correction signals.

[0073] The above process will be explained in detail below.

[0074] The aforementioned complete signal period can refer to the time interval corresponding to the completion of one complete phase change cycle of the two original interference voltage signals. Since both original interference voltage signals exhibit a phase difference... The sinusoidal function, when Traversal Within a certain range, the signal waveform completes one full oscillation cycle. In practical systems, the duration of a complete signal cycle depends on the depth of the laser's sinusoidal frequency modulation and the time delay difference between the unequal arm optical paths. Parameters such as the modulation frequency. The modulation depth is 100kHz, allowing the phase change amplitude to cover... In the above scenario, a complete signal period is approximately on the order of 10 microseconds. This complete signal period can be determined by real-time monitoring of the digital signal sequence output by the signal acquisition module, for example, by detecting when the cumulative phase change reaches a certain value. When this sampling interval is defined as a complete signal period, it is then determined.

[0075] The extreme values ​​mentioned above can refer to the maximum and minimum values ​​reached by the two original interference voltage signals respectively within a complete signal period. As an example, for the first original interference voltage signal, its maximum value within a complete signal period is denoted as... The minimum value is denoted as For the second original interference voltage signal, its maximum value within one complete signal period is denoted as... The minimum value is denoted as These extreme values ​​can be obtained by traversing and comparing the digital signal sequence output by the signal acquisition module over the entire signal period, for example, by scanning point by point and recording the maximum and minimum sample values. In some examples, to improve the robustness of extreme value extraction, preprocessing techniques such as sliding window smoothing or median filtering can be used to reduce the interference of noise spikes on extreme value determination.

[0076] In actual photoelectric detection links, due to factors such as the non-ideal orthogonality of the optical mixer, the difference in DC bias of the photoelectric detector, the inconsistency in amplitude, and the quantization error of the signal acquisition module, the two original interference voltage signals actually acquired are usually not ideally orthogonal signals. In order to quantitatively describe the above system error, the two original interference voltage signals actually acquired can be modeled as shown in the above equation (13): , (13) in, and These are the DC biases of the two original interference voltage signals, which may originate from various factors such as the dark current of the photodetector, the bias voltage of the preamplifier, and the beam splitting imbalance between the output ports of the optical mixer. and These are the AC amplitudes of the two original interference voltage signals, respectively. In actual systems, the amplitudes of the two original interference voltage signals may differ due to the differences in the amplitudes of the photodetectors, amplifiers, and analog-to-digital conversion channels they pass through, and therefore the two are often not equal. The phase of the optical field after transmission through the short arm. The phase of the optical field after long-arm transmission. The orthogonal deviation angle, which deviates from ideal orthogonality, reflects the error introduced by the non-ideal 90-degree phase shift of the optical mixer. Directly performing phase calculation on the aforementioned non-ideal signal containing systematic errors will introduce additional nonlinear measurement errors, leading to distortion of subsequent nonlinear evaluation results.

[0077] The aforementioned DC bias parameters refer to the DC component levels in the two original interference voltage signals that do not change with phase. The presence of DC bias will shift the zero-level reference of the signal; if used directly in subsequent arctangent calculations without correction, it will lead to phase shift errors in the calculated results. As an example, the DC bias parameters of the first original interference voltage signal... It can be based on the maximum value of the signal within a complete signal cycle. and minimum value Confirmed. Due to ,when When taking the maximum value + 1 achieve ,when When taking the minimum value -1 achieve Therefore, the DC bias parameter can be calculated as half the sum of the two, as shown in equation (14) below: (14) Similarly, the DC bias parameters of the second original interference voltage signal It can be shown in the following formula (15): (15) The aforementioned AC amplitude refers to the magnitude of the AC component in the two original interference voltage signals. If there is a gain inconsistency between the two signals, it will lead to asymmetry in their amplitudes, thus introducing a periodic error related to the phase angle in the subsequent arctangent calculation. As an example, the AC amplitude of the first original interference voltage signal... It can be determined based on the maximum and minimum values ​​of the signal within a complete signal cycle. and Therefore, the AC amplitude can be calculated as shown in the following formula (16): (16) Similarly, the AC amplitude of the second original interference voltage signal It can be shown in the following formula (17): (17) As a concrete example, suppose in a certain measurement, the maximum value of the first original interference voltage signal within one complete signal cycle is... It is 4.2 V, the minimum value If the value is 0.6 V, then the DC bias parameter of this signal is... V, AC amplitude V. If the maximum value of the second signal within the same period... It is 5.1 V, the minimum value. If the value is 0.3 V, then its DC bias parameter is... V, AC amplitude V. This shows that there are significant differences in DC bias and amplitude between the two signals. If they are used directly without correction, these differences will seriously affect the accuracy of subsequent phase calculations.

[0078] Based on the DC bias parameters and AC amplitudes of the two original interference voltage signals determined above, the two original interference voltage signals are preprocessed using an ellipse fitting algorithm to generate two target correction signals.

[0079] The above-mentioned ellipse fitting algorithm is used to fit the parameters of the ellipse trajectory, which can deduce the system error parameters such as DC bias, amplitude ratio and orthogonality deviation. Then, these parameters can be used to perform corresponding error correction processing on the original signal.

[0080] The aforementioned preprocessing refers to the process of correcting the two original interference voltage signals using predetermined DC bias parameters and AC amplitudes before the formal phase calculation. The aim is to eliminate or reduce systematic errors such as DC bias differences and amplitude inconsistencies in the signals, making them closer to the form of ideal orthogonal signals. After this preprocessing, the DC biases of both signals are adjusted to near zero, and the AC amplitudes are normalized to near unit amplitude, thus making the two signals comparable in amplitude dimension and providing more standardized input data for subsequent phase calculation.

[0081] It should be added that the above-mentioned method of determining DC bias parameters and AC amplitude based on extreme values ​​is only one approach to estimating elliptic fitting parameters. Its advantage lies in its simple calculation and ease of implementation, making it suitable for scenarios with good signal-to-noise ratio and relatively regular waveforms. In other implementations, the more general least-squares elliptic fitting method can also be used. This involves performing least-squares fitting of the elliptic equation on a two-dimensional data point set formed by the two original interference voltage signals within one or more complete signal cycles. This directly yields geometric parameters such as the center coordinates, major and minor axis lengths, and rotation angles of the ellipse. Based on these geometric parameters, system error parameters such as DC bias, amplitude ratio, and orthogonality deviation are then deduced. This least-squares-based elliptic fitting method has a certain robustness to signal noise and is suitable for scenarios with low signal-to-noise ratio or distorted signal waveforms. Regardless of whether the extreme value method or the least-squares fitting method is used, they both essentially fall under the category of elliptic fitting algorithms, aiming to parameterize and correct system errors through an elliptic geometric model.

[0082] Furthermore, the above-mentioned parameter determination method based on extreme values ​​can be flexibly adapted to different application scenarios. For example, in scenarios where the signal amplitude fluctuates significantly, data from multiple consecutive complete signal cycles can be collected. The extreme values ​​of each cycle can be extracted, and the average value can be taken as the final DC bias parameter and AC amplitude to reduce the impact of random noise within a single cycle on parameter estimation. In scenarios where there are occasional pulse interferences in the signal, the collected data can be sorted by amplitude first, and a certain proportion of outliers at both ends can be removed. Then, the extreme values ​​of the remaining data can be taken to improve the robustness of parameter estimation.

[0083] As described above, this embodiment obtains the maximum and minimum values ​​of the two original interference voltage signals within a complete signal period. Based on the extreme values, it determines the DC bias parameters and AC amplitude of each signal. Then, using an ellipse fitting algorithm as a framework, it performs center shifting and amplitude normalization preprocessing on the original interference voltage signals, generating two target correction signals that eliminate DC bias differences and amplitude inconsistencies. Thus, by using ellipse fitting correction to decouple system errors from the Lissajous figure, the corrected target correction signals can more realistically reflect the phase changes during the laser's sinusoidal frequency modulation process. This avoids the offset and periodic errors introduced by DC bias differences and amplitude inconsistencies in subsequent phase calculations, providing a reliable data foundation for subsequent high-precision phase calculations and nonlinear evaluations.

[0084] Optionally, according to some embodiments of this application, in conjunction with Figure 6 As shown, based on the DC bias parameters and AC amplitudes of the two original interference voltage signals, an ellipse fitting algorithm is used to preprocess the two original interference voltage signals to generate two target correction signals, including: S1101, based on DC bias parameters and AC amplitude, performs center shifting and amplitude normalization on the two original interference voltage signals to obtain two first-stage correction signals after eliminating DC bias differences; S1102, Perform an orthogonal linear transformation on the two first-level correction signals to generate two second-level correction signals; S1103 performs amplitude correction on the two second-stage correction signals to generate two target correction signals. The amplitudes of the two target correction signals are equal and the phase difference is 90 degrees.

[0085] In S1101, the aforementioned center shift can refer to subtracting the DC bias parameter from the signal to eliminate the zero-level offset caused by the DC bias difference, thus returning the signal's oscillation center to the zero-level position. In actual photoelectric detection links, due to factors such as differences in dark current of the photodetector, different bias voltages of the preamplifier, and unbalanced beam splitting at each output port of the optical mixer, the two original interference voltage signals often have different DC bias levels. For example, one signal may have a DC bias of 2.4 V, while the other signal has a DC bias of 2.7 V. This difference in DC bias will cause the center of the ellipse of the Lissajous trajectory formed by the two signals on the plane to deviate from the origin. If this difference is not eliminated, the subsequent arctangent calculation will result in a systematic shift.

[0086] The aforementioned amplitude normalization can refer to dividing the signal after center shift by its AC amplitude to eliminate the amplitude inconsistency between the two signals, thereby unifying the AC oscillation amplitude of the two signals to near the unit amplitude.

[0087] The mathematical expression for the above center translation and amplitude normalization is shown in equation (18): , (18) in, and These are the two first-level correction signals generated after center shifting and amplitude normalization preprocessing. and These are the DC biases for the two original interference voltage signals, respectively. and These represent the AC amplitudes of the two original interference voltage signals, respectively. , These are the two original interference voltage signals acquired.

[0088] Substituting equation (13) into equation (18) above, we can obtain the expression for the two first-stage correction signals after preprocessing as shown in equation (19): , (19) As can be seen from the above formula, after center shifting and amplitude normalization preprocessing, the DC bias difference and amplitude inconsistency have been effectively eliminated. Among them, To eliminate the cosine components of DC bias and amplitude error, To eliminate the sinusoidal components of DC bias and amplitude error, in applications where the orthogonality deviation is small or negligible, the two first-stage correction signals mentioned above have approached the form of ideal orthogonal signals and can be directly used for subsequent phase calculations.

[0089] As can be seen from the above formula, after center shifting and amplitude normalization, the DC bias difference and amplitude inconsistency have been eliminated, but the orthogonality deviation remains. It may still exist in the second-stage correction signal. If If the two first-stage correction signals are not strictly orthogonal, directly using them for subsequent arctangent calculations will still introduce phase calculation errors.

[0090] In S1102, the aforementioned orthogonal linear transformation can refer to performing a linear combination operation on the two first-level correction signals to eliminate the orthogonality deviation between the two signals. The core idea of ​​orthogonalization linear transformation is to use the cosine component that has already undergone DC and amplitude correction in the first-level correction signal as a reference, perform trigonometric identity transformation on the sine component containing orthogonality deviation, and extract the cosine crosstalk component introduced by the orthogonality deviation, thereby recovering the sine component orthogonal to the cosine component.

[0091] The two second-stage correction signals can be represented by the following equations (20) and (21): (20) (twenty one) in, and These are two second-stage correction signals, , These are two first-stage correction signals. After the above orthogonal linear transformation, the two second-stage correction signals have theoretically eliminated orthogonality deviation, forming ideal cosine and sine orthogonal signals.

[0092] It should be noted that the orthogonal deviation angle required in the above orthogonalization linear transformation... This can be obtained through the parameter estimation stage of an ellipse fitting algorithm. As an example, in a Lissajous ellipse formed by two first-level correction signals, there is a definite geometric relationship between the ellipse's rotation angle and the orthogonal deviation angle. By fitting the ellipse and extracting this rotation angle, the result can be deduced. The numerical value can also be estimated by calculating the deviation between the two first-stage correction signals at a specific phase point, utilizing the cross-correlation properties of the two signals. .

[0093] In S1103, the aforementioned amplitude correction can refer to further adjusting the amplitude of the two second-stage correction signals to eliminate residual amplitude differences that may be introduced during the orthogonal linear transformation, ensuring that the two final target correction signals maintain consistent amplitude. In practical systems, because the orthogonal linear transformation may lead to... amplitude and There are slight amplitude deviations. In addition, residual amplitude errors may exist from the aforementioned center shift and amplitude normalization steps.

[0094] As an example, amplitude correction for two second-level correction signals can be performed by: calculating the amplitude or effective value of each signal over a complete signal period, and then scaling the other signal proportionally based on the amplitude of one signal to make their amplitudes equal. Alternatively, both second-level correction signals can be simultaneously normalized to unit amplitude.

[0095] As a specific example, the two target correction signals after amplitude correction through normalization can be represented as shown in equations (22) and (23) below: (twenty two) (twenty three) in, and These are the two target correction signals that are ultimately generated, which meet the ideal conditions of equal amplitude and a phase difference of 90 degrees.

[0096] It should be added that the above three-stage correction process constitutes a progressive error elimination strategy. In practical applications, the correction depth can be flexibly selected according to the specific distribution of system errors: in cases of orthogonality deviation... In smaller applications, only the center shift and amplitude normalization in S1101 and the amplitude correction in S1103 need to be performed, while the orthogonalization linear transformation in S1102 can be omitted to reduce computational overhead; in terms of orthogonality deviation In more significant application scenarios, a complete three-stage correction process is executed to ensure that the two final target corrected signals meet the requirements of equal amplitude and orthogonality. Furthermore, for scenarios with low signal-to-noise ratios, the parameters involved in each correction stage can be obtained through statistical averaging based on data from multiple complete signal cycles, thereby improving the stability of parameter estimation and the consistency of correction results.

[0097] As described above, the embodiments of this application obtain a first-level correction signal by center shifting and amplitude normalization of two original interference voltage signals using DC bias parameters and AC amplitude to eliminate DC bias differences and amplitude inconsistencies. Then, an orthogonal linear transformation is used to eliminate the orthogonality deviation between the two signals to generate a second-level correction signal. Finally, amplitude correction is used to eliminate residual amplitude differences, generating two target correction signals with equal amplitudes and a phase difference of 90 degrees. In this way, various system errors in the photoelectric detection link are eliminated step by step, so that the correction signal can accurately reflect the modulation phase information, laying a reliable foundation for subsequent phase calculation and nonlinear evaluation.

[0098] Optionally, according to some embodiments of this application, in conjunction with Figure 7 As shown, in S120, phase calculation is performed based on the two target correction signals to generate phase information associated with the sinusoidal frequency modulation process of the laser, including: S121, Perform arctangent operation on the two target correction signals to generate initial phase information; S122, perform phase unwrapping processing on the initial phase information to generate phase information.

[0099] In S121, as an example, the two target correction signals can be represented as shown in equations (22) and (23), respectively, where The phase difference between the two arms contains information about the dynamic phase changes during the sinusoidal frequency modulation process of the laser.

[0100] The aforementioned arctangent operation refers to the mathematical process of calculating the corresponding phase angle by using the ratio of two orthogonal signals and the arctangent function. This is because the two target correction signals respectively provide the phase difference. The cosine and sine components of the phase difference can be calculated by taking the arctangent of the ratio of the sine to the cosine components. The initial phase information can refer to the phase quantity obtained directly through the arctangent operation without continuity processing. Its value range is usually limited by the range of the arctangent function and exhibits jump phenomena, hence it is also called the wrapped phase.

[0101] To fully utilize the sign information of the two target correction signals to determine the complete quadrant in which the phase difference lies, in some examples, a four-quadrant arctangent function can be used instead of the basic arctangent function. The four-quadrant arctangent function is a two-parameter arctangent function that determines the phase angle in the four quadrants based on the sign and ratio of the sine and cosine components, ensuring that the generated initial phase information has... or The range of values ​​for .

[0102] It should be noted that the output range of the arctangent function is inherently finite, while the actual phase difference may continuously change and exceed this range during the dynamic process of laser sinusoidal frequency modulation. For example, as the modulation process continues, the phase difference may change from approximately... Gradually increase to more than or from near Gradually reduce to below When the actual phase difference crosses the range boundary, the output of the arctangent operation will jump from the upper limit to the lower limit of the range: when using When the function is called, the jump amplitude is approximately When using basic When the function is called, the jump amplitude is approximately Therefore, the initial phase information presents as a sawtooth or segmented wrapped phase signal. Although it contains real phase change information, it lacks continuity due to abrupt changes, making it difficult to use directly for subsequent spectral analysis and nonlinear evaluation.

[0103] In S122, the aforementioned phase unwrapping process refers to a signal processing operation that restores the continuous phase variation characteristics in the time domain by detecting and compensating for phase jumps between adjacent sampling points in the initial phase information. The aforementioned phase information refers to the phase quantity obtained after phase unwrapping, which is continuous in the time domain and can completely and accurately reflect the dynamic phase changes during the sinusoidal frequency modulation process of the laser. It serves as direct input data for subsequent nonlinear spectrum analysis and nonlinear evaluation.

[0104] The basic principle of phase unwrapping is as follows: Under the premise that the phase change between adjacent sampling points does not exceed half the value range, when a sudden change exceeding a preset threshold is detected between the initial phases of adjacent sampling points, it can be determined that the sudden change is a wrapping jump caused by crossing the value range boundary rather than a real physical process. At this point, compensation is made by adding or subtracting an integer multiple of the value range to the phase values ​​of subsequent sampling points, thereby restoring the continuous phase change curve.

[0105] The aforementioned preset transition threshold can be set based on the range of the arctangent function. As an example, when using the atan2 function and its range is... At this time, the transition threshold can usually be taken as close to The value, for example, about 3.0 rad, is used to determine a package jump when the phase difference between two adjacent sampling points exceeds this threshold.

[0106] As an example, the phase unwrapping process can be performed as follows: starting from the first sampling point of the initial phase information, the phase difference between the current sampling point and the previous sampling point is compared point by point. Let the... The initial phase value of each sampling point is , No. The initial phase value of each sampling point is The difference between the two is .when Greater than the preset positive threshold for transition When this occurs, it indicates a negative jump from the upper limit to the lower limit of the value range. At this point, it can be determined that the current and subsequent sampling points need to be added. The amount of compensation; when Less than the preset negative threshold When this occurs, it indicates a positive jump from the lower limit to the upper limit of the range, at which point it can be determined that the current and subsequent sampling points need to be subtracted. The compensation amount is determined by point-by-point detection and cumulative compensation, ultimately generating phase information that is continuous and without jumps in the time domain.

[0107] As a specific example, the extracted phase difference information is shown in equation (24) below: (twenty four) in, It is an ideal modulation term. It is the second harmonic term caused by modulation nonlinearity. For the fundamental frequency modulation depth, It represents the second harmonic modulation depth.

[0108] In the above equation (24), if the frequency modulation of the laser is linear, then the phase information only contains the phase information related to the modulation fundamental frequency. The corresponding sinusoidal phase change component; if the laser has modulation nonlinearity, then in addition to the fundamental frequency component, this phase information also includes a frequency of , The higher-order harmonic phase components reflect the frequency domain characteristics of the modulation nonlinearity, providing complete and continuous phase data for subsequent quantification of the degree of nonlinear distortion through spectrum analysis.

[0109] It should be noted that the specific algorithm for phase unwrapping is not limited here. In addition to the point-by-point comparison method mentioned above, other algorithms such as two-dimensional unwrapping algorithms based on path tracking, global unwrapping algorithms based on least squares, or adaptive unwrapping algorithms based on Kalman filtering can also be used to adapt to different signal quality and application requirements. For example, in scenarios with low signal-to-noise ratios and significant noise interference near phase transition points, a global optimization algorithm based on least squares can be used to reduce the interference of local noise on the unwrapping results by applying global consistency constraints to the phase gradient of the entire sampling sequence. In scenarios requiring real-time phase processing, recursive estimation algorithms such as Kalman filtering can be used to filter and smooth the phase while unwrapping point by point, improving real-time performance and robustness.

[0110] Optionally, according to some embodiments of this application, in conjunction with Figure 8 As shown, the corresponding nonlinear evaluation results obtained in S120 based on phase information include: S123, Perform a fast Fourier transform on the phase information to obtain the frequency spectrum information of the phase information in the frequency domain; S124, based on the spectrum information, extract the first amplitude parameter corresponding to the fundamental frequency of the initial sinusoidal modulation signal, and the second amplitude parameter corresponding to at least one higher-order harmonic component in the initial sinusoidal modulation signal, wherein the second amplitude parameter includes at least the amplitude of the second-order harmonic component. S125, based on the first amplitude parameter and the second amplitude parameter, generates a nonlinear evaluation result to characterize the modulation nonlinearity intensity.

[0111] In S123, to facilitate the analysis of the frequency components in the phase information, the explanation is based on the aforementioned quadratic polynomial model of the laser's frequency response. As before, the voltage-frequency conversion relationship of the laser can be modeled as shown in equation (2): (2) in, The instantaneous frequency of the laser. These are second-order nonlinear coefficients. The coefficients are first-order linear coefficients. This is a constant term. The initial sinusoidal modulation signal... Substituting into equation (2) above, we can obtain the instantaneous frequency of the laser as shown in equation (3) below: (3) make , We can obtain the following formula (4): (4) As can be seen from the above equation, due to the second-order nonlinear coefficients The presence of this component means that the actual output frequency of the laser includes not only the expected fundamental sinusoidal component. In addition, a second harmonic cosine component also appeared. The phase of the optical field is the integral of frequency over time; therefore, the phase of the optical field of a sinusoidally modulated laser can be represented by the following equation (25): (25) in, The initial phase constant is... The instantaneous phase of the optical field is represented by the ellipsis, which indicates higher-order harmonic phase components that may be introduced by third-order and higher-order nonlinearities. For the center frequency, This is the fundamental frequency modulation amplitude. This represents the second-order harmonic modulation amplitude. After extraction via unequal arm length interferometry and optical mixing, the fundamental frequency component and harmonic components in the time domain are obtained through phase unwrapping. Third-order and higher-order nonlinearities are also introduced accordingly. , Harmonic components of the same frequency.

[0112] Based on the above analysis, by performing a Fast Fourier Transform (FFT) on the phase information, it can be mapped from the time domain to the frequency domain, thereby intuitively revealing the distribution and amplitude of each frequency component.

[0113] The aforementioned spectral information can refer to a complex sequence or amplitude sequence obtained after fast Fourier transform, which reflects the amplitude distribution of each frequency component of phase information in the frequency domain.

[0114] As an example, regarding phase information Discrete sampling sequence ( , The Fast Fourier Transform (FFT) is performed on the number of sampling points, and its mathematical expression is shown in equation (26): (26) in, For spectral information in complex form, its subscript Corresponding to frequency , This indicates the amplitude at the corresponding frequency, where k is the frequency index. Here, j is the sampling frequency, and j is the imaginary unit. In practical applications, modulo operations can also be performed on the spectral information to obtain the amplitude spectrum. Alternatively, the power spectrum can be obtained by taking the modulus and squaring, allowing for a more intuitive analysis of the strength of each frequency component. Furthermore, to reduce spectral leakage, in some examples a window function can be applied to the phase information sequence before performing the FFT to suppress spectral sidelobes and improve the accuracy of frequency resolution.

[0115] Under ideal linear modulation, the laser's frequency response contains only first-order linear terms, and the phase information contains only the fundamental frequency. Single frequency component at the location In the spectrum only It exhibits a single peak value at certain frequencies, while at various harmonic frequencies such as , The amplitude at these locations approaches zero or is at the background noise level.

[0116] However, in practical applications, tunable lasers generally exhibit modulation nonlinearity. When the laser's frequency response contains a second-order nonlinear term, second-order harmonic components will appear in the phase information in addition to the fundamental frequency component. The corresponding spectrum is A peak amplitude will appear at this point. Similarly, when the laser has third-order or higher-order nonlinearities, there will also be a peak amplitude in the spectrum. , Corresponding high-order harmonic peaks appear in places such as [locations].

[0117] As a concrete example, suppose the modulation frequency is... kHz, sampling frequency MHz, for a segment containing Phase information of each sampling point Performing a Fast Fourier Transform yields spectral information that is approximately [value missing] on the frequency axis. A kHz frequency resolution reveals the amplitude distribution of each frequency component. Under ideal linear modulation, only a significant peak appears at 100 kHz, with the amplitudes at other frequencies approaching the noise floor. In the presence of second-order modulation nonlinearity, in addition to the main peak at 100 kHz, a secondary peak appears at 200 kHz; this secondary peak represents the second-order harmonic component caused by the second-order nonlinearity. If the laser also exhibits third-order nonlinearity, a third peak will be observed at 300 kHz.

[0118] In S124, the first amplitude parameter mentioned above can refer to the fundamental frequency. The amplitude corresponding to the spectral information is denoted as This first amplitude parameter reflects the strength of the linear response component in the laser frequency modulation and serves as a reference benchmark for subsequent normalization evaluation of nonlinearity.

[0119] The aforementioned higher-order harmonic components can refer to frequencies that are integer multiples of the fundamental frequency, such as... , , The signal components, such as those mentioned above, originate from the nonlinear characteristics of the laser's frequency response. The second amplitude parameter mentioned above can refer to the amplitude of each higher-order harmonic component in the spectral information, including at least the amplitude of the second-order harmonic component, denoted as... This is because in practical tunable lasers, second-order nonlinearity is usually the dominant component of modulation nonlinearity, and the amplitude of the second-order harmonic component is often the most significant among all harmonics. In scenarios where the laser exhibits third-order or higher-order nonlinearity, the second amplitude parameter can further include the amplitude of the third-order harmonic component. Amplitude of the fourth harmonic component Higher-order amplitude parameters are used to more comprehensively assess the impact of each order of nonlinearity on the modulation process.

[0120] As an example, extracting the first amplitude parameter from the spectral information. Second amplitude parameter And the optional higher-order amplitude parameter can be obtained by: in the amplitude spectrum of the spectral information In the middle, positioning frequency The corresponding amplitude is used as Positioning frequency The corresponding amplitude is used as Positioning frequency The corresponding amplitude is used as And so on. Considering the potential for spectral leakage in actual spectrum analysis, a peak search method can be used when extracting amplitude parameters, i.e., at the fundamental frequency... The maximum amplitude value is searched within the nearby preset frequency window as... At the second harmonic frequency The maximum amplitude value is searched within the nearby preset frequency window as... This process is repeated to improve the accuracy and robustness of amplitude extraction.

[0121] As a concrete example, suppose that after performing an FFT on the phase information, the following is detected in the spectrum: Maximum amplitude within the search window at kHz ;exist Maximum amplitude within the search window at kHz ;exist Maximum amplitude within the search window at kHz This result indicates that the modulation nonlinearity of the laser is dominated by second-order nonlinearity, while a weak residual third-order nonlinearity also exists.

[0122] In S125, based on the first amplitude parameter extracted in S124 With the second amplitude parameter, at least including This generates nonlinear evaluation results to characterize the intensity of modulation nonlinearity. These nonlinear evaluation results can refer to indicators that quantitatively reflect the severity of nonlinear distortion during the sinusoidal frequency modulation of the laser, and are used to guide the generation of subsequent compensation signals.

[0123] As an example, when the modulation nonlinearity is dominated by second-order nonlinearity, the nonlinearity evaluation result can be obtained through the second-order harmonic amplitude. With fundamental frequency amplitude The ratio is used to quantify it, as shown in the following formula (27): (27) in, This is a nonlinear evaluation result. The result has a clear physical meaning: The larger the value, the more severe the modulation nonlinear distortion, and the greater the degree to which the actual frequency modulation of the laser deviates from the ideal sinusoidal law; If the value approaches zero, it indicates that the modulation process is close to an ideal linear state, and the frequency response of the laser is approximately linear. For example, if , ,but This indicates that the second-order nonlinear distortion is approximately 3% of the fundamental frequency component. This quantification result can serve as a direct basis for subsequent judgments on whether pre-distortion compensation needs to be applied and for determining the compensation intensity.

[0124] As another example, when the modulation nonlinearity is dominated by third-order nonlinearity, the nonlinearity evaluation result can be obtained through the third-order harmonic amplitude. With fundamental frequency amplitude The ratio is used to quantify it, as shown in the following formula (28): (28) In other examples, when multiple higher-order harmonic components, such as second-order, third-order and higher-order components, need to be comprehensively evaluated, the nonlinear evaluation results can also be expressed in the form of total harmonic distortion (THD) to fully reflect the overall distortion level of each order of nonlinearity. Its expression is shown in the following equation (29): (29) This index integrates the energy of all harmonic components to reflect the overall proportion of all nonlinear harmonic components relative to the fundamental frequency component. This is in contrast to a single ratio using only the second harmonic. THD can more comprehensively describe the overall distortion degree when multiple nonlinearities exist. For example, if a laser has significant second-order and third-order nonlinearities simultaneously, using only... This may underestimate the actual overall level of nonlinear distortion, while THD can incorporate the energy of each harmonic order into the assessment.

[0125] In other examples, the nonlinear evaluation results can also be expressed as a vector form consisting of the ratios of the amplitudes of each harmonic component to the fundamental frequency amplitude. ,in , , This vector-based evaluation result provides more refined guidance for the independent generation of subsequent compensation components of different orders, enabling the generation of corresponding compensation components for nonlinearities of different orders, such as second and third order.

[0126] The initial amplitude of the aforementioned compensation signal is determined based on the nonlinear evaluation results obtained after the first round without any compensation signal input. Specifically, the initial amplitude of the compensation signal is... , where V is the amplitude corresponding to the initial sinusoidal modulation signal of the laser. That is, equation (1). V in the text.

[0127] It should be added that, in the actual generation of nonlinear evaluation results, phase spectrum data from the spectral information can be combined to extract not only the amplitude parameters of each harmonic component but also their corresponding phase parameters. In this way, the nonlinear evaluation results contain not only amplitude quantization information of the nonlinear intensity but also phase characteristic information of the nonlinear distortion. This allows the subsequent generation of compensation signals to simultaneously perform amplitude matching and phase alignment, thereby more accurately canceling modulation nonlinear distortion.

[0128] As described above, the embodiments of this application obtain spectral information in the frequency domain by performing a fast Fourier transform on the phase information, and extract the fundamental frequency from the spectrum. The corresponding first amplitude parameter And including at least second-order harmonics Corresponding amplitude The second amplitude parameter is used to quantify the modulation nonlinearity intensity by the ratio of harmonic amplitude to fundamental frequency amplitude. This transforms the degree of nonlinear distortion of the laser sinusoidal frequency modulation from a time-domain phase signal into a precisely quantifiable evaluation index in the frequency domain. This index reflects both the nonlinearity intensity and the characteristic distribution of each order of harmonics, providing an accurate quantitative reference for determining the amplitude and phase alignment of each order of compensation components in the subsequent compensation signal.

[0129] Optionally, according to some embodiments of this application, in conjunction with Figure 9 As shown, in S130, a compensation signal for suppressing nonlinear distortion is generated based on the nonlinear evaluation results, including: S131, Based on the nonlinear evaluation results, determine the amplitude and phase of the higher-order harmonic components; S132, based on the amplitude and phase of the higher-order harmonic components, determine the amplitude coefficient and phase offset; S133 generates a compensation signal based on the amplitude coefficient and phase offset.

[0130] In S131, the aforementioned compensation signal can refer to a compensation drive signal superimposed on the initial sinusoidal modulation signal. Its function is to suppress harmonic distortion caused by inherent nonlinearity by introducing a compensation component at the drive end that matches the inherent nonlinear distortion characteristics of the laser beforehand. The aforementioned higher-order harmonic components can refer to those generated in the compensation signal with a fundamental frequency. The sinusoidal compensation signal components are integer multiples of each other, with each higher-order harmonic component corresponding to a certain order of distortion in the laser modulation nonlinearity. For example, at a frequency of... The second harmonic component is used to suppress the frequency distortion introduced by the second-order nonlinearity of the laser, with a frequency of . The third-order harmonic components are used to suppress the frequency distortion introduced by the third-order nonlinearity, and so on.

[0131] In practical implementation, based on the nonlinear evaluation results, the amplitude and phase of each harmonic component in the compensation signal can be determined separately. Taking second-order nonlinear compensation as an example, the amplitude and phase information of the second-order harmonic components can be obtained from the nonlinear evaluation results. This serves as the basis for determining the amplitude and phase of the second-order harmonic component in the compensation signal. The aforementioned amplitude information reflects the strength of the second-order nonlinear distortion: the ratio... The larger the value, the more significant the second-order nonlinearity, and the larger the amplitude of the compensation component that needs to be injected should be; the ratio If the value approaches zero, it indicates that the second-order nonlinearity is relatively weak, and the corresponding compensation component amplitude can be reduced accordingly or even ignored while meeting accuracy requirements. The aforementioned phase... This reflects the phase position characteristics of the second-order nonlinear distortion within the modulation period, and is used to determine the phase reference of the compensation component.

[0132] Similarly, if the nonlinear evaluation results show the existence of significant third-order nonlinearity, then the amplitude and phase information of the third-order harmonic components can be obtained from the evaluation results. This serves as the basis for the third-order compensation component. If the nonlinear evaluation results are expressed in the form of total harmonic distortion (THD) or other comprehensive indices, the specific amplitude and phase information of each harmonic can be further decomposed from them.

[0133] It should be added that when determining the higher-order harmonic components corresponding to the compensation signal, the order to be compensated can be flexibly selected based on the significance of each harmonic component in the nonlinear evaluation results. As an example, an amplitude threshold can be set, generating corresponding compensation components only for higher-order harmonic components with amplitudes exceeding this threshold, while ignoring weak harmonic components with amplitudes below the threshold, thus achieving a balance between compensation effect and signal complexity. For example, if the ratio threshold is set to 0.005, in the aforementioned example, the second-order harmonic ratio... Compensation is needed if the threshold is exceeded, and the third harmonic ratio... If the signal falls within the threshold range, its inclusion in the compensation range can be determined based on actual accuracy requirements. This selective compensation strategy helps reduce the complexity of generating the compensation signal while ensuring compensation accuracy.

[0134] In S132, based on the amplitude and phase of each higher-order harmonic component in the compensation signal determined in S131, the amplitude coefficient and phase offset corresponding to each order compensation component are further determined.

[0135] The aforementioned amplitude coefficient can refer to a proportional parameter used to determine the specific voltage amplitude of each higher-order harmonic component in the compensation signal in the driving signal domain. There is a mapping relationship between this amplitude coefficient and the amplitude of the corresponding higher-order harmonic component. Through the amplitude coefficient, the harmonic amplitude obtained from spectral analysis can be converted into the actual voltage amplitude of the corresponding compensation component in the driving signal domain. In practical systems, because there is a conversion relationship between the dimensions or numerical range of the nonlinear evaluation results and the driving signal domain, it is necessary to establish a proportional mapping between the two through the amplitude coefficient, so that the generated compensation component can produce a pre-distortion effect in the driving signal that matches the inherent nonlinear response amplitude of the laser.

[0136] As an example, for the second harmonic component, the amplitude coefficient It can be shown in the following formula (30): (30) in, The preset voltage conversion factor is a proportionality coefficient that maps the harmonic amplitude in the phase domain to the driving voltage domain, with dimensions in V / unit amplitude. This voltage conversion factor can be determined through preliminary calibration experiments, for example, by measuring the nonlinear response of the laser output at different driving voltage amplitudes, establishing a curve relating the driving voltage increment to the phase harmonic amplitude increment, and taking the slope of this curve near the operating point as... The calibration value.

[0137] In other examples, the magnitude coefficient can also be directly based on the ratio index in the nonlinear evaluation results. Combined with the amplitude of the initial sinusoidal modulation signal To determine. Because of the ratio. The proportional relationship between the second harmonic and the fundamental frequency has already been reflected. When this proportional relationship is mapped to the driving voltage domain, it can be expressed as shown in the following equation (31): (31) in, Empirical adjustment factor ( ), This represents the amplitude of the initial sinusoidal modulation signal. This expression reflects the positive correlation between the amplitude coefficient and the intensity of nonlinear distortion: the nonlinear ratio The larger the amplitude coefficient The larger; conversely The smaller, The smaller.

[0138] The aforementioned phase offset can refer to the amount of phase adjustment required for each higher-order harmonic component in the compensation signal relative to its original harmonic phase obtained from the nonlinear evaluation result, denoted as... This phase offset is used to ensure that the predistortion compensation component, after being superimposed on the initial sinusoidal modulation signal, can form the expected phase relationship with the harmonic distortion generated by the inherent nonlinearity of the laser, thereby achieving a suppression effect.

[0139] As an example, phase offset The determination principle can be based on the following considerations: In order to make the additional harmonics generated by the compensation component during the nonlinear response of the laser mutually weaken the harmonics generated by the inherent nonlinearity of the laser, the phase of the compensation component and the phase of the original nonlinear harmonic component can be set to be out of phase, that is, the phase offset is... Approximately Taking the second harmonic component as an example, if the second harmonic phase obtained from the nonlinear evaluation result is... The compensation phase of the second harmonic component in the compensation signal. It can be expressed as shown in the following formula (32): (32) In other examples, considering the potential additional phase delay in the laser drive circuitry and signal transmission path, the phase offset can be approximately... The compensation amount for this delay is added on top of the existing amount. For example, suppose the first... First harmonic frequency The additional phase delay introduced by the system transmission path is Then the first The phase shift of the first harmonic component can be expressed as shown in equation (33): (33) in, It can be obtained through prior system calibration measurements, for example, by measuring the transmission characteristics from the output of the signal output unit to the modulation input of the laser at different frequencies.

[0140] As a concrete example, taking second-order nonlinear compensation as an example, suppose the second-order harmonic amplitude is obtained from the nonlinear evaluation results. Phase rad, preset voltage conversion factor V / unit amplitude, then the amplitude coefficient of the second-order compensated component V. Simultaneously, the second harmonic frequency was measured through system calibration. Additional phase delay of the transmission path at kHz rad, then the phase shift of the second harmonic component rad, compensated phase rad.

[0141] In S133, a compensation signal is generated based on the amplitude coefficient and phase offset determined in S132. The generation of the compensation signal can refer to the process of combining each order of compensation harmonic components into a complete time-domain compensation signal according to their respective amplitude coefficients and compensation phases.

[0142] As an example, when only second-order nonlinearity needs to be compensated, the compensation signal... It can be represented as a single second-order harmonic component, as shown in equation (34) below: (34) in, The amplitude coefficient of the second harmonic component. Based on the original second-order harmonic phase and phase offset Determined compensation phase, This is the modulation angular frequency.

[0143] Substitute the relationship between the compensated phase, the original phase, and the phase offset. and take The above equation can be further expressed as shown in equation (35): (35) As can be seen from the above formula, when the anti-phase compensation strategy is adopted, the second harmonic component in the compensation signal and the second harmonic distortion generated by the inherent nonlinearity of the laser are in opposite phase on the waveform, which provides a basis for subsequent suppression by superposition.

[0144] When multiple higher-order harmonic components need to be compensated simultaneously, the compensation signal can be composed of multiple harmonic components of corresponding orders superimposed, as shown in the following equation (36): (36) in, and These are the amplitude coefficients and compensation phases corresponding to the third harmonic component, respectively. The ellipsis indicates that it may also include fourth-order and higher-order compensation components.

[0145] As a specific example, taking the parameters determined in S131 and S132 above as an example, the amplitude coefficient of the second harmonic component V, compensation phase rad, modulation angular frequency rad / s; Amplitude coefficient of third harmonic component V, compensation phase rad. The generated compensation signal is: The compensation signal contains a second-order compensation component at 200 kHz and a third-order compensation component at 300 kHz. The amplitudes of both components are matched to the corresponding orders of nonlinear distortion intensity, and their phases are shifted using an anti-phase compensation strategy. This signal will be used in subsequent steps to modulate the initial sinusoidal signal. The signals are superimposed to form the target modulation signal, which drives the laser to achieve active suppression of modulation nonlinearity.

[0146] It should be added that the above-described method for generating compensation signals is not only applicable to generating corresponding compensation components for each identified harmonic, but also to situations where the compensation strategy is dynamically adjusted based on the nonlinear evaluation results. For example, in an iterative compensation process, the first round may only generate compensation signals for the dominant second-order nonlinearity; after applying compensation, the residual nonlinearity is re-evaluated, and if the third-order nonlinearity is still significant, a third-order compensation component is added in the next iteration, forming a progressively refined compensation strategy. Furthermore, the amplitude coefficients and phase shifts of each harmonic component in the compensation signal can also be fine-tuned online according to changes in environmental conditions during actual operation to maintain consistency in the suppression effect.

[0147] As described above, the embodiments of this application extract the amplitude and phase information of each order harmonic component from the nonlinear evaluation results, determine the amplitude coefficient and phase offset of the compensation signal accordingly, and then generate a compensation signal containing the corresponding order harmonic components based on these parameters. This ensures that the compensation signal accurately matches the inherent nonlinear distortion characteristics of the laser in both amplitude and phase dimensions, providing a precise compensation input for the subsequent active suppression of modulation nonlinearity through signal superposition.

[0148] Optionally, according to some embodiments of this application, the amplitude coefficient is positively correlated with the amplitude of the higher-order harmonic component, and the phase offset is 180 degrees out of phase with the higher-order harmonic component.

[0149] Regarding the aforementioned amplitude coefficient, the positive correlation can refer to the trend of the amplitude coefficient increasing as the amplitude of the higher-order harmonic component increases and decreasing as the amplitude decreases.

[0150] In one example, when multiple higher-order harmonic components need to be suppressed, the amplitude coefficients corresponding to each harmonic component can be determined independently according to their respective harmonic amplitudes. For example, the first harmonic component... Amplitude coefficient of first harmonic ,in For the first Voltage conversion factor corresponding to first harmonics, This represents the voltage amplitude corresponding to the m-th harmonic. Different orders... They can be the same or different, depending on the differences in voltage-frequency conversion characteristics of the laser at each order of nonlinearity, which can be determined by calibrating each order of harmonics separately.

[0151] Regarding the aforementioned phase offset, the 180-degree phase difference can refer to the phase difference between the compensated phase of each higher-order harmonic component in the compensated signal and the phase of the corresponding original harmonic component in the nonlinear evaluation result, approximately... The radian dimension causes the compensation signal and the harmonic distortion signal to be suppressed to be out of phase.

[0152] The physical principle behind this phase shift relationship is that when a certain harmonic component of the compensation signal matches the same harmonic distortion of the same order generated by the inherent nonlinearity of the laser in amplitude but is opposite in phase, the two will tend to cancel each other out after being superimposed during the laser modulation response, thereby effectively suppressing the nonlinear harmonic component of that order in the actual output frequency of the laser.

[0153] As a concrete example, suppose the second harmonic phase is obtained from the nonlinear evaluation results. The second harmonic frequency was measured using system calibration in rad. Additional phase delay of the transmission path at kHz If the phase shift of the second harmonic component is rad, then the phase shift of the second harmonic component is taken as rad, compensated phase The compensated phase has an additional phase shift of approximately 182.9 degrees compared to the original harmonic phase. After deducting the effects of transmission path delay, the predistortion compensation component can still maintain a near-out-of-phase relationship with the inherent nonlinear harmonics when it reaches the laser modulation input, thus effectively achieving cancellation.

[0154] As described above, the embodiments of this application make the amplitude coefficient positively correlated with the amplitude of higher-order harmonics, so that the amplitude of the compensation component automatically increases or decreases accordingly with the change of nonlinear distortion intensity. At the same time, the phase offset is set to be about 180 degrees out of phase relative to the original harmonic phase, so that the compensation component and the distortion component form an anti-cancel relationship in the waveform. Thus, the compensation signal and the inherent nonlinear distortion of the laser are accurately matched in both amplitude and phase dimensions, so that the superimposed driving signal can effectively suppress the harmonic errors introduced during the sinusoidal frequency modulation of the laser.

[0155] Optionally, according to some embodiments of this application, in conjunction with Figure 10 As shown, S140 adjusts the initial sinusoidal modulation signal based on the compensation signal to generate the target modulation signal, and drives the laser based on the target modulation signal, including: S141, The compensation signal is superimposed on the initial sinusoidal modulation signal to generate the target modulation signal; S142, apply the target modulation signal to the modulation input of the laser.

[0156] In S141, the aforementioned compensation signal can refer to the compensation drive signal generated in the preceding steps based on the nonlinear evaluation results, which contains harmonic components of various orders that match the inherent nonlinear distortion characteristics of the laser. As an example, when the modulation nonlinearity of the laser is predominantly second-order, the compensation signal can be expressed as... When multiple higher-order harmonic components need to be compensated simultaneously, the compensation signal can be composed of the superposition of multiple harmonic components of corresponding orders, i.e. ,in For the first The amplitude coefficients corresponding to the first harmonic components, For the corresponding phase, This is the modulation angular frequency.

[0157] As an example, the initial sinusoidal modulation signal described above can be represented as follows: ,in The voltage amplitude of the initial sinusoidal modulation signal. This is the modulation angular frequency.

[0158] The aforementioned superposition can refer to the operation of adding the values ​​of two or more time-domain signals at corresponding sampling times to obtain a new composite time-domain signal. The aforementioned target modulation signal can refer to the composite modulation signal generated by superimposing the compensated signal and the initial sinusoidal modulation signal, which is used to drive the laser. It contains both the desired fundamental frequency sinusoidal modulation component and embedded compensation components of various orders used to cancel the modulation nonlinearity of the laser.

[0159] As an example, the compensation signal With the initial sinusoidal modulation signal Superimpose the signals to generate the target modulation signal. The process can be shown by the following formula (37): (37) Among them, the first item The fundamental frequency modulation component is used to drive the laser to generate the desired sinusoidal frequency modulation; the second term... The sum of compensation components of each order. The highest harmonic order requiring compensation is represented by the compensation components of each order, which are used to suppress the corresponding order of nonlinear frequency components generated during the sinusoidal frequency modulation of the laser. Taking second-order nonlinear compensation as an example (i.e....) The target modulation signal can be specifically expanded as shown in equation (38): (38) in The amplitude coefficient of the second harmonic component. This represents the phase of the second harmonic component. When an anti-phase compensation strategy is adopted, i.e. Then, the above formula can be further expressed as ,in The original second-order harmonic phase is obtained from the nonlinear evaluation results.

[0160] Based on the above, the target modulation signal is determined according to the first formula, which is shown below: It should be noted that the specific implementation of the above superposition operation is not limited here. As an example, the superposition operation can be performed in the number field, that is, by... Figure 2 The signal processing and analysis module, when generating the digital waveform data of the target modulation signal, adds the digital sampling sequence of the initial sinusoidal modulation signal and the digital sampling sequence of the compensation signal point by point, and then converts the superimposed digital waveform into an analog voltage signal output through a digital-to-analog converter. Figure 2 The system architecture shown has a signal processing and analysis module 7 that receives the digital signal output by the signal acquisition module 6, completes the correction processing, phase calculation, nonlinear evaluation and compensation signal generation, and then sends the waveform parameters of the target modulation signal to the signal output unit 1, which completes the digital-to-analog conversion and output of the target modulation signal.

[0161] In other examples, analog domain superposition can also be used. For instance, two independent digital-to-analog conversion channels output the initial sinusoidal modulation signal and the compensation signal respectively, and then the signals are superimposed in the analog domain using an analog adder circuit or a signal combiner. The advantage of analog domain superposition is that it can reduce the processing delay in the digital domain, making it suitable for applications with high real-time requirements. The signal output unit 1 can use any circuit or instrument capable of generating and dynamically adjusting the electrically driven signal, such as an arbitrary waveform generator, a programmable signal source, or a digital signal generation module, etc., without any limitations.

[0162] In S142, the aforementioned modulation input terminal can refer to the electrical signal input interface on the laser used to receive external electrical drive signals to modulate its output optical frequency. The specific form of the modulation input terminal may vary depending on the type of tunable laser. For example, for distributed feedback lasers, the modulation input terminal is typically the drive port for its injected current; by changing the magnitude of the injected current, the refractive index of the laser's active region is tuned, thereby changing the output wavelength and frequency. For distributed Bragg reflector lasers, the modulation input terminal can be the current injection port or temperature control port of its grating region. For external cavity tunable lasers, the modulation input terminal can be the control voltage input port of its intracavity tuning element. The specific physical form and interface parameters of the modulation input terminal are not limited here.

[0163] The aforementioned application can refer to the process of feeding the target modulation signal as an electrical signal to the laser modulation input, making it the actual driving signal for laser frequency modulation. Combined with... Figure 2 The system architecture shown describes a system where signal output unit 1 generates a corresponding analog voltage signal based on the target modulation signal waveform parameters provided by signal processing and analysis module 7, and outputs this signal to the modulation input of tunable laser 2. Driven by this target modulation signal, tunable laser 2 outputs laser light that has undergone nonlinear suppression.

[0164] During the application process, the compensation component embedded in the target modulation signal and the inherent nonlinear response of the laser produce the following cancellation effect. This is illustrated by the aforementioned quadratic polynomial model of the laser's frequency response. For example, the nonlinear frequency response of a laser will produce a nonlinear mapping for all frequency components of the driving signal. When the target modulation signal... After being applied to the modulation input of the laser, the instantaneous output frequency of the laser can be expressed as shown in the following equation (39): (39) Will After substituting and expanding, the output frequency includes not only the fundamental frequency component. Through linear terms The desired fundamental frequency modulation component generated and through second-order nonlinear terms Second-order harmonic distortion It also includes compensation components. Through linear terms The resulting additional second-order frequency components This includes the cross-terms between the compensation component and the fundamental frequency component, as well as higher-order terms generated by the nonlinear mapping of the compensation component itself. This can be addressed by appropriately setting the amplitude coefficients of the compensation component. and phase This can make the above terms at the second harmonic frequency. The combined contributions at each point tend to cancel each other out, thereby effectively suppressing the second-order nonlinear harmonic components in the actual output frequency of the laser, making the output frequency approach the ideal sinusoidal modulation law.

[0165] As a concrete example, combined with Figure 2 The system architecture shown indicates that signal output unit 1 outputs the target modulated signal. The signal is fed to the modulation input of the tunable laser 2 via a coaxial cable or other signal transmission line. Driven by the target modulation signal, the tunable laser 2 outputs a nonlinearly suppressed laser beam. This laser beam then enters the unequal arm length optical path 3, is split by an optical fiber coupler, and after being introduced with a fixed time delay difference via a delay fiber, the two beams with the time delay difference are input to the optical mixer 4 for coherent coupling. The photoelectric detection module 5 then converts the interference light signal into an electrical signal, which is then sent to the signal processing and analysis module 7 via the signal acquisition module 6. This forms a complete closed loop from nonlinear assessment to effective suppression and then to effect verification. In actual operation, this closed-loop process can be executed iteratively: after each iteration, the residual nonlinearity is reassessed; if the residual nonlinearity still exceeds a preset threshold, the compensation signal parameters are updated and a new target modulation signal is generated again until the residual nonlinearity is reduced to an acceptable level.

[0166] As described above, the embodiments of this application generate a target modulation signal embedded with anti-phase harmonic compensation components by superimposing the compensation signal and the initial sinusoidal modulation signal in the time domain. This target modulation signal is then applied to the modulation input of the laser to drive the laser to work. This causes the harmonic distortions of the fundamental frequency component caused by the inherent nonlinearity of the laser and the additional harmonics generated by the compensation component after modulation response to tend to cancel each other out at the corresponding frequencies. This effectively suppresses the nonlinear harmonic components in the output laser frequency and improves the linearity of sinusoidal frequency modulation and the accuracy of interferometric measurement.

[0167] Optionally, according to some embodiments of this application, in conjunction with Figure 11 As shown, after adjusting the initial sinusoidal modulation signal of the laser based on the compensation signal in S140 to generate the target modulation signal, and driving the laser based on the target modulation signal, the method further includes: S150, update the target modulation signal to the initial sinusoidal modulation signal, and jump to execute the steps of obtaining the two original interference voltage signals corresponding to the initial sinusoidal modulation signal, and correcting the two original interference voltage signals to obtain the two target correction signals, until the updated nonlinear evaluation result is obtained; S160, If the updated nonlinear evaluation result is greater than the preset threshold, an updated compensation signal is generated based on the updated nonlinear evaluation result; S170: Based on the updated compensation signal and the initial sinusoidal modulation signal of the laser, an updated target modulation signal is generated, and the laser is driven based on the updated target modulation signal. Then, the process jumps to the step of updating the target modulation signal to the initial sinusoidal modulation signal until the updated nonlinear evaluation result is less than a preset threshold.

[0168] In S150, updating the target modulation signal to the initial sinusoidal modulation signal can mean that in the current iteration, the target modulation signal generated after compensation and correction is used as the driving signal for the next iteration, replacing the driving signal used in the current iteration. The purpose of this update is to allow subsequent nonlinear evaluations to be performed again based on the current compensated driving signal, thereby detecting the compensation effect and determining whether residual nonlinearity still exists. This update operation can be performed in the background by the signal processing and analysis module, writing the waveform data or waveform parameters of the current target modulation signal into the storage area corresponding to the driving signal, overwriting the original old value.

[0169] It should be noted that the updated drive signal here differs in waveform from the initial sinusoidal modulation signal in the original concept: the updated signal includes the previously applied compensation component, therefore its waveform is no longer a simple fundamental frequency sine wave, but a composite signal containing compensated harmonics. In subsequent iterations, the modulation nonlinearity characteristics generated by the laser under this updated drive signal will change: under good suppression conditions, the compensation component has offset some of the inherent nonlinearity, and the residual nonlinearity will be weakened compared to the previous round.

[0170] As an example, the updated nonlinear evaluation result can be quantized in the same way as in S120 above, such as the updated ratio of the second harmonic amplitude to the fundamental frequency amplitude. If the compensation in the previous round was effective, the updated nonlinear evaluation result should be lower than that in the previous round; if the compensation parameters are not accurate enough or the nonlinear characteristics of the laser change due to factors such as temperature drift during the iteration, the updated nonlinear evaluation result may still be too high.

[0171] As another example, the process of adjusting the compensation parameters based on the new nonlinear evaluation results can be as follows: First, based on the nonlinear evaluation result of the initial sinusoidal modulation signal corresponding to the laser that has not been compensated, the amplitude of the compensation signal is initialized. The initial amplitude is determined by the product of the nonlinear evaluation result of the initial sinusoidal modulation signal that has not been compensated and the amplitude of the initial sinusoidal modulation signal that has not been compensated. The phase offset is determined by any value between 0 and 360°. The compensation signal is determined based on this. Then, the target modulation signal corresponding to the compensation signal is input to the laser, and the nonlinear evaluation result of the current target modulation signal is obtained. Based on the current nonlinear evaluation and the previous round of nonlinear evaluation results, the adjustment direction is determined. Specifically, if the current nonlinear evaluation result... If the value decreases, it indicates that the current adjustment direction is effective, and the compensation parameters should continue to be optimized along this direction; however, if the current nonlinear evaluation result... An increase indicates that the adjustment direction is unreasonable, requiring a change in the direction of amplitude change of the compensation signal or an adjustment of the phase offset of the compensation signal. This can be achieved through continuous iterative optimization of the compensation signal's amplitude. and phase offset This gradually reduces the nonlinear error index. Finally, when the nonlinear error reaches a preset threshold or further adjustments fail to significantly reduce the error, the optimal compensation parameters are determined to achieve active suppression of modulation nonlinearity.

[0172] As a concrete example, suppose that in the first iteration, the initial sinusoidal modulation signal is V, after detection and evaluation in S110 to S130, yields the nonlinear evaluation result. Based on this, a compensation signal is generated. V, after superposition, yields the target modulation signal. V is applied to the laser. In S150, the target modulation signal is updated to a new driving signal, and then the detection process from S110 to S120 is repeated: the two original interference voltage signals of the laser under the action of the updated driving signal are acquired, and after correction processing and phase calculation, the updated phase information is obtained. Then, the spectrum analysis is performed by fast Fourier transform to extract the updated fundamental frequency amplitude. and second harmonic amplitude The updated nonlinear evaluation results are calculated. If the first round of compensation is effective, It may decrease from the initial 0.03 to about 0.008.

[0173] In S160, the aforementioned preset threshold may refer to a judgment threshold value used to determine whether the residual nonlinearity has been reduced to an acceptable level, denoted as... The preset threshold can be determined based on the accuracy requirements of the modulation linearity of the interferometric measurement system, and its specific value is related to the measurement accuracy requirements of the target application scenario. For example, in ultra-precision displacement measurement scenarios, the preset threshold can be 0.005; in conventional precision measurement scenarios, the preset threshold can be 0.01; and in applications with relatively relaxed linearity requirements, the preset threshold can be 0.02 or higher. The preset threshold can be pre-stored in the memory of the signal processing and analysis module, or it can be set and adjusted by engineers through the human-computer interaction interface according to actual needs; no limitation is made here.

[0174] When the updated nonlinear evaluation results Greater than the preset threshold This indicates that after the previous round of compensation, the modulation nonlinearity of the laser still exceeds the allowable range, and there is residual nonlinearity that requires further compensation. At this point, an updated compensation signal is generated based on the updated nonlinearity evaluation results.

[0175] The specific method for generating the updated compensation signal can be the same as the method for generating the compensation signal in S130 above. That is, the updated amplitude information of each harmonic component (e.g., the updated second harmonic amplitude) is extracted from the updated nonlinear evaluation results. and its ratio to the fundamental frequency amplitude ) and phase information (e.g., updated second-order harmonic phase) Based on this, the updated amplitude coefficients are determined. and phase offset Then, based on these parameters, an updated compensation signal is generated. .

[0176] As an example, taking second-order nonlinear compensation as an example, the updated amplitude coefficients It can be based on the updated harmonic amplitude. Determined by positive correlation, for example ,in This is a preset voltage conversion factor. The updated phase offset can be based on the updated harmonic phase. Determined according to the principle of opposite phase, for example The updated compensation phase The updated compensation signal is thus generated as shown in equation (40): (40) When there is a third-order or higher-order residual nonlinearity, the updated compensation signal can be composed of multiple updated harmonic components of corresponding orders, as shown in equation (41) below: (41) in and The first The updated amplitude coefficients and phases corresponding to the first harmonic components. This represents the highest harmonic order that needs compensation.

[0177] As a concrete example, suppose there is a preset threshold. Updated nonlinear evaluation results after the first round of compensation This indicates that the residual nonlinearity remains significant. At this point, the residual second-order harmonic amplitude is extracted from the updated spectral information. Phase rad, according to amplitude coefficient V, phase offset amount is taken Then phase rad, generating the updated compensation signal as V.

[0178] It should be noted that when the updated nonlinear evaluation results... Less than or equal to the preset threshold When the convergence condition is met, it indicates that the modulation nonlinearity of the laser has decreased to an acceptable level, and the current compensation signal parameters have achieved the expected suppression effect. At this point, the iterative closed-loop process can be terminated, and the current target modulation signal can be maintained to continue driving the laser without further updating the compensation signal. This convergence criterion ensures that the iterative process can terminate in a timely manner after reaching the accuracy target, avoiding unnecessary computational overhead and iteration counts.

[0179] In S170, the updated compensation signal generated in S160, i.e., the current round's compensation signal, is used. The initial sinusoidal modulation signal input to the laser in the previous round is used to generate an updated target modulation signal, and the laser is driven based on the updated target modulation signal. Then, the process jumps to execute S150 to perform the next iteration.

[0180] As an example, the updated compensation signal With the initial sinusoidal modulation signal Superimpose the signals to generate the updated target modulation signal. The process can be represented by the following equation (42): (42) Taking second-order nonlinear compensation as an example, the updated target modulation signal can be expanded as shown in equation (43): (43) After generating the updated target modulation signal, it is applied to the modulation input of the laser to drive the laser. Under this updated drive signal, the laser outputs a frequency-modulated laser with further compensation, aiming to further reduce its residual nonlinearity compared to the previous round. Subsequently, the process jumps to S150, where the updated target modulation signal is updated again to the initial sinusoidal modulation signal, and the detection process is re-executed, thus iterating in this loop.

[0181] The entire iterative closed-loop process described above can be viewed as an optimization mechanism for adaptive compensation parameters based on nonlinear evaluation feedback. Combined with... Figure 2 The system architecture shown involves a closed-loop iterative process involving the cyclical collaboration between the signal processing and analysis module, the signal output unit, the tunable laser, the unequal arm length optical path, the optical mixer, the photoelectric detection module, and the signal acquisition module. In each iteration, the signal acquisition module acquires the interference voltage signal under the current driving signal, the signal processing and analysis module performs correction, calculation, and evaluation, and if the residual nonlinearity exceeds the threshold, it updates the compensation parameters and instructs the signal output unit to adjust the output waveform. This process is repeated until convergence.

[0182] It should be added that the termination condition for the aforementioned iterative closed loop is not limited to the single criterion that the nonlinear evaluation result is less than a preset threshold. In other examples, a maximum number of iterations can also be set as an auxiliary termination condition to prevent the system from entering an infinite loop when the laser's nonlinear characteristics are abnormally severe or a system malfunction occurs. For example, the maximum number of iterations can be set to 5 to 10. When the number of iterations reaches the upper limit and the nonlinear evaluation result is still greater than the preset threshold, the system can issue a warning or prompt, allowing the operator to intervene or make a judgment. In addition, a convergence judgment condition can be set. When the change in the nonlinear evaluation result between two adjacent iterations is less than a preset minimum change threshold, even if the preset threshold is not reached, convergence can be determined and the iteration can be terminated to avoid situations where strict convergence cannot be achieved due to measurement noise.

[0183] As described above, the embodiments of this application update the current modulation signal to a new driving signal and re-execute the detection process after driving the laser with the target modulation signal, and evaluate the residual nonlinearity. If the residual nonlinearity exceeds a preset threshold... An updated compensation signal is generated based on the updated nonlinear evaluation results. This updated compensation signal is then superimposed on the original fundamental frequency sinusoidal signal to form an updated target modulation signal that drives the laser and enters the next iteration. This constructs an iterative closed-loop mechanism of evaluation-suppression-re-evaluation. Each round of compensation is independently generated based on the latest residual nonlinearity and superimposed on the original fundamental frequency signal, avoiding the accumulation of overcompensation of the compensation components. This allows the modulation nonlinearity to gradually converge to the preset accuracy range with each iteration, achieving adaptive closed-loop suppression and dynamic tracking of the laser modulation nonlinearity.

[0184] Figure 12 A schematic diagram of the hardware structure of the control device for the nonlinear suppression method in the sinusoidal frequency modulation provided in the embodiments of this application is shown.

[0185] The control device may include a processor 1201 and a memory 1202 storing computer program instructions.

[0186] Specifically, the processor 1201 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0187] Memory 1202 may include mass storage for data or instructions. For example, and not limitingly, memory 1202 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 1202 may include removable or non-removable (or fixed) media. Where appropriate, memory 1202 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 1202 is non-volatile solid-state memory.

[0188] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the methods according to one aspect of this disclosure.

[0189] The processor 1201 reads and executes computer program instructions stored in the memory 1202 to implement any of the nonlinear suppression methods in sinusoidal frequency modulation in the above embodiments.

[0190] In one example, the control device for the nonlinear suppression method in sinusoidal frequency modulation may further include a communication interface 1203 and a bus 1210. Wherein, as Figure 12 As shown, the processor 1201, memory 1202, and communication interface 1203 are connected through bus 1210 and complete communication with each other.

[0191] The communication interface 1203 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0192] Bus 1210 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 1210 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0193] The control device of the nonlinear suppression method in sinusoidal frequency modulation can execute the nonlinear suppression method in sinusoidal frequency modulation in the embodiments of this application, thereby realizing the nonlinear suppression method in sinusoidal frequency modulation described in the above embodiments.

[0194] Furthermore, in conjunction with the nonlinear suppression method in sinusoidal frequency modulation described in the above embodiments, this application embodiment can provide a computer storage medium for implementation. This computer storage medium stores computer program instructions; when these computer program instructions are executed by a processor, they implement any of the nonlinear suppression methods in sinusoidal frequency modulation described in the above embodiments.

[0195] This application also provides a computer program product, including a computer program that, when executed by a processor, implements any of the nonlinear suppression methods in sinusoidal frequency modulation described in the above embodiments.

[0196] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0197] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0198] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0199] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0200] The above are merely specific embodiments of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for suppressing nonlinearity in sinusoidal frequency modulation, characterized in that, include: Two original interference voltage signals corresponding to the initial sinusoidal modulation signal are obtained, and the two original interference voltage signals are corrected to obtain two target correction signals. The two original interference voltage signals are the signals obtained by optical mixing of the laser corresponding to the initial sinusoidal modulation signal after unequal arm length processing. Phase calculation is performed based on the two target correction signals to generate phase information associated with the sinusoidal frequency modulation process of the laser, and the corresponding nonlinear evaluation result is obtained based on the phase information. The nonlinear evaluation result is used to characterize the degree of nonlinear modulation of the sinusoidal frequency corresponding to the laser. Based on the nonlinear evaluation results, a compensation signal is generated to suppress nonlinear distortion. The initial sinusoidal modulation signal of the laser is adjusted based on the compensation signal to generate a target modulation signal, and the laser is driven based on the target modulation signal.

2. The method according to claim 1, characterized in that, The acquisition of the two original interference voltage signals corresponding to the initial sinusoidal modulation signal includes: The laser corresponding to the initial sinusoidal modulation signal is injected into two optical paths with unequal arm lengths to obtain two beams with a fixed time delay difference. The two beams are input into an optical mixer for coherent coupling to generate multi-channel interference optical signals. Based on the multi-channel interference optical signals, the multi-channel interference optical signals are converted into the two original interference voltage signals.

3. The method according to claim 1, characterized in that, The correction processing of the two original interference voltage signals to obtain two target correction signals includes: Obtain the extreme values ​​of the two original interference voltage signals within the complete signal period, and determine the DC bias parameters and AC amplitude of the two original interference voltage signals based on the extreme values; Based on the DC bias parameters and AC amplitudes of the two original interference voltage signals, the two original interference voltage signals are preprocessed using an ellipse fitting algorithm to generate the two target correction signals.

4. The method according to claim 3, characterized in that, The DC bias parameter and AC amplitude based on the two original interference voltage signals are preprocessed using an ellipse fitting algorithm to generate the two target correction signals, including: Based on the DC bias parameters and the AC amplitude, the two original interference voltage signals are center-shifted and amplitude-normalized to obtain two first-stage correction signals after eliminating DC bias differences. The two first-level correction signals are subjected to an orthogonal linear transformation to generate two second-level correction signals. The amplitude of the two second-level correction signals is corrected to generate the two target correction signals, which have equal amplitudes and a phase difference of 90 degrees.

5. The method according to claim 1, characterized in that, The step of performing phase calculation based on the two target correction signals to generate phase information associated with the sinusoidal frequency modulation process of the laser includes: Perform arctangent operation on the two target correction signals to generate initial phase information; The initial phase information is subjected to phase unwrapping processing to generate the phase information.

6. The method according to claim 1, characterized in that, The process of obtaining the corresponding nonlinear evaluation result based on the phase information includes: Perform a fast Fourier transform on the phase information to obtain the frequency spectrum information of the phase information in the frequency domain; Based on the spectral information, a first amplitude parameter corresponding to the fundamental frequency in the initial sinusoidal modulation signal and a second amplitude parameter corresponding to at least one higher-order harmonic component in the initial sinusoidal modulation signal are extracted. The second amplitude parameter includes at least the amplitude of the second-order harmonic component. The nonlinear evaluation result is generated based on the first amplitude parameter and the second amplitude parameter.

7. The method according to claim 1, characterized in that, The step of generating a compensation signal to suppress nonlinear distortion based on the nonlinear evaluation result includes: Based on the nonlinear evaluation results, the amplitude and phase of the higher-order harmonic components are determined; Based on the amplitude and phase of the higher-order harmonic components, determine the amplitude coefficient and phase offset; The compensation signal is generated based on the amplitude coefficient and the phase offset.

8. The method according to claim 7, characterized in that, The amplitude coefficient is positively correlated with the amplitude of the higher-order harmonic component, and the phase offset is 180 degrees out of phase with the phase of the higher-order harmonic component.

9. The method according to claim 1, characterized in that, The target modulation signal is determined according to a first formula, which is: Among them, S target (t) represents the target modulation signal corresponding to the current time t. For the first The amplitude coefficients corresponding to the first harmonic components, For the first Phase corresponding to the first harmonic component The amplitude corresponding to the initial sinusoidal modulation signal. The modulation angular frequency is the frequency corresponding to the initial sinusoidal modulation signal.

10. The method according to claim 1, characterized in that, After adjusting the initial sinusoidal modulation signal of the laser based on the compensation signal to generate a target modulation signal, and driving the laser based on the target modulation signal, the method further includes: The target modulation signal is updated to the initial sinusoidal modulation signal, and the process jumps to obtain the two original interference voltage signals corresponding to the initial sinusoidal modulation signal, and performs correction processing on the two original interference voltage signals to obtain two target correction signals, until the updated nonlinear evaluation result is obtained. If the updated nonlinear evaluation result is greater than a preset threshold, an updated compensation signal is generated based on the updated nonlinear evaluation result. Based on the updated compensation signal and the initial sinusoidal modulation signal of the laser, an updated target modulation signal is generated, and the laser is driven based on the updated target modulation signal. Then, the process jumps to the step of updating the target modulation signal to the initial sinusoidal modulation signal until the updated nonlinear evaluation result is less than the preset threshold.

Images