Method and apparatus for suppressing jitter path coupling noise in an interferometer inspection quality instrument

Abstract

The application provides a method for suppressing jitter path coupling noise of a proof mass interferometer, comprising: constructing a schematic model of the proof mass interferometer, constructing a reference light beam and a measurement light beam of a four-quadrant detector injected into the proof mass interferometer, calculating LPF path signals and AP path signals, extracting a longitudinal length path signal from a phase signal generated when the reference light beam and the measurement light beam interfere on the surface of the detector, analyzing jitter path coupling noise coupled by high-order aberrations, analyzing the influence of the aberrations on the jitter path coupling noise, drawing a density distribution diagram of the jitter path coupling noise containing the aberrations, determining that the AP path signals are superior to the LPF path signals in reducing the jitter path coupling noise of the proof mass interferometer according to the density distribution diagram, and performing Monte Carlo simulation on the LPF path signals and the AP path signals with three different transverse displacements; and verifying the effectiveness of the method for suppressing the jitter path coupling noise of the proof mass interferometer according to the simulation results.

Description

Technical Field

[0001] This application relates to the field of laser interferometer technology, and in particular to a method and device for suppressing jitter optical path coupling noise in a quality inspection interferometer. Background Technology

[0002] General relativity is one of the most brilliant achievements in the field of natural science in the 20th century, and gravitational waves are the most important prediction of general relativity. Therefore, the detection of gravitational waves is of great scientific significance to the development of physics. Since LIGO first detected gravitational waves in 2016, dozens of gravitational wave events have been detected by ground-based gravitational wave detectors. However, ground-based detectors are affected by ground vibration noise and ambient temperature, making it impossible to detect low-frequency gravitational waves below 1.0 Hz. Space-based gravitational wave detectors can significantly reduce these effects, thus compensating for the limitations of ground-based detection in this regard.

[0003] The two most important technologies for space-based gravitational wave detectors are inertial sensing and space laser interferometry. The core of inertial sensing technology is a test mass probe that undergoes free fall in space, while laser interferometry measures and records the distance changes between the various test mass probes, thereby providing information about gravitational waves.

[0004] Among the main noise sources in the system, jitter optical path coupling noise is the second largest, second only to shot noise. As the name suggests, jitter optical path coupling noise arises because the propagation direction of the light beam fluctuates, causing its propagation path to change, thus introducing additional optical path noise into interferometry. Since space-based gravitational wave detectors are located in outer space, jitter sources are ubiquitous; therefore, a thorough analysis of the impact of jitter optical path coupling noise on the final measurement accuracy is necessary.

[0005] In space interferometric measurement systems, jitter optical path coupling noise primarily originates from two parts. The first part comes from the test mass interferometer. The test mass interferometer consists of the interference of a fixed-propagation Gaussian beam and a Gaussian beam reflected from the test mass surface, used to measure the distance change between the test mass and the spacecraft. Due to the influence of non-conservative forces, deflection jitter between the test mass and the spacecraft is unavoidable. If the test mass exhibits angular jitter... When jitter occurs, the direction of transmission of its reflected light rays will be 2 Jitter, which in turn generates jitter optical path coupling noise.

[0006] The Albert-Einstein Institute (AEI) in Germany is working on the LISA path. The study investigated the jitter optical path coupling noise model in the laser interferometers used in the NDER and GRACE-Follow-On missions. The Sonke-Schuster theory was used to analyze the analytical model of jitter optical path coupling noise in the interference of two Gaussian beams, and ray tracing was performed using their independently developed Ifocad software. An experimental platform was also built for testing. However, the study lacked analysis of the optical path noise caused by aberrations introduced by the quality of the interferometer. Summary of the Invention

[0007] The purpose of this application is to solve the technical problem that the analytical model for analyzing the jitter optical path coupling noise in the interference of two Gaussian beams lacks analysis of the optical path noise caused by the aberrations introduced by the test quality interferometer, and to provide a method and device for suppressing the jitter optical path coupling noise of the test quality interferometer.

[0008] The above-mentioned objective of this application is achieved through the following technical solution:

[0009] S1: Construct a simplified graphical model of the inspection quality interferometer;

[0010] S2: Based on the simplified diagram model, construct the reference beam and the measurement beam that are incident on the four-quadrant detector in the inspection quality interferometer;

[0011] S3: Calculate the LPF optical path signal and AP optical path signal, extract the longitudinal length path signal from the phase signal generated when the reference beam and the measurement beam interfere on the detector surface; analyze the jitter optical path coupling noise of higher-order aberration coupling, and analyze the influence of aberration on jitter optical path coupling noise;

[0012] S4: Plot the density distribution map of jitter optical path coupling noise containing the aberrations, and determine, based on the density distribution map, that the AP optical path signal is superior to the LPF optical path signal in reducing aberration jitter optical path coupling noise in the inspection quality interferometer;

[0013] S5: Monte Carlo simulations were performed on the LPF optical path signal and the AP optical path signal with three different lateral displacements; based on the simulation results of the Monte Carlo simulations, the effectiveness of the method for suppressing the jitter optical path coupling noise of the test quality interferometer was verified.

[0014] Optionally, step S2 includes:

[0015] Both the reference beam and the measurement beam are Gaussian beams, and the beam waist dimensions of the reference beam and the measurement beam are assumed to be... Wavefront curvature radius If they are equal, then the reference beam With the measuring beam It can be represented as:

[0016] (1)

[0017] (2)

[0018] Where t represents time, z represents the direction of beam propagation, k is the wave number, and λ is the wavelength; These are polar coordinates on the detector plane, and α is the coordinate of the beam around the detector plane. Shaft The angle is a small angle of inclination of the line orthogonal to the axis. Radius of the beam hitting the detector surface; phase term Similar to defocusing, whether it equals 0 depends on whether z equals 0; , This represents the wavefront error of a localized beam of light produced by a defective optical element. , It is angular frequency.

[0019] Optionally, step S3 includes:

[0020] S31: The reference beam and the measurement beam interfere on the four-quadrant detector. It is assumed that the centers of the two interfering beams coincide, and the center position is set as the origin of the coordinate system.

[0021] Let D1, D2, D3, and D4 represent the effective integration regions in the four Cartesian coordinate quadrants; the numbers 1, 2, 3, and 4 represent the four segments of the four-quadrant detector, respectively. and It is the eccentricity of the interference beam and the four-quadrant detector in the x and y directions; S1, S2, S3, S4 and S5 represent the changes in the effective integration region of the four segments caused by the eccentricity;

[0022] S32: Assuming that the interference beam is detected without clipping, extract the phase from the integral of the complex overlap term over the detection region;

[0023] set up The integrand becomes:

[0024] (3)

[0025] in, This represents the total wavefront error, including tilt. This represents the static wavefront error of the interferometric beam;

[0026] Phase information is extracted from the independent variable of formula (3); the calculation accuracy is set as: static wavefront error The range is less than 0.1064 Inclination angle The range is Within; based on computational precision, the exponential term Approximately:

[0027] (4)

[0028] S33: Actual detection is performed using LPF optical path signal;

[0029] The complex amplitudes obtained in the four quadrants are summed, and then the phase angle of the summed complex amplitudes is taken to finally obtain the LPF optical path signal, i.e.:

[0030] (5a)

[0031] in, , , , Represents the complex amplitude in the four quadrants;

[0032] Since the effect of the QPD slit on the total complex amplitude is negligible, the QPD slit is not considered in the following calculations. The LPF optical path signal is calculated by directly integrating over the entire circular surface. Therefore:

[0033] (5b)

[0034] in, , Let represent the complex amplitude in each quadrant, and:

[0035] (5c)

[0036] S34: Actual detection is performed using AP optical path signals;

[0037] The complex amplitudes obtained in the four quadrants are summed, and the phase angle of the summed complex amplitude is taken to finally obtain the AP optical path signal, i.e.:

[0038] (6)

[0039] in, , , , These represent the composite complex amplitudes in the four quadrants calculated using the AP method;

[0040] Take the exponent term Approximately first order:

[0041] (7)

[0042] in,

[0043] The calculation of the complex amplitude of the four segments in the QPD is as follows:

[0044] (8a)

[0045] (8b)

[0046] (8c)

[0047] (8d)

[0048] In calculation When the complex amplitude of the area is... and Represented by polar coordinate vectors The AP optical path signal is then expressed as:

[0049] (9)

[0050] S35: Use Zernike circular polynomials to represent the basis functions of wavefront-like functions, as follows:

[0051] (10)

[0052] Among them, the index It is a polynomial ordinal number. It is a radial polynomial, where n and m are positive integers and (nm) ≥ 0; It is a normalized radial coordinate; a function of n and m, as follows:

[0053]

[0054] If the Zernike tilt of both the x-axis and y-axis is used to represent wavefront tilt, the aberration can be written in the following form:

[0055] (12)

[0056] The wavefront tilt magnitude is shown to be The incident axis of the light beam is perpendicular to the x-axis. The straight line of the angle; where, The expansion coefficient before combination; The combined aberration order is indicated by the subscript "j" and the superscript is the abbreviation of the corresponding aberration; the phase term... The effect can be represented by the defocus Zernike term; the wavefront error can be expressed as:

[0057] (13a)

[0058] (13b)

[0059] coefficient of expansion It is given by the following formula:

[0060] (14)

[0061] The aberration variance is given by the following formula:

[0062] (15)

[0063] Substituting equation (13a) into equations 5(b) and 5(c) solves for the longitudinal length path signal of the LPF optical path. Small rotation angle The coupling between phase and, i.e. Find:

[0064]

[0065] in, Indicates containing higher-order aberrations coefficient set Indicates containing higher-order aberrations The set of coefficients for 2;

[0066] S36: Define two aberration vectors as well as ,in This includes first-order coma terms, second-order coma terms, third-order coma terms, and first-order cloverleaf aberration terms and second-order cloverleaf aberration terms. This includes defocus terms, first-order spherical aberration terms, second-order spherical aberration terms, third-order spherical aberration terms, first-order astigmatism terms, second-order astigmatism terms, third-order astigmatism terms, and first-order cloverleaf aberration terms:

[0067] (17)

[0068] (18)

[0069] but , Represented as:

[0070] (19)

[0071] 20)

[0072] Wherein, the coefficient matrix and The elements in the expression are algebraic expressions.

[0073] S37: Expand Only second-order terms not exceeding α and normalized lateral displacements are considered. The first-order term; the longitudinal length path signal of the AP optical path signal. for:

[0074] (twenty one)

[0075] (twenty two)

[0076] (twenty three)

[0077] (twenty four)

[0078] (25)

[0079] Due to the coefficient matrix , , and The elements in the expression are algebraic expressions;

[0080] Coupling coefficient and It is calculated by differentiating formulas (16) and (21) with respect to α, and characterizes the sensitivity of the LPS optical path signal and the AP optical path signal to the tilt angle, that is:

[0081] (26a)

[0082] (26b)

[0083] because The value is small and can be ignored. Satisfying equation (27), The constant term can be eliminated;

[0084] (27)

[0085] Equation (27) shows that the lateral displacement component in the direction perpendicular to the beam jitter axis helps reduce TTL noise associated with aberrations; at the same time, it makes and Two optimal angles for 0 and :

[0086] (28a)

[0087] (28b)

[0088] coefficient , , and Normalized radius and , and The cosine function of the combination of addition and subtraction between them corresponds to and aberration terms; , Normalized radius The function is , and The combination of addition and subtraction of cosine values ​​corresponds to the aberration term. and By setting =1mm, = =0 is used to set the cosine value to 1, and others... It is 0, and in all orders of magnitude Both are equal to λ / 10;

[0089] The conclusions are as follows:

[0090] for Each aberration term has a different effect on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, second-order spherical aberration, and third-order astigmatism having a greater impact.

[0091] for Each aberration term has a different effect on it, with second-order spherical aberration, third-order spherical aberration, third-order astigmatism, and first-order astigmatism having a greater impact.

[0092] for and Each aberration term has a different effect on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, second-order spherical aberration, and third-order astigmatism having a greater impact. Therefore, reducing astigmatism and spherical aberration in the optical system can reduce the magnitude of TTL coupling noise to a certain extent.

[0093] Optionally, step S4 includes:

[0094] Given a beam wavelength λ = 1064 nm, the spot size ω(z) of the interference beam on the detector is = =1 mm; at the same time, in Under the constraint of λ / 20=53.2 nm, according to equation (16), randomly generate except coefficient And randomly generated within the interval [0, 2π] except Direction angle ;

[0095] Plot the coupling coefficient of the AP optical path signal | |Density distribution map and coupling coefficient of LPF optical path signal| | Density distribution map;

[0096] Based on the density distribution map, comparing the effects of the LPF optical path signal and the AP optical path signal in reducing aberration jitter optical path coupling noise, it was determined that the AP optical path signal is superior to the LPF optical path signal in reducing aberration jitter optical path coupling noise in the inspection quality interferometer.

[0097] Optionally, step S5 includes:

[0098] S51: Based on the derived aberration-containing LPS optical path signal and the characterization of sensitivity to tilt angle. The parsing expression determines what makes and Two optimal angles for 0 and and in Medium energy elimination The optimal lateral displacement;

[0099] S52: In Produced in the cases of λ / 40, λ / 20 and λ / 10 Group and ;

[0100] S53: Use wavefront tilt Maximize within a range of 300 μrad | | and | |;

[0101] S54: For AP optical path signals, for three different lateral displacement vectors ε;

[0102] Case 1 is , Consider a compensation mechanism for lateral offset;

[0103] Case 2 is ε = 0, assuming perfect centering;

[0104] Case 3 involves the detector and the interference beam having a lateral offset ε that is randomly generated within a range of ±20 μm. In 0 2 Randomly generated to examine the magnitude of jitter optical path noise under assembly and adjustment tolerances;

[0105] S55: Case 4 indicates the LPF optical path signal;

[0106] By comparing the simulation results of the AP optical path signal and the LPF optical path signal, it was determined that the AP optical path signal is more effective in reducing the optical path coupling noise caused by aberration jitter in the inspection quality interferometer, thus verifying the effectiveness of the method for reducing optical path coupling noise caused by aberration in the inspection quality interferometer.

[0107] An electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform a method for suppressing jitter optical path coupling noise in a quality interferometer.

[0108] A computer-readable storage medium storing instructions that, when executed, perform a method for suppressing jitter optical path coupling noise in a quality interferometer.

[0109] The beneficial effects of the technical solution provided in this application are:

[0110] By constructing a model of an inertial sensor and an incident Gaussian beam in the sensor, the path length definitions for four-quadrant detectors corresponding to different Gaussian beams are analyzed. The jitter optical path coupling noise caused by higher-order aberrations is analyzed, and the influence of aberrations on this noise is investigated. A density distribution map of the jitter optical path coupling noise including these aberrations is plotted, and based on this map, specific methods to reduce the influence of aberrations on the jitter optical path coupling noise are determined. Monte Carlo simulations are performed on the LPF optical path signal and AP optical path signals with three different lateral displacements. Based on the simulation results, the effectiveness of methods for suppressing jitter optical path coupling noise in the test quality interferometer is verified. Further analysis incorporating higher-order aberrations simulates the characteristics of jitter optical path noise with these aberrations, analyzes the most influential terms, and explores methods to effectively suppress jitter optical path coupling noise. This provides a preliminary verification for future theoretical analysis and supports subsequent theoretical research. Attached Figure Description

[0111] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0112] Figure 1 This is a step diagram illustrating the method for suppressing the jitter optical path coupling noise of the inspection quality interferometer in the embodiments of this application;

[0113] Figure 2 This is a schematic diagram of a four-quadrant detector for a method to suppress jitter optical path coupling noise in an interferometer of inspection quality according to an embodiment of this application.

[0114] Figure 3 This application embodiment describes a method for suppressing optical path coupling noise caused by jitter in an interferometer for testing quality. Map affected by a single aberration;

[0115] Figure 4 This application embodiment describes a method for suppressing optical path coupling noise caused by jitter in an interferometer for testing quality. Map affected by a single aberration;

[0116] Figure 5 This application embodiment describes a method for suppressing optical path coupling noise caused by jitter in an interferometer for testing quality. Map showing the effects of a single aberration;

[0117] Figure 6 This application embodiment describes a method for suppressing optical path coupling noise caused by jitter in an interferometer for testing quality. Map showing the effects of a single aberration;

[0118] Figure 7 The coupling coefficients in four cases of the method for suppressing the jitter optical path coupling noise of the inspection quality interferometer in the embodiments of this application are as follows: (Above) and the optimal lateral displacement at Distribution results at λ / 40, λ / 20, and λ / 10;

[0119] Figure 8 This is a simplified model diagram of the inspection quality interferometer used in the method for suppressing jitter optical path coupling noise in the inspection quality interferometer according to the embodiments of this application;

[0120] Figure 9 This is a schematic diagram of the electronic device structure of the method for suppressing the jitter optical path coupling noise of the inspection quality interferometer in the embodiments of this application;

[0121] Figure 10 The completely orthogonal Zernike polynomial in polar coordinates is the method for suppressing the jitter optical path coupling noise of the inspection quality interferometer in the embodiments of this application. picture;

[0122] Figure 11 This is the coupling factor of the method for suppressing the jitter optical path coupling noise of the inspection quality interferometer in the embodiments of this application. The graph shows the proportion of results where the average value is less than 25 pm / μrad. Detailed Implementation

[0123] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0124] Embodiments of this application provide a method and apparatus for suppressing jitter optical path coupling noise in an inspection quality interferometer.

[0125] Please refer to Figure 1 , Figure 1This is a flowchart illustrating the steps of a method for suppressing jitter optical path coupling noise in an inspection quality interferometer according to an embodiment of this application, specifically including the following steps:

[0126] S1: Construct a simplified graphical model of the inspection quality interferometer;

[0127] S2: Based on the simplified diagram model, construct the reference beam and the measurement beam that are injected into the four-quadrant detector in the test quality interferometer;

[0128] S3: Calculate the LPF optical path signal and AP optical path signal, extract the longitudinal length path signal from the phase signal generated when the reference beam and the measurement beam interfere on the detector surface; analyze the jitter optical path coupling noise of higher-order aberration coupling, and analyze the influence of aberration on jitter optical path coupling noise;

[0129] S4: Plot the density distribution map of jitter optical path coupling noise containing the aberrations, and determine, based on the density distribution map, that the AP optical path signal is superior to the LPF optical path signal in reducing aberration jitter optical path coupling noise in the inspection quality interferometer;

[0130] S5: Monte Carlo simulations were performed on the LPF optical path signal and the AP optical path signal with three different lateral displacements; based on the simulation results of the Monte Carlo simulations, the effectiveness of the method for suppressing the jitter optical path coupling noise of the test quality interferometer was verified.

[0131] In this application, the LPF optical path signal is the LISA path. The nder signal, AP optical path signal is the averaged phase optical path signal, QPD is a four-quadrant detector, and optical path tilt (tilt-to-length, TTL) coupling noise.

[0132] Step S2 includes:

[0133] Both the reference beam and the measurement beam are Gaussian beams, and the beam waist dimensions of the reference beam and the measurement beam are assumed to be... Wavefront curvature radius If they are equal, then the reference beam With the measuring beam It can be represented as:

[0134] (1)

[0135] (2)

[0136] Where t represents time, z represents the direction of beam propagation, k is the wave number, and λ is the wavelength; These are polar coordinates on the detector plane, and α is the coordinate of the beam around the detector plane. Shaft The angle is a small angle of inclination of the line orthogonal to the axis. Radius of the beam hitting the detector surface; phase term Similar to defocusing, whether it equals 0 depends on whether z equals 0; , This represents the wavefront error of a localized beam of light produced by a defective optical element. , It is angular frequency.

[0137] Step S3 includes:

[0138] S31: The reference beam and the measurement beam interfere on the four-quadrant detector. It is assumed that the centers of the two interfering beams coincide, and the center position is set as the origin of the coordinate system.

[0139] Let D1, D2, D3, and D4 represent the effective integration regions in the four Cartesian coordinate quadrants; the numbers 1, 2, 3, and 4 represent the four segments of the four-quadrant detector, respectively. and It is the eccentricity of the interference beam and the four-quadrant detector in the x and y directions; S1, S2, S3, S4 and S5 represent the changes in the effective integration region of the four segments caused by the eccentricity;

[0140] S32: Assuming that the interference beam is detected without clipping, extract the phase from the integral of the complex overlap term over the detection region;

[0141] set up The integrand becomes:

[0142] (3)

[0143] in, This represents the total wavefront error, including tilt. This represents the static wavefront error of the interferometric beam;

[0144] Phase information is extracted from the independent variable of formula (3); the calculation accuracy is set as: static wavefront error The range is less than 0.1064 Inclination angle The range is Within; based on computational precision, the exponential term Approximately:

[0145] (4)

[0146] S33: Actual detection is performed using LPF optical path signal;

[0147] The complex amplitudes obtained in the four quadrants are summed, and then the phase angle of the summed complex amplitudes is taken to finally obtain the LPF optical path signal, i.e.:

[0148] (5a)

[0149] in, , , , Represents the complex amplitude in the four quadrants;

[0150] Since the effect of the QPD slit on the total complex amplitude is negligible, the QPD slit is not considered in the following calculations. The LPF optical path signal is calculated by directly integrating over the entire circular surface. Therefore:

[0151] (5b)

[0152] in, , Let represent the complex amplitude in each quadrant, and:

[0153] (5c)

[0154] S34: Actual detection is performed using AP optical path signals;

[0155] The complex amplitudes obtained in the four quadrants are summed, and the phase angle of the summed complex amplitude is taken to finally obtain the AP optical path signal, i.e.:

[0156] (6)

[0157] in, , , , These represent the composite complex amplitudes in the four quadrants calculated using the AP method;

[0158] Take the exponent term Approximately first order:

[0159] (7)

[0160] in,

[0161] The calculation of the complex amplitude of the four segments in the QPD is as follows:

[0162] (8a)

[0163] (8b)

[0164] (8c)

[0165] (8d)

[0166] In calculation When the complex amplitude of the area is... and Represented by polar coordinate vectors The AP optical path signal is then expressed as:

[0167] (9)

[0168] S35: Use Zernike circular polynomials to represent the basis functions of wavefront-like functions, as follows:

[0169] (10)

[0170] Among them, the index It is a polynomial ordinal number. It is a radial polynomial, where n and m are positive integers and (nm) ≥ 0; It is a normalized radial coordinate; a function of n and m, as follows:

[0171]

[0172] If the Zernike tilt of both the x-axis and y-axis is used to represent wavefront tilt, the aberration can be written in the following form:

[0173] (12)

[0174] The wavefront tilt magnitude is shown to be The incident axis of the light beam is perpendicular to the x-axis. The straight line of the angle; where, The expansion coefficient before combination; The combined aberration order is indicated by the subscript "j" and the superscript is the abbreviation of the corresponding aberration; the phase term... The effect can be represented by the defocus Zernike term; the wavefront error can be expressed as:

[0175] (13a)

[0176] (13b)

[0177] coefficient of expansion It is given by the following formula:

[0178] (14)

[0179] The aberration variance is given by the following formula:

[0180] (15)

[0181] Substituting equation (13a) into equations 5(b) and 5(c) solves for the longitudinal length path signal of the LPF optical path. Small rotation angle The coupling between phase and, i.e. Find:

[0182]

[0183] in, Indicates containing higher-order aberrations coefficient set Indicates containing higher-order aberrations The set of coefficients for 2;

[0184] S36: Define two aberration vectors as well as ,in This includes first-order coma terms, second-order coma terms, third-order coma terms, and first-order cloverleaf aberration terms and second-order cloverleaf aberration terms. This includes defocus terms, first-order spherical aberration terms, second-order spherical aberration terms, third-order spherical aberration terms, first-order astigmatism terms, second-order astigmatism terms, third-order astigmatism terms, and first-order cloverleaf aberration terms:

[0185] (17)

[0186] (18)

[0187] but , Represented as:

[0188] (19)

[0189] (20)

[0190] Wherein, the coefficient matrix and The elements in the expression are algebraic expressions.

[0191] S37: Expand Only second-order terms not exceeding α and normalized lateral displacements are considered. The first-order term; the longitudinal length path signal of the AP optical path signal. for:

[0192] (twenty one)

[0193] (twenty two)

[0194] (twenty three)

[0195] (twenty four)

[0196] (25)

[0197] Due to the coefficient matrix , , and The elements in the expression are algebraic expressions;

[0198] Coupling coefficient and It is calculated by differentiating formulas (16) and (21) with respect to α, and characterizes the sensitivity of the LPS optical path signal and the AP optical path signal to the tilt angle, that is:

[0199] (26a)

[0200] (26b)

[0201] because The value is small and can be ignored. Satisfying equation (27), The constant term can be eliminated;

[0202] (27)

[0203] Equation (27) shows that the lateral displacement component in the direction perpendicular to the beam jitter axis helps reduce TTL noise associated with aberrations; at the same time, it makes and Two optimal angles for 0 and :

[0204] (28a)

[0205] (28b)

[0206] coefficient , , and Normalized radius and , and The cosine function of the combination of addition and subtraction between them corresponds to and aberration terms; , Normalized radius The function is , and The combination of addition and subtraction of cosine values ​​corresponds to the aberration term. and By setting =1mm, = =0 is used to set the cosine value to 1, and others... It is 0, and in all orders of magnitude Both are equal to λ / 10;

[0207] The conclusions are as follows:

[0208] for Each aberration term has a different effect on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, second-order spherical aberration, and third-order astigmatism having a greater impact.

[0209] for Each aberration term has a different effect on it, with second-order spherical aberration, third-order spherical aberration, third-order astigmatism, and first-order astigmatism having a greater impact.

[0210] for and Each aberration term has a different effect on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, second-order spherical aberration, and third-order astigmatism having a greater impact. Therefore, reducing astigmatism and spherical aberration in the optical system can reduce the magnitude of TTL coupling noise to a certain extent.

[0211] Step S4 includes:

[0212] Given a beam wavelength λ = 1064 nm, the spot size ω(z) of the interference beam on the detector is = =1 mm; at the same time, in Under the constraint of λ / 20=53.2 nm, according to equation (16), randomly generate except coefficient And randomly generated within the interval [0, 2π] except Direction angle ;

[0213] Plot the coupling coefficient of the AP optical path signal | |Density distribution map and coupling coefficient of LPF optical path signal| | Density distribution map;

[0214] Based on the density distribution map, comparing the effects of the LPF optical path signal and the AP optical path signal in reducing aberration jitter optical path coupling noise, it was determined that the AP optical path signal is superior to the LPF optical path signal in reducing aberration jitter optical path coupling noise in the inspection quality interferometer.

[0215] Step S5 includes:

[0216] S51: Based on the derived aberration-containing LPS optical path signal and the characterization of sensitivity to tilt angle. The parsing expression determines what makes and Two optimal angles for 0 and and in Medium energy elimination The optimal lateral displacement;

[0217] S52: In Produced in the cases of λ / 40, λ / 20 and λ / 10 Group and ;

[0218] S53: Use wavefront tilt Maximize within a range of 300 μrad | | and | |;

[0219] S54: For AP optical path signals, for three different lateral displacement vectors ε;

[0220] Case 1 is , Consider a compensation mechanism for lateral offset;

[0221] Case 2 is ε = 0, assuming perfect centering;

[0222] Case 3 involves the detector and the interference beam having a lateral offset ε that is randomly generated within a range of ±20 μm. In 0 2 Randomly generated to examine the magnitude of jitter optical path noise under assembly and adjustment tolerances;

[0223] S55: Case 4 indicates the LPF optical path signal;

[0224] By comparing the simulation results of the AP optical path signal and the LPF optical path signal, it was determined that the AP optical path signal is more effective in reducing the optical path coupling noise caused by aberration jitter in the inspection quality interferometer, thus verifying the effectiveness of the method for reducing optical path coupling noise caused by aberration in the inspection quality interferometer.

[0225] Specifically, such as Figure 2 As shown in the right figure, assuming Therefore, the shape of the Si region can be considered as rectangular. Thus, it can be calculated using rectangular coordinates. The complex amplitude of the area is more suitable. Because The area is very small, so an exponential term can be taken. It is approximately first-order.

[0226] Specifically, there are several ways to represent Zernike polynomials, one difference being the order of the terms. Here, the fringe Zernike polynomial, currently used by several interferometer and interferometric data analysis software vendors, is selected for the analysis. To fully characterize the manufacturing and adjustment errors of the optical system, the first 25 terms of the fringe Zernike polynomial are used to fit the wavefront error of the interferometric beam (the piston term is omitted). Furthermore, except for the defocus term and three spherical aberration terms, the cosine and sine terms of other Zernike aberrations are combined to represent the magnitude and direction of these aberrations.

[0227] Specifically, by Figure 3 It can be seen that, for Each aberration term has a varying degree of influence on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, third-order spherical aberration, and so on having the greatest impact. Figure 4 It can be seen that, for Each aberration term has a different effect on it, with second-order spherical aberration, third-order spherical aberration, third-order astigmatism, and first-order astigmatism having the largest impact. Figure 5 , 6 It can be seen that the difference between light with astigmatism and light without spherical aberration is as follows: , The deviation is relatively large.

[0228] Figure 11 The coupling factor is shown in four cases. |The average value and proportion are less than the required 25 pm / μrad. For example... Figure 7 The coupling coefficient is shown in the four cases. | (above) and optimal lateral displacement in The distribution results are shown at λ / 40, λ / 20, and λ / 10. The results indicate that only when the wavefront error is less than λ / 20 can the average coupling coefficient of the LPF optical path signal be less than the required 25 pm / μrad. However, even when the RMS value of the wavefront error is less than λ / 20... The average coupling coefficient of the three AP optical path signals is less than the required 25 pm / μrad, and for the AP optical path signal with optimal lateral displacement, the proportion of samples that meet the requirements can reach 97.7%. Therefore, in terms of suppressing the influence of distortion on TTL noise, the AP optical path signal is a better phase determination method than the LPF optical path signal.

[0229] Therefore, if the Zernike coefficients of the fitted fringes of the interference beam wavefront error can be obtained, the analysis results in this paper can be used to predict TTL coupling noise and further calculate the optimal lateral displacement between the interference beam and the QPD to reduce the TTL noise of wavefront aberration coupling.

[0230] This application also discloses an electronic device. (See reference...) Figure 9 , Figure 9 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.

[0231] The communication bus 502 is used to enable communication between these components.

[0232] The user interface 503 may include a display screen and a camera. Optionally, the user interface 503 may also include a standard wired interface and a wireless interface.

[0233] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0234] The processor 501 may include one or more processing cores. The processor 501 connects to various parts of the server using various interfaces and lines, and performs various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory 505, and by calling data stored in memory 505. Optionally, the processor 501 may be implemented using at least one hardware form of Digital Signal Processing (DSP), Field-Programmable Gate Array (FPGA), or Programmable Logic Array (PLA). The processor 501 may integrate one or a combination of several of the following: Central Processing Unit (CPU), Graphics Processing Unit (GPU), and modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content required for display; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 501 and may be implemented as a separate chip.

[0235] The memory 505 may include random access memory (RAM) or read-only memory.

[0236] Optionally, the memory 505 includes a non-transitory computer-readable storage medium. The memory 505 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 505 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch functionality, sound playback functionality, image playback functionality, etc.), instructions for implementing the various method embodiments described above, etc.; the data storage area may store data involved in the various method embodiments described above, etc. The memory 505 may also optionally include, but is not limited to, at least one storage device located remotely from the aforementioned processor 501. (Refer to...) Figure 9 The memory 505, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for a method of suppressing jitter optical path coupling noise in a quality interferometer.

[0237] like Figure 8 As shown, the simplified model of the quality interferometer includes: a laser, a mirror, a beam combiner, and a four-quadrant detector.

[0238] The laser emits a Gaussian beam, which is split into two Gaussian beams by a beam splitter. The downward beam is the reference beam, and the upward beam is the measurement beam. The darker line on the top is the beam trajectory when the quality has not shifted, and the lighter line is the beam trajectory when the quality has shifted. After the reference beam passes through two mirrors, it is combined with the measurement beam by a beam combiner and then injected into a four-quadrant detector.

[0239] exist Figure 9In the illustrated electronic device 500, the user interface 503 is mainly used to provide an input interface for the user and to acquire user input data; while the processor 501 can be used to call an application program stored in the memory 505 for a method to suppress jitter optical path coupling noise in a quality interferometer. When executed by one or more processors 501, the electronic device 500 performs one or more methods as described in the above embodiments. It should be noted that, for the foregoing method embodiments, for the sake of simplicity, they are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, because according to this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0240] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0241] In the various embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed include, but are not limited to, indirect couplings or communication connections between apparatuses or units through some service interfaces, including but not limited to electrical or other forms.

[0242] The units described as separate components include, but are not limited to, physically separate units. The components shown as units include, but are not limited to, physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of these units can be selected to achieve the purpose of this embodiment according to actual needs.

[0243] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or may exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0244] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, portable hard drives, magnetic disks, or optical disks.

[0245] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Other embodiments of this disclosure will readily conceive of those skilled in the art upon consideration of the specification and the disclosure of practical truths.

[0246] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for suppressing jitter optical path coupling noise in an inspection quality interferometer, characterized in that... The method includes the following steps: S1: Construct a simplified graphical model of the inspection quality interferometer; S2: Based on the simplified diagram model, construct the reference beam and the measurement beam that are incident on the four-quadrant detector in the inspection quality interferometer; Step S2 includes: Both the reference beam and the measurement beam are Gaussian beams, and their beam waists are assumed to be... Wavefront curvature radius If they are equal, then the reference beam With the measuring beam It can be represented as: (1) (2) Where t represents time, z represents the direction of beam propagation, and k is the wave number; These are polar coordinates on the detector plane, and α is the coordinate of the beam around the detector plane. Shaft The angle is a small tilt angle of a line orthogonal to the axis; phase term. Similar to defocusing, whether it equals 0 depends on whether z equals 0; This represents the wavefront error of a localized beam of light produced by a defective optical element. It is angular frequency; S3: Calculate the LPF optical path signal and AP optical path signal, extract the longitudinal length path signal from the phase signal generated when the reference beam and the measurement beam interfere on the detector surface; analyze the jitter optical path coupling noise of higher-order aberration coupling, and analyze the influence of aberration on jitter optical path coupling noise; Step S3 includes: S31: The reference beam and the measurement beam interfere on the four-quadrant detector. It is assumed that the centers of the two interfering beams coincide, and the center position is set as the origin of the coordinate system. Let D1, D2, D3, and D4 represent the effective integration regions in the four Cartesian coordinate quadrants; the numbers 1, 2, 3, and 4 represent the four segments of the four-quadrant detector, respectively. and S1 represents the eccentricity of the interference beam and the four-quadrant detector in the x and y directions; S2, S3, S4 and S5 represent the changes in the effective integration region of the four segments caused by the eccentricity. S32: Assuming that the interference beam is detected without clipping, extract the phase from the integral of the complex overlap term over the detection region; set up The integrand becomes: (3) in, This represents the total wavefront error, including tilt. This represents the static wavefront error of the interferometric beam; This represents the wavefront error of a localized beam of light produced by a defective optical element. Phase information is extracted from the independent variable of formula (3); the calculation accuracy is set as: static wavefront error The range is less than 0.1064 tilt angle The range is Within; based on computational precision, the exponential term Approximately: (4) S33: Actual detection is performed using LPF optical path signal; The complex amplitudes obtained in the four quadrants are summed, and then the phase angle of the summed complex amplitudes is taken to finally obtain the LPF optical path signal, i.e.: (5a) in, , , , Represents the complex amplitude in the four quadrants; Since the effect of the QPD slit on the total complex amplitude is negligible, the QPD slit is not considered in the following calculations. The LPF optical path signal is calculated by directly integrating over the entire circular surface. Therefore: (5b) in, , This indicates the radius of the light spot that hits the detector surface. Represents normalized polar coordinates; Let represent the complex amplitude in each quadrant, and: (5c) S34: Actual detection is performed using AP optical path signals; The complex amplitudes obtained in the four quadrants are summed, and the phase angle of the summed complex amplitude is taken to finally obtain the AP optical path signal, i.e.: (6) in, , , , These represent the composite complex amplitudes in the four quadrants calculated using the AP method; Take the exponent term Approximately first order: (7) in, It is in polar coordinates The converted value represents rectangular coordinates; The calculation of the complex amplitude of the four segments in the QPD is as follows: (8a) (8b) (8c) (8d) In calculation When the complex amplitude of the area is... and Represented by polar coordinate vectors The AP optical path signal is then expressed as: (9) S35: Use Zernike circular polynomials to represent the basis functions of wavefront-like functions, as follows: (10) Among them, the index It is a polynomial ordinal number. It is a radial polynomial, where n and m are positive integers and (nm) ≥ 0; These are normalized polar coordinates; functions of n and m, as follows: If the Zernike tilt of both the x-axis and y-axis is used to represent wavefront tilt, the aberration can be written in the following form: (12) The wavefront tilt magnitude is shown to be The incident axis of the light beam is perpendicular to the x-axis. The straight line of the angle; where, The expansion coefficient before combination; The expansion coefficient is indicated by the subscript "j" and the superscript is the abbreviation of the corresponding aberration; the phase term... The effect can be represented by the defocus Zernike term; the wavefront error can be expressed as: (13a) (13b) coefficient of expansion It is given by the following formula: (14) The aberration variance is given by the following formula: (15) Substituting equation (13a) into equations 5(b) and 5(c) solves for the longitudinal length path signal of the LPF optical path. Small rotation angle The coupling between phase and, i.e. Find: (16) in, Indicates containing higher-order aberrations coefficient set Indicates containing higher-order aberrations The set of coefficients for 2; S36: Define two aberration vectors as well as ,in This includes first-order coma terms, second-order coma terms, third-order coma terms, and first-order cloverleaf aberration terms and second-order cloverleaf aberration terms. This includes defocus terms, first-order spherical aberration terms, second-order spherical aberration terms, third-order spherical aberration terms, first-order astigmatism terms, second-order astigmatism terms, third-order astigmatism terms, and first-order cloverleaf aberration terms: (17) (18) but , Represented as: (19) (20) Wherein, the coefficient matrix and The elements in the expression are algebraic expressions; S37: Expand Only second-order terms not exceeding α and normalized lateral displacements are considered. The first-order term; the longitudinal length path signal of the AP optical path signal. for: (21) (22) (23) (24) (25) Due to the coefficient matrix , , and The elements in the expression are algebraic expressions; Coupling coefficient and It is calculated by differentiating formulas (16) and (21) with respect to α, and characterizes the sensitivity of the LPF optical path signal and the AP optical path signal to the tilt angle, that is: (26a) (26b) because The value is small and can be ignored. Satisfying equation (27), The constant term can be eliminated; (27) Equation (27) shows that the lateral displacement component in the direction perpendicular to the beam jitter axis helps reduce TTL noise associated with aberrations; at the same time, it makes and Two optimal angles for 0 and : (28a) (28b) Where the coefficient , , and Normalized radius and , and The cosine function of combinations of addition and subtraction. Indicates the direction angle; , Normalized radius The function; by setting =1mm, = =0 is used to set the cosine value to 1, and others... It is 0, and in all orders of magnitude Both are equal to λ / 10, where λ is the wavelength; for Each aberration term has a different effect on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, second-order spherical aberration, and third-order astigmatism having a greater impact. for Each aberration term has a different effect on it, with second-order spherical aberration, third-order spherical aberration, third-order astigmatism, and first-order astigmatism having a greater impact. for and Each aberration term has a different effect on it, with first-order astigmatism, first-order spherical aberration, second-order astigmatism, second-order spherical aberration, and third-order astigmatism having a greater impact. Therefore, reducing astigmatism and spherical aberration in the optical system can reduce the magnitude of TTL coupling noise to a certain extent. S4: Plot the density distribution map of jitter optical path coupling noise containing the aberrations, and determine, based on the density distribution map, that the AP optical path signal is superior to the LPF optical path signal in reducing aberration jitter optical path coupling noise in the inspection quality interferometer; S5: Monte Carlo simulations were performed on the LPF optical path signal and the AP optical path signal with three different lateral displacements; based on the simulation results of the Monte Carlo simulations, the effectiveness of the method for suppressing the jitter optical path coupling noise of the test quality interferometer was verified.

2. The method for suppressing jitter optical path coupling noise in an inspection quality interferometer as described in claim 1, characterized in that, Step S4 includes: Given a beam wavelength λ = 1064 nm, the spot size ω(z) of the interference beam on the detector is = =1 mm; at the same time, Under the constraint of λ / 20=53.2 nm, according to equation (16), randomly generate except coefficient And randomly generated within the interval [0, 2π] except Direction angle ; Plot the coupling coefficient of the AP optical path signal | |Density distribution map and coupling coefficient of LPF optical path signal| | Density distribution map; Based on the density distribution map, comparing the effects of the LPF optical path signal and the AP optical path signal in reducing aberration jitter optical path coupling noise, it was determined that the AP optical path signal is superior to the LPF optical path signal in reducing aberration jitter optical path coupling noise in the inspection quality interferometer.

3. The method for suppressing jitter optical path coupling noise in an inspection quality interferometer as described in claim 2, characterized in that, Step S5 includes: S51: Based on the derived aberration-containing LPF optical path signal and characterization of sensitivity to tilt angle The parsing expression determines what makes and Two optimal angles for 0 and and in Medium energy elimination The optimal lateral displacement; S52: In Produced in the cases of λ / 40, λ / 20 and λ / 10 Group and ; S53: Use wavefront tilt Maximize within a range of 300 μrad | | and | |; S54: For AP optical path signals, for three different lateral displacement vectors ε; Case 1 is , Consider a compensation mechanism for lateral offset; Case 2 is ε = 0, assuming perfect centering; Case 3 involves the detector and the interference beam having a lateral offset ε that is randomly generated within a range of ±20 μm. In 0 2 Randomly generated to examine the magnitude of jitter optical path noise under assembly and adjustment tolerances; S55: Case 4 indicates the LPF optical path signal; By comparing the simulation results of the AP optical path signal and the LPF optical path signal, it was determined that the AP optical path signal is more effective in reducing the optical path coupling noise caused by aberration jitter in the inspection quality interferometer, thus verifying the effectiveness of the method for reducing optical path coupling noise caused by aberration in the inspection quality interferometer.

4. An electronic device, characterized in that, The device includes a processor (501), a memory (505), a user interface (503), and a network interface (504). The memory (505) is used to store instructions. The user interface (503) and the network interface (504) are used to communicate with other devices. The processor (501) is used to execute the instructions stored in the memory (505) to cause the electronic device (500) to perform the method as described in any one of claims 1-3.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed, perform the steps of the method as described in any one of claims 1-3.

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