A step height and flatness measurement method based on laser interferometry

Abstract

The present invention discloses a step height and flatness measurement method based on laser interferometry, comprising determining to place a calibration step into a laser interferometer measurement device, moving a reflector distance to obtain an interference image, processing the interference image to obtain a step surface phase distribution diagram, determining a calculation point position according to the step boundary and calculating the step measurement result, optimizing device parameters according to the step measurement result and the step calibration value deviation to obtain optimal device parameters, constructing a step device parameter library, matching the device optimal parameters in the step device parameter library according to the step parameters of the step to be measured to obtain reference device parameters and adjust the laser interferometer measurement device, and using the adjusted laser interferometer measurement device to measure the step to be measured to obtain the step height and step flatness. This method can timely and accurately measure step height and flatness, and is of great significance for promoting the development of high-precision measurement technology in the field of micro-nano manufacturing.

Description

Technical Field

[0001] The present invention relates to the field of laser measurement, and in particular to a step height and flatness measurement method based on laser interferometry. Background Art

[0002] With the rapid development of modern precision manufacturing and nanotechnology, high-precision measurement of step height and flatness of tiny structures has become a key link in semiconductor manufacturing, micro-electromechanical system processing, optical component production and other fields. Accurately obtaining step height and flatness parameters not only directly affects product performance and quality, but also provides important technical support for promoting innovation in micro-nano processing technology and ensuring the assembly accuracy of precision equipment.

[0003] The current traditional laser interferometry step measurement technology mainly relies on single-wavelength interference and fixed parameter settings, and has the following limitations: first, the efficiency of single measurement is low, and only a single step height can be obtained. Multi-step measurement requires repeated adjustment of the optical path, which is time-consuming and has poor consistency; second, parameter adjustment relies on experience. For example, key parameters such as refractive index and stage deflection angle need to be calibrated manually by trial and error, which is prone to introduce subjective errors; at the same time, the environmental adaptability is insufficient. When factors such as temperature drift and vibration cause the refractive index drift, the system stability is significantly reduced; finally, there is a lack of intelligent matching. When faced with complex step structures, it is impossible to quickly adapt to the optimal measurement conditions, which restricts the efficiency of batch detection. Based on the above background, the present invention proposes a step height and flatness measurement method based on laser interferometry. By introducing a calibration step into the measurement system, constructing a constraint range of refractive index and deflection angle parameters, and combining interference image phase analysis and parameter optimization strategy, adaptive calibration of measurement device parameters is realized, and a step parameter-device parameter mapping library is constructed. Based on the intelligent matching of rough measurement parameters to the historical optimal configuration, "one-click" high-precision measurement is achieved. This not only significantly improves the measurement accuracy and efficiency, but also effectively solves the measurement deviation problem caused by system parameter errors in traditional laser interferometry. It is of great significance to promote the development of high-precision measurement technology in the field of micro-nano manufacturing. Summary of the Invention

[0004] The purpose of the present invention is to provide a step height and flatness measurement method based on laser interferometry.

[0005] To achieve the above object, the present invention is implemented according to the following technical solutions:

[0006] The present invention comprises the following steps:

[0007] The calibration step is placed in a laser interferometer measurement device, and the refractive index range of the interference lens is determined based on the beam intensity distribution deviation of the incident light in the interference lens, and the deflection angle range of the stage is determined based on the interference fringe parameters; the incident light includes reference light and measurement light;

[0008] Adjusting the distance between the reflectors of the laser interferometer device to obtain an interference image, processing the interference image to obtain a step surface phase distribution map, determining a calculation point position according to a step boundary, and calculating a step measurement result according to the calculation point position and the step surface phase distribution map; the step measurement result includes a step measurement height and a step measurement flatness;

[0009] Optimizing the device parameters within the refractive index range and the stage deflection angle range according to the step measurement results and the step calibration value deviation to obtain the optimal parameters of the device; the step calibration value includes the step calibration height and the step calibration flatness;

[0010] The step parameters and the optimal parameters of the device are combined into a set of step device parameters, and multiple sets of step device parameters of the calibrated steps are obtained to form a step device parameter library; the step parameters include the rough height, rough length, rough width and number of steps;

[0011] According to the step parameters of the step to be measured, the optimal device parameters in the step device parameter library are matched to obtain the reference device parameters and the laser interferometer measurement device is adjusted. The adjusted laser interferometer measurement device is used to measure the step to be measured to obtain the step height and step flatness.

[0012] Furthermore, the method for determining the refractive index range of the interference lens and the method for determining the deflection angle range of the stage include:

[0013] placing the calibration step in a laser interferometer measurement device, passing incident light through an interference lens to obtain a first reflected light and a first transmitted light, and measuring the beam intensities of the incident light, the first reflected light, and the first transmitted light; the incident light includes a reference light and a measurement light; the first reflected light includes a first reference reflected light and a first measurement reflected light; and the first transmitted light includes a first reference transmitted light and a first measurement transmitted light;

[0014] Calculating a ratio of an absolute value of a difference between a first reference reflected light intensity and a first reference transmitted light intensity to the reference light intensity to obtain a reference light distribution deviation; calculating a ratio of an absolute value of a difference between a first measured reflected light intensity and a first measured transmitted light intensity to the measured light intensity to obtain a measured light distribution deviation; calculating an average of the reference light distribution deviation and the measured light distribution deviation to obtain a beam intensity distribution deviation; and selecting a refractive index range of the interference lens corresponding to a beam intensity distribution deviation less than 0.2;

[0015] Adjusting the stage deflection angle to obtain interference fringes and measuring interference fringe parameters; the stage deflection angle includes an x-axis deflection angle and a y-axis deflection angle; the interference fringes are formed by the second reflected light and the third reflected light overlapping at the interference lens; the second reflected light is formed by the first reflected light being reflected along the original path through the step surface; the third reflected light is formed by the first transmitted light being reflected along the original path through the reflector; the interference fringe parameters include contrast, spacing, and tilt;

[0016] The stage deflection angle is adjusted, and the stage deflection angles whose interference fringe parameters conform to the interference fringe parameter rules are selected to form a stage deflection angle range.

[0017] Furthermore, the method for calculating the step measurement result comprises the following steps:

[0018] Adjusting the distance between the reflectors of the laser interferometer device to obtain multiple interference images, and using a phase unwrapping algorithm to process the interference images to obtain a step surface phase distribution diagram; the reflector distance is controlled by a high-precision translation stage; the interference images are collected by a high-definition camera on an imaging lens; the imaging lens is used to receive interference fringes formed by the interference lens;

[0019] The specific steps of obtaining the step surface phase distribution map include: denoising and distortion correction of each interference image, calculating the initial phase information in each interference image using a spatial carrier phase shift method, and calculating the phase distribution map of the interference fringes using a five-step phase unwrapping algorithm to obtain the step surface phase distribution map; the step surface phase distribution map includes multiple step surface interference regions and invalid regions;

[0020] Determine the center point of each step surface according to the step boundary, set the center point of each step surface as the calculation point, calculate the height difference between adjacent calculation points based on the interference principle, the reference light wavelength, the measurement light wavelength and the position of adjacent calculation points, and define the height difference between adjacent calculation points as the corresponding step measurement height;

[0021] The data points of each step surface are extracted according to the phase distribution diagram of the step surface, and the ideal plane of each step surface is fitted using the least squares method to obtain the step measurement flatness.

[0022] Furthermore, the method for obtaining the optimal parameters of the device includes:

[0023] The device optimization objective function is determined based on the step measurement results and the step calibration value deviation:

[0024]

[0025] in Optimize the objective function for the device, is a set of device parameters, including the reference light wavelength , measure light wavelength , refractive index of interference lens , stage x-axis deflection angle , stage y-axis deflection angle Distance from reflector , is the bias weight, is the stability weight, is the number of stages, 、 No. The measured height and the calibrated height of the steps, 、 Respectively The measured flatness and calibrated flatness of the steps, is the standard deviation of the height of repeated measurements, is the standard deviation of flatness from repeated measurements;

[0026] Determine the device optimization objective function constraint conditions based on the refractive index range, stage deflection angle range, laser transmitter performance, and optical path interference principle;

[0027] The parameters of the laser interferometry device are optimized according to the device optimization objective function and the corresponding constraints. The improved whale optimization algorithm is used to search for the optimal parameters of the device. The whale population is divided into the main population and the auxiliary population, and the initial positions of the main and auxiliary populations are generated by hybrid chaotic mapping:

[0028]

[0029]

[0030] in The first chaotic map The chaotic sequence value after iterations, For the The chaotic sequence value after iterations, For the The chaotic sequence value after iterations, is the maximum number of iterations;

[0031] Calculate the objective function value and record the The optimal position of the population in the iteration , and enter the prey encirclement stage to update the particle position, the expression is:

[0032]

[0033]

[0034]

[0035] in Surrounding the prey The particle update positions in the main and auxiliary particle groups are is the best random position of the population, 、 is the vector coefficient, 、 is a randomly generated vector in [0,1], is a parameter that decreases linearly during the iteration process. represents the distance vector between the whale and the optimal solution, is the best random position of the population, is a random number in [0,1], is the average best position of the population, is the contraction-expansion coefficient;

[0036] Entering the bubble net predation stage, the particle position is updated using the shrinking and surrounding mechanism and the spiral position update mechanism. The expression is:

[0037]

[0038] in The first stage of bubble net predation The position of particles in the main and auxiliary particle groups are updated in the iteration. For the The distance between the whale and its prey, is a constant of the shape of the logarithmic spiral, is a random number between [-1,1];

[0039] Perform adaptive step size and mixed perturbation on the auxiliary population to update the position of the auxiliary population:

[0040]

[0041]

[0042] in For the The second iteration is the auxiliary population particle in Position component update, is the Lévy step length, is a Gaussian perturbation, is the standard deviation, for The maximum value of the position component, for The minimum value of the position component, is the step size coefficient, which has an initial value of 0.1 and increases linearly to 0.5 with the number of iterations. is the Levy distribution function;

[0043] Entering the prey search phase, a dynamic strategy is used to update the particle position, and the expression is:

[0044]

[0045]

[0046] in Searching for prey The position of particles in the main and auxiliary particle groups are updated in the iteration. A random whale in the current population;

[0047] The ratio of the main and auxiliary populations is updated every 10 generations, and the expression is:

[0048]

[0049]

[0050] in The proportion of the main population, The proportion of auxiliary populations;

[0051] Repeat the above steps for multiple iterations until the device optimization objective function is minimized or the maximum number of iterations is reached, and then stop the iteration and output the optimal parameters of the device; the optimal parameters of the device include the wavelength of the incident light, the refractive index of the interference lens, the deflection angle of the stage, and the distance of the reflector; the wavelength of the incident light includes the wavelength of the reference light and the wavelength of the measurement light.

[0052] Furthermore, the method for obtaining the step height and step flatness includes:

[0053] Perform Min-Max standardization on the step parameters of the measurement step and all step parameter entries in the step device parameter library:

[0054]

[0055] in After Min-Max normalization Class parameters The standardized results, is the minimum value of the corresponding parameter in the parameter library, is the maximum value of the corresponding parameter in the parameter library;

[0056] According to the distribution characteristics of the data in the parameter library, the weights of different types of parameters are dynamically adjusted. The expression is:

[0057]

[0058] in for Dynamically modified weights of class parameters, for The base weight of the class parameters, For parameter library Standard deviation of class parameters, parameter category The collection includes rough height , Rough length measurement , Rough measurement of width and order ;

[0059] The Euclidean distance and cosine similarity between the step parameters of the measured step after Min-Max normalization and the step parameters in the step device parameter library are calculated to obtain the comprehensive similarity:

[0060]

[0061] in is the comprehensive similarity, 、 is the similarity weight, Steps to be measured Class parameter normalization results, Parameter library for step devices Class parameter normalization results, is the maximum possible distance between all entries in the parameter library and the step parameter of the step to be measured;

[0062] The optimal parameters corresponding to the step parameters in the step device parameter library with the highest comprehensive similarity are taken as the reference device parameters. The reference device parameters are used to set the laser interferometer measurement device. The adjusted laser interferometer measurement device is used to measure the step to be measured to obtain multiple interference images. The above operations are repeated to calculate the step height and step flatness.

[0063] In the second aspect, a laser interferometer measurement device includes: a reference light emitter, a measuring light emitter, an optical fiber, a beam expander lens, an interference lens, a stage, a step gauge, a reflector, an imaging lens and a high-definition camera; the reference light emitter and the measuring light emitter are used to emit reference light and measuring light, respectively; the optical fiber connects the reference light emitter and the measuring light emitter to project the reference light and the measuring light to the beam expander lens; the beam expander lens is used to perform chromatic aberration correction on the reference light and the measuring light and expand the beam into parallel incident light; the interference lens is at an angle of 45° to the incident light, and is used to split the incident light into a first reflected light and a first transmitted light, and form an interference beam through the second reflected light and the third reflected light stripes; the stage is parallel to the incident light and is used to adjust the deflection angle and place the step gauge; the step gauge is used to fix steps to be measured of different specifications; the reflector is perpendicular to the incident light and is used to return the first transmitted light along the original path to form a third reflected light; the imaging lens is parallel to the incident light and is used to receive the interference stripes; the high-definition camera is used to collect the interference stripes on the imaging lens to form an interference image; the step surface of the step to be measured is used to return the first reflected light along the original path to form a third reflected light; the first reflected light and the second reflected light are perpendicular to the incident light, and the directions of the two are opposite; the first transmitted light and the third reflected light are parallel to the incident light, and the directions of the two are opposite.

[0064] The beneficial effects of the present invention are:

[0065] The present invention is a step height and flatness measurement method based on laser interferometry. Compared with the prior art, the present invention has the following technical effects:

[0066] The present invention can improve the data preprocessing capability and enhance the model adaptability in step height and flatness measurement through the steps of phase distribution diagram solution, determination of calculation point position, measurement result solution, device parameter optimization and database parameter matching, thereby improving the efficiency and accuracy of step height and flatness measurement. Optimizing the step height and flatness measurement technology can greatly save resources, improve work efficiency, and realize the measurement of step height and flatness, providing strong support for the development of modern precision manufacturing and nanotechnology, and is of great significance to promoting the development of high-precision measurement technology in the field of micro-nano manufacturing. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is a flowchart of a step height and flatness measurement method based on laser interferometry of the present invention;

[0068] Figure 2 A schematic diagram of a laser interferometry measurement device provided by the present invention;

[0069] Figure 3A schematic diagram of the optical path of a laser interferometer measurement device provided by the present invention;

[0070] In the figure: 1-reference light emitter; 2-measuring light emitter; 3-optical fiber; 4-beam expansion lens; 5-interference lens; 6-stage; 7-step gauge; 8-reflector; 9-imaging lens; 10-high-definition camera; A-reference light; B-measuring light; C-incident light; D-first reflected light; E-first transmitted light; F-second reflected light; G-third reflected light; H-interference fringes. DETAILED DESCRIPTION

[0071] The present invention will be further described below through specific examples. The illustrative examples and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0072] The present invention provides a step height and flatness measurement method based on laser interferometry, comprising the following steps:

[0073] like Figure 1 As shown, in this embodiment, the following steps are included:

[0074] The calibration step is placed in a laser interferometer measurement device, and the refractive index range of the interference lens is determined based on the beam intensity distribution deviation of the incident light in the interference lens, and the deflection angle range of the stage is determined based on the interference fringe parameters; the incident light includes reference light and measurement light;

[0075] Adjusting the distance between the reflectors of the laser interferometer device to obtain an interference image, processing the interference image to obtain a step surface phase distribution map, determining a calculation point position according to a step boundary, and calculating a step measurement result according to the calculation point position and the step surface phase distribution map; the step measurement result includes a step measurement height and a step measurement flatness;

[0076] Optimizing the device parameters within the refractive index range and the stage deflection angle range according to the step measurement results and the step calibration value deviation to obtain the optimal parameters of the device; the step calibration value includes the step calibration height and the step calibration flatness;

[0077] The step parameters and the optimal parameters of the device are combined into a set of step device parameters, and multiple sets of step device parameters of the calibrated steps are obtained to form a step device parameter library; the step parameters include the rough height, rough length, rough width and number of steps;

[0078] According to the step parameters of the step to be measured, the optimal device parameters in the step device parameter library are matched to obtain the reference device parameters and the laser interferometer measurement device is adjusted. The adjusted laser interferometer measurement device is used to measure the step to be measured to obtain the step height and step flatness.

[0079] In this embodiment, the method for determining the refractive index range of the interference lens and the method for determining the deflection angle range of the stage include:

[0080] placing the calibration step in a laser interferometer measurement device, passing incident light through an interference lens to obtain a first reflected light and a first transmitted light, and measuring the beam intensities of the incident light, the first reflected light, and the first transmitted light; the incident light includes a reference light and a measurement light; the first reflected light includes a first reference reflected light and a first measurement reflected light; and the first transmitted light includes a first reference transmitted light and a first measurement transmitted light;

[0081] Calculating a ratio of an absolute value of a difference between a first reference reflected light intensity and a first reference transmitted light intensity to the reference light intensity to obtain a reference light distribution deviation; calculating a ratio of an absolute value of a difference between a first measured reflected light intensity and a first measured transmitted light intensity to the measured light intensity to obtain a measured light distribution deviation; calculating an average of the reference light distribution deviation and the measured light distribution deviation to obtain a beam intensity distribution deviation; and selecting a refractive index range of the interference lens corresponding to a beam intensity distribution deviation less than 0.2;

[0082] Adjusting the stage deflection angle to obtain interference fringes and measuring interference fringe parameters; the stage deflection angle includes an x-axis deflection angle and a y-axis deflection angle; the interference fringes are formed by the second reflected light and the third reflected light overlapping at the interference lens; the second reflected light is formed by the first reflected light being reflected along the original path through the step surface; the third reflected light is formed by the first transmitted light being reflected along the original path through the reflector; the interference fringe parameters include contrast, spacing, and tilt;

[0083] Adjusting the stage deflection angle, and selecting the stage deflection angle whose interference fringe parameters meet the interference fringe parameter rules to form the stage deflection angle range;

[0084] In the actual evaluation, the height and flatness of four steps calibrated in a factory were obtained (unit: nm): 100.1 / 0.2, 200.3 / 0.1, 300.2 / 0.1, and 400.2 / 0.2. For the calibrated steps, when the lens refractive index was 0.1, the control variable method was used to set the reference light and measurement light to the wavelengths at 1 / 4 and 3 / 4 of the laser transmitter emission band (1000nm and 2000nm), with a light intensity of 100lux. Only the reference light was emitted to measure the first reference reflected light intensity and the first reference transmitted light intensity, which were 40l. ux, 56lux, the corresponding reference light distribution deviation is 0.16, only the measurement light is emitted to measure the first measurement reflected light intensity and the first measurement transmitted light intensity are 51lux and 45lux, corresponding to the measurement light distribution deviation of 0.06lux, the calculated beam intensity distribution deviation is (0.16+0.06) / 2=0.11<0.2, then the lens refractive index of 0.1 meets the requirements of the calibration step measurement, and the lens refractive index is continuously adjusted to select the refractive index of the interference lens corresponding to the beam intensity distribution deviation less than 0.2 to determine the refractive index range of the interference lens is 0.1-0.2;

[0085] The interference fringe parameter rules include the interference fringe contrast greater than 0.5, the interference fringe spacing between [10,100] (unit: pixel), and the interference fringe tilt less than 5°;

[0086] An interference lens with a refractive index of 0.1 is selected. At this time, the x / y-axis deflection angle of the stage is 0.5° / 0.3°, and the corresponding interference fringe parameters are 0.6, 30 pixels, and 3°, which conforms to the interference fringe parameter rules. The stage deflection angle is continuously adjusted to obtain a stage deflection angle range of 0.5-2.5° / 0.3-2.8°. Similarly, an interference lens with a refractive index of 0.2 is selected to adjust the stage deflection angle to obtain a stage deflection angle range of 0.8-2.7° / 0.5-2.5°. The intersection of the two deflection angle ranges is taken to determine the adjusted stage deflection angle range of 0.8-2.5° / 0.5-2.5°.

[0087] In this embodiment, the method for calculating the step measurement result includes the following steps:

[0088] Adjusting the distance between the reflectors of the laser interferometer device to obtain multiple interference images, and using a phase unwrapping algorithm to process the interference images to obtain a step surface phase distribution diagram; the reflector distance is controlled by a high-precision translation stage; the interference images are collected by a high-definition camera on an imaging lens; the imaging lens is used to receive interference fringes formed by the interference lens;

[0089] The specific steps of obtaining the step surface phase distribution map include: denoising and distortion correction of each interference image, calculating the initial phase information in each interference image using a spatial carrier phase shift method, and calculating the phase distribution map of the interference fringes using a five-step phase unwrapping algorithm to obtain the step surface phase distribution map; the step surface phase distribution map includes multiple step surface interference regions and invalid regions;

[0090] Determine the center point of each step surface according to the step boundary, set the center point of each step surface as the calculation point, calculate the height difference between adjacent calculation points based on the interference principle, the reference light wavelength, the measurement light wavelength and the position of adjacent calculation points, and define the height difference between adjacent calculation points as the corresponding step measurement height;

[0091] The data points of each step surface are extracted according to the phase distribution diagram of the step surface, and the ideal plane of each step surface is fitted by the least square method to obtain the step measurement flatness;

[0092] In the actual evaluation, the median of the interference lens refractive index range of 0.15, the median of the stage deflection angle of 1.65° / 1.5°, the reference light (1000nm, 100lux), and the measurement light (2000nm, 100lux) were used as the calibration steps for the device parameters of the laser interferometer measurement device. A high-precision translation stage was used to coarsely adjust the reflection lens distance from left to right (1mm / step) until interference fringes were generated and an interference image could be captured on the imaging lens using a high-definition camera. The reflection lens distance was then fine-tuned from left to right (10μm / step, 500nm / step, 100nm / step) to obtain multiple interference images. The phase unwrapping algorithm was used to process the interference images to obtain the phase distribution map of the step surface.

[0093] According to the calibrated step boundary, the center point of each step surface is determined as the step surface centroid, and the step surface centroid is set as the calculation point. The phase differences between adjacent calculation points are calculated according to the reference light wavelength, the measurement light wavelength and the position of adjacent calculation points, which are 0.628π, 1.256π, 1.884π, and 2.512π. According to the interference principle, the step heights of each level are calculated to be 100.3, 200.4, 299.8, and 400.1 nm, respectively. The data points of each step surface are extracted according to the step surface phase distribution diagram, and the least squares method is used to fit the ideal plane of each step surface to obtain the step measurement flatness of 0.22, 0.19, 0.15, and 0.24 nm.

[0094] In this embodiment, the method for obtaining the optimal parameters of the device includes:

[0095] The device optimization objective function is determined based on the step measurement results and the step calibration value deviation:

[0096]

[0097] in Optimize the objective function for the device, is a set of device parameters, including the reference light wavelength , measure light wavelength , refractive index of interference lens , stage x-axis deflection angle , stage y-axis deflection angle Distance from reflector , is the bias weight, is the stability weight, is the number of stages, 、 Respectively The measured height and the calibrated height of the steps, 、 Respectively The measured flatness and calibrated flatness of the steps, is the standard deviation of the height of repeated measurements, is the standard deviation of flatness from repeated measurements;

[0098] Determine the device optimization objective function constraint conditions based on the refractive index range, stage deflection angle range, laser transmitter performance, and optical path interference principle;

[0099] The parameters of the laser interferometry device are optimized according to the device optimization objective function and the corresponding constraints. The improved whale optimization algorithm is used to search for the optimal parameters of the device. The whale population is divided into the main population and the auxiliary population, and the initial positions of the main and auxiliary populations are generated by hybrid chaotic mapping:

[0100]

[0101]

[0102] in The first chaotic map The chaotic sequence value after iterations, For the The chaotic sequence value after iterations, For the The chaotic sequence value after iterations, is the maximum number of iterations;

[0103] Calculate the objective function value and record the The optimal position of the population in the iteration , and enter the prey encirclement stage to update the particle position, the expression is:

[0104]

[0105]

[0106]

[0107] in Surrounding the prey The particle update positions in the main and auxiliary particle groups are is the best random position of the population, 、 is the vector coefficient, 、 is a randomly generated vector in [0,1], is a parameter that decreases linearly during the iteration process. represents the distance vector between the whale and the optimal solution, is the best random position of the population, is a random number in [0,1], is the average best position of the population, is the contraction-expansion coefficient;

[0108] Entering the bubble net predation stage, the particle position is updated using the shrinking and surrounding mechanism and the spiral position update mechanism. The expression is:

[0109]

[0110] in The first stage of bubble net predation The position of particles in the main and auxiliary particle groups are updated in the iteration. For the The distance between the whale and its prey, is a constant of the shape of the logarithmic spiral, is a random number between [-1,1];

[0111] Perform adaptive step size and mixed perturbation on the auxiliary population to update the position of the auxiliary population:

[0112]

[0113]

[0114] in For the The second iteration is the auxiliary population particle in Position component update, is the Lévy step length, is a Gaussian perturbation, is the standard deviation, for The maximum value of the position component, for The minimum value of the position component, is the step size coefficient, which has an initial value of 0.1 and increases linearly to 0.5 with the number of iterations. is the Levy distribution function;

[0115] Entering the prey search phase, a dynamic strategy is used to update the particle position, and the expression is:

[0116]

[0117]

[0118] in Searching for prey The position of particles in the main and auxiliary particle groups are updated in the iteration. A random whale in the current population;

[0119] The ratio of the main and auxiliary populations is updated every 10 generations, and the expression is:

[0120]

[0121]

[0122] in The proportion of the main population, The proportion of auxiliary populations;

[0123] Repeat the above steps for multiple iterations until the device optimization objective function is minimized or the maximum number of iterations is reached, and then stop the iteration and output the optimal parameters of the device; the optimal parameters of the device include the wavelength of the incident light, the refractive index of the interference lens, the deflection angle of the stage, and the distance of the reflector; the wavelength of the incident light includes the wavelength of the reference light and the wavelength of the measurement light;

[0124] In the actual evaluation, the constraints of the device optimization objective function include: the optimized refractive index belongs to the refractive index range, the optimized deflection angle belongs to the stage deflection angle range, the reference light wavelength and the measurement light wavelength are within the laser transmitter emission band, and the reflector distance is Phase difference should be ensured It must be at least a certain ratio greater than the phase change (2π) corresponding to one wavelength;

[0125] Take bias weight , stability weight , the standard deviation of the height of repeated measurements and flatness standard deviation They are (0.5, 0.6, 0.4, 0.5) and (0.02, 0.03, 0.02, 0.03) respectively. According to the measurement results of the calibration step and the calibration value calculation device, the optimization objective function is 1.344545;

[0126] The improved whale optimization algorithm is used to search for the optimal parameters of the device, where the contraction and expansion coefficients , the constant of the shape of the logarithmic spiral , maximum number of iterations The optimal position of the initial population is the particle position corresponding to the median refractive index range of the interference lens of 0.15, the median deflection angle of the stage of 1.65° / 1.5°, the reference light (1000nm, 100lux), the measurement light (2000nm, 100lux) and the reflector distance of 100-250mm. , iterate repeatedly, and when the iteration reaches the 14th, 15th, and 16th times, the device optimization objective function is 1.258, 1.251, and 1.29 respectively, and the optimal position of the population at the 15th iteration is taken The device parameters corresponding to the particles are the optimal parameters of the device: interference lens refractive index 1.47, stage deflection angle 1.25° / 0.75°, reflector distance 150-300 mm, reference light (736 nm, 100 lux), measurement light (1545 nm, 100 lux);

[0127] The step parameters of the calibration step (400nm, 5mm, 3mm, 4) and the corresponding device optimal parameters are combined into a set of step device parameters, and multiple sets of step device parameters of the calibration steps are obtained to form a step device parameter library.

[0128] In this embodiment, the method for obtaining the step height and the step flatness includes:

[0129] Perform Min-Max standardization on the step parameters of the measurement step and all step parameter entries in the step device parameter library:

[0130]

[0131] in After Min-Max normalization Class parameters The standardized results, is the minimum value of the corresponding parameter in the parameter library, is the maximum value of the corresponding parameter in the parameter library;

[0132] According to the distribution characteristics of the data in the parameter library, the weights of different types of parameters are dynamically adjusted. The expression is:

[0133]

[0134] in for Dynamically modified weights of class parameters, for The base weight of the class parameters, For parameter library Standard deviation of class parameters, parameter category The collection includes rough height , Rough length measurement , Rough measurement of width and order ;

[0135] The Euclidean distance and cosine similarity between the step parameters of the measured step after Min-Max normalization and the step parameters in the step device parameter library are calculated to obtain the comprehensive similarity:

[0136]

[0137] in is the comprehensive similarity, 、 is the similarity weight, Steps to be measured Class parameter normalization results, Parameter library for step devices Class parameter normalization results, is the maximum possible distance between all entries in the parameter library and the step parameter of the step to be measured;

[0138] The optimal parameters corresponding to the step parameters in the step device parameter library with the highest comprehensive similarity are taken as the reference device parameters. The reference device parameters are used to set the laser interferometer measurement device. The adjusted laser interferometer measurement device is used to measure the step to be measured to obtain multiple interference images. The above operation is repeated to calculate the step height and step flatness.

[0139] In the actual evaluation, the step parameters of the step to be measured are obtained (380nm, 4.5mm, 3mm, 4). The minimum and maximum values ​​of the step parameters in the step device parameter library are 200nm / 2μm, 3mm / 10mm, 1mm / 5mm, and 2 / 10, respectively. The step parameters of the measured step and all step parameter entries in the step device parameter library are normalized by Min-Max to obtain the normalized step parameters (1 / 10, 3 / 14, 1 / 2, 3 / 8).

[0140] According to the basic weights of the step parameters (0.4, 0.15, 0.15, 0.3) and the standard deviation of the step parameters in the parameter library, the weights of different types of parameters are dynamically adjusted to obtain dynamic correction weights (0.45, 0.11, 0.12, 0.32). The maximum possible distance between all entries in the parameter library and the step parameters of the step to be measured is , calculate the Euclidean distance and cosine similarity between the step parameters of the measured step after Min-Max normalization and the step parameters in the step device parameter library to obtain the comprehensive similarity, and take the optimal parameters corresponding to the step parameters in the step device parameter library with the highest comprehensive similarity of 0.88 as the reference device parameters: interference lens refractive index 1.36, stage deflection angle 1.10° / 0.9°, reflector distance 125-325mm, reference light (1200nm, 100lux), measurement light (1730nm, 100lux);

[0141] The laser interferometer measurement device was set up using the reference device parameters. The adjusted laser interferometer measurement device was used to measure the step to be measured to obtain multiple interference images. The above operation was repeated to calculate the step height and step flatness (unit: nm): 95.05 / 0.15, 190.1 / 0.1, 285.2 / 0.15, 380.25 / 0.05, respectively.

[0142] like Figures 2-3 As shown, in this embodiment, a cable based on optical fiber technology includes: a reference light emitter 1, a measuring light emitter 2, an optical fiber 3, a beam expander lens 4, an interference lens 5, a stage 6, a step gauge 7, a reflector 8, an imaging lens 9 and a high-definition camera 10; the reference light emitter 1 and the measuring light emitter 2 are respectively used to emit reference light A and measuring light B; the optical fiber 3 connects the reference light emitter 1 and the measuring light emitter 2, and projects the reference light A and the measuring light B to the beam expander lens 4; the beam expander lens 4 is used to perform chromatic aberration correction on the reference light A and the measuring light B and expand them into parallel incident light C; the interference lens 5 is at an angle of 45° with the incident light C, and is used to split the incident light C into a first reflected light D and a first transmitted light E, and transmit the second reflected light F and the third The reflected light G forms interference fringes H; the stage 6 is parallel to the incident light C, and is used to adjust the deflection angle and place the step gauge 7; the step gauge 7 is used to fix steps to be measured of different specifications; the reflector 8 is perpendicular to the incident light C, and is used to return the first transmitted light E along the original path to form a third reflected light G; the imaging lens 9 is parallel to the incident light C, and is used to receive the interference fringes H; the high-definition camera is used to collect the interference fringes H on the imaging lens 9 to form an interference image; the step surface of the step to be measured is used to return the first reflected light D along the original path to form a third reflected light F; the first reflected light D and the second reflected light F are perpendicular to the incident light C, and the directions of the two are opposite; the first transmitted light E and the third reflected light G are parallel to the incident light C, and the directions of the two are opposite.

[0143] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for measuring step height and flatness based on laser interferometry, comprising the following steps: S1. Place the calibration step in a laser interferometer measurement device, pass the incident light through an interference lens to obtain a first reflected light and a first transmitted light, and measure the intensities of the incident light, the first reflected light, and the first transmitted light; the incident light includes a reference light and a measurement light; the first reflected light includes a first reference light and a first measurement reflected light; and the first transmitted light includes a first reference light and a first measurement transmitted light; Calculating a ratio of an absolute value of a difference between a first reference reflected light intensity and a first reference transmitted light intensity to the reference light intensity to obtain a reference light distribution deviation; calculating a ratio of an absolute value of a difference between a first measured reflected light intensity and a first measured transmitted light intensity to the measured light intensity to obtain a measured light distribution deviation; calculating an average of the reference light distribution deviation and the measured light distribution deviation to obtain a beam intensity distribution deviation; and selecting a refractive index range of the interference lens corresponding to a beam intensity distribution deviation less than 0.2; Adjusting the stage deflection angle, including the x- and y-axes, to obtain interference fringes and measure the interference fringe parameters. The interference fringes are formed by the superposition of the second reflected light and the third reflected light at the interference lens. The second reflected light is formed by the first reflected light reflecting along its original path through the step surface. The third reflected light is formed by the first transmitted light reflecting along its original path through the reflector. The interference fringe parameters include contrast, pitch, and tilt. Adjusting the stage deflection angle, and selecting the stage deflection angle whose interference fringe parameters meet the interference fringe parameter rules to form the stage deflection angle range; S2. Adjust the distance between the reflectors of the laser interferometer device to obtain an interference image, process the interference image to obtain a step surface phase distribution map, determine the calculation point position according to the step boundary, and calculate the step measurement results including the step measurement height and flatness according to the calculation point position and the step surface phase distribution map; S3. Optimizing the device parameters within the refractive index range and the stage deflection angle range according to the step measurement results and the calibration value deviation to obtain the optimal parameters of the device; the step calibration value includes the step calibration height and flatness; S4. Combining the step parameters including the roughly measured height, length, width, and number of steps with the optimal parameters of the device into a set of step device parameters, and obtaining multiple sets of step device parameters of calibrated steps to form a step device parameter library; S5. According to the step parameters of the step to be measured, the optimal device parameters in the step device parameter library are matched to obtain reference device parameters and the laser interferometer measurement device is adjusted. The adjusted laser interferometer measurement device is used to measure the step to be measured to obtain the step height and flatness.

2. The step height and flatness measurement method based on laser interferometry according to claim 1, characterized in that: The method for calculating the step measurement result comprises the following steps: Adjusting the distance between the reflectors of the laser interferometer device to obtain multiple interference images, and using a phase unwrapping algorithm to process the interference images to obtain a step surface phase distribution diagram; the reflector distance is controlled by a high-precision translation stage; the interference images are collected by a high-definition camera on an imaging lens; the imaging lens is used to receive interference fringes formed by the interference lens; The specific steps of obtaining the step surface phase distribution map include: denoising and distortion correction of each interference image, calculating the initial phase information in each interference image using a spatial carrier phase shift method, and calculating the phase distribution map of the interference fringes using a five-step phase unwrapping algorithm to obtain the step surface phase distribution map; the step surface phase distribution map includes multiple step surface interference regions and invalid regions; Determine the center point of each step surface according to the step boundary, set the center point of each step surface as the calculation point, calculate the height difference between adjacent calculation points based on the interference principle, the reference light wavelength, the measurement light wavelength and the position of adjacent calculation points, and define the height difference between adjacent calculation points as the corresponding step measurement height; The data points of each step surface are extracted according to the phase distribution diagram of the step surface, and the ideal plane of each step surface is fitted using the least squares method to obtain the step measurement flatness.

3. The step height and flatness measurement method based on laser interferometry according to claim 1, characterized in that: The method for obtaining optimal parameters of the device includes: The device optimization objective function is determined based on the step measurement results and the step calibration value deviation: in Optimize the objective function for the device, is a set of device parameters, including the reference light wavelength , measure light wavelength , refractive index of interference lens , stage x-axis deflection angle , stage y-axis deflection angle Distance from reflector , is the bias weight, is the stability weight, is the number of stages, 、 Respectively The measured height and the calibrated height of the steps, 、 Respectively The measured flatness and calibrated flatness of the steps, is the standard deviation of the height of repeated measurements, is the standard deviation of flatness from repeated measurements; Determine the device optimization objective function constraint conditions based on the refractive index range, stage deflection angle range, laser transmitter performance, and optical path interference principle; The parameters of the laser interferometry device are optimized according to the device optimization objective function and the corresponding constraints. The improved whale optimization algorithm is used to search for the optimal parameters of the device. The whale population is divided into the main population and the auxiliary population, and the initial positions of the main and auxiliary populations are generated by hybrid chaotic mapping: in The first chaotic map The chaotic sequence value after iterations, For the The chaotic sequence value after iterations, For the The chaotic sequence value after iterations, is the maximum number of iterations; Calculate the objective function value and record the The optimal position of the population in the iteration , and enter the prey encirclement stage to update the particle position, the expression is: in Surrounding the prey The particle update positions in the main and auxiliary particle groups are is the best random position of the population, 、 is the vector coefficient, 、 is a randomly generated vector in [0,1], is a parameter that decreases linearly during the iteration process. represents the distance vector between the whale and the optimal solution, is the best random position of the population, is a random number in [0,1], is the average best position of the population, is the contraction-expansion coefficient; Entering the bubble net predation stage, the particle position is updated using the shrinking and surrounding mechanism and the spiral position update mechanism. The expression is: in The first stage of bubble net predation The position of particles in the main and auxiliary particle groups are updated in the iteration. For the The distance between the whale and its prey, is a constant of the shape of the logarithmic spiral, is a random number between [-1,1]; Perform adaptive step size and mixed perturbation on the auxiliary population to update the position of the auxiliary population: in For the The second iteration is the auxiliary population particle in Position component update, is the Lévy step length, is a Gaussian perturbation, is the standard deviation, for The maximum value of the position component, for The minimum value of the position component, is the step size coefficient, which has an initial value of 0.1 and increases linearly to 0.5 with the number of iterations. is the Levy distribution function; Entering the prey search phase, a dynamic strategy is used to update the particle position, and the expression is: in Searching for prey The position of particles in the main and auxiliary particle groups are updated in the iteration. A random whale in the current population; The ratio of the main and auxiliary populations is updated every 10 generations, and the expression is: in The proportion of the main population, The proportion of auxiliary populations; Repeat the above steps for multiple iterations until the device optimization objective function is minimized or the maximum number of iterations is reached, and then stop the iteration and output the optimal parameters of the device; the optimal parameters of the device include the wavelength of the incident light, the refractive index of the interference lens, the deflection angle of the stage, and the distance of the reflector; the wavelength of the incident light includes the wavelength of the reference light and the wavelength of the measurement light.

4. The step height and flatness measurement method based on laser interferometry according to claim 1, characterized in that: The method for obtaining step height and flatness includes: Perform Min-Max standardization on the step parameters of the measurement step and all step parameter entries in the step device parameter library: in After Min-Max normalization Class parameters The standardized results, is the minimum value of the corresponding parameter in the parameter library, is the maximum value of the corresponding parameter in the parameter library; According to the distribution characteristics of the data in the parameter library, the weights of different types of parameters are dynamically adjusted. The expression is: in for Dynamically modified weights of class parameters, for The base weight of the class parameters, For parameter library Standard deviation of class parameters, parameter category The collection includes rough height , Rough length measurement , Rough measurement of width and order ; The Euclidean distance and cosine similarity between the step parameters of the measured step after Min-Max normalization and the step parameters in the step device parameter library are calculated to obtain the comprehensive similarity: in is the comprehensive similarity, 、 is the similarity weight, Steps to be measured Class parameter normalization results, Parameter library for step devices Class parameter normalization results, is the maximum possible distance between all entries in the parameter library and the step parameter of the step to be measured; The optimal parameters corresponding to the step parameters in the step device parameter library with the highest comprehensive similarity are taken as the reference device parameters. The reference device parameters are used to set the laser interferometer measurement device. The adjusted laser interferometer measurement device is used to measure the step to be measured to obtain multiple interference images. The above operations are repeated to calculate the step height and step flatness.

5. A laser interferometer measuring device for executing the method according to any one of claims 1 to 4, characterized in that: include: Reference light emitter, measurement light emitter, optical fiber, beam expander lens, interference lens, stage, step gauge, reflector, imaging lens and high-definition camera; The reference light emitter and the measuring light emitter are used to emit reference light and measuring light, respectively; the optical fiber connects the reference light emitter and the measuring light emitter, and projects the reference light and the measuring light to the beam expander lens; the beam expander lens is used to perform chromatic aberration correction on the reference light and the measuring light and expand the beams into parallel incident light; the interference lens forms a 45° angle with the incident light, and is used to split the incident light into a first reflected light and a first transmitted light, and form interference fringes through the second reflected light and the third reflected light; the stage is parallel to the incident light, and is used to adjust the deflection angle and place the step gauge; The step gauge is used to fix steps to be measured of different specifications; the reflector is perpendicular to the incident light, and is used to return the first transmitted light along the original path to form a third reflected light; the imaging lens is parallel to the incident light, and is used to receive the interference fringes; the high-definition camera is used to collect the interference fringes on the imaging lens to form an interference image; the step surface of the step to be measured is used to return the first reflected light along the original path to form a third reflected light; the first reflected light and the second reflected light are perpendicular to the incident light, and the directions of the two are opposite; the first transmitted light and the third reflected light are parallel to the incident light, and the directions of the two are opposite.

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