CN116756477B - Precise measurement method based on Fresnel diffraction edge characteristics - Google Patents
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Abstract
The invention relates to a precise measurement method based on Fresnel diffraction edge characteristics, which comprises the following steps: acquiring a forward discrete sequence and a reverse discrete sequence of a projection light intensity signal of a target object; constructing a first Fresnel diffraction characteristic expression matrix of a forward discrete sequence and a second Fresnel diffraction characteristic expression matrix of an inverse discrete sequence; determining an average offset between the forward discrete sequence and the reverse discrete sequence based on a similarity between each first expression vector in the first fresnel diffraction property expression matrix and each second expression vector in the second fresnel diffraction property expression matrix; based on the average offset, compensating discrete points of the forward discrete sequence in the symmetric compensation area by utilizing the reverse discrete sequence; and performing curve fitting on the compensated discrete points, and determining the edge position of the target object by using a fitting curve obtained by fitting so as to determine the target size of the target object based on the edge position.
Description
Technical Field
The present disclosure relates generally to the field of optical measurement technology, and more particularly, to a precise measurement method based on fresnel diffraction edge characteristics.
Background
The structural size is the most basic characteristic of various entity products, and in order to ensure the specification quality of the high consistency of the products, the size measurement and verification of the products can be carried out in the industrial production process. Optical measurement methods are widely used in industrial manufacturing due to their non-contact and rapid advantages.
The measuring method based on parallel light projection is a common optical measuring method, and the size of a target is calculated by receiving a projected light intensity signal of the target object under the irradiation of parallel light and judging the edge position of the target object according to the range of a shielded area of the parallel light in the light intensity signal. However, the method has a relatively large bottleneck in the micro-nano level precise measurement application scene.
On the one hand, for the application scene with micro-nano precision requirement, one milli edge positioning deviation can cause great increase of measurement errors during light intensity signal processing. And the existence of system noise and random noise in the optical measurement system is unavoidable, which affects the accuracy and stability of measurement. On the other hand, when the parallel light irradiates the target object, fresnel diffraction occurs at the edge position of the target, the light intensity is not completely clear, but the rising edge with a gentle gradient is formed, the real edge position is hidden, the difficulty of determining the edge position in the light intensity signal is increased, and the accuracy of size measurement is limited. Furthermore, the intensity fluctuations caused by fresnel diffraction itself can also make the noise signal more difficult to remove. To overcome these effects, it is necessary to study more robust and accurate measurement methods.
Disclosure of Invention
The precise measurement method based on the Fresnel diffraction edge characteristics can be used for carrying out high-precision edge positioning in a symmetrical compensation mode, and accurate measurement of the target size is achieved.
In one general aspect, there is provided a method of precisely measuring edge characteristics based on fresnel diffraction, comprising: acquiring a forward discrete sequence and an inverse discrete sequence of a projection light intensity signal of a target object, wherein the forward discrete sequence and the inverse discrete sequence are in reverse order; constructing a first Fresnel diffraction characteristic expression matrix of the forward discrete sequence and a second Fresnel diffraction characteristic expression matrix of the reverse discrete sequence; determining an average offset between the forward discrete sequence and the reverse discrete sequence based on a similarity between each first expression vector in the first fresnel diffraction property expression matrix and each second expression vector in the second fresnel diffraction property expression matrix; based on the average offset, performing compensation processing on discrete points of the forward discrete sequence in a symmetric compensation area by utilizing the reverse discrete sequence; and performing curve fitting on the compensated discrete points, and determining the edge position of the target object by using a fitting curve obtained by fitting so as to determine the target size of the target object based on the edge position.
Optionally, the constructing the first fresnel diffraction property expression matrix of the forward discrete sequence includes: determining a first Fresnel diffraction characteristic expression point in the forward discrete sequence, wherein the first Fresnel diffraction characteristic expression point is a local extreme point corresponding to a peak or a trough in the forward discrete sequence; and converting the first Fresnel diffraction characteristic expression point into the first expression vector so as to obtain the first Fresnel diffraction characteristic expression matrix based on the first expression vector.
Optionally, each first expression vector includes a first expression element, a second expression element, a third expression element, and a fourth expression element, wherein the converting the first fresnel diffraction property expression point into the first expression vector includes: for any one first Fresnel diffraction characteristic expression point, determining a first average value of a first number of discrete points in the forward discrete sequence with the first Fresnel diffraction characteristic expression point as a center, and determining the first expression element based on a first quantization coefficient and the first average value; performing normal distribution fitting on a second number of discrete points taking the first Fresnel diffraction characteristic expression point as a center in the forward discrete sequence to obtain a first standard deviation, and determining the second expression element based on a second quantization coefficient and the first standard deviation; performing normal distribution fitting on a third number of discrete points taking the first Fresnel diffraction characteristic expression point as a center in the forward discrete sequence to obtain a second standard deviation, and determining the third expression element based on a third quantization coefficient and the second standard deviation; determining the sequence number of the first Fresnel diffraction characteristic expression point in the forward discrete sequence, and taking the sequence number as the fourth expression element.
Optionally, the determining the average offset between the forward discrete sequence and the reverse discrete sequence based on the similarity between each first expression vector in the first fresnel diffraction property expression matrix and each second expression vector in the second fresnel diffraction property expression matrix includes: respectively carrying out difference calculation on each first expression vector and each second expression vector to obtain a first difference vector of each first expression vector relative to each second expression vector, wherein each first difference vector comprises a first difference element, a second difference element, a third difference element and a fourth difference element; determining a second difference vector in the first difference vector, wherein a first difference element, a second difference element and a third difference element of the second difference vector are all 0; taking a fourth difference element of each second difference vector as a positive and negative sequence offset element; performing frequency statistics on all positive and negative sequence offset elements to determine a first offset element, wherein the first offset element is a positive and negative sequence offset element corresponding to a frequency maximum value; determining a second offset element in the positive and negative sequence offset elements based on the first offset element, wherein an absolute value of a difference value between the second offset element and the first offset element is smaller than a first threshold value; and determining a second average value of the second offset element, and taking the second average value as the average offset.
Optionally, the symmetric compensation area is an area between a first discrete point and a second discrete point in the forward discrete sequence, wherein the first discrete point corresponds to a highest diffraction peak on the left side of the forward discrete sequence, and the second discrete point corresponds to a highest diffraction peak on the right side of the forward discrete sequence, and the compensating the discrete points of the forward discrete sequence in the symmetric compensation area with the reverse discrete sequence based on the average offset comprises: determining a first symmetric compensation local data matrix of any one discrete point in the symmetric compensation area; performing decentering treatment on the first symmetrical compensation local data matrix in the column direction to obtain a second symmetrical compensation local data matrix; determining a symmetric compensated local covariance matrix based on the second symmetric compensated local data matrix; performing eigenvalue decomposition on the symmetrical compensation local covariance matrix to obtain an eigenvector corresponding to the maximum eigenvalue; multiplying the feature vector by the second symmetrical compensation local data matrix to obtain a deviation value vector; denoising the first symmetrical compensation local data matrix based on the deviation value vector to obtain a third symmetrical compensation local data matrix, and determining a gravity center vector of the third symmetrical compensation local data matrix; and compensating the discrete point based on the gravity center vector and the characteristic vector.
Optionally, the determining the first symmetric compensated local data matrix for the discrete point includes: the discrete point is determined by the following first equationIs a first symmetric compensated local data matrix +.>：
Wherein,representing discrete points in the forward discrete sequence, Z +.>Representing discrete points in the inverse discrete sequence,representing the discrete point as the first +.>Discrete points->Representing window range values, ++>Represents the average offset, +.>Representing rounding operations; wherein the determining a symmetric compensated local covariance matrix comprises: determining a symmetrically compensated local covariance matrix by the following second equation>：
Wherein,representing a second symmetric compensated local data matrix, < >>Representation->Is a transposed matrix of (a).
Optionally, the offset value vector includesThe gravity center vector comprises a first gravity center element and a second gravity center element, wherein the denoising processing is performed on the first symmetrical compensation local data matrix based on the gravity center vector to obtain a third symmetrical compensation local data matrix, and the gravity center vector of the third symmetrical compensation local data matrix is determined, and the method comprises the following steps: comparing each deviation value element with a second threshold value to determine a noise element among the deviation value elements, wherein an absolute value of the noise element is greater than the second threshold value; removing row vectors in the first symmetrical compensation local data matrix corresponding to the noise element to obtain the third symmetrical compensation local data matrix; determining a first column element of the third symmetrically compensated local data matrix A third mean value of the elements, and taking the third mean value as the first barycenter element; determining a fourth mean value of the second column matrix elements of the third symmetrical compensation local data matrix, and taking the fourth mean value as the second center element, wherein the compensation processing for the discrete point comprises the following steps: the discrete point is +.>And (3) performing compensation treatment:
wherein,representing the first barycenter element->Representing a second concentric element, ">First feature element representing a feature vector, +.>And a second feature element representing a feature vector.
Optionally, the fitting curves include a first fitting curve and a second fitting curve, the edge positions include a left edge position and a right edge position, wherein the performing curve fitting on the compensated discrete points and determining the edge position of the target object by using the fitting curve obtained by fitting to determine the target size of the target object based on the edge positions includes: dividing the symmetrical compensation area into a left edge fitting area and a right edge fitting area; performing curve fitting on the compensated discrete points in the left edge fitting area to obtain a first fitting curve, and determining the left edge position by using the first fitting curve; performing curve fitting on the compensated discrete points in the right edge fitting area to obtain a second fitting curve, and determining the right edge position by using the second fitting curve; a distance between the left edge position and the right edge position is determined as the target size.
Alternatively, the curve fitting is performed by the following fourth equation:
wherein,representing the number of sequences of discrete points +.>Representing the light intensity value +.>Representing the first fitting parameters, +.>Representing the second fitting parameters, +.>Representing the third fitting parameter, +.>Representing the fourth fitting parameter, +.>Representing a hyperbolic tangent function.
Optionally, the determining the edge position of the target object by using the fitted curve includes: determining a first maximum value of a first derivative and a second maximum value of a second derivative of the fitted curve, and determining a target sequence number corresponding to the first maximum value; determining an edge position of the target object based on the first maximum value, the second maximum value, and the target sequence number in combination with a first calibration parameter and a second calibration parameter, wherein the edge position is determined by a fifth equation：
Wherein,representing the number of target sequences, +.>Represents a first maximum, +.>Representing a second maximum, +.>Representing a first calibration parameter,/->Representing a second calibration parameter.
According to the precise measurement method based on the Fresnel diffraction edge characteristics, through determining the average offset between the forward discrete sequence and the reverse discrete sequence of the projected light intensity signals and combining the reverse discrete sequence to compensate discrete points in the forward discrete sequence, the theoretical consistency of the Fresnel diffraction characteristics of the left edge and the right edge can be fully utilized, the original light intensity signals are symmetrically compensated, abrupt noise is effectively removed, the processed signal trend is more consistent with the Fresnel diffraction characteristics, a more accurate fitting curve is obtained to calculate the edge position of a target object, and when the fitting curve is utilized to calculate the edge position, calibration compensation is designed based on the influence of the Fresnel diffraction, so that the calculated edge position is more accurate.
Additional aspects and/or advantages of the present general inventive concept will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the general inventive concept.
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The foregoing and other objects and features of embodiments of the present disclosure will become more apparent from the following description taken in conjunction with the accompanying drawings in which the embodiments are shown, in which:
FIG. 1 is a schematic diagram illustrating parallel light projection optical measurement according to an embodiment of the present disclosure;
FIG. 2 is a waveform diagram illustrating a projected light intensity signal disturbed by noise in accordance with an embodiment of the present disclosure;
FIG. 3 is a flow chart illustrating a method of precision measurement based on Fresnel diffraction edge characteristics according to an embodiment of the present disclosure;
FIG. 4 is a graph illustrating a projected light intensity signal scatter plot according to an embodiment of the present disclosure;
FIG. 5 is a diagram illustrating similarity statistics of an expression matrix according to an embodiment of the present disclosure;
FIG. 6 is a schematic diagram illustrating a symmetric compensation region according to an embodiment of the present disclosure;
fig. 7 is a schematic diagram illustrating edge fitting according to an embodiment of the present disclosure.
Detailed Description
The following detailed description is provided to assist the reader in obtaining a thorough understanding of the methods, apparatus, and/or systems described herein. However, various changes, modifications, and equivalents of the methods, apparatuses, and/or systems described herein will be apparent after an understanding of the disclosure of the present application. For example, the order of operations described herein is merely an example and is not limited to those set forth herein, but may be altered as will be apparent after an understanding of the disclosure of the present application, except for operations that must occur in a particular order. Furthermore, descriptions of features known in the art may be omitted for clarity and conciseness.
The features described herein may be embodied in different forms and should not be construed as limited to the examples described herein. Rather, the examples described herein have been provided to illustrate only some of the many possible ways to implement the methods, devices, and/or systems described herein, which will be apparent after an understanding of the present disclosure.
Unless defined otherwise, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs after understanding this disclosure. Unless explicitly so defined herein, terms (such as those defined in a general dictionary) should be construed to have meanings consistent with their meanings in the context of the relevant art and the present disclosure, and should not be interpreted idealized or overly formal.
In addition, in the description of the examples, when it is considered that detailed descriptions of well-known related structures or functions will cause a ambiguous explanation of the present disclosure, such detailed descriptions will be omitted.
A precise measurement method based on fresnel diffraction edge characteristics according to an embodiment of the present disclosure will be described in detail with reference to fig. 1 to 7.
FIG. 1 is a schematic diagram illustrating parallel light projection optical measurement according to an embodiment of the present disclosure; fig. 2 is a waveform diagram illustrating a projected light intensity signal disturbed by noise according to an embodiment of the present disclosure.
Referring to fig. 1, the principle of the parallel light projection optical measurement method is as follows: parallel light irradiates an object from one side, and the other side is received by a light intensity signal receiver to obtain a light intensity signal waveform. In the area shielded by the object, the parallel light can not reach the light intensity signal receiver, and trough areas with lower values can be formed on the light intensity signal waveform; in the area which is not shielded by the object, the parallel light is collected by the light intensity signal receiver, and the area with larger value outside the trough is formed on the light intensity signal. At the edge of the object, a fluctuating fresnel diffraction peak waveform is formed due to the fresnel diffraction effect. And due to the existence of diffraction effect, the dark and bright juncture is not clear but becomes a gentle slope rising edge, and the real edge position is hidden in the gentle rising edge.
In addition, referring to fig. 2, in practice, due to noise interference, many burrs, deformations, and distortions occur in the projected light intensity signal waveform, which also affects the accuracy of edge positioning and measurement.
Therefore, in order to suppress noise and accurately position the edge position in the rising edge of the fresnel diffraction peak, the waveform consistency (or symmetry) of the two diffraction peaks can be used to compensate each other to refine effective information, so as to suppress noise, specifically, the material structures of the two edges of the measurement target are generally consistent, and the fresnel diffraction waveform formed under parallel light is theoretically consistent, so that the prior information can be fully used to perform signal denoising; and then, establishing an edge model based on the Fresnel rising edge, acquiring an initial edge position through data fitting, correcting the initial edge position through parameter calibration to obtain a final accurate edge position, and obtaining a target size according to the distance between the left edge position and the right edge position.
Fig. 3 is a flowchart illustrating a precise measurement method based on fresnel diffraction edge characteristics according to an embodiment of the present disclosure.
Referring to fig. 3, in step S301, a forward discrete sequence and an inverse discrete sequence of the projected light intensity signal of the target object may be acquired. Here, the forward discrete sequence is the reverse of the ordering of the discrete points in the reverse discrete sequence.
Fig. 4 is a graph illustrating a projected light intensity signal scatter plot according to an embodiment of the present disclosure.
Referring to fig. 4, discretization may be performed on the projected light intensity signal waveform, so that all points after discretization of the light intensity signal form a discrete sequence, and when the point sequence is arranged from left to right, a forward discrete sequence is formed, and when the point sequence is arranged from right to left, an inverse discrete sequence is formed. Here, discrete points in the forward discrete sequence are availableTo express, in particular, < >>Can represent the +.>Discrete points->The dot value of (2) is +.>Light intensity values corresponding to the discrete points; similarly, discrete points in the inverted discrete sequence can be used +.>To represent. Further, the projection beam is generally collected through a linear array CMOS device, the collection interval and the discrete point depend on hardware parameters of the linear array CMOS device, and the type selection of the linear array CMOS device is based on the measurement accuracy requirement, so that a person skilled in the art can determine the number of discrete points in the forward discrete sequence and/or the reverse discrete sequence by determining the type selection of the linear array CMOS device, and the disclosure is not limited to this.
Referring back to fig. 3, next, in step S302, a first fresnel diffraction property expression matrix of the forward discrete sequence and a second fresnel diffraction property expression matrix of the reverse discrete sequence may be constructed.
According to embodiments of the present disclosure, when constructing a first fresnel diffraction property expression matrix of a forward discrete sequence, a first fresnel diffraction property expression point in the forward discrete sequence may be determined; then, the first Fresnel diffraction characteristic expression point is converted into a first expression vector to obtain a first Fresnel diffraction characteristic expression matrix based on the first expression vector. Here, the first fresnel diffraction characteristic expression point is a local extremum point corresponding to a peak (local maximum value) or a trough (local minimum value) in the forward discrete sequence, reflects a trend of a sequence fluctuation change, and all the local extremum points of the sequence can express fresnel diffraction waveform characteristics.
According to an embodiment of the present disclosure, each first expression vector may include a first expression element, a second expression element, a third expression element, and a fourth expression element, so that when converting a first fresnel diffraction characteristic expression point into a first expression vector, for any one first fresnel diffraction characteristic expression point, it may be determined that the first fresnel diffraction characteristic expression point is the center in the forward discrete sequenceA first mean of a first number of discrete points of the heart, and determining a first expression element based on the first quantization coefficient and the first mean; performing normal distribution fitting on a second number of discrete points taking the first Fresnel diffraction characteristic expression point as a center in the forward discrete sequence to obtain a first standard deviation, and determining a second expression element based on a second quantization coefficient and the first standard deviation; performing normal distribution fitting on a third number of discrete points taking the first Fresnel diffraction characteristic expression point as a center in the forward discrete sequence to obtain a second standard deviation, and determining a third expression element based on a third quantization coefficient and the second standard deviation; determining the sequence number of the first Fresnel diffraction characteristic expression point in the forward discrete sequence, and taking the sequence number as a fourth expression element. Further, all the first expression vectors corresponding to the forward discrete sequences may be sequentially arranged according to rows to obtain a first fresnel diffraction characteristic expression matrix, and if the forward discrete sequences correspond to the L first expression vectors, the dimension of the first fresnel diffraction characteristic expression matrix is 。
In one possible implementation, for the first in the forward discrete sequenceDiscrete points->The first expression vector may be expressed as:
here, the length of the first expression vector is 4; the first expression element isThe local mean value of the expression point of the first Fresnel diffraction characteristic is embodied, and the expression point is +.>Representation ofFirst window interval parameter,/->I.e. a first number,/->Representing the maximum point value in the forward discrete sequence,/->Representing a first quantization coefficient; the second expression element isA local normal fitting standard deviation of the first Fresnel diffraction characteristic expression point is embodied, specifically, < >>Represents a first standard deviation,/->Representing the second quantization factor, ">Description of->Is a forward discrete sequence with the sequence number [ -degree ]>]Standard deviation of the normal distribution fitting result of all interval points, +.>I.e. a second number; the third expression element is->The window interval of the partial normal fitting is one time larger than that of the second expression element, and the partial normal fitting is carried out by +.>Represents the second standard deviation->A third quantized coefficient is represented and is used to represent,description of->Is a forward discrete sequence with the sequence number [ -degree ]>]Standard deviation of the normal distribution fitting result of all interval points, +.>I.e. a third number; the fourth expression element is->，/>Represents the number of sequences, embody->Sequence positions in the forward discrete sequence.
Further, when constructing the second fresnel diffraction characteristic expression matrix of the reverse discrete sequence, a manner similar to the manner of constructing the first fresnel diffraction characteristic expression matrix of the forward discrete sequence described above may be used to determine second fresnel diffraction characteristic expression points in the reverse discrete sequence, and then the second fresnel diffraction characteristic expression points are converted into second expression vectors to obtain the second fresnel diffraction characteristic expression matrix based on the second expression vectors; and, the second fresnel diffraction property expression points may be converted into second expression vectors in a manner similar to the determination of the first expression vectors described above, and the disclosure is not repeated here.
It should be understood that the first number, the second number, the third number, the first quantization coefficient, the second quantization coefficient, and the third quantization coefficient described above may be determined by one skilled in the art according to actual circumstances, which is not limited by the present disclosure. In addition, when a first expression vector corresponding to the first Fresnel diffraction characteristic expression point is determined, the characteristic of the local wave crest and wave trough curve can be extracted by adopting normal fitting, and the first quantization coefficient, the second quantization coefficient and the third quantization coefficient are combined to play roles in suppressing noise interference and accelerating calculation speed.
Next, in step 303, an average offset between the forward discrete sequence and the reverse discrete sequence may be determined based on a similarity between each first expression vector in the first fresnel diffraction property expression matrix and each second expression vector in the second fresnel diffraction property expression matrix.
According to an embodiment of the disclosure, each first expression vector and each second expression vector may be subjected to difference calculation to obtain a first difference vector of each first expression vector relative to each second expression vector, where each first difference vector includes a first difference element, a second difference element, a third difference element, and a fourth difference element; then, a second difference vector may be determined in the first difference vector, where the first difference element, the second difference element, and the third difference element of the second difference vector are all 0; then, the fourth difference element of each second difference vector can be used as a positive and negative sequence offset element; then, frequency statistics can be performed on all positive and negative sequence offset elements to determine a first offset element, wherein the first offset element is a positive and negative sequence offset element corresponding to the maximum frequency value; then, a second offset element may be determined among the positive and negative sequence offset elements based on the first offset element, where an absolute value of a difference value of the second offset element and the first offset element is less than a first threshold; then, a second average of the second offset elements may be determined and used as an average offset. Further, the first threshold may be determined by one skilled in the art according to the actual situation, which is not limited by the present disclosure.
For a better understanding of the above embodiments, the following description is made in connection with fig. 5. Fig. 5 is a similarity statistics schematic diagram illustrating an expression matrix according to an embodiment of the present disclosure.
Referring to fig. 5, in one possible implementation, the average offset may be determined by:
1) And traversing each first expression vector in the first Fresnel diffraction characteristic expression matrix Dx, and calculating the difference value between each first expression vector and all second expression vectors in the second Fresnel diffraction characteristic expression matrix Dz to obtain a difference value matrix. Here, if the Dx dimension isThe Dz dimension is->L difference matrixes are obtained, and the dimension of each difference matrix isAs shown in fig. 5. In fig. 5, (1) represents a first fresnel diffraction property expression matrix Dx of the forward discrete sequence, and each row represents a first expression vector corresponding to one first fresnel diffraction property expression point. The 1 st element (i.e. the first expression element) of the first expression vector represents the local mean value of the expression points, the 2 nd and 3 rd elements (i.e. the second expression element and the third expression element) represent the local normal fitting standard deviation of the expression points, and the 4 th element (i.e. the fourth expression element) represents the sequence number of the expression points The method comprises the steps of carrying out a first treatment on the surface of the (2) And (3) a second Fresnel diffraction characteristic expression matrix Dz representing an inverse discrete sequence, wherein a dx1 vector is differenced with each second expression vector in the Dz matrix, a dx2 vector is differenced with each second vector in the Dz matrix, and the like, so as to obtain a difference matrix in (3).
2) And counting all first difference vectors in all difference matrixes, and screening out vectors with all first three elements being 0 as second difference vectors to form a similarity expression vector difference matrix, referring to (4) in fig. 5. The first three elements of the first difference vector (or the second difference vector) represent the similarity of the expression vectors to each other in Dx and Dz, the closer the three elements are to 0, the more similar.
3) All elements in the fourth column of the similarity expression vector difference matrix are extracted as positive and negative sequence offset elements to form a positive and negative sequence offset vector, refer to (5) in fig. 5. Here, the positive and negative sequence offset element represents the sequence position offset between the expression points corresponding to the second expression vector.
4) Performing frequency histogram statistics on all positive and negative sequence offset elements in the positive and negative sequence offset vector to obtain a first offset element with highest occurrence frequency, and marking the first offset element asThen screening out all second offset elements in the positive and negative sequence offset vectors satisfying the following inequality (1) >：
（1）
Here the number of the elements is the number,representing a first threshold. Further, all second offset elements satisfying inequality (1) are statistically +.>The average value of (a) is the average offset, and is recorded as +.>，/>In decimal. The average offset reflects the sequence distance between the forward and reverse discrete sequences that needs to be moved to achieve optimal coincidence of the fresnel diffraction waveforms of the two sequences.
Referring back to fig. 3, next, in step S304, a compensation process may be performed on discrete points of the forward discrete sequence in the symmetric compensation area using the reverse discrete sequence based on the average offset. Here, the symmetric compensation region is a region between a first discrete point in the forward discrete sequence, which corresponds to the highest diffraction peak on the left side of the forward discrete sequence, and a second discrete point, which corresponds to the highest diffraction peak on the right side of the forward discrete sequence.
Fig. 6 is a schematic diagram illustrating a symmetric compensation region according to an embodiment of the present disclosure.
Referring to fig. 6, in determining the symmetric compensation area, a start and end position of the symmetric compensation area may be determined, the start position corresponding to a first discrete point and the end position corresponding to a second discrete point. As shown in fig. 6, the first two highest maximum points in the forward discrete sequence are the start and end positions of the symmetric compensation region, corresponding to the left highest diffraction peak and the right highest diffraction peak, respectively.
According to the embodiment of the disclosure, when the discrete points of the forward discrete sequence in the symmetric compensation area are compensated, each discrete point of the forward discrete sequence in the symmetric compensation area can be traversed, the local area with similar Fresnel diffraction waveforms in the reverse discrete sequence is used for compensation, and the value of the current discrete point of the forward discrete sequence is subjected to denoising updating. Specifically, for any one discrete point in the symmetric compensation region, the discrete point may be subjected to compensation processing by:
1) A first symmetric compensated local data matrix of the discrete points is determined. Here, in one possible implementation, the first of the forward discrete sequencesTwo sides of the discrete point>The discrete points are window ranges, which can be determined by the following first equation (2)>Is a first symmetric compensated local data matrix +.>：
（2）
Further, the method comprises the steps of,is +.>，/>Representing discrete points in the forward discrete sequence, Z +.>Representing discrete points in the inverse discrete sequence, +.>Representing the discrete point as the first +.>Discrete points->Representing window range values, ++>Represents the average offset, +.>Representing a rounding operation.
2) And performing decentering treatment on the first symmetrical compensation local data matrix in the column direction to obtain a second symmetrical compensation local data matrix. Here, the second symmetric compensated local data matrix may be obtained by subtracting the average value of each column of the first symmetric compensated local data matrix from each column element.
3) A symmetric compensated local covariance matrix is determined based on the second symmetric compensated local data matrix. Here, in one possible implementation, the symmetric compensated local covariance matrix may be determined by the following second equation (3)：
（3）
Further, the method comprises the steps of,is +.>，/>Representing a second symmetric compensated local data matrix, < >>Representation->Is a transposed matrix of (a).
4) And decomposing the eigenvalue of the symmetrical compensation local covariance matrix to obtain an eigenvector corresponding to the maximum eigenvalue. Here, the feature vector has dimensions of。
5) And multiplying the characteristic vector by a second symmetrical compensation local data matrix to obtain a deviation value vector. Here, the offset value vector，/>Representing feature vectors +_>Is +.>I.e. the offset vector comprises->The offset value element. Further, & gt, deviating value vector>The offset value element reflects the first of the forward discrete sequencesThe compensation of the discrete points takes place by +.>The local discrete points (i.e.)>Around the discrete point +.>Dots, and +.>Individual points) and the extent of deviation from the direction of change in the extension of the local fresnel diffraction waveform.
6) Denoising the first symmetrical compensation local data matrix based on the offset value vector to obtain a third symmetrical compensation local data matrix, and determining the gravity center vector of the third symmetrical compensation local data matrix. Here, the gravity center vector has a dimension of Comprising a first center of gravity element and a second center of gravity element. Further, each of the deviation value elements may be compared with a second threshold value to determine a noise element among the deviation value elements, where an absolute value of the noise element is greater than the second threshold value; then, row vectors in the first symmetrical compensation local data matrix corresponding to the noise element can be removed to obtain a third symmetrical compensation local data matrix; then, a third average value of the first column matrix elements of the third symmetrical compensation local data matrix can be determined, and the third average value is used as a first gravity center element; then, a third symmetrically compensated local data moment may be determinedAnd taking the fourth average value of the second column of matrix elements of the matrix as a second center element. Still further, the second threshold may be determined by one skilled in the art according to the actual situation, which is not limited by the present disclosure.
7) And compensating the discrete point based on the gravity center vector and the characteristic vector. Here, in one possible implementation, the discrete point can be determined by the following third equation (4)And (3) performing compensation treatment:
（4）
further, the method comprises the steps of,representing the first barycenter element->Representing a second concentric element, " >First feature element representing a feature vector, +.>And a second feature element representing a feature vector.
Referring back to fig. 3, next, in step S305, curve fitting may be performed on the compensated discrete points, and an edge position of the target object may be determined using a fitted curve obtained by the fitting to determine a target size of the target object based on the edge position.
According to embodiments of the present disclosure, the fitted curve may include a first fitted curve and a second fitted curve, and accordingly, the edge positions may include a left edge position and a right edge position.
Fig. 7 is a schematic diagram illustrating edge fitting according to an embodiment of the present disclosure.
Referring to fig. 7, the symmetric compensation region may be equally divided into a left edge fitting region and a right edge fitting region; then, curve fitting can be carried out on the compensated discrete points in the left edge fitting area to obtain a first fitting curve, and the left edge position is determined by utilizing the first fitting curve; then, curve fitting can be carried out on the compensated discrete points in the right edge fitting area to obtain a second fitting curve, and the right edge position is determined by utilizing the second fitting curve; then, the distance between the left edge position and the right edge position may be determined as the target size. Here, in one possible implementation, curve fitting may be performed by the following fourth equation (5):
（5）
Further, the method comprises the steps of,representing the number of sequences of discrete points +.>Representing the light intensity value +.>Representing the first fitting parameters, +.>Representing the second fitting parameters, +.>Representing the third fitting parameter, +.>Representing the fourth fitting parameter, +.>Representing a hyperbolic tangent function. It should be appreciated that the above-described manner of curve fitting is merely an example, and that a person skilled in the art may determine the specific manner of curve fitting according to the actual situation, for example, polynomial fitting may also be used.
According to the embodiment of the disclosure, inWhen the edge position of the target object is determined by using the fitted curve obtained by fitting, a first maximum value of a first derivative and a second maximum value of a second derivative of the fitted curve can be determined, and the number of target sequences corresponding to the first maximum value can be determined; then, the edge position of the target object may be determined based on the first maximum value, the second maximum value, and the target sequence number, in combination with the first calibration parameter and the second calibration parameter. Here, in one possible implementation, the edge position can be determined by the following fifth equation (6)：
（6）
Further, the method comprises the steps of,representing the number of target sequences, +.>Represents a first maximum, +.>Representing a second maximum, +.>Representing a first calibration parameter,/->Representing a second calibration parameter. Still further, the first calibration parameter and the second calibration parameter may be obtained by calibrating a standard of known dimensions for compensating for the exact position. In the related art, only the maximum position of the first derivative is generally used as the edge position, but the true edge position has deviated from the maximum position of the first derivative due to the influence of the fresnel diffraction which is reflected on the variation of the first derivative value and the second derivative value, and therefore, by compensating with the calibrated correction values of the first derivative and the second derivative, the effect of the fresnel diffraction is improved A more accurate edge position can be obtained.
According to the precise measurement method based on the Fresnel diffraction edge characteristics, through determining the average offset between the forward discrete sequence and the reverse discrete sequence of the projected light intensity signals and combining the reverse discrete sequence to compensate discrete points in the forward discrete sequence, the theoretical consistency of the Fresnel diffraction characteristics of the left edge and the right edge can be fully utilized, the original light intensity signals are symmetrically compensated, abrupt noise is effectively removed, the processed signal trend is more consistent with the Fresnel diffraction characteristics, a more accurate fitting curve is obtained to calculate the edge position of a target object, and when the fitting curve is utilized to calculate the edge position, calibration compensation is designed based on the influence of the Fresnel diffraction, so that the calculated edge position is more accurate.
Although a few embodiments of the present disclosure have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the disclosure, the scope of which is defined in the claims and their equivalents.
Claims (10)
1. A precise measurement method based on Fresnel diffraction edge characteristics is characterized by comprising the following steps:
Acquiring a forward discrete sequence and an inverse discrete sequence of a projection light intensity signal of a target object, wherein the forward discrete sequence and the inverse discrete sequence are in reverse order;
constructing a first Fresnel diffraction characteristic expression matrix of the forward discrete sequence and a second Fresnel diffraction characteristic expression matrix of the reverse discrete sequence;
determining an average offset between the forward discrete sequence and the reverse discrete sequence based on a similarity between each first expression vector in the first fresnel diffraction property expression matrix and each second expression vector in the second fresnel diffraction property expression matrix;
based on the average offset, performing compensation processing on discrete points of the forward discrete sequence in a symmetric compensation area by utilizing the reverse discrete sequence;
and performing curve fitting on the compensated discrete points, and determining the edge position of the target object by using a fitting curve obtained by fitting so as to determine the target size of the target object based on the edge position.
2. The method of precision measurement according to claim 1, wherein said constructing a first fresnel diffraction property expression matrix of the forward discrete sequence comprises:
Determining a first Fresnel diffraction characteristic expression point in the forward discrete sequence, wherein the first Fresnel diffraction characteristic expression point is a local extreme point corresponding to a peak or a trough in the forward discrete sequence;
and converting the first Fresnel diffraction characteristic expression point into the first expression vector so as to obtain the first Fresnel diffraction characteristic expression matrix based on the first expression vector.
3. The precision measurement method according to claim 2, wherein each first expression vector comprises a first expression element, a second expression element, a third expression element and a fourth expression element,
wherein said converting said first fresnel diffraction property expression point into said first expression vector comprises:
for any one first Fresnel diffraction characteristic expression point, determining a first average value of a first number of discrete points in the forward discrete sequence with the first Fresnel diffraction characteristic expression point as a center, and determining the first expression element based on a first quantization coefficient and the first average value;
performing normal distribution fitting on a second number of discrete points taking the first Fresnel diffraction characteristic expression point as a center in the forward discrete sequence to obtain a first standard deviation, and determining the second expression element based on a second quantization coefficient and the first standard deviation;
Performing normal distribution fitting on a third number of discrete points taking the first Fresnel diffraction characteristic expression point as a center in the forward discrete sequence to obtain a second standard deviation, and determining the third expression element based on a third quantization coefficient and the second standard deviation;
determining the sequence number of the first Fresnel diffraction characteristic expression point in the forward discrete sequence, and taking the sequence number as the fourth expression element.
4. The precise measurement method of claim 1, wherein the determining the average offset between the forward discrete sequence and the reverse discrete sequence based on the similarity between each first expression vector in the first fresnel diffraction property expression matrix and each second expression vector in the second fresnel diffraction property expression matrix comprises:
respectively carrying out difference calculation on each first expression vector and each second expression vector to obtain a first difference vector of each first expression vector relative to each second expression vector, wherein each first difference vector comprises a first difference element, a second difference element, a third difference element and a fourth difference element;
Determining a second difference vector in the first difference vector, wherein a first difference element, a second difference element and a third difference element of the second difference vector are all 0;
taking a fourth difference element of each second difference vector as a positive and negative sequence offset element;
performing frequency statistics on all positive and negative sequence offset elements to determine a first offset element, wherein the first offset element is a positive and negative sequence offset element corresponding to a frequency maximum value;
determining a second offset element in the positive and negative sequence offset elements based on the first offset element, wherein an absolute value of a difference value between the second offset element and the first offset element is smaller than a first threshold value;
and determining a second average value of the second offset element, and taking the second average value as the average offset.
5. The precision measurement method according to claim 1, wherein the symmetric compensation region is a region between a first discrete point in the forward discrete sequence corresponding to a left highest diffraction peak of the forward discrete sequence and a second discrete point corresponding to a right highest diffraction peak of the forward discrete sequence,
Wherein the compensating the discrete points of the forward discrete sequence in the symmetric compensation area by using the reverse discrete sequence based on the average offset comprises:
determining a first symmetric compensation local data matrix of any one discrete point in the symmetric compensation area;
performing decentering treatment on the first symmetrical compensation local data matrix in the column direction to obtain a second symmetrical compensation local data matrix;
determining a symmetric compensated local covariance matrix based on the second symmetric compensated local data matrix;
performing eigenvalue decomposition on the symmetrical compensation local covariance matrix to obtain an eigenvector corresponding to the maximum eigenvalue;
multiplying the feature vector by the second symmetrical compensation local data matrix to obtain a deviation value vector;
denoising the first symmetrical compensation local data matrix based on the deviation value vector to obtain a third symmetrical compensation local data matrix, and determining a gravity center vector of the third symmetrical compensation local data matrix;
and compensating the discrete point based on the gravity center vector and the characteristic vector.
6. The method of precision measurement according to claim 5, wherein said determining a first symmetric compensated local data matrix for the discrete point comprises:
The discrete point is determined by the following first equationIs a first symmetric compensated local data matrix +.>：
Wherein (1)>Representing discrete points in the forward discrete sequence, Z +.>Representing discrete points in the inverse discrete sequence, +.>Representing the discrete point as the first +.>Discrete points->Representing window range values, ++>Represents the average offset, +.>Representing rounding operations; wherein the determining a symmetric compensated local covariance matrix comprises: determining a symmetrically compensated local covariance matrix by the following second equation>：/>The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Representing a second symmetric compensated local data matrix, < >>Representation->Is a transposed matrix of (a).
7. The precise measurement method according to claim 6, wherein the offset value vector comprisesA bias value element, the centroid vector including a first centroid element and a second centroid element,
denoising the first symmetrical compensation local data matrix based on the offset value vector to obtain a third symmetrical compensation local data matrix, and determining a gravity center vector of the third symmetrical compensation local data matrix, wherein the denoising processing comprises the following steps:
comparing each deviation value element with a second threshold value to determine a noise element among the deviation value elements, wherein an absolute value of the noise element is greater than the second threshold value;
Removing row vectors in the first symmetrical compensation local data matrix corresponding to the noise element to obtain the third symmetrical compensation local data matrix;
determining a third average value of first column matrix elements of the third symmetrical compensation local data matrix, and taking the third average value as the first gravity center element;
determining a fourth mean value of the second column matrix elements of the third symmetrical compensation local data matrix, and taking the fourth mean value as the second center element, wherein the compensation processing for the discrete point comprises the following steps: the discrete point is calculated by the following third equationAnd (3) performing compensation treatment: />The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Representing the first barycenter element->Representing a second concentric element, ">First feature element representing a feature vector, +.>And a second feature element representing a feature vector.
8. The precision measurement method according to any one of claim 1 to 7, wherein the fitted curve comprises a first fitted curve and a second fitted curve, the edge positions comprise a left edge position and a right edge position,
the curve fitting is performed on the compensated discrete points, and the edge position of the target object is determined by using a fitting curve obtained by fitting, so as to determine the target size of the target object based on the edge position, which comprises the following steps:
Dividing the symmetrical compensation area into a left edge fitting area and a right edge fitting area;
performing curve fitting on the compensated discrete points in the left edge fitting area to obtain a first fitting curve, and determining the left edge position by using the first fitting curve;
performing curve fitting on the compensated discrete points in the right edge fitting area to obtain a second fitting curve, and determining the right edge position by using the second fitting curve;
a distance between the left edge position and the right edge position is determined as the target size.
9. The precision measurement method according to claim 8, wherein curve fitting is performed by the following fourth equation:the method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Representing the number of sequences of discrete points +.>Representing the light intensity value +.>Representing the first fitting parameters, +.>Representing the second fitting parameters, +.>Representing the third fitting parameter, +.>Representing the fourth fitting parameter, +.>Representing a hyperbolic tangent function.
10. The precise measurement method according to any one of claims 1 to 7, wherein the determining the edge position of the target object using the fitted curve obtained by fitting comprises:
Determining a first maximum value of a first derivative and a second maximum value of a second derivative of the fitted curve, and determining a target sequence number corresponding to the first maximum value; based on the first maximum value, the second maximum value and the target number of sequences,determining an edge position of the target object in combination with the first calibration parameter and the second calibration parameter, wherein the edge position is determined by the following fifth equation：/>The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Representing the number of target sequences, +.>Represents a first maximum, +.>Representing a second maximum, +.>Representing a first calibration parameter,/->Representing a second calibration parameter.
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