JP2015139126A - Correction formula calculation device, correction formula calculation method, inspection device and inspection method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a correction formula calculation device being capable of calculating correction formulae for performing highly accurate correction while suppressing an increase of the correction formulae and parameters included in the correction formulae.SOLUTION: A correction formula calculation device comprises: a detection section detecting a plurality of reference points related to a predetermined pattern in an image imaged with the predetermined pattern; a first calculation section 20 calculating an even-ordered polynomial expression representing components of a first direction of distortion generated in a planar manner in the image due to aberrations of lenses used for imaging on the basis of the plurality of reference points detected by the detection section; a second calculation section 22 calculating an odd-order polynomial expression of third order or more representing a coefficient of an even-ordered polynomial expression representing a distribution of the components of the first direction in a second direction different from the first direction; and a third calculation section 23 calculating correction formulae correcting the distortion on the basis of calculation results by the second calculation section.

Description

  The present invention relates to a correction formula calculation apparatus, a correction formula calculation method, an inspection apparatus, and an inspection method.

  In the picked-up image picked up by the image pickup unit, distortion due to aberration of the imaging lens occurs. This distortion affects measurement that requires high measurement accuracy, such as measurement of the length of a microscopic structure of the observation target, measurement of a remote observation target, and the like. For this reason, there has been proposed a method for obtaining sufficient measurement accuracy by correcting distortion caused by aberration of the imaging lens.

  In this regard, a distortion correction apparatus that corrects distortion of a captured image by capturing a lattice pattern and calculating a correction expression that corrects an aberration amount at each point of the captured image is known (Patent Document 1). reference.).

JP 2007-288724 A

  However, in the conventional distortion correction apparatus, in order to increase the accuracy of correction, there is a problem that the correction formula for performing correction and the parameters included in the correction formula increase.

  Accordingly, the present invention has been made in view of the above-described problems of the prior art, and calculates a correction formula for performing high-precision correction while suppressing an increase in the correction formula and parameters included in the correction formula. A correction formula calculation device, a correction formula calculation method, an inspection device, and an inspection method are provided.

According to one aspect of the present invention, in an image in which a predetermined pattern is captured, a detection unit that detects a plurality of reference points related to the predetermined pattern, and the plurality of reference points detected by the detection unit, A first calculation unit that calculates an even-order polynomial that expresses a first-direction component of distortion generated in a plane in the image due to aberration of a lens used for imaging; and a second direction different from the first direction. A second calculation unit that calculates a third-order or higher-order odd-order polynomial that represents a coefficient of the even-order polynomial that expresses the distribution of the component in the first direction; And a third calculation unit that calculates a correction formula to be corrected.
With this configuration, the correction formula calculation apparatus detects a plurality of reference points related to a predetermined pattern in an image obtained by capturing a predetermined pattern, and based on the detected plurality of reference points, the lens used for imaging is detected. An even-order polynomial that expresses a first-order component that expresses a first-direction component of distortion that occurs in a plane in an image due to aberration, and that expresses a distribution of the first-direction component in a second direction that is different from the first direction. A third-order or higher-order odd-order polynomial representing a coefficient is calculated, and a correction formula for correcting the distortion is calculated based on the calculated third-order or higher-order odd-order polynomial. As a result, the correction formula calculation apparatus can calculate a correction formula for performing highly accurate correction while suppressing an increase in the correction formula and parameters included in the correction formula.

According to one aspect of the present invention, in the correction formula calculation apparatus, a configuration in which the predetermined pattern is a lattice pattern may be used.
With this configuration, in the correction formula calculation apparatus, the predetermined pattern is a lattice pattern. Accordingly, the correction formula calculation apparatus can calculate a correction formula for performing highly accurate correction using the distortion of the pattern of the lattice.

One aspect of the present invention may be configured such that, in the correction formula calculation apparatus, the plurality of reference points are lattice points of a lattice corresponding to the lattice pattern.
With this configuration, in the correction formula calculation apparatus, the plurality of reference points are lattice points of the lattice corresponding to the lattice pattern. Thus, the correction formula calculation apparatus can generate a reference grid pattern having grid points and calculate a correction formula based on the generated reference grid pattern.

One embodiment of the present invention is the correction formula calculation apparatus, wherein the detection unit detects the plurality of reference points based on four lattice points of one lattice including a position corresponding to the center of the lens in the image. A configuration may be used.
With this configuration, the correction formula calculation apparatus detects a plurality of reference points based on four lattice points of one lattice including a position corresponding to the center of the lens in the image. Accordingly, the correction formula calculation apparatus can generate a reference grid pattern having the detected plurality of reference points as grid points, and can calculate a correction formula based on the generated reference grid pattern.

One aspect of the present invention is the correction formula calculation apparatus, wherein the detection unit calculates a distance between the lattice points in the image and corresponds to the center of the lens based on the calculated distance between the lattice points. A configuration that detects the position may be used.
With this configuration, the correction formula calculation apparatus calculates the distance between the lattice points in the image, and detects the position corresponding to the center of the lens based on the calculated distance between the lattice points. Thereby, the correction formula calculation apparatus can accurately detect the position of the center of distortion in the image accurately without using the information of the aberration characteristics of the lens used for imaging, and as a result, A correction formula for performing highly accurate correction can be calculated.

One aspect of the present invention is that in the correction formula calculation apparatus, the detection unit fits the distance data between the lattice points with an even-order polynomial, and the value of the even-order polynomial obtained as a result of the fitting is a pole. A configuration in which a position corresponding to the center of the lens is detected based on a position serving as a value may be used.
With this configuration, the correction formula calculation apparatus fits the distance data between the lattice points with an even-order polynomial, and based on the position where the value of the even-order polynomial obtained as a result of the fitting becomes an extreme value, the center of the lens The position corresponding to is detected. Thereby, the correction formula calculation apparatus can calculate a correction formula for performing correction with high accuracy by fitting.

One aspect of the present invention is the correction formula calculation apparatus, wherein the first calculation unit corresponds to the position of each grid point of the reference grid pattern based on the plurality of reference points and each grid point of the reference grid pattern. A configuration may be used in which the even-order polynomial is calculated using a difference between the position of each lattice point of the predetermined pattern as distortion due to aberration of the lens.
With this configuration, the correction formula calculation apparatus allows the position of each grid point of the reference grid pattern based on a plurality of reference points and the position of each grid point of the predetermined pattern corresponding to each grid point of the reference grid pattern. Is calculated as an even-order polynomial. Accordingly, the correction formula calculation apparatus can accurately detect distortion in an image without using information on the aberration characteristics of the lens used for imaging, and as a result, performs high-accuracy correction. The correction formula can be calculated.

In one aspect of the present invention, in the correction formula calculation apparatus, the first calculation unit fits distortion data due to aberration of the lens with an even-order polynomial, and calculates the even-order polynomial as a result of the fitting. A configuration may be used.
With this configuration, the correction equation calculation apparatus fits distortion data due to lens aberration with an even-order polynomial, and calculates an even-order polynomial as a result of the fitting. As a result, the correction formula calculation apparatus can represent distortion due to lens aberration by an even-order polynomial, and as a result, a correction formula for performing highly accurate correction can be calculated.

One aspect of the present invention is the correction formula calculation apparatus, wherein the second calculation unit fits the coefficient of the even-order polynomial by the odd-order polynomial of the third or higher order, and the third or higher-order is obtained as a result of the fitting. A configuration may be used that calculates an odd-order polynomial.
With this configuration, the correction formula calculation apparatus fits the coefficients of the even-order polynomials with the third-order or higher-order odd-order polynomials, and calculates third-order or higher-order odd-order polynomials as a result of the fitting. Thereby, in the correction formula calculation apparatus, the coefficients of the even-order polynomial can be collected as one odd-order polynomial, and as a result, an increase in the number of correction formulas can be suppressed.

One aspect of the present invention is to detect a plurality of reference points related to the predetermined pattern in an image in which a predetermined pattern is captured, and based on the plurality of reference points, the aberration of the lens used for the imaging An even-order polynomial that expresses an even-order polynomial that expresses a first-direction component of distortion generated in a plane in an image, and that expresses a distribution of the component in the first direction in a second direction different from the first direction 3 is a correction formula calculation method for calculating a third-order or higher-order odd-order polynomial representing a coefficient of the first and second, and calculating a correction formula for correcting the distortion based on the third-order or higher-order odd-order polynomial.
With this configuration, in the correction formula calculation method, a plurality of reference points related to a predetermined pattern are detected in an image obtained by capturing a predetermined pattern, and an image is obtained based on the aberration of the lens used for imaging based on the plurality of reference points. An even-order polynomial that expresses the first-direction component of the distortion that occurs in a plane in FIG. 2 is calculated, and represents the coefficient of the even-order polynomial that expresses the distribution of the first-direction component in the second direction different from the first direction A third-order or higher odd-order polynomial is calculated, and a correction formula for correcting distortion is calculated based on the third-order or higher odd-order polynomial. Thereby, in the correction formula calculation method, it is possible to calculate a correction formula for performing highly accurate correction while suppressing an increase in the correction formula and parameters included in the correction formula.

One aspect of the present invention includes a correction formula calculation device, an image correction unit that corrects an image to be inspected using the correction formula calculated by the third calculation unit of the correction formula calculation device, and the image correction And an inspection unit that inspects an image corrected by the unit.
With this configuration, the inspection apparatus corrects the image to be inspected using the correction formula, and inspects the corrected image. As a result, the inspection apparatus can perform a highly accurate inspection in addition to shortening the calculation time associated with the number of correction equations and the number of parameters being suppressed.

One embodiment of the present invention is an inspection method in which an image to be inspected is corrected using the correction formula calculated by a correction formula calculation method, and the corrected image is inspected.
With this configuration, in the inspection method, the image to be inspected is corrected using the correction formula, and the corrected image is inspected. Thereby, in the inspection method, in addition to shortening the calculation time associated with the number of correction formulas and the number of parameters being suppressed, highly accurate inspection can be performed.

  As described above, the correction formula calculation apparatus, the correction formula calculation method, the inspection apparatus, and the inspection method detect a plurality of reference points related to a predetermined pattern in an image obtained by capturing a predetermined pattern, and set the detected reference points as a plurality of reference points. Based on this, an even-order polynomial expressing a first direction component of distortion generated in a plane in the image due to the aberration of the lens used for imaging is calculated, and the first direction in a second direction different from the first direction is calculated. A third-order or higher-order odd-order polynomial representing a coefficient of an even-order polynomial expressing the component distribution is calculated, and a correction formula for correcting the distortion is calculated based on the calculated third-order or higher odd-order polynomial. Thereby, it is possible to calculate a correction formula and a correction formula for performing highly accurate correction while suppressing an increase in parameters included in the correction formula.

It is a figure which shows an example of a function structure of the correction formula calculation apparatus 1 which concerns on 1st Embodiment. It is a figure which shows an example of the pattern L imaged by the imaging part 2, and an example of the captured image P by which the pattern L was imaged. A pattern L imaged on the captured image P1, which is a lattice pattern CL1 distorted by pincushion aberrations and a pattern L imaged on the captured image P2, which is distorted by barrel aberrations It is a figure which shows CL2. When the pattern L in the tilted state is picked up by the image pickup unit 2, the pattern CL3 is rotated so that the example of the picked-up image P3 picked up and the pattern CL3 become the pattern CL4 picked up in the state not in the tilted state. It is a figure which shows an example of image P3 '. 6 is a flowchart illustrating an example of a procedure of processing performed in a control unit 6. FIG. It is a figure which shows an example of the pattern CL in the captured image P. FIG. It is a figure which shows an example of table | surface T1 which stored each grid point distance in each line of the pattern CL calculated by the grid point distance calculation part 14. FIG. It is a figure which shows an example of the line graph which plotted the distance between lattice points for every lattice point in row R1 of the pattern CL shown by FIG. It is a figure which shows an example of the graph which fitted the data of the distance between the lattice points for every lattice point in row R1 of the pattern CL shown by FIG. 7 using a quadratic polynomial. It is an example of the graph which plotted the minimum distance between lattice points for every column in pattern CL. It is a figure which shows an example of the pattern CL in the captured image P. FIG. It is a figure which shows an example of the captured image P which overlap | superposed the reference | standard grid pattern BL on the pattern CL. FIG. 13 is an enlarged view of an area ZA shown in FIG. 12. Among the aberration amounts calculated by the aberration amount calculation unit 18, the aberration amount Δx in the X-axis direction for each lattice point included in each column in the reference lattice pattern BL is set for each Y coordinate value indicating the position of each lattice point. It is a figure which shows the graph plotted by (1). It is a figure which shows Table T2 which described an example of each coefficient of the quadratic polynomial calculated as a result of fitting by the 1st calculation part. It is a figure which shows an example of the graph which plotted the coefficient a shown by 2nd column T2-2 of Table T2 for every X coordinate of 1st column T2-1. It is a figure which shows an example of the graph which plotted the coefficient b shown by the 3rd row | line | column T2-3 of Table T2 for every X coordinate of the 1st row | line | column T2-1. It is a figure which shows an example of the graph which plotted the coefficient c shown by 4th row | line | column T2-4 of Table T2 for every X coordinate of 1st row | line | column T2-1. It is a figure which shows an example of a function structure of the test | inspection apparatus 3 which concerns on 2nd Embodiment. It is a figure for demonstrating the outline of correction | amendment of the captured image by the image correction part 27. FIG.

<First Embodiment>
Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a diagram illustrating an example of a functional configuration of a correction formula calculation apparatus 1 according to the present embodiment. The correction formula calculation apparatus 1 is connected to the imaging unit 2 so as to be communicable. In the present embodiment, the correction formula calculation device 1 and the imaging unit 2 will be described as separate units. However, these components may be integrally configured as integrated hardware.

The correction formula calculation apparatus 1 calculates a correction formula for correcting distortion of a captured image captured by the imaging unit 2. Here, in the present embodiment, the distortion of the captured image is described as the distortion caused by the aberration caused by the imaging lens included in the imaging unit 2, but as another example, the distortion of the captured image is other than the imaging lens. Even when the distortion is caused by the influence of the optical system, it is possible to apply the same correction formula calculation processing as that of the present embodiment to the distortion having the same characteristics as the distortion caused by the aberration caused by the imaging lens. .
When calculating the correction formula, the correction formula calculation apparatus 1 acquires an image captured by the imaging unit 2 and captured by the grid pattern shown in FIG.

  FIG. 2A is a diagram illustrating an example of a pattern L imaged by the imaging unit 2. The pattern L is installed in an area where the image capturing unit 2 can capture an image, for example, by a user or a device. FIG. 2B is a diagram illustrating an example of a captured image P in which the pattern L is captured. As shown in FIGS. 2A and 2B, the pattern L is imaged as a lattice-like pattern CL that is distorted by the aberration caused by the imaging lens. The correction formula calculation apparatus 1 calculates a correction formula for correcting distortion of the captured image based on the pattern CL.

  With reference to FIG. 3A and FIG. 3B, the captured image P distorted by the aberration caused by the imaging lens will be described. 3A and 3B, the position (center corresponding position) CP corresponding to the center of the imaging lens on the captured image P is assumed to be positioned at the center of the image. Will be described as being located at the intersection. As the aberration caused by the imaging lens, there are pincushion aberration and barrel aberration.

  FIG. 3A is a diagram showing a pattern L1 captured on the captured image P1 and a lattice pattern CL1 distorted by pincushion aberration. The dotted line in FIG. 3A indicates the position of the lattice-like pattern PL1 that is imaged in an ideal case where there is no aberration due to the imaging lens. As shown in FIG. 3A, each lattice point of the lattice pattern CL1 distorted by pincushion aberration is farther away from the center corresponding position CP of the imaging lens than the lattice points of the pattern PL1. Displace as follows. As a result, the distance between the lattice points becomes long.

  FIG. 3B is a diagram showing a pattern L2 captured on the captured image P2 and a lattice pattern CL2 distorted by barrel aberration. The dotted line in FIG. 3B indicates the position of the grid pattern PL2 that is imaged when there is no aberration due to the imaging lens. As shown in FIG. 3B, each lattice point of the lattice pattern CL2 distorted by the barrel aberration is closer to the center corresponding position CP of the imaging lens than each lattice point of the pattern PL2. Displace. As a result, the distance between grid points is shortened.

A correction formula calculation apparatus 1 according to this embodiment shown in FIG. 1 includes an image acquisition unit 4, a control unit 6, a display unit 8, a storage unit 10, and an operation unit 11.
The control unit 6 includes a lens center detection unit 12, an aberration amount calculation unit 18, a first calculation unit 20, a second calculation unit 22, and a third calculation unit 23. Note that some or all of the functional units included in the control unit 6 are realized by, for example, a CPU (Central Processing Unit) (not illustrated) executing various programs stored in the storage unit 10. Also, some or all of the functional units included in the control unit 6 may be hardware functional units such as LSI (Large Scale Integration) and ASIC (Application Specific Integrated Circuit).

The imaging unit 2 captures an image of a lattice pattern.
The image acquisition unit 4 acquires an image captured by the imaging unit 2.
The lens center detection unit 12 includes a lattice point distance calculation unit 14 and a rotation correction unit 16.
The inter-grid point distance calculation unit 14 detects the lattice points of the distorted lattice pattern CL reflected in the captured image P acquired by the image acquisition unit 4, and calculates the inter-lattice point distance based on each detected lattice point. calculate. The distance between lattice points indicates the distance between two adjacent lattice points. The lens center detection unit 12 detects the center-corresponding position CP of the imaging lens in the captured image P based on the inter-lattice distance calculated by the inter-lattice distance calculation unit 14.

  Based on the grid point distance calculated by the grid point distance calculation unit 14, the rotation correction unit 16 and the X axis or Y axis on the image sensor of the imaging unit 2 and the row direction of the pattern L that is the imaging target or A rotation determination process is performed to determine whether or not the column direction is parallel at the time of imaging. In the present embodiment, a state in which these are not parallel is referred to as an inclined state.

Here, the rotation determination process will be described with reference to FIGS. 4 (A) and 4 (B).
FIG. 4A is a diagram illustrating an example of a captured image P3 captured when the pattern L in the tilted state is captured by the imaging unit 2. When the rotation correction unit 16 performs the rotation determination process and determines that the inclination is based on the distance between the lattice points of the pattern CL3 shown in the captured image P3, as illustrated in FIG. An image P3 ′ obtained by rotating the pattern CL3 so as to be a pattern CL4 captured in a state other than the tilt state is generated.

  FIG. 4B is a diagram illustrating an example of an image P3 ′ obtained by rotating the pattern CL3 so that the pattern CL3 is a pattern CL4 that is captured in a state that is not in an inclined state. After generating the image P3 ', the rotation correction unit 16 causes the lens center detection unit 12 to re-detect the center corresponding position CP. Note that the rotation correction unit 16 performs the rotation determination process, and when it is determined that the pattern CL3 is not in the tilted state, the rotation process is not performed as it is.

  The aberration amount calculation unit 18 generates a reference lattice pattern BL based on the center corresponding position CP detected by the lens center detection unit 12. The reference lattice pattern BL is a pattern that is used as a reference for correcting the aberration caused by the imaging lens of the captured image P, and has a lattice point corresponding to each lattice point of the pattern CL. The aberration amount calculation unit 18 calculates the aberration amount at each lattice point of the captured image P based on the generated reference lattice pattern BL. The aberration amount at each lattice point is an amount representing the magnitude of the influence (distortion) of the aberration caused by the imaging lens at each lattice point. Each grid point of the reference grid pattern BL is an example of a plurality of reference points.

Based on the aberration amount calculated by the aberration amount calculation unit 18, the first calculation unit 20 uses a first approximate expression that represents the aberration of the imaging lens along each row and each column of the reference grating pattern BL. Calculate as
The second calculation unit 22 is based on the first approximate expression calculated by the first calculation unit 20, and represents the aberration of the imaging lens along each row and the imaging lens along each column. A second approximate expression is calculated, in which the expressions representing the aberrations are summarized as expressions representing the aberration of one imaging lens for each row and column.

The third calculation unit 23 calculates a correction formula for correcting distortion caused by the aberration caused by the imaging lens based on the second approximate formula calculated by the second calculation unit 22. And the 3rd calculation part 23 outputs the information showing the calculated correction formula to the memory | storage part 10, and makes it memorize | store it. In addition, the third calculation unit 23 may output and display information representing the calculated correction formula on the display unit 8.
The display unit 8 is configured using, for example, a liquid crystal display panel or an organic EL (ElectroLuminescence) display panel, and displays various types of information.
The operation unit 11 includes, for example, various operation buttons, operation keys, a touch panel, and the like that receive instructions from the user.

  The storage unit 10 includes, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), an EEPROM (Electrically Erasable Programmable Read-Only Memory), and a ROM (Read-Only Memory). Various information and programs processed by the control unit 6, information indicating the position XY of the imaged point determined in advance, and the like are stored. Further, the storage unit 10 stores information representing a correction formula calculated by the control unit 6. The storage unit 10 may be an external storage device connected by a digital input / output port such as a USB (Universal Serial Bus) instead of the one built in the correction formula calculation apparatus 1.

With reference to FIG. 5, an example of a procedure of processing performed in the control unit 6 will be described. FIG. 5 is a flowchart illustrating an example of a procedure of processing performed in the control unit 6.
First, the control unit 6 acquires the captured image P from the image acquisition unit 4 (step S100). Next, the inter-grid point distance calculation unit 14 calculates the inter-lattice distance (step S110).

With reference to FIG. 6, the process of calculating the distance between grid points will be described. FIG. 6 is a diagram illustrating an example of the pattern CL in the captured image P. For convenience of explanation, symbols R1 to R6 are given to the rows of the pattern CL, and symbols C1 to C8 are given to the columns of the pattern CL.
In FIG. 6, an example of the pattern CL is shown as an 8-by-6 grid so that the entire pattern CL can be grasped. However, the actual number of rows and columns of the pattern L and the pattern CL are arbitrary It may be.

  The inter-grid point distance calculation unit 14 detects each lattice point of the pattern CL and calculates a distance between two adjacent lattice points. Specifically, the inter-grid point distance calculation unit 14 calculates the distance between the lattice point a and the lattice point b shown in FIG. 6 based on the coordinates on the captured image P of these lattice points. Calculated as an inter-distance H23. Similarly, the inter-grid point distance calculation unit 14 calculates the distance between the lattice points c and d shown in FIG. 6 based on the coordinates on the captured image P of these lattice points. Calculated as V34.

With reference to FIG. 7, the inter-grid point distance calculated by the inter-lattice distance calculation unit 14 will be described. FIG. 7 is a diagram illustrating an example of a table T1 that stores the distances between grid points in each row of the pattern CL calculated by the grid point distance calculation unit 14.
Each column in the table T1 indicates the distance between each lattice point for each row of the pattern CL, and indicates the position of the lattice using the column number. For example, the column “1” indicates the distance between the lattice points between the column C1 and the column C2 shown in FIG. In addition, as the symbol indicating each row of the pattern CL, the same symbol as the symbol shown in FIG. 6 (for example, the symbol “R1” indicating “first row”) is used. In addition, since the distance between lattice points corresponding to the pattern L actually used for calculation of the distance between lattice points is shown in the table T1, the number of rows and the number of columns are larger than those of the pattern CL shown in FIG. Many. The inter-grid point distance calculation unit 14 calculates the inter-grid point distances in each column of the pattern CL in the same manner as the inter-grid point distances in each row of the pattern CL shown in Table T1.

  After the inter-lattice distance calculation unit 14 calculates the inter-lattice distances in each row and each column of the pattern CL, the lens center detection unit 12 is based on the calculated inter-lattice distances in each row and each column of the pattern CL. Then, the minimum distance between grid points in each row and each column of the pattern CL is calculated (step S120). The minimum distance between grid points is the position of a point showing a minimum value in a curve indicated by a quadratic polynomial fitted to the data of the distance between grid points in each row and each column of the pattern CL. Note that the polynomial to be fitted to the data on the distance between lattice points may be a polynomial of another order instead of the quadratic polynomial. In addition, since the correction formula calculation apparatus 1 according to the present embodiment describes the case where the aberration due to the imaging lens is a pincushion type aberration, the minimum distance between lattice points is fitted to the above-described distance between lattice points data. It was a point showing a minimum value in the curve indicated by the second-order polynomial. As another example, when the aberration due to the imaging lens is barrel aberration, in the correction formula calculation apparatus 1, the minimum position between the lattice points is represented by a quadratic polynomial fitted to the data on the distance between lattice points described above. It becomes a point showing the maximum value in the curve.

With reference to FIG. 8 and FIG. 9, processing for detecting the minimum distance between lattice points will be described.
FIG. 8 is a diagram showing an example of a line graph in which the distance between lattice points is plotted for each lattice point in the row R1 of the pattern CL shown in FIG. Here, the horizontal axis of the line graph shown in FIG. 8 indicates the position between each grid point for each row of the pattern CL in the table T1 shown in FIG. Further, the vertical axis of the line graph shown in FIG. 8 indicates the distance between lattice points for each lattice point in the row R1 of the pattern CL shown in FIG.

  When the aberration due to the imaging lens is pincushion aberration, the distance between the lattice points becomes longer outside the center corresponding position CP. Therefore, the center corresponding position CP corresponds to the minimum distance between lattice points of the pattern CL in the captured image P. Here, as shown in the line graph of FIG. 8, the data shown in FIG. 7 looks like a quadratic function, but includes an error. In many cases, it is difficult to detect the position where the distance between the contacts is minimized. Therefore, the lens center detection unit 12 fits the data of the inter-lattice distance shown in FIG. 7 with a quadratic polynomial as shown in FIG. The lens center detection unit 12 fits the inter-grid point distance data shown in FIG. 7 with a quadratic or higher order even number polynomial instead of fitting with a quadratic polynomial as shown in FIG. May be.

  FIG. 9 is a diagram illustrating an example of a graph obtained by fitting data on the distance between lattice points in the row R1 of the pattern CL illustrated in FIG. 7 using a quadratic polynomial. As shown in FIG. 9, the lens center detection unit 12 calculates a position where the value of the fitted quadratic polynomial becomes a minimum, and detects the calculated position as the minimum position between the lattice points. Similarly to the row R1, the lens center detection unit 12 calculates the minimum distance between lattice points for each of all the rows and columns of CL.

After the minimum grid point distance position is calculated for each of all the rows and columns of the pattern CL, the rotation correction unit 16 captures the captured image P based on the calculated minimum grid point distance position. , A rotation determination process is performed (step S130).
The rotation determination process will be described with reference to FIG. FIG. 10 is an example of a graph in which the minimum position between grid points is plotted for each column in the pattern CL. Here, on the horizontal axis of the graph, symbols indicating the columns of the pattern CL are arranged in the order in which the columns are arranged. In addition, the vertical axis of this graph indicates the minimum distance between lattice points. The position of each lattice point distorted by the pincushion aberration on the captured image P is displaced so as to move away from the position corresponding to the center of the imaging lens. For this reason, when the pattern L is not in an inclined state, the minimum distance between grid points is the same position (excluding errors during measurement) in all columns. On the other hand, in the tilted state, the minimum position between the grid points is different for each column.

  Therefore, the rotation correction unit 16 can determine whether or not the pattern L is in an inclined state based on a graph in which the minimum position between grid points is plotted for each row and column. For example, the rotation correction unit 16 plots the minimum distance between grid points for each column of the pattern CL as shown in FIG. 10, and a straight line L1 indicated by a first-order polynomial fitted to the plotted data is a graph. It is determined whether or not it is parallel to a straight line (a first order polynomial with a slope of zero) representing the horizontal axis.

  Then, when the straight line indicated by the fitted first-order polynomial is tilted at an angle θ with respect to the X axis of the graph like the straight line L2, the rotation correction unit 16 takes a captured image based on the detected angle θ. The lattice-like pattern CL on P is rotated by an angle −θ, and an image in a state similar to the pattern CL4 captured in a state that is not in an inclined state as shown in FIG. 4B is generated. Then, the rotation correction unit 16 causes the lens center detection unit 12 to re-detect the minimum distance between lattice points based on the generated image. By this re-detection, the lens center detection unit 12 can detect the center-corresponding position CP on the captured image P with higher accuracy than when no re-detection is performed.

  If the rotation correction unit 16 determines that the pattern L is in an inclined state (step S130—Yes), the rotation correction unit 16 rotates the pattern CL on the captured image P (step S190), and the process proceeds to step S110 to calculate the distance between lattice points. Let the unit 14 recalculate the distance between grid points. Here, the rotation correction unit 16 rotates the pattern CL on the captured image P with the normal passing through the center corresponding position CP of the captured image P as a rotation axis. The detection of the center corresponding position CP is performed by the same process as step S140 described below. In the present embodiment, as a preferred example, the rotation correction unit 16 transitions to step S110 after step S190, but as another example, the rotation correction unit 16 transitions to step S120 after step S190. May be. On the other hand, when it is determined that the pattern L is not in the tilted state (No at Step S130), the lens center detecting unit 12 detects the center corresponding position CP based on the minimum distance between lattice points (Step S140).

  Specifically, the lens center detection unit 12 calculates the average value of the minimum distance between lattice points detected for each row and column. The lens center detection unit 12 is a straight line that passes through the minimum average grid point distance position in the row and is parallel to the Y axis of the captured image P, and a straight line that passes through the minimum average grid point distance position in the column. Then, the intersection point where the straight line parallel to the X axis of the captured image P intersects is detected as the center corresponding position CP. If the pattern CL is rotated in step S190 before the processing in step S140 is performed, the lens center detection unit 12 detects the center corresponding position CP detected in order to perform the rotation in step S140. It may be used instead of the corresponding position CP.

Next, the aberration amount calculation unit 18 calculates an aberration amount based on the center-corresponding position CP of the imaging lens on the captured image P detected by the lens center detection unit 12 (step S150).
Processing for calculating the aberration amount will be described with reference to FIGS. FIG. 11 is a diagram illustrating an example of a pattern CL in the captured image P.
The aberration amount calculation unit 18 detects a lattice including the center corresponding position CP detected by the lens center detection unit 12 from the captured image P.

  An alternate long and short dash line L3 illustrated in FIG. 11 indicates a straight line parallel to the X axis of the captured image P that passes through the average position between the average lattice points in the column calculated by the lens center detection unit 12. Also, an alternate long and short dash line L4 shown in FIG. 11 indicates a straight line parallel to the Y axis of the captured image P passing through the minimum average inter-grid point distance position of the row calculated by the lens center detection unit 12. The center corresponding position CP is the position of the intersection where the straight line L3 and the straight line L4 intersect.

  The aberration amount calculation unit 18 detects four lattice points constituting a minimum quadrangle including the center corresponding position CP, that is, a lattice constituted by the lattice points BP1 to BP4 shown in FIG. Then, the aberration amount calculation unit 18 calculates an average value of the distances between the four lattice points at the detected lattice points BP1 to BP4. The aberration amount calculation unit 18 generates a square having the calculated average value as one side. Then, the aberration amount calculation unit 18 overlaps the pattern CL in the captured image P so that the position of the center of gravity of the generated square matches the center corresponding position CP of the pattern CL. The aberration amount calculation unit 18 further repeatedly generates the reference lattice pattern BL shown in FIG. 12 over the pattern CL in the captured image P by repeatedly transferring the square in the X direction and the Y direction of the captured image P. . FIG. 12 is a diagram illustrating an example of the captured image P in which the reference lattice pattern BL is superimposed on the pattern CL. Here, the number of rows and the number of columns of the reference lattice pattern BL are the same as the number of rows and the columns of the pattern CL.

  Then, the aberration amount calculation unit 18 associates the lattice points closest to each other among the lattice points of the pattern CL and the lattice points of the reference lattice pattern BL. Note that the aberration amount calculation unit 18 uses other association methods instead of associating the lattice points closest to each other to associate each lattice point of the pattern CL and each lattice point of the reference lattice pattern BL. One-to-one correspondence may be used. The aberration amount calculation unit 18 calculates a difference value of coordinate values between the lattice points of the associated pattern CL and the reference lattice pattern BL as an aberration amount of each lattice point of the reference lattice pattern BL. Here, the aberration amount calculation unit 18 calculates the aberration amount for each of the X-axis direction and the Y-axis direction of the captured image P.

  FIG. 13 is an enlarged view of the area ZA shown in FIG. The lattice point A ′ located at the coordinates (x ′, y ′) on the captured image P of the pattern CL is connected to the lattice point A located at the coordinates (x, y) on the captured image P of the reference lattice pattern BL. The lattice points are displaced by the aberration caused by the image lens. Therefore, the aberration amount calculation unit 18 determines the displacement amounts Δx = f (x, y) of the x coordinate and the y coordinate between the lattice point A (x, y) and the lattice point A ′ (x ′, y ′). ), Δy = g (x, y) is calculated as an aberration amount. The aberration amount calculation unit 18, for example, based on the coordinate value of the point A ′ (x ′, y ′) and the coordinate value of the point A (x, y), as shown in the following formula (1), the aberration amount Δx And an aberration amount Δy is calculated.

Note that the aberration amount between the lattice point A (x, y) and the lattice point A ′ (x ′, y ′) is not calculated as a difference value of coordinate values, but by other coordinate conversion or the like. The resulting value may be used.
After the aberration amount is calculated by the aberration amount calculation unit 18, the first calculation unit 20 represents an aberration due to the imaging lens along each row and each column of the reference grating pattern BL based on the calculated aberration amount. Is calculated as a first approximate expression (step S160).

  With reference to FIG. 14, a process for calculating an expression representing the aberration caused by the imaging lens will be described. FIG. 14 shows the aberration amount Δx in the X-axis direction for each lattice point included in each column in the reference lattice pattern BL among the aberration amounts calculated by the aberration amount calculation unit 18, and indicates the position of each lattice point. It is a figure which shows the graph plotted for every Y coordinate value. The shape of each line graph shown in FIG. 14 represents the shape of distortion caused by the aberration of the imaging lens on each column of the reference lattice pattern BL.

  The first calculation unit 20 fits an even-order polynomial to the line graph regarding the aberration amount Δx in the X-axis direction for each lattice point included in each column. The even-order polynomial is a second-order polynomial shown in Equation (2), but may be a polynomial of another order as long as it is an even-order polynomial such as a fourth or sixth order.

  FIG. 15 is a diagram illustrating a table T2 in which an example of each coefficient of the second-order polynomial calculated as a result of the fitting by the first calculation unit 20 is described. A first column T2-1 in Table T2 indicates an X coordinate indicating the position of each column of the reference lattice pattern BL. The second column T2-2 in Table T2 indicates the value of the coefficient a in the first approximate expression (Equation (1)) calculated for each column of the reference lattice pattern BL. A third column T2-3 of Table T2 indicates the value of the coefficient b in the first approximate expression calculated for each column of the reference lattice pattern BL. A fourth column T2-4 in Table T2 indicates the value of the coefficient c in the first approximate expression calculated for each column of the reference lattice pattern BL.

  As described above, the first calculation unit 20 calculates the first approximate expression for each column of the reference lattice pattern BL. Similarly, the first calculator 20 calculates a first approximate expression for each row of the reference lattice pattern BL. Note that the number of first approximate expressions increases in the same manner as the number of rows and columns of the pattern L to be imaged increases.

Therefore, the control unit 6 uses the second calculation unit 22 to calculate a second approximate expression in which the first approximate expressions are combined into one for the rows of the reference lattice pattern BL and one for the columns. .
After the first approximate expression is calculated by the first calculation unit 20, the second calculation unit 22 calculates the second approximate expression based on each coefficient of the calculated first approximate expression (step S170). Specifically, the second calculator 22 calculates the coefficients a, b, and c shown in the second column T2-2, the third column 2-3, and the fourth column 2-4 of the table T2 shown in FIG. Are each calculated as a function of the X coordinate on the captured image P. Here, the process of calculating the second approximate expression will be described with reference to FIGS.

  FIG. 16 is a diagram illustrating an example of a graph in which the coefficient a shown in the second column T2-2 of the table T2 is plotted for each X coordinate of the first column T2-1. As illustrated in FIG. 16, the coefficient a of the quadratic term included in the first approximate expression for each column of the reference lattice pattern BL behaves as a linear function with respect to the X coordinate on the captured image P. FIG. 17 is a diagram illustrating an example of a graph in which the coefficient b shown in the third column T2-3 of the table T2 is plotted for each X coordinate of the first column T2-1. As shown in FIG. 17, the coefficient b of the first-order term included in the first approximate expression for each column of the reference grid pattern BL behaves as a linear function with respect to the X coordinate on the captured image P.

  FIG. 18 is a diagram illustrating an example of a graph in which the coefficient c shown in the fourth column T2-4 of the table T2 is plotted for each X coordinate of the first column T2-1. As illustrated in FIG. 18, the coefficient c of the 0th-order term included in the first approximate expression for each column of the reference lattice pattern BL behaves as a cubic function with respect to the X coordinate on the captured image P.

  For example, the second calculation unit 22 fits the graph shown in FIG. 16 with a cubic polynomial including a linear function, and calculates each coefficient included in the fitted cubic polynomial. Note that the second calculation unit 22 may perform fitting with an odd-order polynomial of 5th order or higher instead of fitting with a third-order polynomial for this calculation.

  For example, the second calculation unit 22 fits the graph illustrated in FIG. 17 with a cubic polynomial including a linear function, and calculates each coefficient included in the fitted cubic polynomial. Note that the second calculation unit 22 may perform fitting with an odd-order polynomial of 5th order or higher instead of fitting with a third-order polynomial for this calculation. Further, for example, the second calculation unit 22 fits the graph shown in FIG. 18 with a cubic polynomial, and calculates each coefficient included in the fitted cubic polynomial. Note that the second calculation unit 22 may perform fitting with an odd-order polynomial of 5th order or higher instead of fitting with a third-order polynomial for this calculation.

  The second calculation unit 22 uses the third-order polynomial calculated by fitting the coefficients included in the first approximate expression corresponding to each row and each column of the reference lattice pattern BL, using Expression (3) and Expression (3). The second approximate expression summarized as in (4) is calculated.

  After the second approximate expression is calculated by the second calculation unit 22, the third calculation unit 23 calculates a correction formula based on the second approximate expression. Here, the X coordinate of an arbitrary point C on the captured image P before correcting the aberration due to the imaging lens is Xn, and the X coordinate of the point C ′ on the captured image P after correcting the aberration with respect to this point C If X is Xm, the aberration at that point is expressed by Equation (5) using the second approximate equation.

  Formula (6) is obtained by rearranging Formula (5) with Xm. The third calculation unit 23 calculates Expression (6) as a correction expression related to the X-axis direction.

  Similarly, the third calculation unit 23 calculates Expression (7) as a correction expression regarding the Y-axis direction.

  In this embodiment, the case where the aberration due to the imaging lens is pincushion aberration has been described, but the same processing can be performed when the aberration due to the imaging lens is barrel aberration. In this case, in the captured image, each lattice point of the lattice pattern distorted by barrel aberration is displaced so as to approach the center corresponding position CP of the imaging lens. Therefore, in this case, each functional unit of the control unit 6 detects the maximum inter-grid point distance position instead of the minimum inter-grid point distance position, and the center corresponding position based on the detected maximum inter-grid point distance position. The configuration is such that the CP is detected, and the subsequent processing is the same as in this embodiment.

  In addition, each functional unit of the control unit 6 calculates a correction formula for each of the X-axis direction and the Y-axis direction on the captured image P, but instead of this, a correction formula for only the X-axis direction or the Y-axis direction is used. It may be calculated. In addition to the correction equations for the X-axis direction and the Y-axis direction on the captured image P, each functional unit of the control unit 6 further has a correction equation for another direction different from the X-axis direction and the Y-axis direction. It may be calculated. In that case, as an example, the correction formula calculation apparatus 1 replaces the captured image P obtained by capturing the grid pattern CL with the captured image obtained by capturing the triangular lattice, and the X-axis direction and the Y-axis direction. A correction formula for another different direction is calculated.

  As described above, the correction formula calculation apparatus 1 according to the first embodiment detects a plurality of reference points related to a predetermined pattern in the captured image P obtained by capturing the predetermined pattern, and detects the plurality of detected reference points. Based on the above, for at least one first direction among a plurality of different directions, coefficients of a plurality of even-order polynomials representing distortion due to aberration of the lens used for imaging are calculated, and the first direction among the plurality of directions is calculated. A third-order or higher-order odd-order polynomial representing coefficients of a plurality of even-order polynomials is calculated in a second direction different from the above, and a correction equation for correcting the distortion is calculated based on the calculated third-order or higher odd-order polynomial. calculate. As a result, the correction formula calculation apparatus 1 can calculate a correction formula for performing highly accurate correction while suppressing an increase in the correction formula and parameters included in the correction formula.

In the correction formula calculation apparatus 1, the predetermined pattern is a lattice pattern. Thereby, the correction formula calculation apparatus 1 can calculate a correction formula for performing highly accurate correction using the distortion of the pattern of the lattice.
In the correction formula calculation apparatus 1, the plurality of reference points are lattice points of the lattice corresponding to the lattice pattern. Accordingly, the correction formula calculation apparatus 1 can generate a reference grid pattern having the grid points and calculate a correction formula based on the generated reference grid pattern.
Further, the correction formula calculation apparatus 1 detects a plurality of reference points based on four grid points of one grid including the center corresponding position CP in the captured image P. Accordingly, the correction formula calculation apparatus 1 can generate a reference grid pattern BL having a plurality of detected reference points as grid points, and can calculate a correction formula based on the generated reference grid pattern BL.

  In addition, the correction formula calculation apparatus 1 calculates the distance between the lattice points in the captured image P, and detects the center corresponding position CP based on the calculated distance between the lattice points. The position of the center of distortion in the captured image P is accurately detected without requiring details of the system. As a result, the correction formula calculation apparatus 1 can accurately detect the position of the distortion center in the image accurately without using the information on the aberration characteristics of the lens used for imaging. A correction formula for performing highly accurate correction can be calculated.

  Further, the correction formula calculation apparatus 1 fits the distance data between the lattice points of the pattern CL with an even-order polynomial, and based on the position where the value of the even-order polynomial obtained as a result of the fitting becomes an extreme value, Corresponding position CP is detected. As a result, the correction formula calculation apparatus 1 can calculate a correction formula for performing correction with high accuracy by fitting.

  In addition, the correction formula calculation apparatus 1 includes a position between each lattice point of the reference lattice pattern BL based on a plurality of reference points and a position of each lattice point of the pattern CL corresponding to each lattice point of the reference lattice pattern BL. Is used as the distortion due to the aberration of the lens, and the coefficients of a plurality of even-order polynomials are calculated. Therefore, the distortion in the captured image P is accurately detected without requiring the details of the optical system used for imaging. As a result, the correction formula calculation apparatus 1 can accurately detect distortion in the image without using information on the aberration characteristics of the lens used for imaging. As a result, high-precision correction is performed. The correction formula for this can be calculated.

  Further, the correction formula calculation apparatus 1 fits distortion data due to lens aberration with an even-order polynomial, and calculates a plurality of even-order polynomial coefficients as a result of the fitting. Thereby, in the correction formula calculation apparatus 1, distortion due to lens aberration can be represented by a plurality of even-order polynomials. As a result, a correction formula for performing highly accurate correction can be calculated.

  In addition, the correction formula calculation apparatus 1 fits the coefficients of a plurality of even-order polynomials using a third-order or higher-order odd-order polynomial, and calculates a third-order or higher-order odd-order polynomial as a result of the fitting. Thereby, in the correction | amendment formula calculation apparatus 1, a some even-order polynomial can be put together as one even-order polynomial, As a result, it can suppress that the number of correction formulas increases.

Second Embodiment
Hereinafter, a second embodiment of the present invention will be described with reference to the drawings.
FIG. 19 is a diagram illustrating an example of a functional configuration of the inspection apparatus 3 according to the second embodiment. The inspection apparatus 3 according to the present embodiment includes the correction formula calculation apparatus 1, an image acquisition unit 26, an image correction unit 27, an inspection unit 28, a display unit 29, an operation unit 30, and a storage unit 31. The correction formula calculation device 1 and the imaging unit 2 are communicably connected.
The correction formula calculation apparatus 1 and the imaging unit 2 included in the inspection apparatus 3 according to the present embodiment are the same as those illustrated in FIG. 1 and will be described with the same reference numerals. In addition, the image acquisition unit 26, the display unit 29, the operation unit 30, and the storage unit 31 provided in the inspection device 3 are respectively similar functional units (the image acquisition unit 4 and the display unit 8) provided in the correction formula calculation device 1. The operation unit 11 and the storage unit 10) have the same functions, and may be configured as a functional unit common to the correction formula calculation apparatus 1.

In the present embodiment, the correction formula calculation apparatus 1 outputs the correction formula stored in the storage unit 10 to the image correction unit 27 in response to a request from the image correction unit 27 included in the inspection apparatus 3.
The image correction unit 27 reads the correction formula stored in the storage unit 10 of the correction formula calculation apparatus 1. In addition, the image correction unit 27 acquires the captured image P from the image acquisition unit 26. Then, the image correction unit 27 uses the correction formula read from the correction formula calculation device 1 to generate an image (corrected image) in which the distortion caused by the aberration due to the imaging lens in the acquired captured image is corrected. The image correction unit 27 outputs the generated corrected image to the inspection unit 28.

  Upon obtaining the corrected image from the image correction unit 27, the inspection unit 28 performs an inspection such as determining whether or not there is an abnormality on the surface of the work WK shown in the corrected image based on the corrected image. And the test | inspection part 28 outputs the information which shows the result of a test | inspection on the display part 29, and displays it. The workpiece WK is an example of an object to be inspected. For example, the workpiece WK is a plate sample such as a printer nozzle plate or a silicon wafer, but may be various other objects.

  With reference to FIG. 20A and FIG. 20B, correction of a captured image by the image correction unit 27 will be described. 20A and 20B are diagrams for explaining an outline of correction of a captured image by the image correction unit 27. FIG. The image correction unit 27 was not affected by the aberration at the points A1 and A2 of the image distorted due to the aberration by the imaging lens shown in FIG. 20A based on the equations (6) and (7). The positions B1 and B2 in the case are calculated. The image correction unit 27 performs this calculation by solving simultaneous equations based on the equations (6) and (7). The image correction unit 27 moves (converts) the points A1 and A2 of the image distorted by the aberration caused by the imaging lens to the positions B1 and B2 when not affected by the aberration as shown in FIG. To do. The image correction unit 27 performs this movement for all points in the acquired captured image, thereby correcting the captured image.

  As described above, the inspection apparatus 3 according to the second embodiment corrects an image to be inspected using the correction formula calculated by the correction formula calculation apparatus 1 and inspects the corrected image. As a result, the inspection apparatus 3 can perform a highly accurate inspection in addition to reducing the calculation time associated with the number of correction equations and the number of parameters being suppressed.

  In the correction formula calculation apparatus 1 described above, the center corresponding position CP is detected by the lens center detection unit 12, but instead, the center corresponding position CP is input from the operation unit 11 or the operation unit 30 by the user. The correction formula may be calculated based on the input center corresponding position CP.

  In addition, when it is determined in step S130 that the pattern CL on the captured image P is in an inclined state, the correction formula calculating apparatus 1 replaces the pattern CL on the captured image P with the pattern CL in step S190. These grid point coordinates may be subjected to rotational coordinate conversion based on the angle θ described above, and thereafter, the processing after step S110 may be performed based on the respective grid point coordinates subjected to the rotational coordinate conversion. Normally, a digital error occurs when the pattern CL is rotated on the captured image P. In this configuration, a method of rotating each grid point coordinate can be used as a method that does not cause the digital error. As a result, the correction formula calculation apparatus 1 can calculate a correction formula for performing correction with higher accuracy than when the pattern CL is rotated on the captured image P in step S190.

  Further, a program for realizing the function of an arbitrary component in the above-described apparatuses (for example, the correction formula calculation apparatus 1 and the inspection apparatus 3) is recorded on a computer-readable recording medium, and the program is stored in a computer system. You may make it read and execute. Here, the “computer system” includes hardware such as an OS (Operating System) and peripheral devices. “Computer-readable recording medium” means a portable disk such as a flexible disk, a magneto-optical disk, a ROM (Read Only Memory), a CD (Compact Disk) -ROM, or a hard disk built in a computer system. Refers to the device. Further, the “computer-readable recording medium” means a volatile memory (RAM: Random Access) inside a computer system that becomes a server or a client when a program is transmitted via a network such as the Internet or a communication line such as a telephone line. Memory that holds a program for a certain period of time, such as Memory).

In addition, the above program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the “transmission medium” for transmitting the program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.
Further, the above program may be for realizing a part of the functions described above. Further, the program may be a so-called difference file (difference program) that can realize the above-described functions in combination with a program already recorded in the computer system.

DESCRIPTION OF SYMBOLS 1 Correction formula calculation apparatus, 2 Imaging part, 3 Inspection apparatus, 4, 26 Image acquisition part, 6 Control part, 8, 29 Display part, 10, 31 Storage part, 11, 30 Operation part, 12 Lens center detection part, 14 Interstitial point distance calculation unit, 16 rotation correction unit, 18 aberration amount calculation unit, 20 first calculation unit, 22 second calculation unit, 23 third calculation unit, 27 image correction unit, 28 inspection unit

Claims (12)

A detection unit for detecting a plurality of reference points related to the predetermined pattern in an image obtained by capturing the predetermined pattern;
Based on the plurality of reference points detected by the detection unit, an even-order polynomial expressing a first direction component of distortion generated in a plane in the image due to the aberration of the lens used for the imaging is calculated. A first calculation unit;
A second calculation unit that calculates a third-order or higher-order odd-order polynomial that represents a coefficient of the even-order polynomial that expresses a distribution of components in the first direction in a second direction different from the first direction;
A third calculation unit that calculates a correction formula for correcting the distortion based on a calculation result by the second calculation unit;
A correction formula calculation apparatus comprising: The predetermined pattern is a lattice pattern,
The correction formula calculation apparatus according to claim 1. The plurality of reference points are lattice points of a lattice corresponding to the lattice pattern,
The correction formula calculation apparatus according to claim 2. The detection unit detects the plurality of reference points based on four lattice points of one lattice including a position corresponding to the center of the lens in the image.
The correction formula calculation apparatus according to claim 3. The detection unit calculates a distance between the lattice points in the image, and detects a position corresponding to the center of the lens based on the calculated distance between the lattice points.
The correction formula calculation apparatus according to claim 3 or 4. The detection unit fits the distance data between the lattice points with an even-order polynomial, and based on the position where the value of the even-order polynomial obtained as a result of the fitting is an extreme value, Detect the corresponding position,
The correction formula calculation apparatus according to claim 5. The first calculator is configured to determine a position between each grid point position of the reference grid pattern based on the plurality of reference points and each grid point position of the predetermined pattern corresponding to each grid point of the reference grid pattern. And calculating the even-order polynomial as a distortion due to the aberration of the lens,
The correction formula calculation apparatus according to any one of claims 3 to 6. The first calculation unit fits distortion data due to the aberration of the lens with an even-order polynomial, and calculates the even-order polynomial as a result of the fitting.
The correction formula calculation apparatus according to any one of claims 1 to 7. The second calculating unit fits the coefficient of the even-order polynomial by the odd-order polynomial of the third order or higher, and calculates the odd-order polynomial of the third order or higher as a result of the fitting.
The correction formula calculation apparatus according to any one of claims 1 to 8. A plurality of reference points related to the predetermined pattern are detected in an image obtained by capturing the predetermined pattern;
Based on the plurality of reference points, an even-order polynomial expressing a first direction component of distortion generated in a plane in the image due to aberration of the lens used for the imaging is calculated,
Calculating a third or higher order odd-order polynomial representing a coefficient of the even-order polynomial expressing a distribution of components in the first direction in a second direction different from the first direction;
Calculating a correction formula for correcting the distortion, based on the third-order or higher-order odd-order polynomial;
Correction formula calculation method. The correction formula calculation apparatus according to any one of claims 1 to 9,
An image correction unit that corrects an image to be inspected using the correction formula calculated by the third calculation unit of the correction formula calculation device;
An inspection unit for inspecting the image corrected by the image correction unit;
An inspection apparatus comprising: An image to be inspected is corrected using the correction formula calculated by the correction formula calculation method according to claim 10,
Inspecting the corrected image;
Inspection method.

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