Calibration method of displacement sensor

Abstract

To provide a calibration method of a displacement sensor capable of realizing high measurement accuracy, despite calibration work having a small number of test measurement, and not requiring complicating arithmetic processing.SOLUTION: In two-dimensional coordinates, an intersection point of an optical axis of a light source which irradiates a detection object with light, a surface including a principal plane of a light receiving lens which forms an image on a light receiving plane of a detection element by reflected light from the detection object, and the surface including the light receiving plane, is set as a base point, and a principal point of the light receiving lens is set as an original point. A mathematical model which shows a distance from the base point of the detection object, by a position in a first straight line in which an inclination angle becomes the angle formed by the optical axis of the light source and the principal plane, and shows the distance from the base point to an image forming position in the light receiving plane, by the position in a second straight line in which the inclination angle becomes the angle formed by the principal plane and the light receiving plane, is used. A parameter in a correlation equation of the distance from the detection object and the distance between the image forming position and the base point is calculated, based on the plurality of distances from the detection object acquired by test measurement through a filter obtained on the basis of any setting value of the distance between the image forming position and the base point.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a method for calibrating a displacement sensor that measures the distance / displacement (hereinafter referred to as "displacement") of a measurement object by triangulation.

[0002] Displacement sensors that calculate the displacement of a detection target object based on the reflected light from the detection target utilize the correlation between the distance to the detection target and the reflected light, but the parameters that indicate this correlation are obtained through calibration using a test object with a known distance. However, it is difficult to make the geometric relationship between the light source that irradiates the detection target and the detection unit that obtains the reflected light from the detection target, which are included in the displacement sensor, the same for all displacement sensors, and individual differences occur. Therefore, the calibration process requires test measurements of more than 10,000 points for each individual displacement sensor in some cases.

[0003] Therefore, JP 2022-128878 A (Patent Document 1) proposes a displacement sensor that enables high measurement accuracy to be achieved even in calibration work involving a small number of test measurement points. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent Publication No. 2022-128878 Summary of the Invention [Problem to be solved by the invention]

[0005] The displacement sensor disclosed in Patent Document 1 uses a mathematical model obtained from the relationship between the change in the imaging position of the reflected light in the detection unit and the distance between the light-projecting unit, which includes a light source, and the object to be detected in order to determine the distance between the light-projecting unit and the object to be detected, thereby enabling a significant reduction in the number of test measurement points in the calibration process.

[0006] However, in the mathematical model disclosed in Patent Document 1, the relationship between the distance to the detection object to be calculated and the measured image formation position is nonlinear. Therefore, although the number of test measurement points can be reduced, there is a problem that complex arithmetic processing is required to calculate the parameters indicating the correlation between the distance to the detection object and the image formation position of the reflected light.

[0007] Therefore, an object of the present invention is to provide a calibration method for a displacement sensor that enables high measurement accuracy even in test measurements with a small number of points and does not require complex arithmetic processing. [Means for solving the problem]

[0008] The calibration method for a displacement sensor according to the present invention uses a mathematical model in which the intersection point between the optical axis of a light source that irradiates light onto an object to be detected and a plane including a principal plane of a light receiving lens that images reflected light from the object to be detected on a light receiving plane of a detection element and a plane including the light receiving plane is used as a base point, the distance of the object to be detected from the base point is represented as a position on a first line in a two-dimensional coordinate system having the principal point of the light receiving lens as the origin, the tilt angle of which is the angle between the optical axis of the light source and the principal plane, and the distance from the base point to the image position on the light receiving plane is represented as a position on a second line in the two-dimensional coordinate system, the tilt angle of which is the angle between the principal plane and the light receiving plane.

[0009] Then, the distance to the object to be detected when the distance between the base point and the imaging position of the reflected light from the object to be detected by the light receiving lens of the detection element becomes an arbitrary set value is obtained by test measurement involving movement of the object to be detected, and parameters of a correlation equation between the distance to the object to be detected and the distance between the imaging position and the base point are calculated based on multiple distances to the object to be detected obtained by the test measurement, via a filter obtained based on the arbitrary set value of the distance between the imaging position and the base point.

[0010] The correlation equation may vary depending on the distance to the object to be detected.

[0011] The parameters of the correlation equation may be calculated using floating point numbers and then converted to a fixed point representation. Effect of the Invention

[0012] The calibration method for a displacement sensor according to the present invention uses a mathematical model in which the intersection point between the optical axis of a light source that irradiates light onto an object to be detected and a plane including the principal plane of a light-receiving lens that images reflected light from the object to be detected on the light-receiving plane of a detection element and a plane including the light-receiving plane is used as a base point, the distance of the object to be detected from the base point is represented as a position on a first line in a two-dimensional coordinate system with the principal point of the light-receiving lens as the origin, the tilt angle of which is the angle between the optical axis of the light source and the principal plane, and the distance from the base point to the image position on the light-receiving plane is represented as a position on a second line in the two-dimensional coordinate system, the tilt angle of which is the angle between the principal plane and the light-receiving plane. Therefore, the measurement accuracy of the displacement sensor can be increased even in test measurements with a small number of points.

[0013] Furthermore, the distance to the object to be detected when the distance between the imaging position and the base point becomes an arbitrary set value is obtained by test measurement involving movement of the object to be detected, and based on multiple distances to the object to be detected obtained by test measurement through a filter obtained based on the arbitrary set value of the distance between the imaging position and the base point, the parameters of the correlation equation between the distance to the object to be detected and the distance between the imaging position by the receiving lens at the receiving plane of the reflected light from the object to be detected and the base point can be calculated without the need for complex arithmetic processing. [Brief description of the drawings]

[0014] [Figure 1] 11 is a diagram illustrating a filter for calculating parameters of a correlation equation between the distance to a detection object and the distance between a base point and the position where light reflected from the detection object is focused by a light receiving lens on a light receiving plane. FIG. [Diagram 2] FIG. 2 is a schematic diagram showing the positional relationship of elements constituting a mathematical model. [Diagram 3] FIG. 2 is a diagram showing a mathematical model in two-dimensional coordinates. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] An embodiment of a method for calibrating a displacement sensor according to the present invention will be described. First, the mathematical model used in this embodiment will be described. In this mathematical model, as shown in Figure 2, the base point BP is the intersection of the optical axis AE of the light source E that irradiates light onto the detection object D, the plane SL that includes the principal plane of the light-receiving lens LR that images the reflected light from the detection object D onto the light-receiving plane SR of the detection element, and the plane SS that includes the light-receiving plane SR.

[0016] Then, the distance s from the base point BP of the object to be detected D is expressed as the position on a first line in a two-dimensional coordinate system with the origin O being the principal point OP, which is the intersection of the light receiving axis of the light receiving lens LR and the principal plane, and whose inclination angle with respect to the vertical axis is the angle θ (theta) between the optical axis AE of the light source E and the principal plane.

[0017] In addition, the distance t from the base point BP to the imaging position on the light-receiving plane SR is expressed as the position on a second line in the two-dimensional coordinate system, whose tilt angle with respect to the vertical axis is the angle φ (phi) between the principal plane and the light-receiving plane SR, and whose tilt direction with respect to the vertical axis is opposite to the tilt direction of the first line.

[0018] In FIG. 2, the subscript of the symbol D indicating the detection object indicates the number of the test measurement described later. That is, in FIG. 2, the detection object D1 is at the measurement position in the first (first) measurement, and the detection object Dk is at the measurement position in the kth measurement. Similarly, the subscript of the symbol s indicating the distance to the detection object (hereinafter referred to as the "calculation target distance") also indicates the number of the test measurement. That is, in FIG. 2, the calculation target distance s1 indicates the distance in the first (first) measurement, and the calculation target distance sk indicates the distance in the kth measurement. Furthermore, the subscript of the symbol t indicating the distance between the imaging position by the light receiving lens LR on the light receiving plane SR and the base point BP (hereinafter referred to as the "calculation source distance") also indicates the number of the test measurement. That is, in FIG. 2, the calculation source distance t1 indicates the distance in the first (first) measurement, and the calculation source distance tk indicates the distance in the kth measurement.

[0019] In a two-dimensional coordinate system with the origin O being the principal point OP of the light receiving lens LR, the horizontal direction is represented by the x coordinate, the vertical direction is represented by the y coordinate, and the first line is represented by y=ax+b and the second line is represented by y=cx+d, then the line connecting the position (x1, y1) on the first line and the position (x2, y2) on the second line corresponds to the reflected light from the detection object D to the light receiving plane SR, and passes through the origin O, which is the principal point OP of the light receiving lens LR. Therefore, from these geometric relationships, the mathematical model shown in the following formula (1) can be obtained. FIG. 3 shows an example of the mathematical model shown in formula (1) expressed in two-dimensional coordinates.

[0020]

number

[0021] In Fig. 3, the inclination of the first straight line is angle θ counterclockwise with respect to the vertical axis (y-axis), and the inclination of the second straight line is angle φ clockwise with respect to the vertical axis, i.e., the first straight line has a negative inclination and the second straight line has a positive inclination. However, the inclinations of the first straight line and the second straight line only need to be in the opposite direction. Therefore, the first straight line may have a positive inclination and the second straight line may have a negative inclination.

[0022] According to this mathematical model, the relationship between the reciprocal of the calculation target distance s and the reciprocal of the calculation source distance t is linear. In addition, a, b, c, d, θ, and φ, which determine the coefficients and constant terms on the right side, are fixed values ​​determined by the positional relationship between the light source, the light receiving lens, and the detection element. In addition, a, which is the slope of the first straight line, is -1 / tan θ, and c, which is the slope of the second straight line, is 1 / tan φ. Therefore, the unknowns in the correlation equation between the calculation target distance s and the calculation source distance t are b, d, θ, and φ. Therefore, the number of test measurements to obtain the parameters is theoretically four.

[0023] However, in FIG. 3, the relative positional relationship between a point on the second line corresponding to a point on the first line is fixed. Therefore, it is possible to draw the first line and the second line by measuring two points. That is, the number of test measurement points required to obtain the parameters is essentially two. However, in actual test measurement, taking into account the limits of measurement accuracy, it is preferable to have 10 or more measurement points.

[0024] Next, a procedure for calculating the parameters of the correlation equation used in this embodiment will be described. In this embodiment, a high-order polynomial with the inverse of the calculation source distance t as a variable (hereinafter referred to as "variable x") is used as the correlation equation between the calculation target distance s and the calculation source distance t, and the coefficients of each term of this high-order polynomial correspond to the parameters of the correlation equation.

[0025] The filter used to calculate the coefficients of each term of a high-order polynomial of the variable x, i.e., the parameters of the correlation equation, can be generated based on a matrix obtained by partial differentiation of each coefficient of the high-order polynomial, as shown in the following equation (2).

number

[0026] Equation (2) can be expressed as a simultaneous equation. For example, when expressed as a fourth-order polynomial, it can be expressed as a determinant shown in the following equation (3). In addition, in equation (3), y is the reciprocal of the distance s to be calculated.

number

[0027] Then, a determinant for calculating the coefficients of a high-order polynomial can be obtained from the determinant shown in equation (3). For example, when expressed as a fourth-order polynomial, the determinant shown in the following equation (4) can be obtained.

number

[0028] In the calibration process, the variable x, which is the reciprocal of the calculation source distance t, is set arbitrarily, so that the set value can be substituted for the variable x in formula (4). For example, if the calculation source distance t in the calibration process is set to have reciprocals of -3, -2, -1, 0, 1, 2, and 3, the inverse matrix of one item on the left side of formula (4) will be a matrix whose elements are all quantified, as shown as matrix 2a constituting filter 2 in Fig. 1.

[0029] The matrix including the variable y in the two items on the left side of equation (4) (matrix 1 shown in Fig. 1) can be divided into matrix 2b constituting filter 2, and a matrix whose element is only variable y, as shown in Fig. 1. By substituting a set value for variable x included in matrix 2b constituting filter 2, it becomes a matrix whose elements are all quantified.

[0030] As shown in Figure 1, by using the product of matrix 2a and matrix 2b, all of whose elements have been quantified, as a default filter 2, the coefficients of a high-order polynomial in which variable y indicating the detection target distance s is the inverse of the calculation source distance t as variable x, i.e., the parameters of the correlation equation between the detection target distance s and the calculation source distance t, can be easily calculated without the need for complex arithmetic processing.

[0031] The order of the correlation equation can be set appropriately taking into consideration the test measurement conditions of the calibration work and the displacement measurement conditions. It may be a linear equation. The equation including a filter for calculating the coefficient of the linear equation is shown below.

[0032]

number

[0033] In the calibration process for calculating the filter shown in equation (5), seven points, namely, −3, −2, −1, 0, 1, 2, and 3, are set as the variable x.

[0034] Test measurements are performed for each individual displacement sensor, but by determining in advance the setting values ​​of the variable x for which the test measurements are performed (in this embodiment, -3, -2, -1, 0, 1, 2, 3) and calculating the filter, it is not necessary to calculate the filter in the test measurements performed for each individual sensor, and it is possible to calculate the parameters of the correlation equation in a short time.

[0035] The order of the correlation equation may differ depending on the distance to the detection object D. For example, a sixth-order polynomial (sixth-order approximation) may be used in the range of distances from the detection object from -1 to 1, and a second-order polynomial (second-order approximation) may be used in the other ranges.

[0036] The correlation equation between the calculation target distance s and the calculation source distance t is stored in a storage device mounted on the displacement sensor and used. Then, in a calculation processing device mounted on the displacement sensor, calculation processing is performed to calculate the calculation target distance s from the calculation source distance t obtained by measurement, and in many cases, the calculation processing device performs processing using a fixed point. Therefore, it is preferable that the correlation equation is displayed in a format using a fixed point, taking into account the processing capacity of the calculation processing device mounted on the displacement sensor. On the other hand, a calculation processing device separate from the displacement sensor that performs processing using a floating point can be used to calculate the coefficients. Therefore, it is preferable that the parameters of the correlation equation are calculated by processing using a floating point, taking into account the accuracy of the calculated calculation basis value.

[0037] In addition, when the arithmetic processing device mounted on the displacement sensor has sufficient processing power to obtain the required measurement accuracy, the arithmetic processing device mounted on the displacement sensor may be used to calculate the parameters of the correlation equation.

[0038] Furthermore, if the accuracy and calculation time can be ensured, the filter may be calculated in a calculation processing device mounted on the displacement sensor. [Explanation of symbols]

[0039] 1 Matrix containing calculation basis values 2. Filters 2a, 2b Filter configuration matrices Optical axis of AE light source BP base point D. Object to be detected E light source LR receiving lens OP Principal point of receiving lens SL: The surface including the principal plane of the receiving lens SR receiving plane SS Surface including the light receiving plane s Distance from the base point of the object to be detected (calculated distance) t is the distance from the base point to the image position on the light receiving plane (the calculation source distance)

Claims

1. a point of intersection between an optical axis of a light source that irradiates light onto the detection object, a plane including a principal plane of a light-receiving lens that forms an image of reflected light from the detection object on a light-receiving plane of a detection element, and a plane including the light-receiving plane is used as a base point, and the distance of the detection object from the base point is expressed as a position on a first straight line whose inclination angle is the angle between the optical axis of the light source and the principal plane in a two-dimensional coordinate system having an origin at the principal point of the light-receiving lens; using a mathematical model that expresses the distance from the base point to an image position on the light receiving plane as a position on a second line whose inclination angle is an angle between the principal plane and the light receiving plane in the two-dimensional coordinate system; acquiring a distance to the detection object when a distance between an image position of the reflected light from the detection object on the light receiving plane formed by the light receiving lens and the base point becomes an arbitrary set value by performing a test measurement involving movement of the detection object; A method for calibrating a displacement sensor, characterized in that parameters of a correlation equation between the distance to the detection object and the distance between the imaging position and the base point are calculated based on multiple distances to the detection object obtained by the test measurement, via a filter obtained based on an arbitrary set value of the distance between the imaging position and the base point, for which the test measurement was performed.

2. 2. The method for calibrating a displacement sensor according to claim 1, wherein the correlation equation varies depending on a distance to the object to be detected.

3. 3. The method for calibrating a displacement sensor according to claim 1, wherein the parameters of the correlation equation are calculated using floating point numbers and then converted into a representation using fixed point numbers.

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