JPH06265611A - Magnetic-field measuring apparatus - Google Patents

Abstract

PURPOSE:To improve measuring accuracy by multiplying the correcting coefficients including the parameters corresponding to the inclination and the sensitivity of a magnetic sensor on the output from each magnetic sensor, and performing the correction. CONSTITUTION:The voltages from the magnetic field sensors (in general, Hall elements) of probes 6a, 6b and 6c are converted into the magnetic field values with a Gauss meter 8. A constant current is made to flow into a sample 9 to be measured from a stabilized Power supply 10. An operator 11 stores the magnetic field values from the Gauss meter 8. The operator 11 operates the correcting coefficients including the parameters corresponding to the inclination and the sensitivity of each magnetic field sensor based on the output from each magnetic field sensor obtained by forcibly applying the magnetic field in each directed direction of the magnetic field sensor. The output from each magnetic field sensor is multiplied by the computed correcting coefficient, and the correction is performed. A display device 12 is used for displaying the distribution of the magnetic field and for monitoring the measuring state.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a magnetic field measuring device,
In particular, it relates to a magnetic field measuring device for measuring a magnetic field in a two-dimensional space or a three-dimensional space.

[0002]

2. Description of the Related Art For example, a magnetic field measuring apparatus for measuring a magnetic field in a three-dimensional space is provided with three magnetic field sensors arranged in directions (x, y, z directions) orthogonal to each other. The magnetic field component in each direction is calculated from each output from the sensor, and the magnetic field in the three-dimensional space is measured.

[0003]

However, it has been pointed out that the measurement accuracy of the magnetic field measuring device having such a structure is not sufficient.

That is, as the magnetic field sensor, for example, a Hall element is used, and there is a case where there is a variation in sensitivity between the Hall elements and a sufficient measurement accuracy cannot be obtained.

Further, in the case of accurately detecting a magnetic field in the direction in which the Hall element is in charge, the Hall element must be arranged so as to be completely perpendicular to the direction, but for example, in that direction. However, there was a case in which sufficient measurement accuracy could not be obtained due to a slight inclination (arrangement with respect to the base).

Therefore, the present invention has been made under such circumstances, and an object of the present invention is to provide a magnetic field measuring apparatus capable of greatly improving the measurement accuracy. .

[0007]

In order to achieve such an object, the present invention is basically arranged such that at least two magnetic field sensors are arranged in different directions. In the magnetic field measuring device for measuring the magnetic field within the dimension determined in each of the directions from the output from, the correction means for performing the correction by multiplying the output from each of the magnetic field sensors by the correction coefficient, and A correction coefficient including each parameter corresponding to the inclination and sensitivity of the magnetic field sensor is calculated from the output from each magnetic field sensor obtained by forcibly applying the magnetic field in each direction, and the calculated value is corrected by the correction means. It is characterized in that it is provided with a computing means used as a coefficient.

[0008]

In the magnetic field measuring device having such a structure, first, the inclination of the magnetic field sensor is calculated from the output from each magnetic field sensor obtained by forcibly applying the magnetic field in each direction in which the magnetic field sensor is oriented. There is provided calculation means for calculating a correction coefficient including each parameter corresponding to the sensitivity.

That is, since the output corresponding to the number of magnetic field sensors used (the number of forced magnetic fields applied in different directions) is obtained for one magnetic field sensor, The squared number of outputs will be obtained.

On the other hand, the factors that impede the measurement accuracy for one magnetic field sensor are its inclination (one component in the case of a two-dimensional space, two components in the case of a three-dimensional space) and sensitivity (one component).
The number of correction components in all magnetic field sensors is the same as the number of outputs of the magnetic field sensors.

Therefore, it is possible to calculate a correction coefficient including an element that hinders measurement accuracy from the output of each magnetic field sensor.

Since the correction means performs the correction by multiplying the output from each magnetic field sensor by the correction coefficient calculated in this way, the measurement accuracy of the output is significantly improved. Will be able to.

[0013]

FIG. 2 is a schematic configuration diagram showing an embodiment of a magnetic field measuring apparatus according to the present invention. (A) is the figure seen from the x direction, (b) is the figure seen from the y direction. In each figure,
Reference numeral 1 is a base on which a measurement sample and a measuring device are installed, 2 is a measuring device base, 3 is a y-direction moving base, 4 is an x-direction moving base, 5a,
Reference numerals 5b and 5c are z-direction moving bases, and 6a, 6b and 6c are magnetic field measuring probes. Here, 5a and 6a are for x-direction magnetic field measurement, 5b and 6b are for y-direction magnetic field measurement, and 5c and 6c are z.
It is for directional magnetic field measurement. A magnetic field measuring element (magnetic field sensor) is embedded at the tip of the measuring probes 6a, 6b, 6c.

A hall element is usually used as a magnetic field measuring element (magnetic field sensor) embedded in the measuring probes 6a, 6b and 6c. As shown in FIG. 3, this element is formed of a thin plate (thickness d) rectangular parallelepiped semiconductor.
When a constant current J is applied in the opposing surface directions along the thin plate surface and a magnetic field H is applied in a direction perpendicular to the thin plate surface, a potential difference V is generated in the current and the magnetic field in the vertical direction (this phenomenon). Is called the Hall effect).

This potential difference V is

[0016]

[Equation 1]

It is expressed as follows, and is proportional to the strength H of the magnetic field.

Here, the proportional constant R _H is a value peculiar to a substance and is called a Hall coefficient. By measuring this potential difference, the magnetic field component in the direction orthogonal to the thin plate surface can be obtained.

The direction of the electric current is t, the direction perpendicular to the thin plate surface is n,
If the direction perpendicular to t and n is denoted by b, the rotation of the Hall element around the n direction does not affect the measurement. That is, the setting of the t or b direction is arbitrary, but it is necessary to accurately orient the n direction in the direction of the component to be measured.

Here, regarding the Hall element, for example,
Kyoritsu Shuppan Co., Ltd., Laboratory of Experimental Physics "Magnetic", edited by Satoshi Chikaku, June 1968 (first edition), pages 175-1
76, in detail.

The correction method of the embodiment of the present invention will be described in detail below. The explanation is (1) general theory of conversion rule of vector quantity by rotation of coordinate system (this corresponds to rotation or inclination of magnetic field measuring element), (2) rotation of magnetic field measuring element using Helmholtz coil (inclination) ) Angle measurement method, and (3) a method of correcting the inclination of the magnetic field measuring element to obtain an accurate magnetic field value.

(1) of vector quantity for rotation of coordinate system
A unit vector (referred to as a base vector) in the coordinate axis direction of a Cartesian coordinate system with a conversion rule is defined as e ₁ , e ₂ , and e ₃ (where subscripts 1, 2, and 3 correspond to x, y, and z directions). ). An arbitrary vector B can be expressed as follows using a basis vector.

[0023]

[Equation 2]

Here, B ₁ , B ₂ and B ₃ are called vector components. It is assumed that the transformation from the (e ₁ , e ₂ , e ₃ ) coordinate system to another orthogonal coordinate system (e ₁ ′, e ₂ ′, e ₃ ′) is given as follows.

[0025]

[Equation 3]

Since the matrix R is an orthogonal matrix, its inverse is a transposed matrix. Therefore, the equation (3) is changed to (e ₁ , e ₂ , e
Solving for ₃ ) gives the following equation.

[0027]

[Equation 4]

On the other hand, the components of the vector B are also transformed by the transformation of the coordinate system. That is, by substituting equation (4) into equation (2),

[0029]

[Equation 5]

Therefore, another orthogonal coordinate system (e ₁ ′,
e ₂ ′, e ₃ ′) of the vector B components (B ₁ ′, B ₂ ′,
B ₃ ′) is expressed as follows.

[0031]

[Equation 6]

If the (e ₁ , e ₂ , e ₃ ) system is (e ₁ ′,
If the conversion to the e ₂ ′, e ₃ ′) system is rotation (rotation angle θ) in the (x, y) plane as shown in FIG. 4A,
The transformation matrix R ₁ (θ) is as follows.

[0033]

[Equation 7]

If the transformation is shown in FIG. 3 (b) (z,
x) rotation in the plane (rotation angle φ), the transformation matrix R ₂
(Φ) is as follows.

[0035]

[Equation 8]

Then, the conversion R (θ, φ) when the conversions of (7) and (8) are sequentially performed are as follows.

[0037]

[Equation 9]

The direction of the basis vectors e ₁ , e ₂ , e ₃ is x,
It is possible to identify the direction of the magnetic field measuring element in the y and z directions and the vector B with the magnetic flux density. At this time, the rotation matrix of the magnetic field measurement element when the three directions of the measurement element are rotated by θ in the (x, y) plane and further rotated by the angle φ from the z axis (toward the new x direction after rotation). Is given by equation (9).

[0039] Accordingly, the true (x, y, z) direction of the magnetic flux density _{(B x, B y, B} z) When to, magnetic field measuring element (x, y) rotates θ in the plane, further z New x from axis
Flux density measurements false when the rotation angle φ in the direction _{(B x ', B y'} , B z ') relationship with is as follows.

[0040]

[Equation 10]

Equation (9) or (10) can be used to describe the rotation of the magnetic field measuring element measuring the magnetic field in the x or z direction, but the rotation of the magnetic field measuring element measuring the magnetic field in the y direction is Not enough to describe. I mean,
The second transformation z and rotation R ₂ (φ) in the x plane is y
This is because the magnetic field measuring element for measuring the directional magnetic field does not affect the measured value of the magnetic field because it only rotates in the bt plane shown in FIG.

Therefore, for the magnetic field measuring element for measuring the y-direction magnetic field, rotation in the z and y planes is used for the second conversion. That is, rotation (rotation angle φ) from the z axis to the y axis is taken as the second conversion R _2y .

[0043]

[Equation 11]

Therefore, the transformation R _y (θ, φ) obtained by sequentially performing the transformations of (7) and (11) is as follows.

[0045]

[Equation 12]

That is, the magnetic flux density measurement value (B _x ′, when the magnetic field measuring element rotates θ in the (x, y) plane and further rotates by the angle φ in the new y direction from the z axis.
The relation with B _y ′, B _z ′) is as follows.

[0047]

[Equation 13]

(2) Magnetic field measurement using Helmholtz coil
Method of Measuring Rotation Angle of Constant Element When circular coils having the same diameter as shown in FIG. 5 (a) are coaxially separated by a radius r and electric currents are passed in the same direction, the midpoints on the central axes of the two coils In the vicinity of O, a uniform magnetic field having a component only in the axial direction (A) is formed. This is called the Helmholtz coil. If the current x number of windings is I (ampere turn), the magnitude B of the magnetic flux density in the axial direction is

[0049]

[Equation 14]

Is given by Here, μ ₀ is the magnetic permeability of vacuum. When an electric current is passed counterclockwise when viewed from the upper side of the coil, the direction of the magnetic field is from the lower side to the upper side of the coil. The value B of the magnetic flux density at this time is positive.

FIG. 5 (b) is an external sketch of the Helmholtz coil case actually used. The Helmholtz coil is embedded in a cube C made of aluminum (nonmagnetic material). The center of the cube and the center O of the Helmholtz coil coincide with each other, and the axis A of the coil is placed perpendicular to the two opposing surfaces of the cube. Further, round holes 7a and 7b are provided in the aluminum cube so that the magnetic field measuring probe can be inserted in the axial direction of the Helmholtz coil and in the direction perpendicular to the axis.
When generating a magnetic field in the z direction, the hole 7a in the coil axial direction
Is directed in the z direction, and the coil is installed on the measurement sample installation base 1 of FIG. When a magnetic field is generated in the x (or y) direction, the hole 7b in the direction perpendicular to the coil axis is formed in the z direction,
The hole 7a in the coil axial direction is installed so as to face the x (or y) direction.

Using this coil, the inclination of the magnetic field measuring element for measuring the magnetic field in each of the x, y and z directions from the normal direction,
(Θ _x , φ _x ), (θ _y , φ _y ), (θ _z , φ _z ) can be obtained. However, it is assumed that the rotation of the magnetic field measuring element for measuring the magnetic fields in the x and z directions is described by Expression (9), and the rotation of the magnetic field measuring element for measuring the y direction magnetic field is described by Expression (12).

First, the axis of the coil is oriented in the x direction. The true magnetic flux density in the (x, y, z) direction near the center of the coil is (B, 0, 0). However, the direction of the current was determined so that B was positive. If the magnetic field from the x-direction magnetic field measuring element at this time is B _1x ′, from equation (10),

[0054]

[Equation 15]

It is

Here, ′ is the value of the magnetic flux density from the measuring device (false value), and S _x is the value indicating the sensitivity correction of the x-direction magnetic field measuring element. When the magnetic field measuring probe in the x direction is calibrated accurately, the value of S _x is 1, but a deviation from 1 indicates a calibration error. Similarly, the measuring magnetic fields B _2x ′ and B _3x ′ of the x-direction magnetic field measuring element when the axes of the coils are oriented in the y-direction and the z-direction are

[0057]

[Equation 16]

[0058]

[Equation 17]

It becomes

Here, the subscripts 1, 2 and 3 are x,
This means that the axes of the Helmholtz coils are oriented in the y and z directions. Further, the subscript x indicates the reading from the x-direction magnetic field measuring element. From the equations (15) to (17), the rotation angle (θ _x , φ _x ) of the x-direction magnetic field measuring element and the value of the sensitivity correction S _x can be obtained as follows.

[0061]

[Equation 18]

[0062]

[Formula 19]

[0063]

[Equation 20]

The inclinations θ _x and φ _x can be considered to be sufficiently small, usually not exceeding 10 °, and the inverse trigonometric function ar
It is defined that c tan takes the principal value (-π / 2 to π / 2). Similarly, measuring magnetic fields B _1y ′, B _2y ′ from the y-direction magnetic field measuring element when the axes of the coils are oriented in the x, y and z directions,
B _3y ′ can be expressed as follows using the equation (13).

[0065]

[Equation 21]

[0066]

[Equation 22]

[0067]

[Equation 23]

From the equations (21) to (23), the rotation angle (θ _y , φ _y ) of the y-direction magnetic field measuring element and the value of the sensitivity correction S _y can be calculated as follows.

[0069]

[Equation 24]

[0070]

[Equation 25]

[0071]

[Equation 26]

Similarly, the measurement magnetic fields B _1z ′, B from the z direction magnetic field measuring element when the axes of the coils are oriented in the x, y and z directions.
_2z and _B3z 'can be expressed as follows using the equation (10).

[0073]

[Equation 27]

[0074]

[Equation 28]

[0075]

[Equation 29]

From the equations (27) to (29), the rotation angle (θ _z , φ _z ) of the z-direction magnetic field measuring element and the value of the sensitivity correction S _z can be obtained as follows.

[0077]

[Equation 30]

[0078]

[Equation 31]

[0079]

[Equation 32]

Therefore, the rotation angle and sensitivity correction of each x-, y-, and z-direction magnetic field measuring element, (θ _x , φ _x ), S _x , (θ _y ,
φ _y ), S _y , (θ _z , φ _z ), S _z are expressed by equations (18) to (20),
It is given by (24) ~ (26), (30) ~ (32).

(3) Correct the accuracy by correcting the rotation angle of the magnetic field measuring element
A method for obtaining a good magnetic field value of the rotation angle and sensitivity correction of each x, y, z direction magnetic field measuring element obtained by the above method, (θ _x , φ _x ), S _x , (θ _y ,
A method of obtaining the measured value of the magnetic flux density with improved accuracy by using φ _y ), S _y , (θ _z , φ _z ), and S _z will be described.

[0082] the magnetic flux density of all components _{(B x, B y, B} z)
When the (true value) is applied, the magnetic flux density from the measuring element (false _{value) (B x ', B y} ', B z ') when to, x
The direction component can be obtained by using the equation (10), the y direction component can be obtained by using the equation (13), and the z direction component can be obtained by using the equation (10). When described collectively,

[0083]

[Expression 33]

The transformation matrix R (θ _x , φ _x , S _x ; θ _y ,
[phi] _y , _Sy ; [theta] _z , [phi] _z , _Sz ) is not generally an orthogonal matrix because the n-axes of each magnetic field measurement element are not always orthogonal to each other. Transformation matrix R (θ _x , φ _x , S _x ;
θ _y , φ _y , S _y ; θ _z , φ _z , S _z )
^{_{1 (θ x, φ x,}} S x; θ y, φ y, S y; θ z, φ z, S z) is represented as the true magnetic flux density _{(B x, B y, B} z) is measured magnetic flux density _{(B x ', B y'} , B z ') can be expressed as follows using.

[0085]

[Equation 34]

According to the equation (34), 3 from the magnetic field measuring element is obtained.
One of the values of the magnetic flux density and _{(B x ', B y'} , B z ') of the column,
By applying a 3 3 matrix R ~ ^1, it is possible to obtain accuracy improved magnetic flux density _{(B x, B y, B} z) of.
It should be noted that the matrix R ~ ¹ has six parameters (θ _x , φ _x , θ _y , φ _y , representing the inclination of each magnetic field measuring element from the normal direction).
θ _z , φ _z ) and three parameters of sensitivity correction (S _x , S _y ,
A total of 9 parameters of S _z ) are included. It has the same degrees of freedom as the 9 elements of the matrix,
Given the components, the nine parameters can be uniquely determined. Therefore, giving the value of each component of the matrix is equivalent to giving the nine parameters of the inclination of the magnetic field measuring element and the sensitivity correction.

FIG. 6 is a block diagram of the correction means and the like in the magnetic field measuring apparatus according to the present invention.

In addition to the configuration shown in FIG. 2, the apparatus has a Gauss meter 8 for converting the voltage from the magnetic field measuring element (generally a Hall element) of the probes 6a, 6b, 6c into a magnetic field value, and a constant measurement sample 9. Stabilized power supply 10 for passing current, calculator 11 for storing and calculating magnetic field values from the Hall element and Gauss meter (commercially available microcomputer can be used), displaying magnetic field distribution and measuring state And a display device 12 (for example, a cathode ray tube or a liquid crystal display device is used) for monitoring.

A flowchart of FIG. 1 shows a procedure for correcting the inclination or the difference in sensitivity of the magnetic field measuring element to obtain a magnetic field value with improved accuracy, using the above apparatus and the magnetic field correction method described above.

(1) First, the Helmholtz coil is connected to the stabilized current source 10, and x, y, z is applied to the point (x ₀ , y ₀ , z ₀ ).
Uniform magnetic field (B, 0,0), (0, B, 0),
(0,0, B) is generated. At that time, the magnetic field value (B _1x ′, each of the magnetic field measuring elements in the x, y, and z directions (hereinafter referred to as “elements”)
B _1y ′, B _1z ′), (B _2x ′, B _2y ′, B _2z ′), (B _3x ′, B
_3y ′, B _3z ′) is measured and stored in the _computer 11. However, the magnetic field value shall always be the one from which the contribution of the geomagnetism or the external magnetic field has been removed. For this purpose, the magnetic field when there is no magnetic field measurement sample (including the Helmholtz coil) is measured in advance by the element, and the value is subtracted from the subsequent magnetic field value. Since the spatial variation of the geomagnetism or the external magnetic field is gradual, it is possible to use the average value in a certain range. Hereinafter, the magnetic field value is assumed to be the value obtained by subtracting the value of the geomagnetism or the external magnetic field.

(2) Expressions (18) to (20) and (24) to (2
6), (30) to (32) are used to calculate x, y, z in the computer 11.
Rotation angle of directional element and parameters for sensitivity correction (θ _x ,
φ _x ), S _x , (θ _y , φ _y ), S _y , (θ _z , φ _z ), S _z are calculated and stored.

(3) The above nine parameters are converted into the equation (33).
And the transformation matrix R and its inverse matrix R ~ ¹ are substituted into
Calculate with and store.

The above is the preparation for setting the parameters for correcting the inclination and sensitivity of the element and for error correction. Next, the method of measuring the magnetic field value of the measurement sample and the error correction method will be described.

(4) The magnetic field measurement sample 9 is accurately set on the table 1 in a predetermined direction. At this time, when a current is applied to the sample, it is connected to the stabilized current source 10 and a predetermined current is applied.

(5) A set of points {(x _n , y _n , z _n ): n = 1, 2, ..., N} given in advance has x, y,
Each element in the z direction is moved, the magnetic field value from the element at that time is measured, and {(B _xn ′, B _yn ′, B _zn ′): n = 1,
2 ..., N} and stored in the computer 11.

(6) Magnetic field values from the device (B _xn ′, B _yn ′,
B _zn ′) is converted according to the equation (34) to obtain a magnetic field value (B _xn , B _yn , B _zn ) with improved accuracy and stored in the _computer .

(7) Using the corrected magnetic field value, the magnetic field distribution is visually displayed on the display device 12 or the corrected magnetic field value is output to another device.

As described above, according to the above-described embodiment, the output from each magnetic field sensor obtained by forcibly applying the magnetic field in each direction in which the magnetic field sensor is oriented corresponds to the inclination and sensitivity of the magnetic field sensor. There is provided a calculating means for calculating a correction coefficient including each parameter to be set.

That is, for one magnetic field sensor, an output corresponding to the number of magnetic field sensors used (the number of forced magnetic fields applied in different directions) can be obtained. The squared number of outputs will be obtained.

On the other hand, the factors that impede the measurement accuracy for one magnetic field sensor are its inclination (one component in the case of a two-dimensional space, two components in the case of a three-dimensional space) and sensitivity (one component).
The number of correction components in all magnetic field sensors is the same as the number of outputs of the magnetic field sensors.

Therefore, it is possible to calculate a correction coefficient including an element (sensor inclination and sensitivity difference) that hinders measurement accuracy from the output of each magnetic field sensor.

Since the correction means performs the correction by multiplying the output from each magnetic field sensor by the correction coefficient thus calculated, the measurement accuracy of the output is significantly improved. Will be able to.

In the above-mentioned embodiment, three magnetic field sensors oriented in directions orthogonal to each other are provided and the magnetic field measurement in the three-dimensional space is explained, but the present invention is not limited to this. That is, using two magnetic field sensors,
It goes without saying that it can also be applied to the case of measuring a magnetic field in a dimensional space.

Further, in the above-mentioned embodiment, the magnetic field sensors arranged in the respective directions are individually arranged, but the arrangement of one magnetic field sensor is moved (the direction is changed). It goes without saying that it may be configured so that it also serves as at least two other magnetic field sensors. In this case, there is an effect that the measurement accuracy can be sufficiently secured even if the moving mechanism has an accuracy error.

[0105]

As is apparent from the above description,
According to the magnetic field measuring device of the present invention, the accuracy of the magnetic field measurement can be significantly improved.

[Brief description of drawings]

FIG. 1 is a flowchart showing an embodiment of a magnetic field measuring apparatus according to the present invention.

2 is a schematic view of a magnetic field measuring apparatus according to the present invention, FIG.
Is a view as seen from the y direction, and (b) is a view as seen from the x direction.

FIG. 3 is a schematic view of a magnetic field measuring element (magnetic field sensor) used in the present invention.

4A and 4B are explanatory diagrams for performing a correction calculation of the magnetic field measuring apparatus according to the present invention, in which FIG. 4A is a diagram showing the rotation of a basis vector in the xy plane, and FIG. 4B is a basis in the zx plane. It is a figure showing the rotation of a vector.

5A and 5B are explanatory views of a forced magnetic field applied for correction calculation of the magnetic field measuring apparatus according to the present invention, FIG. 5A is a schematic view of a Helmholtz coil, and FIG. 5B is a schematic view showing a housing of the Helmholtz coil. is there.

FIG. 6 is a configuration diagram showing correction means and the like of the magnetic field measuring apparatus according to the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Stand for setting measurement sample and measuring instrument, 2 ... Measuring instrument base, 3 ... y-direction moving stand, 4 ... x-direction moving stand, 5a, 5
b, 5c ... Z-direction moving table, 6a, 6b, 6c ... Magnetic field measuring probe, D ... Hall element, d ... Hall element thickness, J
... current flowing through the hall element, H ... magnetic field applied to the hall element, V ... potential difference in the hall element, t ... direction of current, n
... directions perpendicular to the thin plate surface, b ... directions perpendicular to t and n, r ...
Radius of a circular coil, O ... midpoint on the central axes of two coils, A ... axial direction of Helmholtz coil, I ... current flowing in Helmholtz coil × number of windings (ampere turn),
C ... Aluminum casing, 7a, 7b ... Round hole provided in aluminum casing, 8 ... Gauss meter, 9 ... Measurement sample,
10 ... Stabilized power source, 11 ... Computing machine, 12 ... Display device.

Claims (1)

[Claims] 1. A magnetic field measuring apparatus in which at least two magnetic field sensors are arranged so as to be oriented in different directions, and a magnetic field within a dimension determined in each direction is measured from outputs from these magnetic field sensors. Compensation means for compensating by multiplying the output from the magnetic field sensor by a compensation coefficient, and the magnetic field from the output from each magnetic field sensor obtained by forcibly applying the magnetic field in each direction in which the magnetic field sensor is oriented. A magnetic field measuring apparatus comprising: a correction coefficient including a parameter corresponding to the inclination and sensitivity of the sensor, and a calculation means that uses the calculated value as a correction coefficient of the correction means.