CN113156354A - Non-orthogonal error measurement method for triaxial Helmholtz coil in unshielded environment - Google Patents
Non-orthogonal error measurement method for triaxial Helmholtz coil in unshielded environment Download PDFInfo
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Abstract
The invention belongs to the field of non-orthogonal error measurement of three-axis Helmholtz coils, in particular to a non-orthogonal error measurement method of three-axis Helmholtz coils in an unshielded environment under the condition that a background geomagnetic field exists in the unshielded environment.
Description
Technical Field
The invention belongs to the field of non-orthogonal error measurement of a triaxial Helmholtz coil, and particularly relates to a non-orthogonal error measurement method of a triaxial Helmholtz coil in an unshielded environment under the condition that a background geomagnetic field exists in the unshielded environment.
Background
The triaxial Helmholtz coil is an instrument and device widely applied to multiple subjects such as materials, electronics, biology, medical treatment, aerospace, chemistry, applied physics and the like because the triaxial Helmholtz coil can provide a uniform magnetic field in a certain region. One controls the current in the helmholtz coil so that the coil produces the desired magnetic field.
The single-shaft Helmholtz coil is composed of two current-carrying coils which are identical in structure, size and number of turns, coaxial and parallel, connected in series and have the same current flowing direction. The triaxial Helmholtz coil is formed by vertically arranging and combining three groups of uniaxial Helmholtz coils two by two. However, due to the limitation of the processing technology, non-orthogonal errors inevitably exist in the coils in the three axial directions, and particularly, error parameters of the three-axis helmholtz coil are changed under the action of long-distance transportation and external force, so that the non-orthogonal error angle of the three-axis helmholtz coil needs to be measured before each use.
CN102116852A discloses a method for measuring the orthogonality of a three-axis magnetic field coil through a magnetic field, which measures a combined field by reproducing the combination of magnetic fields in different directions of the magnetic axis and calculates the orthogonality between different magnetic axes of the three-axis magnetic field coil, but this method is only suitable for the environment of absolute no magnetism under the condition of electromagnetic shielding, and the method is no longer suitable for the case of the existence of a background magnetic field.
Disclosure of Invention
The invention aims to solve the technical problem of providing a triaxial Helmholtz coil non-orthogonal error measuring method in an unshielded environment, which is not only suitable for an absolutely nonmagnetic environment under an electromagnetic shielding condition, but also suitable for an unshielded environment in a geomagnetic field.
The present invention is achieved in such a way that,
a non-orthogonal error measuring method of a three-axis Helmholtz coil in an unshielded environment comprises the following steps:
the method comprises the steps of respectively introducing forward or reverse current into every two axial coils of a three-axis Helmholtz coil by utilizing a constant current source so as to reproduce a synthetic magnetic field under 4 conditions, recording data before and after the two coils generate 4 synthetic magnetic fields through a three-axis DC-SQUID magnetometer sensor, and calculating an included angle between the two axial coils according to the data before and after the 4 synthetic magnetic fields, wherein the 4 conditions comprise in sequence: the first step is as follows: constant current is respectively led into the two axial coils; the second step is that: fixing the current magnitude and direction of one axial coil unchanged, and changing the current direction of the other axial coil; the third step: fixing the current magnitude and direction of the axial coil changing the current direction in the second step, and changing the current direction of the other axial coil; the fourth step: and fixing the current magnitude and direction of the axial coil changing the current direction in the third step, and changing the current passing direction of the other axial coil.
Further, the included angle includes: the included angle alpha of the X-axis coil and the Y-axis coil, the included angle beta of the X-axis coil and the Z-axis coil and the included angle gamma of the Y-axis coil and the Z-axis coil.
Further, measuring the included angle α between the X-axis coil and the Y-axis coil comprises:
1a, fixing a three-axis DC-SQUID magnetometer sensor in a magnetic field uniform region of a three-axis Helmholtz coil at any random angle, and recording three axial outputs of the three-axis DC-SQUID magnetometer sensor as BXY-X0、BXY-Y0And BXY-Z0；
1b, respectively passing constant current I to an X axial coil and a Y axial coil of the triaxial Helmholtz coil by using a current source1And I2Reproducing a constant magnetic field BXAnd a constant magnetic field BYRecording the outputs of three axial coils of the sensor of the three-axis DC-SQUID magnetometer as BXY1-X、BXY1-YAnd BXY1-Z；
1c, keeping the current magnitude and direction of the X axial coil unchanged, changing the direction of the current introduced into the Y axial coil, keeping the magnitude unchanged, and reproducing the constant magnetic field BXAnd a constant magnetic field-BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY2-X、BXY2-YAnd BXY2-Z；
1d, keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the X-axis coil, keeping the magnitude unchanged, and reproducing the current constantlyConstant magnetic field-BXAnd a constant magnetic field-BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY3-X、BXY3-YAnd BXY3-Z；
1e, keeping the current magnitude and direction of the X axial coil unchanged, changing the direction of the current introduced into the Y axial coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY4-X、BXY4-YAnd BXY4-Z；
1f, calculating an included angle alpha between the X-axis coil and the Y-axis coil according to the following formula:
wherein:
M1＝(BXY1-X-BXY-X0)2+(BXY1-Y-BXY-Y0)2+(BXY1-Z-BXY-Z0)2
M2＝(BXY2-X-BXY-X0)2+(BXY2-Y-BXY-Y0)2+(BXY2-Z-BXY-Z0)2
M3＝(BXY3-X-BXY-X0)2+(BXY3-Y-BXY-Y0)2+(BXY3-Z-BXY-Z0)2
M4＝(BXY4-X-BXY-X0)2+(BXY4-Y-BXY-Y0)2+(BXY4-Z-BXY-Z0)2。
further, measuring the included angle β between the X-axis coil and the Z-axis coil comprises:
2a, three axial coils of the three-axis Helmholtz coil are not electrified, and three axial outputs of the three-axis DC-SQUID magnetometer sensor are recorded as BXZ-X0、BXZ-Y0And BXZ-Z0；
2b, respectively passing constant current I to an X axial coil and a Z axial coil of the triaxial Helmholtz coil by using a current source1And a constant current I3Reproducing a constant magnetic field BXAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ1-X、BXZ1-YAnd BXZ1-Z；
2c, keeping the current magnitude and direction of the X-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing the constant magnetic field BXAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ2-X、BXZ2-YAnd BXZ2-Z；
2d, keeping the magnitude and direction of the current of the Z-axis coil unchanged, changing the direction of the current introduced into the X-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ3-X、BXZ3-YAnd BXZ3-Z；
2e, keeping the current magnitude and direction of the X axial coil unchanged, changing the direction of the current introduced into the Z axial coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ4-X、BXZ4-YAnd BXZ4-Z；
2f, calculating an included angle beta of the X-axis coil and the Z-axis coil according to the following formula:
wherein:
N1＝(BXZ1-X-BXZ-X0)2+(BXZ1-Y-BXZ-Y0)2+(BXZ1-Z-BXZ-Z0)2
N2＝(BXZ2-X-BXZ-X0)2+(BXZ2-Y-BXZ-Y0)2+(BXZ2-Z-BXZ-Z0)2
N3＝(BXZ3-X-BXZ-X0)2+(BXZ3-Y-BXZ-Y0)2+(BXZ3-Z-BXZ-Z0)2
N4＝(BXZ4-X-BXZ-X0)2+(BXZ4-Y-BXZ-Y0)2+(BXZ4-Z-BXZ-Z0)2。
further, measuring the included angle γ between the Y-axis coil and the Z-axis coil comprises:
3a, three axial coils of the three-axis Helmholtz coil are not electrified, and three axial outputs of the three-axis DC-SQUID magnetometer sensor are recorded as BYZ-X0、BYZ-Y0And BYZ-Z0；
3b, respectively passing constant current I to a Y-axis coil and a Z-axis coil of the triaxial Helmholtz coil by using a current source2And a constant current I3Reproducing a constant magnetic field BYAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ1-X、BYZ1-YAnd BYZ1-Z；
3c, keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing the constant magnetic field BYAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ2-X、BYZ2-YAnd BYZ2-Z；
3d, keeping the magnitude and direction of the current of the Z-axis coil unchanged, changing the direction of the current introduced into the Y-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BYAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ3-X、BYZ3-YAnd BYZ3-Z；
3e, keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BYAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ4-X、BYZ4-YAnd BYZ4-Z；
And 3f, calculating an included angle gamma between the Y-axis coil and the Z-axis coil according to the following formula:
wherein:
Q1＝(BYZ1-X-BYZ-X0)2+(BYZ1-Y-BYZ-Y0)2+(BYZ1-Z-BYZ-Z0)2
Q2＝(BYZ2-X-BYZ-X0)2+(BYZ2-Y-BYZ-Y0)2+(BYZ2-Z-BYZ-Z0)2
Q3＝(BYZ3-X-BYZ-X0)2+(BYZ3-Y-BYZ-Y0)2+(BYZ3-Z-BYZ-Z0)2
Q4＝(BYZ4-X-BYZ-X0)2+(BYZ4-Y-BYZ-Y0)2+(BYZ4-Z-BYZ-Z0)2。
compared with the prior art, the invention has the beneficial effects that:
1) compared with the traditional method, the method of the invention gets rid of the dependence on an electromagnetic shielding chamber and an absolute nonmagnetic environment, and is also suitable for the environment with the background geomagnetic field. 2) The method is applicable to the background geomagnetic field environment, and the triaxial Helmholtz coil can change the triaxial non-orthogonality error parameters under the action of long-distance transportation and external force and needs to be corrected before being used every time, so that the method provides possibility for field measurement of the field triaxial Helmholtz coil non-orthogonality error angle. 3) The SQUID magnetometer vector sensor utilized by the method has the measurement accuracy of 10pT, and is higher by one order of magnitude compared with the measurement accuracy of 0.1nT of a proton magnetometer scalar sensor utilized by the traditional method, so the measurement accuracy of a non-orthogonal error angle is higher by one order of magnitude.
Drawings
FIG. 1 is a schematic diagram of a non-orthogonal angle measurement between the X-axis and the Y-axis of a three-axis Helmholtz coil of the present invention;
FIG. 2 is a schematic diagram of a non-orthogonal angle measurement between the X-axis and the Z-axis of a three-axis Helmholtz coil of the present invention;
FIG. 3 is a schematic diagram of a non-orthogonal angle measurement between the Y-axis and the Z-axis of a three-axis Helmholtz coil of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A non-orthogonal error measuring method of a three-axis Helmholtz coil in an unshielded environment comprises the following steps:
the method comprises the steps of respectively introducing forward or reverse current into every two axial coils of a three-axis Helmholtz coil by utilizing a constant current source so as to reproduce a synthetic magnetic field under 4 conditions, recording data before and after the two coils generate 4 synthetic magnetic fields through a three-axis DC-SQUID magnetometer sensor, and calculating an included angle between the two axial coils according to the data before and after the 4 synthetic magnetic fields, wherein the 4 conditions comprise in sequence: the first step is as follows: constant current is respectively led into the two axial coils; the second step is that: fixing the current magnitude and direction of one axial coil unchanged, and changing the current direction of the other axial coil; the third step: fixing the current magnitude and direction of the axial coil changing the current direction in the second step, and changing the current direction of the other axial coil; the fourth step: and fixing the current magnitude and direction of the axial coil changing the current direction in the third step, and changing the current passing direction of the other axial coil. The included angle includes: the included angle alpha of the X-axis coil and the Y-axis coil, the included angle beta of the X-axis coil and the Z-axis coil and the included angle gamma of the Y-axis coil and the Z-axis coil.
The method specifically comprises the following steps:
a. fixing the three-axis DC-SQUID magnetometer sensor in a magnetic field uniform region of the three-axis Helmholtz coil at any random angle, and recording three axial outputs of the three-axis DC-SQUID magnetometer sensor as BXY-X0、BXY-Y0And BXY-Z0；
b. As shown in figure 1, a current source is used for respectively passing constant current I to the X axis and the Y axis of a three-axis Helmholtz coil1And I2Reproducing a constant magnetic field BXAnd BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY1-X、BXY1-YAnd BXY1-Z；
c. Keeping the current magnitude and direction of the X-axis coil unchanged, changing the current direction of the Y-axis coil, and reproducing the constant magnetic field BXand-BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY2-X、BXY2-YAnd BXY2-Z；
d. Keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the X-axis coil, and reproducing the constant magnetic field-BXand-BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY3-X、BXY3-YAnd BXY3-Z；
e. Keeping the current magnitude and direction of the X-axis coil unchanged, changing the current direction of the Y-axis coil, and reproducing the constant magnetic field-BXAnd BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY4-X、BXY4-YAnd BXY4-Z；
f. The angle α between the X-axis coil and the Y-axis coil is calculated according to the following formula:
wherein: m1＝(BXY1-X-BXY-X0)2+(BXY1-Y-BXY-Y0)2+(BXY1-Z-BXY-Z0)2
M2＝(BXY2-X-BXY-X0)2+(BXY2-Y-BXY-Y0)2+(BXY2-Z-BXY-Z0)2
M3＝(BXY3-X-BXY-X0)2+(BXY3-Y-BXY-Y0)2+(BXY3-Z-BXY-Z0)2
M4＝(BXY4-X-BXY-X0)2+(BXY4-Y-BXY-Y0)2+(BXY4-Z-BXY-Z0)2
g. Three axial directions of the three-axis Helmholtz coil are not electrified, and three axial outputs of the three-axis DC-SQUID magnetometer sensor are recorded as BXZ-X0、BXZ-Y0And BXZ-Z0；
h. As shown in FIG. 2, a current source is used to supply constant current I to the X-axis and Z-axis of the three-axis Helmholtz coil1And I3Reproducing a constant magnetic field BXAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ1-X、BXZ1-YAnd BXZ1-Z；
i. Keeping the current magnitude and direction of the X-axis coil unchanged, changing the current direction of the Z-axis coil, and reproducing the constant magnetic field BXAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ2-X、BXZ2-YAnd BXZ2-Z；
j. Keeping the current magnitude and direction of the Z-axis coil unchanged, changing the direction of the current introduced into the X-axis coil, and reproducing the constant magnetic field-BXand-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ2-X、BXZ2-YAnd BXZ2-Z；
k. Health-care productKeeping the current magnitude and direction of the X-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ4-X、BXZ4-YAnd BXZ4-Z；
And l, calculating an included angle beta of the X-axis coil and the Z-axis coil according to the following formula:
wherein: n is a radical of1＝(BXZ1-X-BXZ-X0)2+(BXZ1-Y-BXZ-Y0)2+(BXZ1-Z-BXZ-Z0)2
N2＝(BXZ2-X-BXZ-X0)2+(BXZ2-Y-BXZ-Y0)2+(BXZ2-Z-BXZ-Z0)2
N3＝(BXZ3-X-BXZ-X0)2+(BXZ3-Y-BXZ-Y0)2+(BXZ3-Z-BXZ-Z0)2
N4＝(BXZ4-X-BXZ-X0)2+(BXZ4-Y-BXZ-Y0)2+(BXZ4-Z-BXZ-Z0)2
No current flows in three axial directions of the m and three-axis Helmholtz coils, and three axial outputs of the three-axis DC-SQUID magnetometer sensor are recorded as BYZ-X0、BYZ-Y0And BYZ-Z0；
n, as shown in fig. 3, constant current I is respectively supplied to the Y-axis coil and the Z-axis of the triaxial Helmholtz coil by a current source2And I3Reproducing a constant magnetic field BYAnd BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ1-X、BYZ1-YAnd BYZ1-Z；
o, keeping the current of the Y-axis coilThe sum direction is unchanged, the direction of the current led into the Z-axis coil is changed, the magnitude is unchanged, and the constant magnetic field B is reproducedYand-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ2-X、BYZ2-YAnd BYZ2-Z；
p, keeping the current magnitude and direction of the Z-axis coil unchanged, changing the direction of the current introduced into the Y-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BYand-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ3-X、BYZ3-YAnd BYZ3-Z；
q, keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BYAnd BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ4-X、BYZ4-YAnd BYZ4-Z；
r, calculating an included angle gamma of the Y-axis coil and the Z-axis coil according to the following formula:
wherein: q1＝(BYZ1-X-BYZ-X0)2+(BYZ1-Y-BYZ-Y0)2+(BYZ1-Z-BYZ-Z0)2
Q2＝(BYZ2-X-BYZ-X0)2+(BYZ2-Y-BYZ-Y0)2+(BYZ2-Z-BYZ-Z0)2
Q3＝(BYZ3-X-BYZ-X0)2+(BYZ3-Y-BYZ-Y0)2+(BYZ3-Z-BYZ-Z0)2
Q4＝(BYZ4-X-BYZ-X0)2+(BYZ4-Y-BYZ-Y0)2+(BYZ4-Z-BYZ-Z0)2。
Application example:
a three-axis DC-SQUID magnetometer sensor formed by MAG-09 type DC-SQUID magnetometer manufactured by CSIRO Australia is used for measuring the orthogonality between the Y axis and the Z axis of a certain three-axis Helmholtz coil. The measurement results were as follows:
BY＝7000.1nT，BZ＝6999.3nT，BYZ-X0＝34.56nT，BYZ-Y0＝45.15nT，BYZ-Z0＝-28.31nT，BYZ1-X＝6347.68nT，BYZ1-Y＝7716.77nT，BYZ1-Z＝-1064.28nT，BYZ2-X＝-5423.30nT，BYZ2-Y＝5432.27nT，BYZ2-Z＝6162.79nT，BYZ3-X＝-6209.44nT，BYZ3-Y＝-7536.17nT，BYZ3-Z＝951.04nT，BYZ4-X＝5561.54nT，BYZ4-Y＝-5251.67nT，BYZ4-Z＝-6276.03nT。
the angle γ between the Y and Z axes of the triaxial helmholtz coil is 89.645 ° as calculated by the formula.
In the same way, other two angles are obtained, and the orthogonality of the three-axis Helmholtz coil can be obtained through 3 experiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A triaxial Helmholtz coil non-orthogonal error measurement method under an unshielded environment is characterized by comprising the following steps:
the method comprises the steps of respectively introducing forward or reverse current into every two axial coils of a three-axis Helmholtz coil by utilizing a constant current source so as to reproduce a synthetic magnetic field under 4 conditions, recording data before and after the two coils generate 4 synthetic magnetic fields through a three-axis DC-SQUID magnetometer sensor, and calculating an included angle between the two axial coils according to the data before and after the 4 synthetic magnetic fields, wherein the 4 conditions comprise in sequence: the first step is as follows: constant current is respectively led into the two axial coils; the second step is that: fixing the current magnitude and direction of one axial coil unchanged, and changing the current direction of the other axial coil; the third step: fixing the current magnitude and direction of the axial coil changing the current direction in the second step, and changing the current direction of the other axial coil; the fourth step: and fixing the current magnitude and direction of the axial coil changing the current direction in the third step, and changing the current passing direction of the other axial coil.
2. The method of claim 1, wherein said angle comprises: the included angle alpha of the X-axis coil and the Y-axis coil, the included angle beta of the X-axis coil and the Z-axis coil and the included angle gamma of the Y-axis coil and the Z-axis coil.
3. The method of claim 2, wherein measuring the included angle α between the X-axis coil and the Y-axis coil comprises:
1a, fixing a three-axis DC-SQUID magnetometer sensor in a magnetic field uniform region of a three-axis Helmholtz coil at any random angle, and recording three axial outputs of the three-axis DC-SQUID magnetometer sensor as BXY-X0、BXY-Y0And BXY-Z0；
1b, respectively passing constant current I to an X axial coil and a Y axial coil of the triaxial Helmholtz coil by using a current source1And I2Reproducing a constant magnetic field BXAnd a constant magnetic field BYRecording the outputs of three axial coils of the sensor of the three-axis DC-SQUID magnetometer as BXY1-X、BXY1-YAnd BXY1-Z；
1c, keeping the current magnitude and direction of the X axial coil unchanged, changing the direction of the current introduced into the Y axial coil, keeping the magnitude unchanged, and reproducing the constant magnetic field BXAnd a constant magnetic field-BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY2-X、BXY2-YAnd BXY2-Z；
1d, keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the X-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field-BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY3-X、BXY3-YAnd BXY3-Z；
1e, keeping the current magnitude and direction of the X axial coil unchanged, changing the direction of the current introduced into the Y axial coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field BYRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXY4-X、BXY4-YAnd BXY4-Z；
1f, calculating an included angle alpha between the X-axis coil and the Y-axis coil according to the following formula:
wherein:
M1＝(BXY1-X-BXY-X0)2+(BXY1-Y-BXY-Y0)2+(BXY1-Z-BXY-Z0)2
M2＝(BXY2-X-BXY-X0)2+(BXY2-Y-BXY-Y0)2+(BXY2-Z-BXY-Z0)2
M3＝(BXY3-X-BXY-X0)2+(BXY3-Y-BXY-Y0)2+(BXY3-Z-BXY-Z0)2
M4＝(BXY4-X-BXY-X0)2+(BXY4-Y-BXY-Y0)2+(BXY4-Z-BXY-Z0)2。
4. the method of claim 2, wherein measuring the included angle β of the X-axis coil and the Z-axis coil comprises:
2a, three axial coils of the three-axis Helmholtz coil are not electrified, and three axial outputs of the three-axis DC-SQUID magnetometer sensor are recorded as BXZ-X0、BXZ-Y0And BXZ-Z0；
2b, respectively passing constant current I to an X axial coil and a Z axial coil of the triaxial Helmholtz coil by using a current source1And a constant current I3Reproducing a constant magnetic field BXAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ1-X、BXZ1-YAnd BXZ1-Z；
2c, keeping the current magnitude and direction of the X-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing the constant magnetic field BXAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ2-X、BXZ2-YAnd BXZ2-Z；
2d, keeping the magnitude and direction of the current of the Z-axis coil unchanged, changing the direction of the current introduced into the X-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ3-X、BXZ3-YAnd BXZ3-Z；
2e, keeping the current magnitude and direction of the X axial coil unchanged, changing the direction of the current introduced into the Z axial coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BXAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BXZ4-X、BXZ4-YAnd BXZ4-Z；
2f, calculating an included angle beta of the X-axis coil and the Z-axis coil according to the following formula:
wherein:
N1＝(BXZ1-X-BXZ-X0)2+(BXZ1-Y-BXZ-Y0)2+(BXZ1-Z-BXZ-Z0)2
N2＝(BXZ2-X-BXZ-X0)2+(BXZ2-Y-BXZ-Y0)2+(BXZ2-Z-BXZ-Z0)2
N3＝(BXZ3-X-BXZ-X0)2+(BXZ3-Y-BXZ-Y0)2+(BXZ3-Z-BXZ-Z0)2
N4＝(BXZ4-X-BXZ-X0)2+(BXZ4-Y-BXZ-Y0)2+(BXZ4-Z-BXZ-Z0)2。
5. the method of claim 2, wherein measuring the included angle γ of the Y-axis coil and the Z-axis coil comprises:
3a, three axial coils of the three-axis Helmholtz coil are not electrified, and three axial outputs of the three-axis DC-SQUID magnetometer sensor are recorded as BYZ-X0、BYZ-Y0And BYZ-Z0；
3b, respectively passing constant current I to a Y-axis coil and a Z-axis coil of the triaxial Helmholtz coil by using a current source2And a constant current I3Reproducing a constant magnetic field BYAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ1-X、BYZ1-YAnd BYZ1-Z；
3c, keeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing the constant magnetic field BYAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ2-X、BYZ2-YAnd BYZ2-Z；
3d, keeping the magnitude and direction of the current of the Z-axis coil unchanged, changing the direction of the current introduced into the Y-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BYAnd a constant magnetic field-BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ3-X、BYZ3-YAnd BYZ3-Z；
3eKeeping the current magnitude and direction of the Y-axis coil unchanged, changing the direction of the current introduced into the Z-axis coil, keeping the magnitude unchanged, and reproducing a constant magnetic field-BYAnd a constant magnetic field BZRecording three axial outputs of the three-axis DC-SQUID magnetometer sensor at the moment as BYZ4-X、BYZ4-YAnd BYZ4-Z；
And 3f, calculating an included angle gamma between the Y-axis coil and the Z-axis coil according to the following formula:
wherein:
Q1＝(BYZ1-X-BYZ-X0)2+(BYZ1-Y-BYZ-Y0)2+(BYZ1-Z-BYZ-Z0)2
Q2＝(BYZ2-X-BYZ-X0)2+(BYZ2-Y-BYZ-Y0)2+(BYZ2-Z-BYZ-Z0)2
Q3＝(BYZ3-X-BYZ-X0)2+(BYZ3-Y-BYZ-Y0)2+(BYZ3-Z-BYZ-Z0)2
Q4＝(BYZ4-X-BYZ-X0)2+(BYZ4-Y-BYZ-Y0)2+(BYZ4-Z-BYZ-Z0)2。
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