Modeling of a magnetic field
A method, including generating a magnetic field in a region from a first magnetic field radiator located at a first position and a second magnetic field radiator located at a second position. A volume having a multiplicity of vertices is delineated within the region, and respective values of the magnetic field at the multiplicity of vertices are measured. In response to the respective values, respective first dipole moments to the first magnetic field radiator and respective second dipole moments to the second magnetic field radiator are assigned. A value of the magnetic field within the volume is calculated in terms of the first dipole moments and the second dipole moments.
1. A method, comprising:
generating a magnetic field in a region from a first magnetic field radiator located at a first position and a second magnetic field radiator located at a second position;
delineating within the region a volume having a multiplicity of vertices;
measuring respective values of the magnetic field at the multiplicity of vertices;
in response to the respective values and in response to displacements of the multiplicity of vertices from an origin of a frame of reference defined by the first position and the second position, assigning respective first dipole moments to the first magnetic field radiator and assigning respective second dipole moments to the second magnetic field radiator; and
calculating a value of the magnetic field within the volume in terms of the first dipole moments and the second dipole moments.
2. The method according to claim 1 , and comprising, subsequent to calculating the value, inserting into the region a probe, configured to measure the value of the magnetic field, and determining a location of the probe within the region in response to the measured value.
3. The method according to claim 1 , wherein the volume is a cube having eight vertices.
4. The method according to claim 1 , wherein calculating the value of the magnetic field comprises the first and second magnetic radiators operating as simple dipoles having poles obeying an inverse square law.
5. The method according to claim 1 , wherein the value of the magnetic field for a point within the volume is calculated in terms of a first average of the first dipole moments assigned for the multiplicity of vertices and of a second average of the second dipole moments assigned for the multiplicity of vertices.
6. The method according to claim 5 , wherein the first and second averages are respective linear weighted averages calculated in terms of a location of the point within the volume.
7. The method according to claim 1 , wherein the first magnetic field radiator and the second magnetic field radiator respectively transmit a first alternating magnetic field at a first frequency and a second alternating magnetic field at a second frequency different from the first frequency.
8. An apparatus, comprising:
a first magnetic field radiator located at a first position and a second magnetic field radiator located at a second position, the radiators being configured to generate a magnetic field in a region; and
a processor, configured to:
delineate within the region a volume having a multiplicity of vertices,
measure respective values of the magnetic field at the multiplicity of vertices,
in response to the respective values and in response to displacements of the multiplicity of vertices from an origin of a frame of reference defined by the first position and the second position, assign respective first dipole moments to the first magnetic field radiator and assign respective second dipole moments to the second magnetic field radiator, and
calculate a value of the magnetic field within the volume in terms of the first dipole moments and the second dipole moments.
9. The apparatus according to claim 8 , and comprising a probe that is inserted into the region subsequent to calculating the value, and wherein the probe is configured to measure the value of the magnetic field, and wherein the processor is configured to determine a location of the probe within the region in response to the measured value.
10. The apparatus according to claim 8 , wherein the volume is a cube having eight vertices.
11. The apparatus according to claim 8 , wherein the first and second magnetic radiators operate as simple dipoles having poles obeying an inverse square law.
12. The apparatus according to claim 8 , wherein the value of the magnetic field for a point within the volume is calculated in terms of a first average of the first dipole moments assigned for the multiplicity of vertices and of a second average of the second dipole moments assigned for the multiplicity of vertices.
13. The apparatus according to claim 12 , wherein the first and second averages are respective linear weighted averages calculated in terms of a location of the point within the volume.
14. The apparatus according to claim 8 , wherein the first magnetic field radiator and the second magnetic field radiator respectively transmit a first alternating magnetic field at a first frequency and a second alternating magnetic field at a second frequency different from the first frequency.
15. A method, comprising:
generating a magnetic field in a region from a first magnetic field radiator located at a first position and a second magnetic field radiator located at a second position;
delineating within the region a volume having a multiplicity of vertices;
measuring respective values of the magnetic field at the multiplicity of vertices;
in response to the respective values, assigning respective first dipole moments to the first magnetic field radiator and assigning respective second dipole moments to the second magnetic field radiator; and
calculating a value of the magnetic field within the volume in terms of the first dipole moments and the second dipole moments;
wherein the value of the magnetic field for a point within the volume is calculated in terms of a first average of the first dipole moments assigned for the multiplicity of vertices and of a second average of the second dipole moments assigned for the multiplicity of vertices.
16. The method according to claim 15 , and comprising, subsequent to calculating the value, inserting into the region a probe, configured to measure the value of the magnetic field, and determining a location of the probe within the region in response to the measured value.
17. The method according to claim 15 , wherein the volume is a cube having eight vertices.
18. The method according to claim 15 , wherein calculating the value of the magnetic field comprises the first and second magnetic radiators operating as simple dipoles having poles obeying an inverse square law.
19. The method according to claim 15 , and comprising assigning the respective first dipole moments to the first magnetic field radiator and assigning the respective second dipole moments to the second magnetic field radiator in response to displacements of the multiplicity of vertices from an origin of a frame of reference defined by the first position and the second position.
20. The method according to claim 15 , wherein the first and second averages are respective linear weighted averages calculated in terms of a location of the point within the volume.
21. The method according to claim 15 , wherein the first magnetic field radiator and the second magnetic field radiator respectively transmit a first alternating magnetic field at a first frequency and a second alternating magnetic field at a second frequency different from the first frequency.
22. An Apparatus, comprising:
a first magnetic field radiator located at a first position and a second magnetic field radiator located at a second position, the radiators being configured to generate a magnetic field in a region; and
a processor, configured to:
delineate within the region a volume having a multiplicity of vertices,
measure respective values of the magnetic field at the multiplicity of vertices,
in response to the respective values, assign respective first dipole moments to the first magnetic field radiator and assign respective second dipole moments to the second magnetic field radiator, and
calculate a value of the magnetic field within the volume in terms of the first dipole moments and the second dipole moments;
wherein the value of the magnetic field for a point within the volume is calculated in terms of a first average of the first dipole moments assigned for the multiplicity of vertices and of a second average of the second dipole moments assigned for the multiplicity of vertices.
23. The apparatus according to claim 22 , and comprising a probe that is inserted into the region subsequent to calculating the value, and wherein the probe is configured to measure the value of the magnetic field, and wherein the processor is configured to determine a location of the probe within the region in response to the measured value.
24. The apparatus according to claim 22 , wherein the volume is a cube having eight vertices.
25. The apparatus according to claim 22 , wherein the first and second magnetic radiators operate as simple dipoles having poles obeying an inverse square law.
26. The apparatus according to claim 22 , wherein the processor is configured to assign the respective first dipole moments to the first magnetic field radiator and assign the respective second dipole moments to the second magnetic field radiator in response to displacements of the multiplicity of vertices from an origin of a frame of reference defined by the first position and the second position.
27. The apparatus according to claim 22 , wherein the first and second averages are respective linear weighted averages calculated in terms of a location of the point within the volume.
28. The apparatus according to claim 8 , wherein the first magnetic field radiator and the second magnetic field radiator respectively transmit a first alternating magnetic field at a first frequency and a second alternating magnetic field at a second frequency different from the first frequency.