System and method for heading error correction in a pulsed Rb-87 magnetometer at geomagnetic fields
According to various embodiments, a method for reducing heading error in a magnetometer that uses Rb-87 atoms is disclosed. The method includes varying a direction and magnitude of a magnetic field at different spin polarization regimes. According to various embodiments, a magnetometer adapted for reduced heading error is disclosed. The magnetometer includes a multipass cell containing Rb-87 vapor, a pump laser operated in a pulse mode that is synchronous with a Larmor frequency, and two orthogonal probe lasers configured to rotate to vary a direction and magnitude of a magnetic field at different spin polarization regimes.
1. A method for reducing heading error in a magnetometer that uses Rb-87 atoms, the method comprising:
exposing the magnetometer to a magnetic field;
measuring a precession frequency and determining an angle θ that is an angular deviation of a pump laser beam from a nominal magnetometer orientation where the pump laser beam is perpendicular to the magnetic field; and
determining heading error-free magnetic field based on
B
=
4
h
υ
(
g
s
-
3
g
l
)
μ
B
[
1
-
3
υ
υ
h
f
sin
θ
P
(
7
+
P
2
)
5
+
3
P
2
]
wherein B is the magnetic field strength, g s and g l are the electronic and nuclear Landé factors, respectively, μ B is the Bohr Magneton, υ=ω/2π is the measured precession frequency, υ hf is a hyperfine splitting frequency, and P is a degree of initial spin polarization.
2. The method of claim 1 , further comprising determining an average Larmor frequency via an analytical expression that depends on an angle between the pump laser beam and the magnetic field.
3. The method of claim 1 , further comprising measuring opposite relative phases between two hyperfine states during a spin precession via two orthogonal probe beams.
4. The method of claim 3 , further comprising averaging the measured opposite relative phases to cancel frequency shifts.
5. The method of claim 1 , further comprising using pulsed pumping via a pump laser to achieve higher initial spin polarization.
6. The method of claim 1 , further comprising calculating heading error in real time.
7. The method of claim 1 , further comprising:
measuring an AC signal and a DC signal based on the vertical probe laser and/or horizontal probe laser; and
determining the angle θ based on a ratio of the AC signal to the DC signal.
8. A magnetometer, comprising:
a multipass cell containing Rb-87 vapor;
a pump laser operated in a pulse mode that is synchronous with a Larmor frequency and oriented to pass a pump beam through the multi-pass cell in a first direction;
a horizontal probe laser configured to pass a first probe beam through the multipass cell in a direction parallel to the pump beam; and
a vertical probe laser configured to pass a second probe beam through the multipass cell in a direction perpendicular to the pump beam; and
one or more processing units configured to:
determine a direction of a magnetic field based on a ratio of an AC signal to an DC signal measured based on the vertical probe laser and/or horizontal probe laser; and
determine heading error-free magnetic field based on
B
=
4
h
υ
(
g
s
-
3
g
l
)
μ
B
[
1
-
3
υ
υ
h
f
sin
θ
P
(
7
+
P
2
)
5
+
3
P
2
]
wherein B is the magnetic field strength, g s and g l are the electronic and nuclear Landé factors, respectively, μ B is the Bohr Magneton, υ=ω/2π is a measured precession frequency, υ hf is a hyperfine splitting frequency, P is a degree of initial spin polarization, and θ is an angular deviation of the pump beam from a nominal magnetometer orientation where the pump beam is perpendicular to the magnetic field.
9. The magnetometer of claim 8 , wherein the multipass cell further contains a buffer gas.
10. The magnetometer of claim 8 , wherein the multipass cell further comprises internal mirrors.
11. The magnetometer of claim 10 , further comprising two polarimeters, each disposed in an optical path of the first probe beam or the second probe beam after the multipass cell, wherein each polarimeter comprises a half-wave plate to receive the first probe beam or the second probe beam and direct it towards a polarizing beam-splitter, which directs the first probe beam or the second probe beam towards two photodiodes with differential amplification.
12. The magnetometer of claim 8 , wherein one probe laser propagates parallel to the pump laser and the other probe laser propagates orthogonal to the pump laser.
13. The magnetometer of claim 8 , wherein an angle between the pump laser and the magnetic field determines an average Larmor frequency via an analytical expression.
14. The magnetometer of claim 8 , wherein the two probe lasers are configured to measure opposite relative phases between two hyperfine states during a spin precession for a lower polarization.
15. The magnetometer of claim 14 , wherein opposite relative phases are averaged to cancel frequency shifts.
16. The magnetometer of claim 8 , wherein heading error is calculated in real time.
17. The magnetometer of claim 8 , further comprising an electric heater to heat the Rb-87 vapor.