Dokumentenidentifikation 
EP1847846 06.12.2007 
EPVeröffentlichungsnummer 
0001847846 
Titel 
KernmagnetresonanzGyroskop 
Anmelder 
Northrop Grumman Corp., Los Angeles, Calif., US 
Erfinder 
Kanegsberg, Edward, Pacific Palisades, CA 90272, US 
Vertreter 
derzeit kein Vertreter bestellt 
Vertragsstaaten 
AT, BE, BG, CH, CY, CZ, DE, DK, EE, ES, FI, FR, GB, GR, HU, IE, IS, IT, LI, LT, LU, LV, MC, MT, NL, PL, PT, RO, SE, SI, SK, TR 
Sprache des Dokument 
EN 
EPAnmeldetag 
12.03.2007 
EPAktenzeichen 
071039713 
EPOffenlegungsdatum 
24.10.2007 
Veröffentlichungstag im Patentblatt 
06.12.2007 
IPCHauptklasse 
G01R 33/26(2006.01)A, F, I, 20070925, B, H, EP

IPCNebenklasse 
G01C 19/62(2006.01)A, L, I, 20070925, B, H, EP

Beschreibung[en] 
TECHNICAL FIELD
The invention relates generally to nuclear magnetic resonance
and more particularly to nuclear magnetic resonance gyroscopes.
BACKGROUND
A nuclear magnetic resonance (hereinafter referred to as
NMR) angular rate sensor or gyroscope is described in
U.S. Pat. No. 4,157,495
, the disclosure of which is hereby incorporated by reference into this
document. A NMR gyroscope operates on the principle of sensing inertial angular
rotation rate or angular displacement about a sensitive axis of the device as a
shift in the Larmor precession frequency or phase, respectively, of one or more
isotopes that possess nuclear magnetic moments.
The gyroscope is composed of an angular rotation sensor
and associated electronics. The principal elements of the sensor are a light source,
an NMR cell, a photodetector, a set of magnetic shields and a set of magnetic field
coils. The principal elements of the electronics are signal processing circuits
for extracting the Larmor precession frequency and phase information as well as
circuits for generating and controlling various magnetic fields, both steady and
varying sinusoidally with time, that are necessary for the proper operation of the
device.
The NMR cell is mounted within a set of magnetic shields
in order to attenuate external magnetic fields to acceptable low levels. Magnetic
field coils are used to apply very uniform magnetic fields to the NMR cell. Both
a steady field and an ac carrier field are applied along the sensitive axis of the
device and AC feedback fields are applied along one of the transverse axes. The
DC magnetic fields along both transverse axes are controlled to be substantially
zero. The NMR cell contains one or more alkali metal vapors, such as rubidium, together
with two isotopes of one or more noble gases, such as krypton83, and xenon129,
or xenon131. One or more buffer gases such as helium and nitrogen may also be contained
in the cell. The NMR cell is illuminated by a beam of circularly polarized light
that originates from a source such as a rubidium lamp and which passes through the
cell at an angle with respect to the steady magnetic field. Absorption of some of
this light causes the atomic magnetic moments of the rubidium atoms to be partly
aligned in the direction of the steady magnetic field. This alignment is partly
transferred to the nuclear magnetic moments of the noble gases, and these moments
are caused to precess about the direction of the steady magnetic field, which in
turn creates magnetic fields that rotate at the respective Larmor precession frequencies
of the two noble gases. These rotating fields modulate the precessional motions
of the rubidium magnetic moments, which in turn produce corresponding modulations
of the transmitted light, thereby making it possible to optically detect the Larmor
precession frequencies of the two noble gases.
The modulations of the light intensity are converted into
electrical signals by a photodetector, and these signals are then electronically
demodulated and filtered to provide signals at the Larmor precession frequencies
of the two noble gases. The difference between the two precession frequencies is
used to accurately control the steady magnetic field so that it is constant. One
of the noble gas precession frequencies is subtracted from a precision reference
frequency. The resulting difference frequency is a measure of the angular rotation
rate of the gyroscope. The magnitude of an individual nuclear magnetic moment is
extremely small and the natural equilibrium condition is one in which a nearly random
orientation of moments exists in an ensemble of atoms. Techniques must be used to
orient a significant fraction of these magnetic moments in a single direction so
that a macroscopic magnetic moment, and consequently a measurable signal, will be
produced.
SUMMARY
The invention in one implementation encompasses a method.
A nuclear magnetic resonance cell with first, second, and third nuclear moment gases
and at least one optically pumpable substance is provided. First, second, and third
measured precession frequencies that correspond to the first, second, and third
nuclear moment gases are obtained. The first, second, and third measured precession
frequencies are altered from corresponding first, second, and third Larmor precession
frequencies by a rotational rate and corresponding first, second, and third local
magnetic fields. The rotational rate is determined with compensation for the first,
second, and third local magnetic fields through employment of the first, second,
and third measured precession frequencies.
Another implementation of the invention encompasses an
apparatus. The apparatus comprises a nuclear magnetic resonance cell and a photodetector.
The nuclear magnetic resonance cell comprises first, second, and third nuclear moment
gases and at least one optically pumpable substance. The nuclear magnetic resonance
cell receives detection light that passes through the nuclear magnetic resonance
cell. The first, second, and third nuclear moment gases and the at least one optically
pumpable substance cooperate to modulate the detection light based on local magnetic
fields and pass transmitted light to the photodetector. The photodetector receives
the transmitted light through the nuclear magnetic cell and determines a rotational
rate with compensation for the first, second, and third local magnetic fields.
Accordingly the invention provides a method according to
claim 1 with advantageous embodiments provided in the dependent claims. The invention
also provides an apparatus according to claim 11 with advantageous embodiments provided
in the dependent claims thereto.
DESCRIPTION OF THE DRAWINGS
Features of various implementations of the invention will
become apparent from the description, the claims, and the accompanying drawings
in which:
The figure is a representation of one implementation of
an apparatus that comprises a nuclear magnetic resonance cell and a photodetector.
DETAILED DESCRIPTION
The nuclear magnetic resonance ("NMR") gyro disclosed in
U.S. Patent No. 4,157,495
employs two noble gas species as rotation detectors based on the following
equations of precession:
$${\mathrm{\&ohgr;}}_{1}={\mathrm{\&ggr;}}_{1}H\mathrm{\&OHgr;}$$
$${\mathrm{\&ohgr;}}_{2}={\mathrm{\&ggr;}}_{2}H\mathrm{\&OHgr;}$$
where the subscripts refer to one or the other of the noble
gas species, and where H is the applied magnetic field, &ggr; is the gyromagnetic
ratio for the noble gas nuclear spin, &OHgr; is the vehicle rotation rate and &ohgr;
is the measured precession frequency.
Since equations (1) and (2) are a system of linear equations
with two unknowns, H and &OHgr;, unique solutions, depending only on the measured
precession frequencies &ohgr; and constants &ggr; , can be found for both H and
&OHgr;. Implicit in equations (1) and (2) is the assumption that the magnetic field
"experienced" by both nuclear spin systems is the same.
In the practice of the NMR gyro, however, this assumption
of both systems experiencing the same field is not quite true. During interactions
(e.g., collisions) between a noble gas atom and an alkali, there are small local
magnetic fields. The macroscopic effect of these fields depends on both the spin
polarization of the alkali and on the collision rate. The spin polarization is light
dependent and the collision rate is temperature dependent due to vapor pressure
of the alkali. These collisionbased fields are also dependent on the noble gas
and alkali isotope, leading to different effective magnetic fields for each nuclear
species present. Accordingly, equations (1) and (2) can be modified to:
$${\mathrm{\&ohgr;}}_{1}={\mathrm{\&ggr;}}_{1}(H+{h}_{1})\mathrm{\&OHgr;}$$
$${\mathrm{\&ohgr;}}_{2}={\mathrm{\&ggr;}}_{2}(H+{h}_{2})\mathrm{\&OHgr;}$$
where h
_{1} and h
_{2} are the local collisional fields and in general h
_{1} ≠ h
_{2}. The thermal and light intensity dependence of h
_{1} and h
_{2} lead to perturbations to &ohgr;_{1} and &ohgr;_{2},
which cause gyro bias errors. At first, it appears that this is a system of two
equations with four unknowns: H, h
_{1}
, h
_{2}
, and &OHgr;. However, h
_{1} and h
_{2} are related to each other because both are due to interactions with
the same alkali atom system. The fields h
_{1} and h
_{2} are both proportional to the frequency of alkali atomic collisions
which is proportional to alkali density and alkali spin polarization with a constant
of proportionality that depends on which nuclear specie is interacting with the
alkali. The alkali density is temperature dependent and the alkali spin polarization
is light dependent. Accordingly, equations (3) and (4) can be rewritten as:
$${\mathrm{\&ohgr;}}_{1}={\mathrm{\&ggr;}}_{1}H+{b}_{1}c\mathrm{\&OHgr;}$$
$${\mathrm{\&ohgr;}}_{2}={\mathrm{\&ggr;}}_{2}H+{b}_{2}c\mathrm{\&OHgr;}$$
where b
_{1}
c = &ggr;_{1}
h
_{1} and b
_{2}
c = &ggr;
_{2}
h
_{2} and where c is a function of the alkali density and alkali spin polarization
and is not a function of which nuclear specie is being considered. The proportionality
factor b will be a constant with a different value for each nuclear specie.
Adding a third nuclear specie and thus a third equation
does not introduce any more unknown variables:
$${\mathrm{\&ohgr;}}_{3}={\mathrm{\&ggr;}}_{3}H+{b}_{3}c\mathrm{\&OHgr;}$$
Equations 5, 6, and 7 comprise a system of three linear
equations in three unknown variables H, c, and &OHgr; so there are unique solutions.
Solving for each unknown variable as functions of the measurable frequencies &ohgr;
and known or calibratable constants results in:
$$H=\frac{({\mathit{\&ohgr;}}_{1}{\mathit{\&ohgr;}}_{2})\left({b}_{2},,{b}_{3}\right)({\mathit{\&ohgr;}}_{2}{\mathit{\&ohgr;}}_{3})\left({b}_{1},,{b}_{2}\right)}{\left({\mathrm{\&ggr;}}_{1},,{\mathrm{\&ggr;}}_{2},\left),\right(,{b}_{2},,{b}_{3},),,(,{\mathrm{\&ggr;}}_{2},,{\mathrm{\&ggr;}}_{3},\left),\right(,{b}_{1},,{b}_{2}\right)}$$
$$c=\frac{({\mathit{\&ohgr;}}_{1}{\mathit{\&ohgr;}}_{2})\left({\mathrm{\&ggr;}}_{2},,{\mathrm{\&ggr;}}_{3}\right)({\mathit{\&ohgr;}}_{2}{\mathit{\&ohgr;}}_{3})\left({\mathrm{\&ggr;}}_{1},,{\mathrm{\&ggr;}}_{2}\right)}{\left({\mathrm{\&ggr;}}_{2},,{\mathrm{\&ggr;}}_{1},\left),\right(,{b}_{1},,{b}_{2},),,(,{\mathrm{\&ggr;}}_{1},,{\mathrm{\&ggr;}}_{2},\left),\right(,{b}_{2},,{b}_{3}\right)}$$
$$\mathrm{\&OHgr;}={\mathrm{\&ggr;}}_{1}H+{b}_{1}c{\mathit{\&ohgr;}}_{1}$$
The parameters &ggr; and b can be obtained during gyro
calibration and entered into an operational system model. The dependency of &ggr;
can be determined by observing the effects of a changing magnetic field. The dependency
of b can be determined by observing the effects of a changing temperature and light
level.
Turning to the figure, an apparatus 100 in one example
comprises a nuclear magnetic resonance ("NMR") gyroscope. The apparatus 100 comprises
a NMR cell 102, a pumping light generator 111, a steady magnetic field generator
119, a feedback magnetic field generator 121, a detection light generator 123, a
carrier magnetic field generator 125, and a photodetector 134. The NMR cell 102
comprises at least one optically pumpable substance, for example, an alkali metal
vapor 104. The NMR cell 102 also comprises first, second, and third nuclear magnetic
moment gases 106, 108, and 110. The alkali metal vapor 104 in one example comprises
rubidium. The nuclear magnetic moment gases 106, 108, and 110 in one example comprise
isotopes of noble gases such as xenon and/or krypton. The NMR cell 102 in a further
example comprises at least one buffer gas, such as helium or nitrogen. The photodetector
134 in one example comprises an instance of a computerreadable signal bearing medium
136.
An illustrative description of operation of the apparatus
100 is presented, for explanatory purposes. The pumping light generator 111 directs
optical pumping light 112 into the NMR cell 102 along the zaxis. The optical pumping
light 112 in one example comprises circularly polarized light. The steady magnetic
field generator 119 applies a steady magnetic field 120 along the zaxis. The optical
pumping light 112 and the steady magnetic field 120 cooperate to align magnetic
moments of atoms of the alkali metal vapor 104 in the zdirection. The atoms of
the alkali metal vapor 104 transfer the magnetic moment alignment to nuclei of the
nuclear magnetic moment gases 106, 108, and 110 through interatomic collisions.
The feedback magnetic field generator 121 applies a sinusoidal
AC feedback magnetic field 122 in the xdirection and serves to torque the magnetic
moment of the nuclear magnetic moment gases 106, 108, and 110 to the xy plane.
The sinusoidal AC feedback magnetic field 122 comprises three feedback signals of
different frequencies that are superimposed, for example, one feedback signal per
nuclear magnetic moment gas. The frequency and phase of each signal are matched
to a Larmor precession frequency of collective magnetic moments of the respective
nuclear magnetic moment gases 106, 108, and 110. The collective magnetic moments
of the nuclear magnetic moment gases 106, 108, and 110 then precess in the xy plane
at their Larmor precession frequencies &ohgr;_{a1}, &ohgr;_{a2},
and &ohgr;_{a3} about the steady magnetic field 120. The precessing nuclear
magnetic moments create nuclear precession magnetic fields of strength h_{a1},
h_{a2}, and h_{a3} that rotate in the xy plane and which therefore
have a component in the ydirection that is equal to h_{a}cos &ohgr;_{a}t.
The detection light generator 123 directs detection light
124 through the nuclear magnetic resonance cell. The detection light 124 interacts
with the atoms of the alkali vapor 104, which are under the influence of the steady
magnetic field 120, a superimposed AC carrier magnetic field 126, and the ycomponent
of the nuclear precession fields h_{a}. The carrier magnetic field generator
125 applies the superimposed AC carrier magnetic field 126. The superimposed AC
carrier magnetic field comprises a frequency of &ohgr;, which is close to the Larmor
precession frequency for an alkali magnetic moment of the alkali metal vapor 104.
This interaction of the detection light 124 and the alkali vapor 104 causes the
intensity of the xcomponent of transmitted light 130 to be modulated at the precession
frequency &ohgr;, with a modulation envelope 132 at the nuclear precession frequencies
&ohgr;_{a} (&ohgr;_{a1}, &ohgr;_{a2}, and &ohgr;_{a3}).
For example, the transmitted light 130 comprises the superimposed AC carrier magnetic
field that comprises the nuclear precession frequencies &ohgr;_{a} as sidebands.
The silicon photodetector 134 receives the transmitted light 130 and converts the
transmitted light 130 into electrical signals.
The silicon photodetector 134 in one example processes
the electrical signals to obtain angular rate information for the apparatus 100.
For example, the silicon photodetector 134 employs one or more of equations (5)(10)
to determine the angular rate information where &ohgr;_{a} (e.g., &ohgr;_{a1},
&ohgr;_{a2}, &ohgr;_{a3}) is the measured precession frequency.
The computerreadable signal bearing medium 136 of the silicon photodetector 134
in one example comprises software, firmware, and/or other executable code for processing
the electrical signals.
The apparatus 100 in one example comprises a plurality
of components such as one or more of electronic components, hardware components,
and computer software components. A number of such components can be combined or
divided in the apparatus 100. One or more components of the apparatus 100 may employ
and/or comprise a set and/or series of computer instructions written in or implemented
with any of a number of programming languages, as will be appreciated by those skilled
in the art.
The apparatus 100 in one example employs one or more computerreadable
signalbearing media. The computerreadable signalbearing media store software,
firmware and/or assembly language for performing one or more portions of one or
more implementations of the invention. Examples of a computerreadable signalbearing
medium for the apparatus 100 comprise the recordable data storage medium 136 of
the silicon photodetector 134. The computerreadable signalbearing medium for the
apparatus 100 in one example comprise one or more of a magnetic, electrical, optical,
biological, and atomic data storage medium. For example, the computerreadable signalbearing
medium comprise floppy disks, magnetic tapes, CDROMs, DVDROMs, hard disk drives,
and electronic memory. In another example, the computerreadable signalbearing
medium comprises a modulated carrier signal transmitted over a network comprising
or coupled with the apparatus 100, for instance, one or more of a telephone network,
a local area network ("LAN"), a wide area network ("WAN"), the Internet, and a wireless
network.
The steps or operations described herein are just exemplary.
There may be many variations to these steps or operations without departing from
the spirit of the invention. For instance, the steps may be performed in a differing
order, or steps may be added, deleted, or modified.
Although exemplary implementations of the invention have
been depicted and described in detail herein, it will be apparent to those skilled
in the relevant art that various modifications, additions, substitutions, and the
like can be made without departing from the spirit of the invention and these are
therefore considered to be within the scope of the invention as defined in the following
claims.

Anspruch[en] 
A method, comprising the steps of:
providing a nuclear magnetic resonance cell with first, second, and
third nuclear moment gases and at least one optically pumpable substance;
obtaining first, second, and third measured precession frequencies that
correspond to the first, second, and third nuclear moment gases, wherein the first,
second, and third measured precession frequencies are altered from corresponding
first, second, and third Larmor precession frequencies by a rotational rate and
corresponding first, second, and third local magnetic fields; and
determining the rotational rate with compensation for the first, second,
and third local magnetic fields through employment of the first, second, and third
measured precession frequencies.
The method of claim 1, wherein the step of determining the rotational
rate with compensation for the first, second, and third local magnetic fields through
employment of the first, second, and third measured precession frequencies comprises
the step of:
approximating the first, second, and third local magnetic fields as
a base magnetic field multiplied by corresponding first, second, and third proportionality
factors.
The method of claim 2, wherein the step of approximating the first,
second, and third local magnetic fields as the base magnetic field multiplied by
the corresponding first, second, and third proportionally factors comprises the
step of:
determining the base magnetic field as a function of density of the
at least one optically pumpable substance and spin polarization of the at least
one optically pumpable substance.
The method of claim 3, wherein the step of approximating the first,
second, and third local magnetic fields as the base magnetic field multiplied by
the first, second, and third proportionality factors comprises the steps of:
modeling the first measured precession frequency as:
$${\mathrm{\&ohgr;}}_{1}={\mathrm{\&ggr;}}_{1}H+{b}_{1}c\mathrm{\&OHgr;}$$
modeling the second measured precession frequency as:
$${\mathrm{\&ohgr;}}_{2}={\mathrm{\&ggr;}}_{2}H+{b}_{2}c\mathrm{\&OHgr;}$$
modeling the third measured precession frequency as:
$${\mathrm{\&ohgr;}}_{3}={\mathrm{\&ggr;}}_{3}H+{b}_{3}c\mathrm{\&OHgr;}$$
where &ohgr;
_{n}
is the measured precession frequency for the three nuclear moment gases, &ggr;
_{n}
is a gyromagnetic ratio for nuclear spin for the three nuclear moment gases,
H is an applied magnetic field, b_{n} is the proportionality factor for
the three nuclear moment gases, c is the base magnetic field, and &OHgr; is the
rotational rate information.
The method of claim 4, further comprising the steps of:
determining the gyromagnetic ratios for nuclear spin for the three nuclear
moment gases &ggr;
_{n}
and the proportionality factor b through calibration.
The method of claim 5, wherein the step of determining the gyromagnetic
ratios for nuclear spin for the three nuclear moment gases &ggr;
_{n}
and the proportionality factors b_{n} through calibration comprises
the step of:
adjusting the applied magnetic field to determine the gyromagnetic ratios
for nuclear spin for the three nuclear moment gases &ggr;
_{n}
.
The method of claim 5, wherein the step of determining the gyromagnetic
ratios for nuclear spin for the three nuclear moment gases &ggr;
_{n}
and the proportionality factor b through calibration comprises the step of:
adjusting a temperature within the nuclear magnetic resonance cell to
determine the proportionality factors b_{n}.
The method of claim 5, wherein the step of determining the gyromagnetic
ratios for nuclear spin for the three nuclear moment gases &ggr;
_{n}
, and the proportionality factor b through calibration comprises the step of:
adjusting a light level within the nuclear magnetic resonance cell to
determine the proportionality factors b_{n}.
The method of claim 5, wherein the step of determining the gyromagnetic
ratios for nuclear spin for the three nuclear moment gases &ggr;
_{n}
and the proportionality factor b through calibration comprises the step of:
adjusting a temperature within the nuclear magnetic resonance cell and
a light level within the nuclear magnetic resonance cell to determine the proportionality
factors b_{n}.
The method of claim 5, further comprising the step of determining the
rotational rate information as:
$$\mathrm{\&OHgr;}={\mathrm{\&ggr;}}_{1}H+{b}_{1}c{\mathit{\&ohgr;}}_{1}$$
where
$$H=\frac{({\mathit{\&ohgr;}}_{1}{\mathit{\&ohgr;}}_{2})\left({b}_{2},,{b}_{3}\right)({\mathit{\&ohgr;}}_{2}{\mathit{\&ohgr;}}_{3})\left({b}_{1},,{b}_{2}\right)}{\left({\mathrm{\&ggr;}}_{1},,{\mathrm{\&ggr;}}_{2},\left),\right(,{b}_{2},,{b}_{3},),,(,{\mathrm{\&ggr;}}_{2},,{\mathrm{\&ggr;}}_{3},\left),\right(,{b}_{1},,{b}_{2}\right)}$$
and
$$c=\frac{({\mathit{\&ohgr;}}_{1}{\mathit{\&ohgr;}}_{2})\left({\mathrm{\&ggr;}}_{2},,{\mathrm{\&ggr;}}_{3}\right)({\mathit{\&ohgr;}}_{2}{\mathit{\&ohgr;}}_{3})\left({\mathrm{\&ggr;}}_{1},,{\mathrm{\&ggr;}}_{2}\right)}{\left({\mathrm{\&ggr;}}_{2},,{\mathrm{\&ggr;}}_{1},\left),\right(,{b}_{1},,{b}_{2},),,(,{\mathrm{\&ggr;}}_{1},,{\mathrm{\&ggr;}}_{2},\left),\right(,{b}_{2},,{b}_{3}\right)}\mathrm{.}$$
An apparatus, comprising:
a nuclear magnetic resonance cell; and
a photodetector;
wherein the nuclear magnetic resonance cell comprises first, second, and third nuclear
moment gases and at least one optically pumpable substance;
wherein the nuclear magnetic resonance cell receives detection light that passes
through the nuclear magnetic resonance cell;
wherein the first, second, and third nuclear moment gases and the at least one optically
pumpable substance cooperate to modulate the detection light based on local magnetic
fields and pass transmitted light to the photodetector;
wherein the photodetector receives the transmitted light through the nuclear magnetic
cell and determines a rotational rate with compensation for the first, second, and
third local magnetic fields.
The apparatus of claim 11, wherein the at least one optically pumpable
substance comprises an alkali vapor.
The apparatus of claim 12, wherein the alkali vapor comprises rubidium.
The apparatus of claim 11, wherein at least one of the first, second,
and third nuclear moment gases comprise isotopes of at least one noble gas.
The apparatus of claim 14, wherein the at least one noble gas comprises
krypton83, xenon129, or xenon131.
The apparatus of claim 11, wherein the nuclear magnetic resonance cell
comprises at least one buffer gas of helium or nitrogen.
The apparatus of claim 11, further comprising:
a pumping light generator that directs circularly polarized optical
pumping light through the nuclear magnetic resonance cell;
a steady magnetic field generator that applies a steady magnetic field
along a zaxis of the nuclear magnetic resonance cell;
a feedback magnetic field generator that applies a sinusoidal AC feedback
magnetic field in an xdirection of the nuclear magnetic resonance cell;
a detection light generator that directs detection light through the
nuclear magnetic resonance cell, wherein the detection light comprises a wavelength
approximately equal to a wavelength which can be absorbed by the at least one optically
pumpable substance; and
a carrier magnetic field generator that applies a superimposed AC carrier
magnetic field.
The apparatus of claim 17, wherein the sinusoidal AC feedback magnetic
field comprises first, second, and third feedback signals of different frequencies;
wherein the feedback magnetic field generator superimposes the first, second, and
third feedback signals.
The apparatus of claim 18, wherein the feedback magnetic field generator
matches a frequency and phase of the first feedback signal with a Larmor precession
frequency of the first nuclear moment gas;
wherein the feedback magnetic field generator matches a frequency and phase of the
second feedback signal with a Larmor precession frequency of the second nuclear
moment gas;
wherein the feedback magnetic field generator matches a frequency and phase of the
third feedback signal with a Larmor precession frequency of the third nuclear moment
gas.
The apparatus of claim 19, wherein the superimposed AC carrier magnetic
field comprises a frequency &ohgr; that is close to a Larmor precession frequency
of the at least one optically pumpable substance.


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