Auxiliary DC field coil for improving rate bias instability of magnetic resonance gyroscopes

A magnetic resonance gyroscope has auxiliary coils mounted adjacent the coils which normally produce the DC H.sub.o field for the gyro spin generators. The auxiliary coils establish an inhomogeneous H.sub.o field which results in a reduction of the rate bias shifts due to readout lamp plasma shifts. Alternately, rate bias shifts may be reduced by introducing a temperature differential between the two absorption cells employed in the gyro.

FIELD OF THE INVENTION 
The present invention relates to magnetic resonance gyroscopes and more 
particularly to an apparatus employed in the readout beam section of the 
gyroscope for reducing the rate bias shift due to readout lamp plasma 
shifts. 
BRIEF DESCRIPTION OF THE PRIOR ART 
Magnetic resonance glyroscopes are well established in the art. A basic 
configuration for such a gyroscope is described in U.S. Pat. No. 
3,778,700, assigned to the present assignee. In a gyroscope of the type 
described, a readout plasma lamp is employed as a source of light which 
undergoes beam splitting and subsequent redirection through a pair of 
absorption cells filled with isotopes of Hg. The lamp is dumbbell shaped, 
with the intermediate connecting portion of the lamp containing plasma. 
Because the readout beam originates from an extended source, any changes 
in the source may produce polarization, beam division, and beam direction 
effects in the gyro which are major sources of rate bias instability. Lamp 
plasma shifts can occur due to factors including electrical changes in the 
RF lamp driving system, movement of the lamp and/or coil position, changes 
in the magnet position, temperature changes in the lamp housing, plasma 
striation phenomena, or magnetic deflections of the plasma due to movement 
of the magnet. 
A number of corrections have been attempted previously with limited success 
in decreasing the effects of these sources of rate bias instability. 
However, such corrections have generally resulted in a decrease of 
signal-to-noise ratio. 
BRIEF DESCRIPTION OF THE PRESENT INVENTION 
The present invention utilizes auxiliary coils, which are placed in close 
proximity to the coils generating the DC field H.sub.o for an absorption 
cell. This results in the creation of an inhomogeneous H.sub.o field which 
corrects the rate bias instability. This is achieved without a compromise 
of the signal-to-noise ratio. 
An alternate correction is achieved by accomplishing a temperature 
differential between the absorption cells to an extent resulting in 
substantial decrease of rate bias instability.

DETAILED DESCRIPTION 
Prior to an explanation of the improvement in magnetic resonance gyros as 
discussed in the following text in connection with FIGS. 3-5, it will be 
instructive to review the general structure of a prior art gyro as shown 
in FIGS. 1 and 2. 
FIG. 1 illustrates a basic configuration of a prior art gyroscope as 
described in U.S. Pat. No. 3,778,700, assigned to the present assignee. 
The gyroscope is generally indicated by reference numeral 10 and comprises 
a first spin generator designated generally by the reference numeral 11 
and a second spin generator designated generally by the reference numeral 
12. Each spin generator acts as a basic sensing unit for the gyroscope and 
serves as an oscillator which effectively simultaneously operates at two 
frequencies .omega..sub.1 and .omega..sub.2. The output frequencies of 
each spin generator are influenced by the rate of rotation of the 
gyroscope about the predetermined sensitive axis 22 so that the angle of 
rotation is added algebraically to the phase of each oscillation from the 
spin generator. Each output frequency of each spin generator is 
proportional to its magnetic field, H.sub.o, so that the ratio of the 
frequencies in each spin generator remains constant in the absence of 
rotation. 
The phases of the oscillation signals from each spin generator are given by 
the following equations: 
EQU .phi..sub.11 =.intg..gamma..sub.1 H.sub.01 dt+.phi..sub.0 
EQU .phi..sub.21 =.intg..gamma..sub.2 H.sub.01 dt-.phi..sub.0 (1) 
EQU .phi..sub.12 =.intg..gamma..sub.1 H.sub.02 dt-.phi..sub.0 
EQU .phi..sub.22 =.intg..gamma..sub.2 H.sub.02 dt+.phi..sub.0 (1) 
where .gamma..sub.1 and .gamma..sub.2 are the absolute gyromagnetic ratios 
of the Hg nuclei in the absorption cell; H.sub.01 and H.sub.02 are the 
respective magnetic fields proportional to the current applied to the 
coils which produce the fields; .phi..sub.0 is the common angle of 
rotation of the spin generators about the predetermined sensitive axis; 
.phi..sub.11 and .phi..sub.21 are the phases of the output signals from 
spin generator 11 and .phi..sub.12 and .phi..sub.22 are the phases of the 
output signals of spin generator 12; .phi..sub.11 and .phi..sub.12 are the 
phases of the signals whose frequency is .omega..sub.1, while .phi..sub.21 
and .phi..sub.22 are the phases of the signals whose frequency is 
.omega..sub.2. 
The angle of rotation is obtained by comparing the phases of pairs of 
signals. Neglecting error terms, if the phase difference in the signals of 
one frequency from the two spin generators is maintained equal and 
opposite in sign to the phase difference between the signals of the other 
frequency, the phase difference at either frequency is twice the angle of 
rotation of the gyroscope about the sensitive axis. Thus, if 
EQU (.phi..sub.11 -.phi..sub.12)+(.phi..sub.21 -.phi..sub.22)=0 (2) 
then 
EQU .phi..sub.11 -.phi..sub.12 =2.phi..sub.0 and .phi..sub.21 -.phi..sub.22 
=2.phi..sub.0 (3) 
The condition of equation (2) above may be maintained by developing an 
error signal from the sum of the respective phase differences of the 
corresponding outputs from the two spin generators. Th error signal is 
used as a differential control signal to control the current through one 
or more coils which generates the H.sub.o magnetic fields to maintain the 
error signal at a null. This forces H.sub.01 to equal H.sub.02. 
The gyroscope 10 includes circuitry (not shown) for comparing the phases of 
the output signals from the two spin generators 11 and 12 and for 
generating control and output signals as described above. The output 
signal produced is proportional to the angle of rotation of the gyroscope 
10 about the sensitive axis. 
The spin generator 11 includes an optically pumped and an optically 
monitored magnetic resonance element which comprises a coil assembly (not 
shown in FIG. 1) having a mercury absorption cell 14 at its center. 
Similarly, the spin generator 12 includes a mercury absorption cell 15 
located at the center of a multiple coil assembly (not shown in FIG. 1). A 
first field coil (shown in FIGS. 3 and 4) generates a DC magnetic H.sub.o 
field designated generally by the reference numeral 17, for the spin 
generator 11 while a second field coil of the same type as the first 
generates a second DC magnetic H.sub.o field, designated generally by the 
reference numeral 18, for the spin generator 12. 
For clarity, the orientation of the components in the apparatus shown in 
FIG. 1 will be related to an arbitrary x, y, z-axis coordinate system to 
aid in visualizing the spatial relationship of the components and to 
indicate the polarization of the pumping and readout light beams which 
will be described in detail. The x, y, and z-axes are designated generally 
by the reference numerals 20, 21 and 22, respectively. Thus, the H.sub.o 
field 17 is in the positive z direction, while the H.sub.o field 18 is in 
the negative z direction, so that the field 18 is thus antiparallel to the 
field 17. 
Each of the mercury absorption cells 14 and 15 preferably contains two odd 
isotopes of mercury, i.e., .sup.199 Hg and .sup.201 Hg. When the DC 
H.sub.o magnetic field has a strength of about 1.3 gauss, the resonance 
frequency of .sup.199 Hg is approximately 1 kHz and the resonance 
frequency of .sup.201 Hg is about 369 Hz. When each mercury cell is 
illuminated by light in a waveband having a nominal optical center at 
253.7 nm, the mercury atoms in the cell may absorb light in this region 
and be excited from the ground state to the first excited level by any 
light at a wavelength which is in resonance with transitions from the 
ground state mercury atoms in the mercury cell. 
The ground state atoms of mercury in each absorption cell possess magnetic 
moments due only to their intrinsic nuclear angular momentum or spin 
properties, since all electronic moments cancel out. When a collection or 
ensemble of such spins is subjected to the influence of a substantially 
homogenous static magnetic field H.sub.o, the orientations of the magnetic 
moments will be quantized or split into a series of ground states or 
levels having predeterminable energy separations. In the absence of very 
strong magnetic fields or optical pumping, the moments are randomly 
distributed and produce no net magnetic moment. A macroscopic magnetic 
moment may be produced in the mercury vapor by the process of optical 
pumping. Circularly polarized light of precise wavelengths to be absorbed 
by the mercury atoms adds its angular momentum to the mercury atoms when 
it is absorbed. Some of this angular momentum remains behind when the 
excited atoms reemit the absorbed electronic excitation energy. This 
corresponds to a redistribution of population among the ground state 
magnetic quantum levels. For .sup.199 Hg, there are only two such levels, 
m.sub.f =.+-.1/2, and any asymmetry of populations corresponds only to an 
orientation moment, with a resultant macroscopic nuclear magnetic moment. 
For .sup.201 Hg, having a nuclear spin of 3/2, there are four levels, 
m.sub.f =.+-.3/2 and .+-.1/2. For such atoms, the orientation moment is 
proportional to 3(n.sub.+3/2 -n.sub.-3/2)+(n.sub.1/2 -n.sub.-1/2), where 
the n's represent the populations in the respective magnetic levels. 
Again, the orientation moment is observable as a net magnetic moment. 
There is also an alignment moment proportional to (n.sub.3/2 
+n.sub.-3/2)-(n.sub.1/2 +n.sub.-1/2). The alignment moment leads to a 
variety of effects in the magnetic resonance gyro, most of them tending to 
produce errors in rate. 
A pumping lamp 23 provides a beam 24 of randomly polarized absorbable light 
which may be resolved into components polarized in a first plane 
designated by the numeral 25 and in a second plane designated by the 
numeral 26. The light output from the lamp 23 is directed upon a Brewster 
angle polarizer 27 which also acts as a beam splitter. The components of 
the light in the plane 26 are transmitted therethrough and are reflected 
from a mirror 29 in a direction parallel to the z axis 22. The components 
of the light in the plane 25 are reflected from the Brewster angle 
polarizer 27 and are reflected from the mirror 30 in a direction parallel 
to the z axis 22. The linearly polarized light reflected from the mirror 
29 is circularly polarized by the quarter wave plate 32 and intersects the 
mercury absorption cell 14, where it performs the function of optical 
pumping. The linearly polarized light reflected from the mirror 30 is 
circularly polarized by the quarter wave plate 33 and intersects the 
mercury absorption cell 15, producing optical pumping in this cell. 
A readout lamp 35 produces a beam of randomly polarized off-resonance light 
which contains components of light polarized in the plane designated by 
the reference numeral 37 and light polarized in the plane designated by 
the reference numeral 38. The beam from the lamp 35 undergoes filtering by 
a filter cell 36 containing .sup.199 Hg and .sup.201 Hg atoms. The 
filtered beam then intersects the Brewster angle polarizer 40 which 
transmits the components of light polarized in the plane 38 to intersect 
the mercury cell 14. Similarly, the components of light polarized in the 
plane 37 in the readout beam are reflected from the Brewster angle 
polarizer 40 and intersect the mercury absorption cell 15. 
The geometry shown in FIG. 1 is determined in large part by the Brewster 
angle. Preferably, each Brewster angle polarizer is made from stacks of 
thin plates of fused silica. When the incident light beam is at the 
Brewster angle, the reflected light beam is linearly polarized with its 
electric vector parallel to the plane of the reflecting surface and the 
transmitted beam is partially linearly polarized perpendicularly to the 
polarization of the reflected beam. 
Each of the mercury absorption cells 14 and 15 is also subjected to an AC 
H.sub.1 field produced by field coils (not shown). The H.sub.1 fields are 
perpendicular to the H.sub.o fields and the readout beams, as shown in 
FIG. 2. 
The H.sub.1 field applied to cell 14 is produced by the field generator 16 
in circuit with the output of the spin generator 11 while the H.sub.1 
field applied to cell 15 is produced by the field generator 19 in circuit 
with the output of the spin generator 12. Each field generator 16 and 19 
includes a phase-stable amplifier for receiving and amplifying the output 
of its respective photodetector, and a field coil oriented with respect to 
the absorption cell which produces an H.sub.1 field along the axis of the 
field coil and perpendicular to the H.sub.o field. 
The alternating magnetic field H.sub.1 has the effect of applying a torque 
to the net magnetic moment of the mercury in the absorption cell, causing 
it to tilt away from the H.sub.o field and to process about the axis of 
the H.sub.o field at the frequency of the applied H.sub.1 field. The 
Larmor precessional frequency is given by: 
EQU .omega.=-.gamma.H.sub.o (4) 
where .omega. is the Larmor precession frequency, .gamma. is the gyro 
magnetic ratio, and H.sub.o is the applied DC magnetic field. The negative 
sign in equation (4) demonstrates that a nucleus with a positive 
gyromagnetic ratio will precess in a counter-clockwise direction when 
viewed along a direction parallel to the direction of H.sub.o, i.e., 
according to the left-hand rule with the thumb in the direction of H.sub.o 
and the fingers in the direction of .omega.. 
The precessing magnetic moment will have a component which is perpendicular 
to the H.sub.o field and may be considered to rotate about the axis of the 
H.sub.o field. 
The readout beams 38 and 37 pass through respective half wavelength plates 
to the mercury cells 14 and 15, respectively, and the angle of the plane 
of polarization is modulated at the precessional frequency by the Faraday 
effect on the readout beam caused by the perpendicular or transverse 
magnetic moment component rotating about the H.sub.o axis. The modulation 
of the angle of the plane of polarization of the readout beam 38 is 
converted to an amplitude modulation by passing the polarization modulated 
beam through the linear analyzer 42 and the amplitude modulation is 
detected in the photomultiplier 43. Similarly, the readout beam 37 is 
polarization modulated in the mercury cell 15 and is passed through the 
linear analyzer 45 and is detected in the photodetector 46. The output 
current from each of the photodetectors is amplified and used to generate 
the alternating field H.sub.1. 
When all of the conditions of loop closure (such as proper gains and no 
phase shifts) are precisely met, each of the mercury isotopes in the spin 
generators 11 and 12 will cause the spin generator to oscillate at its 
respective Larmor precessional frequency as indicated above. 
When a beam of plane polarized light having a direction of propagation 
parallel to a component of magnetization of a magnetized medium is caused 
to pass through the medium, the plane of oscillation of the light may be 
rotated through an angle as a result of the Faraday effect. When a plane 
polarized beam 38 of light is caused to pass through the mercury cell 14, 
it will be affected by a magnetic moment component rotating at the Larmor 
frequency about the H.sub.o axis and as a result the angular orientation 
of the plane of polarization of the light will oscillate with respect to 
time at the Larmor frequency. Thus, the polarization angle of the light 
beams 37 and 38 will be modulated by the cells 15 and 14, respectively. 
The analyzers 45 and 42 convert this polarization angle modulation to 
intensity modulation. By properly orienting the direction of the analyzers 
45 and 42, the components of this intensity modulation at a Larmor 
frequency can be maximized. 
Since two isotopes of mercury are contained within each absorption cell, 
two such signals are produced by each absorption cell, each having been 
modulated at the characteristic Larmor precessional frequency in 
accordance with the gyromagnetic ratio for each isotope. Thus, each output 
beam is amplitude modulated simultaneously at two frequencies which 
correspond to each of the characteristic frequencies of the isotopes in 
the mercury cell. 
Thus far, the gyroscope operation has been described for a gyroscope which 
is fixed in inertial space. 
When the gyroscope rotates about the H.sub.o axis, the phase relationships 
are affected in accordance with equation (1) above. That is, the relative 
phase of the signal at each frequency at the output of each spin generator 
after rotation is displaced in phase from the signal which would have been 
received under non-rotation conditions. This relative displacement is thus 
used to provide an output representative of the degree of rotation of the 
gyroscope. 
The readout lamp 35 as shown in FIG. 2 is in preferred practice an 
electrodeless r-f excited dumbbell shaped device having an intermediate 
elongated portion filled with plasma. Since the readout beam originates 
from an extended source, any changes in this source may produce beam 
division and beam direction effects in the gyro which are major sources of 
rate bias instability. As previously mentioned, changes in the light 
source are due mainly to plasma shifts in the lamp. 
Referring to FIG. 2, there is shown a diagram of the light translation 
problems which the present invention addresses. 
When the readout lamp 35 is normally positioned in location 50, there is an 
even division of beam intensity reaching absorption cells 14 and 15. 
However, due to the reasons mentioned, the plasma in the readout lamp may 
undergo translation to a new location as indicated by 52. In this new 
position beam 38 will move counterclockwise, as indicated by reference 
numeral 54, while beam 37 moves to a new location as indicated by 
reference numeral 58. The point of intersection 56 between the center of 
the newly directed readout beam and beam splitting polarizer 40 produces 
the beams 54 and 58 of unequal intensity because the reflection 
coefficient of the beam splitting polarizer changes. This change in the 
beam intensity division causes a rate bias shift which requires 
correction. Since the beams have finite angular widths, the variable 
reflection coefficient of the splitter 40 causes the effective shifts in 
the directions of the two beams to be unequal, also leading to rate 
changes. 
Referring to FIGS. 3 and 4, a shielded can 60 is illustrated for enclosing 
absorption cell 15. A similar can would enclose absorption cell 14. Series 
connected coils 62 and 64 of modified Helmholtz type conduct DC current 
therethrough for generating the H.sub.o field 18, previously mentioned in 
connection with FIG. 1. The conventional dot (.cndot.) and plus sign (+) 
symbols indicate the direction of the current flow through coils 62 and 64 
as being out from the plane of the paper on the right end of the coils, 
and into the plane of the paper on the opposite ends. This generates the 
indicated direction for the H.sub.o field, utilizing the right-hand rule. 
The spacing between coils 62 and 64 is changed from the normal Helmholtz 
spacing to compensate for the effects of the shielding enclosure 60, 
yielding better homogeneity for the shielded assembly. 
The auxiliary coils 66 and 68 also of the modified Helmholtz type, are 
mounted in proximity to the series connected coils 62 and 64. Auxiliary 
coils 66 and 68 are connected in series but the current flow through these 
coils is in opposite directions. Thus, the DC field generated by auxiliary 
coil 66 adds to the component of the H.sub.o generated by coil 62 but the 
DC field generated by auxiliary coil 68 subtracts from the H.sub.o 
component generated by coil 64. The opposing current flow in coil 64 and 
auxiliary coil 68 is indicated by the symbols denoting current flow in and 
out of the plane of the paper in FIG. 3. The result is a controllable 
inhomogeneity of the H.sub.o field along the axis of the shielded can 60. 
It is this controlled inhomogeneity which does correct the plasma 
translation error of the readout lamp. It will be noted that the 
absorption cell 15 is located in the center of the shielded can 60 
although FIGS. 3 and 4 are not intended to represent true dimensional 
relationships between the illustrated coils and the absorption cells. An 
identical configuration of coils within a shield can exists for absorption 
cell 14. 
Current drivers 70 and 72 respectively drive the H.sub.o coils and 
auxiliary coils. These drivers are conventional regulated power supply 
current drivers. 
The amount of current delivered by auxiliary coil current driver 72 to 
correct the plasma translation problem may be determined empirically. For 
example, it is possible to translate the readout lamp 35 by placing a 
mechanical shim against the housing for lamp 35 which will translate the 
housing so as to produce a reproducible translation in space of the entire 
readout light assembly. Based on the magnitude of mechanical translation, 
one measures the change in gyro rate. Then, the auxiliary coils associated 
with one of the cells are provided with increasing current until the gyro 
rate change approaches zero. If, after delivering current to an auxiliary 
coil, the gyro rate change with lamp translation worsens, then the 
auxiliary coil corresponding to the other absorption cell is driven 
instead. Thus, by driving the auxiliary coils around one or the other of 
absorption cells 14, 15, a current level may be determined which solves 
the plasma translation problem. 
Now that a preferred embodiment has been discussed which creates an 
inhomogeneous H.sub.o field through one of the absorption cells 14, 15, 
the theory relating to the plasma translation theory will be discussed. 
The rate bias equation associated with inner loop mechanical phase angle 
errors is given by 
##EQU1## 
where subscripts 1, 2 are mercury isotope labels; subscripts A, B are 
corresponding labels for spin generators 11 and 12; M refers to mechanical 
as opposed to electronic phase angles; .gamma..sub.1 and .gamma..sub.2 are 
the absolute magnitudes of the gyromagnetic ratios for the two mercury 
isotopes in the absorption cells 14 and 15; .tau..sub.ij is the transverse 
relaxation time for isotope i (i=1, 2) in spin generator j (j=A, B), and 
.omega..sub.B is the rate bias due to these error sources. The mechanical 
phase angle changes are .DELTA..phi..sub.ijM. Mechanical phase angles 
represent differences from 90.degree. of the angle between the effective 
or mean direction of each readout beam and the direction of its respective 
H.sub.1 field. The change in mechanical phase angle, due to a lamp plasma 
shift, is the same for both isotopes in the same loop, i.e., 
EQU .DELTA..phi..sub.1AM =.DELTA..phi..sub.2AM =.DELTA..phi..sub.AM 
and 
EQU .DELTA..phi..sub.1BM =.DELTA..phi..sub.2BM =.DELTA..phi..sub.BM. 
Thus, the equation becomes 
##EQU2## 
In order that .omega..sub.B =0, the relationship between 
.DELTA..phi..sub.AM and .DELTA..phi..sub.BM and the .tau.'s must be: 
##EQU3## 
By driving one of the auxiliary coils, which creates an inhomogeneous 
H.sub.o field, either the numerator or the denominator of the last 
expression will be changed due to a reduction of the relaxation times 
corresponding to the auxiliary coils being driven with current. The 
directional effects of lamp plasma shifts are completely compensated for 
when the ratios appearing in the last expression are equated. These ratios 
are both close to unity, but as noted previously, -.DELTA..phi..sub.AM 
will not be exactly equal to .DELTA..phi..sub.BM because of the finite 
beam widths interacting with the variable reflectance of the beam 
splitter. 
In addition to allowing the beam direction errors to be compensated, this 
adjustment also provides compensation for the beam-intensity-division 
differential-light-induced-frequency-shift errors arising from lamp plasma 
translations. In achieving the translation null rate shift by 
inhomogeneity trim, one error offsets the other so their sum is nulled. 
An alternate embodiment for achieving the inhomogeneous H.sub.o field is to 
employ a single set of Helmholtz coils 78 and 80, as shown in FIG. 5, for 
generating the H.sub.o field. Such a structure could be employed in 
connection with each absorption cell 14 and 15. Each of the coils 78 and 
80 is provided with a separate current driver (74, 76) so that different 
levels of current drive the coils. This would create an inhomogeneous 
H.sub.o field through the absorption cells. The current differential is 
adjusted empirically, as in the case of the structure shown in FIG. 4, 
until the gyro rate change due to plasma shift approaches zero. 
An alternate approach to solution of plasma shift error is to introduce a 
differential temperature between the absorption cells 14 and 15 and 
thereby tune the relaxation times in the two cells. Utilizing this 
approach, the H.sub.o field may be uniform or, a temperature differential 
could be employed in conjunction with an inhomogeneous H.sub.o field. 
Accordingly, a number of approaches have been disclosed which successfully 
cure the problem of readout lamp plasma shifts which would ordinarily 
cause rate bias instability. With this problem eliminated, the output of a 
nuclear magnetic resonance gyroscope is more error free. 
It should be understood that the invention is not limited to the exact 
details of construction shown and described herein for obvious 
modifications will occur to persons skilled in the art.