LASER GYRO WITH PHASED DITHERED MIRRORS

GYROSCOPE A LASER AVEC MIROIRS OSCILLANTS A COMMANDE DE PHASE

English Abstract

ABSTRACT OF THE DISCLOSURE
Disclosed herein is a ring laser gyroscope having two
oppositely traveling laser beams and is provided with
mechanically dithered mirrors at its three or four reflection
points. At least two of the mirrors are mounted for movement
in and out as the result of the expansion and contraction of
stacks of piezoelectric elements associated with these mirrors.
These mirrors are thus dithered, i.e. oscillated in and out,
in phased relationship with one another so that the total
length of the laser cavity is held at a fixed number of wave-
lengths, but the laser beam translates back and forth across
the surfaces of the mirrors. By this technique, the undesired
phenomenon of lock-in at low rotation rates of the gyroscope
is avoided, without the need for special optical or magnetic
structures in the path of the laser beam.

Claims

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. A ring laser gyroscope having at least three mirrors
for setting up a closed-loop path for one and the other of two
light beams which, in operation of the gyroscope, propagate
in mutually opposite directions in an active laser medium
of the gyroscope, there being means for driving each of the
mirrors into vibratory motion perpendicular to the reflective
surface of the mirror, means for controlling the vibratory
motions of the mirrors to maintain constant laser beam path
lengths, and wherein each mirror can be vibrated at a phase
difference with respect to an adjacent mirror which is equal
to 360° divided by the number of mirrors.
2. A gyroscope according to claim 1, wherein all the
mirrors have substantially uniform amplitudes of vibratory motion
3. A gyroscope according to claim 1, wherein the
vibratory motion of all mirrors is substantially sinusoidal
with respect to time.
4. A gyroscope according to claim 1, claim 2 or claim 3,
wherein the translational displacement of each mirror is of
the order of ? 0.19 <IMG>, wherein .lambda. is the wavelength of the
laser light and .THETA. is the angle formed between the direction
of incidence of the light beams on each mirror and a plane
oriented perpendicularly to the mirror surface.
13

5. A gyroscope according to claim 1, claim 2 or claim 3,
and comprising an individual transducer for driving each
of the mirrors into vibratory motion.
6. A gyroscope according to claim 1, claim 2 or claim 3,
wherein each mirror is associated with a stack of piezo-
electric elements constituting an individual transducer
for driving a said mirror into vibratory motion.
7. A ring laser comprising:
means forming a closed loop optical cavity containing
an active lasing medium for generating primary counterrotating
laser light beams therein, the frequency difference between
the light beams having a measure of the rate of rotation
experienced by the ring laser, said cavity forming means
including a plurality of mirrors for reflecting said light
beams; and
means for vibrating a plurality of said mirrors in
translation at the same frequency in a direction only
perpendicular to the surface of the mirror with said
vibrating mirrors having nonzero amplitudes of vibration and
phases of vibration to cause the total distance around said
closed loop to remain substantially constant.
8. A ring laser as recited in claim 7 wherein the
amplitudes of vibration of said vibrating mirrors are
substantially equal.
14

9. A ring laser as recited in claim 8 wherein the
phase difference between the oscillation of said vibrating
mirrors is substantially equal to 360 degrees divided by the
number of vibrating mirrors.
10. A ring laser as defined in claims 7, 8, or 9 wherein
said vibrating means comprises means for causing the
displacement of said vibrating mirrors to be substantially
sinusoidal with respect to time.
.
11. A ring laser as defined in claim 8 wherein the
magnitude from a neutral position of the translational
vibration of each "i"th vibrating mirror is in the order
of:
<IMG>
Where .lambda. is the wavelength of the laser light beam, and
.THETA.i is equal to the angle of incidence of the light beams
on the "i"th vibrating mirror relative to the perpendicular
from the mirror at the point of incidence, and .beta. is an
argument of Bessel's function of the first kind and zero
order which makes J0(.beta.) = 0.
12. A ring laser as defined in claim 7 wherein said
vibrating means comprises a transducer.
13. A ring laser as defined in claim 12 wherein said
transducer comprises a stack of piezoelectric elements.

14. A ring laser comprising:
a ring laser structure of the single mode type
having two counterrotating laser beams and including at least
three mirrors;
means for translating at least two of said mirrors
in an oscillating mode at the same frequency substantially
only in the direction of a line bisecting the beams
incident on each said vibrating mirror; and
means for phasing the movement of all of said
vibrating mirrors to maintain constant primary laser beam
path length as said vibrating mirrors are displaced.
15. A ring laser as defined in claim 14 wherein the
magnitude from a neutral position of the translational
oscillation of each "i"ith vibrating mirror is in the order
of:
<IMG>
where .lambda. is the wavelength of the laser light beam and
.THETA.i is equal to the angle of incidence of the light beams
on the "i"th vibrating mirror relative to the perpendicular
from such mirror at the point of incidence, and .beta. is an
argument of Bessels function of the first kind of zero
order which makes the function J0(.beta.) = 0.
16. A ring laser as defined in claim 14 wherein the
magnitude of the translational vibration of each "i"th
vibrating mirror is in the order of:
16

<IMG>
where .lambda. is the wavelength of the laser light beam and
.THETA.i is equal to the angle of incidence of the light beams
on the "i"th vibrating mirror relative to the perpendicular
from such mirror at the point of incidence.
17. A ring laser as defined in claim 16 wherein
said vibration is substantially sinusoidal.
18. A ring laser as defined in claim 14 wherein all
of the trigonometric Fourier components of said vibration
are phased the same as the fundamental component.
19. A ring laser as defined in claim 14 in which
said vibrating mirrors vibrate open-loop.
20. A ring laser as defined in claim 14 in which
all of said vibrating mirrors are closed-loop servoed to
control their amplitude and phasing.
21. A ring laser as recited in claim 14 wherein the
phases of the n vibrating mirrors of a generalized closed
laser path are related one to another by 2 .pi./n radians and
the amplitudes of the vibrating mirror displacements, x,
are described by
<IMG>
where .beta.m is a value of the argument of the zero order Bessel
function of the first kind,
J0(.beta.m)=0 for m=1, 2, 3...., .THETA.i=angle of incidence at the
"i"th vibrating mirror, .omega.=the dither angular frequency which
17

is large compared to typical lock-in frequencies of said
laser.
18

Description

) 7 ~ 5
This invention rel.ate~s to ring laser gyroscopes
which are known to have a closed-loop path optical cavity
containing an active lasing medium for generating two
light beams which travel in opposite dlrections along the
path, the diEference between the frequencies of the light in
the beams being a measure of the rate or rotation experienced
by the ring laser gyroscope. In these instruments, the closed-
loop path for the beams is formed by means of at least three
mirrors which reilect the light beams. ; ;
~. 10 In the field of such ring laser gyros~opes, it is
~, ~
well known to use triangular:or rectangular~paths for the
~:; lase.r beams,~with mirrors located:at the~apeces oE the t:ri-
angular path or at the corne:rs of the ;rectangular path. ~During
operatlon, rotation of the gyroscope in the pla~ne of the :
:laser paths gives rise to a beat frequency between:the two
; oppositely dlrected laser ~bea~s, aDd thls beat~frequency~is
used to determine the rotation associated with a cha:nge:in~
,, : ~ ~ .
orientatio~n of;the gyroscope. ~o.wever, at~ v~ery slow~rota~tion
rate~s~, the two~beams tend to lock one~into the~other~ so; that
20; ~no~di:ference~f~requency is observed. Th~is ls~ ln part;:a
result of back:scattering,:with some of the:energy~from
each oL the~ lase~r beams being ref~lected bac:X~alDng~the path
:of~the other~beam a~nd tendi:ng to make the~two beams lock~in
; step ~i.e. in phase.
Varicus techniques have been pro~osed for avoiding
thls disturbi.ng phenomenon, frequently;called ring laser:
gyroscope lock-ln, and these have included~vibrating~ the
: entire body of the laser gyroscope~ and the use of non- :
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reciprocal phase-shifting arrangements, such as Faraday
rotating elements. Of course vibrating the entire body of
the laser device is not the most elegant manner of
handling the lock-in problem, and the use oE Faraday
rotation or other magnetic or optical devices in the
laser path makes for a more complex structure than
might be desired.
In accordance with the invention, there is provided
a ring laser comprising means forming a closed loop optical
~: .
cavity containing an active lasing medium for generating
primary counterrotating laser light beams therein, the
frequency difference bet~een the light beams havin~ a
measure of the rate of rotation experienced by the ring
laser, the cavity forminq means including a plurali-ty of
mirrors for reflecting the light beams; and means for
vibrating a plurality of the mirrors in translation of
the same frequency in a direction only perpendicuIar to
the surface of the mirror with the vibrating mirrors having
; nonze~ro amplltudes of vibration and phases of vibration to ~ -
~cause the total distance around the closed loop to remain
substantially constant.
Each mlrror may be vibrated at a phase difference
- with respect to an adjacent mirror which is equal to 360
divided by the number of mirrors. Moreover, it is~possible
to provide for substantially uniform amplitudes of
vibratory motion for all mirrors. Additionally, the
; vibratory motion of all mirrors can be substantially sinusidal
with respect to time. The translational displacement of each
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mirror is sui.tably of the order of ~ 0.19 sin ~ wherein ~
is the wavelength of the laser light and ~ is the angle formed
between the direction of incidence oE the light beams on
each mirror and a plane oriented perpendicularly to the
` ,
mirror surface.
In accordance with a speciic embodiment of the
invention an individual transducer is used for driving each
.;'~:~ .
of the mirrors into vibratory motion, with each transducer
being preferably a stack of piezoelectric elements.
Thus, lt can be seen that in accordance with an
: exemplary embodiment of the present invention, the mirrors
.at all the refl.ection points of a ring Iaser gyroscope are
dithered in and o~t, with the phase o o:c_1la~:ion of the~
mirrors being staggered around the periphery of the laser
gyroscope structure such that the phase difference between
two adja~cent mirrors is equal to 360 degrees divided~
by the number of mirrors, this condition resulting in a
: constant path length for the oppositely~orlented beams,
a~ccomp~anied ~by the point of incidence of each~laser beam
: 20 sh~ifting across the surface of each:of the mirr:ors. This
~:, ~ : . . : ~
: i:s found to~shift the frequency of the back-scatter~ed;l~ight:,
thu~s~reducing., if not avoiding, the coupllng between the laser
beams:and~sub~st~antially preventing the l~ock-in phenomenon.
For a better understanding of the invention a~nd to ~
show how the same may be carried into effect, ~eference will-
: now be~mad.e, by way of example, to the accompanying drawlngs,n whlch:
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Figure l is a schematic illustration of a
ri.ng laser gyroscope;
- Figure 2 is a detail view of mirror-and-transducer
assemblies oE which one is located at each reflection
point of the laser gyroscope; and
Figure 3 is a diagram schematically illustrating
, , .
~ the movement of each of the three mirrors of Figure l
3~-:
with respect to the others.
With referenoe to the drawlngs, Figure l schem~atically
illustrates a laser body 12 which may be made of quartz,
for example. Three peripheral chaDnels 14, 16 and 18
forming the closed-loop path in the configuration oE a
trian~ie, as shown, have been bored through ~he quartz body
12. Within the channels l4, 16 and~18 ~is a gaseous laser
medium, such as~a mixture of gases suitable for laser ~
action. Mo~e specifically, the gas in one embodlment is~;
approximately 90~ helium and lO~ neon, and it may be~ at
a~pressure of approximately 3 torr.
'In accorda~nce with known laser techn~ology two ~
20~ cathodes 20 and 22, and two anodes 24 and 26 are secure~ to
the quartz body 12, so that a gas discharge can;be
e~stablished~between cathode 20 and anode 24, as~well as
between cathode 22 and anode 26, in channels 16~ and 18,
r~espectiv~ely.-
Mirror-a~nd-transducer assembl1és~ 28~, 30 and-3Z are
mo~unted at the three re;flection points~of the~1llustrated
` triangular ring laser~gyroscope structure.
All of the~i~nte~rnal elements of ~the rin~ laser
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gyroscope assembly, as descrlbed above, including the
mirrors, cathodes and anodes, are tigh-tly sealed into the
quartz body 12, so thak the gas wi.thin the channels of the
quartz body is maintained at the proper pressure and free
~ .
~ from contaminati.on. Laser action occurs in a single mode
:~ 14
~:~ at a frequency of approximately 5 x 10 ~z. This
corresponds to a wavelength of approximately 0.633
microns, i.e. the resulting illumination is brilliant
~ light red in color.
:~ 10: The structure of one mirror-and-transducer
~ - assemblies 28, 30 or 32, mentioned above is shown in
. ~ .
: detail in Figure 2. In Figure 2, the mirror-and- :
; trar.sducer assembly 2~ has a mirror 64 who~se`Ieflectlve,
partially coated surface 34 faces the laser beams and
reflects thelr light from one of the cha~nels 14,:16, 1~8
into another. The mirror 64 is fa:stened to the quartz
: body 12 along its rim 36. The mirror is thinned down in
an~ànnular zone 38 which extends around the mirror on its:
: ba~ck su:rface~just within the heavier outer rim 36. Secured
~20~ : to the rim 36 is a rigid housing 40, suitably cylindrical
in shape. This:cylindrical housing 40 is provided with a
: heavy bottom 42.
: Extend;ing between the bottom 42 of the housing
and the central portion 46 of the mirror~is~a stack 44 :
:of piezoélectric:transducer elements. The piezoelectric
tr~ansducer stack 44 is made up of a number of thin flat
piezoelectric wafers. These wafers have the property that~ -
: : :
~ when a voltage is applied across them, they become slightly
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thicker or slightly thinner, depending on the polarity of the
voltage. The stack 44 may be made up oE fifteen piezo-
electric wafers, each oE which is about 10 mils thick. The
:
`~ wafers have electrodes on their top and bottom surfaces and
are connected "back-to-back"-, which means that alternate-
;~ . ..
common electrodes forming one set of electrodes, are connected
` to the driving lead - of opposite polarity. With the wafers
; ~ .
being connected "back-to-back", when having oppositely directed
e]ectric fields applied across alternate wafers, they expand
and contract in thickness together, exerting substantial
pressure on the mirror center portion 46 and causlng it to
flex the thin annular section 38 of the mirror 64, in a manner
; similar to the displacement of a dia,~hrag.n secured to a frame
along its edge.
; The stacks of piezoelectric transducer elements may
be made up of piezoelectric wafers available from Gulton
as Gulton Type No. 1408. The approximate level of voltage
found to produce the magnitude of displacement dis-cussed
below is approximately 160 volts peak-to-peak. This provides
20~ the dlsplacement of the proper order of magnitude to obtain
the~amp~lltudes~needed for the practice~of the present~
invention, as developed below. ~ ~
Returnl~ng to Figure 1, the electrical driving circults
include the two~ power supplies 52 and 54 of known types for ~
starting and maintaining the gas discharges between the anodes
~ ~:
a~nd cathodes of the laser device. ~
The mirror surfaces of the assemblies 28j 30~ and 32
are driven into vibratory motion by the transducers which are
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,~, energized by the three-phase bias excita~,ion circui-t 56. Each
of the piezoelectric transducer stacks, s~ch as stack 44
shown in Figure 2, is excited such that .its vibration is
120 out of phase with each of the others.
In Figure 2, the laser beams 57 and 58 are shown to
~ - . . . . ..
,~; pass through the partially coated mirror surface 34 and
respectively through the apertures 59 and 60 in housing 40.
; As shown in Figure'1, they impinge upon external~mirrors 61
and 62. From these mirrors 61 and 62, the beams are directed
10: to a detector 63 which detects the beats between the two
: oppositely directed laser beams, which beats occur wh~eD the
structure rotates, in a manner known in the~art. ~:
In Figure 3, the three mirrors of the~ ring:laser
gyroscope~ are~shown'schematically as mi:rror~64, wlth~
: additional mirrors 65 and 66. The neutraI position of each :~
of:the~mirrors i9 shown at:64', 65' an~d~66'. As indicated ~ ~
by~the arrows 68, each~of the mirrors moves in:and~out, toward
: an:d:~away~ from ~the center of the laser gyroscope~assembly. In
Fi~gure 3~ the~heavy line 70 represents the path of the laser
20~ ;gyro beam wlth the mirrors in the positian shown. More ~ :
specl~fically, ln that position the mirror 65 is~close tO~Its
furthe:st retracted position,~whlle~ each of the~mlrrors~ 64
:and 66 is displaced~from the mirror 65 by successive 120~
increments and:therefore it lS more advanced in its posltlons.
Thus~ th~e~arrangement lS controlled to malntaln the~.tr~iangular~ :
lase~r beam~paths.substantially constant as the three mirrors
progressivel~y move in and~out of thelr~phasea relationships
of vibratory motion.
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For a four-mlrror ring laser gyroscope geometry,
the four mirrors would be driven by transducers which are
energized by a four phase supply, and the successive
mirrors would be operated to perform vibratory motion 90
out ofphase with that of each adjacent mirror.
More generally, the phase dispIacement between
adjacent mirrors should be equal to 360 dlvided by the-
~; number of mirrors.
With regard to the frequency of the excitation
source 56 of Figure 1, it is desirable that the frequency ~
be relatively high, suitably in the order of so~e tens of kilocycles
up to several hundreds of kilocycles. However,~frequencies
a~s low as l or 2 kilocycles may be employed.
Further, as illustrated in Figure 3, when the mirrors
move~ln~and out~from thelr extreme retracted positlon to their~
extreme advanced positi~ons, the points of ~incidence of the laser
beams move back~and~f~orth across the mir~ror surfaces~from;one
extr~eme position,;;the~correspondlng;paths of~a~beam being~glven~
by lines 72, 74~and 76 to the other extreme position o these
20~ paths~g1ven by llnes 78,~ 80 an~d 82. Of~course~,~as ~indic~ated~by;
; the tr~iangular path 70, shown in Figure 3, the~beams reach the
extreme p~ositions~ given by lines 72, 74 and 7.6! and subsequently
reach the~inner boundaries~78~ 80 and~8~2 at~different~polnts in~ ;
time, always maintaining the~laser path precisely the~;same 1~eng~th.
A somewhat related prior art disclosure~is found in
U.S. Patent No.~3,533,014, issued October 6! 1970-to Coccoli et al.
and entitled "Gas Ring Laser Using Oscillating Radiation Scattering
Sources Within~the~Laser Cavity". This patent discloses an
8 -
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an arrangemenk wherein the mirrors and other scattering
sources are caused to oscillate parallel to their surfaces,
` rathex than perpendicular to their surfaces as taught by the
present invention. It was found to be extremely difficult to
~-~ implement arrangements for moving the mirrors of a laser
`~ gyroscope in their own plane, while concurrently keeping the
laser cavities sealed and meeting the other necessary
requirements.
~;~ In contrast, the present invention, using vibratory
motlon of the mirrors perpendicular to their surfaces shifts
the laser beams back and forth across the surfaces o the
mirrors iD a manner which may be analyzed mathematically
by the teohnique employed in accordance~with U.S. Patent
No. 3,533,014. More specifically, the formula set forth
in Column 6j lines 53 to 55 of that~patent is precisely
applicable to the amplitude of the mirrors employed in the
present invention. This surprising result arises from the
fact~that the polnts or incide~nce of the laser~beams are
translated back and forth across the surfaces of the mirrors
;2~0 ~by~ exactly the same distance that the mlrrors are osolllated
inwardly and outwardly i.e. toward and away from the center
of the assembly.
The formula glven ln U.S. Patent No. 3,533,014,
me~ntioned above, in an abridged form, would read
4 ~ (sin ~)
Wherein "A'i is the maximum displacement of each~
mirror in each direction from a neutral position, ~ is the
wavelength ~f the laser light, ~ is the angle between the
direction of incidence of the laser beams and a plane
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perpendicular to the mirror surface, and ~ is any number
; which, when taken as the argument of the Bessel function
~ of zero order, yields a value of the Bessel function which
~:~
is zero.
~,:
For the embodiment of trlangular configuration,
as shown in Figure 1, 9 is 30, and Sin ~ is equal to one-
half. From mathematical tables it can be seen that ~ is
~1 equal to 2.405 of the lowest order Bessel function.
Substituting these values into equation (l) the following
results are obtained =
0.191 ~ ~ (2)
sin
A= 0.382 ~ ; 13)
When using the neon-helium gas~mixture mentioned
above, the wavelength is 0.633 microns and the displacement
amplitude "A" i9 equal to about 0.242 microns, i.e. 0.242
10- oentlmeters~, ln each dlrection from the neutral
positlo~n~of the mlrrors.
Recapitulating, with the three~mirrors ~ibratinq
20~ ; exactly 120 out~of phase wlth respect to each other,;there~
is~no~chang~e in the instantaneous optical cavity length
Thus,~laser operat~ion is~maintained at a frequency position~
at the center of~the gain curve with a m~inimum length
perturbation due to the effect achieved by the invention whi~h
may conveniently be referre~d to as "microdither" modulation.
:~ ~:~ :: : :
The microdither amplitude are of subwavelength~dimensions.
Geometrlcal analysis shows that the standing wave
field assoc~ated wlth the triangular configuration shown in
1 0
:: :
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: .. ,
Figure 3 is caused to perform translational motion, bu-t not
; to rotate, in a manner such that the apeces of the triangIe,
describe circles, as shown by the arrows in E'igure 3, while
the points of incidence describe lines on the surfaces of the
mirrors, inasmuch as the mirrors move in and out so that each
laser beam moves back and forth across the mirror surfaces~
This results in the scatter centers being displaced with
reepect to the translated i.e. position - shiftea standing
wave field modes, hence satisfying the phase shif~ requirement
: ~
of phase modulation. This displacement also results in the
standing wave field being displaced wit-h respect to a body-fixed
~:.
aperture, as is well known in the art.
In addition, the distance from one scatter group
~:, ,
to the next group on the next mirror can be seen to be varying
with tlme. It i~s the vector summation of the optically back-
scattered light from all the scattering surfaces of the laser
- cavity that determines the magnitude of the~ "lock-in" effect~
as well as the fin~al phase position. Thus,; the microdither
of the mirrors~ causes~the net scatter vecto~r to be time-modulated.
~ This effect further reduces the "lock~in" effect.
For completeness, reference is also made~to U S.
Patent No. 3,581,227, issued May 25, 1971 to Podgorski, which
is of~interest inasmuch as it shows a~stack of piezoeleotric
elements and wherein the position of a mirror is shifted to
accurately change the length of a laser cavity~ This is known
technlque, and could be used in the apparatus of the present
inve~ntion as a DC bias upon which the properly phased alternating
current signals could be superimposed. Of course, U.S. Patent
dm :\~J`~\~
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No. 3,581,227 does not disclose a plurality of mirrors of
whlch each has a pieæoelectric control, nor does it disclose
the phased vibration, i.e. oscillation of the mirrors. It
is evident that transducers o-ther than piezoelectric elements
'
could be employed for oscillating the mirrors in the proper
phase relationship. For example, magnetostrictive transducers
~could be employed. In addition, other lasi.ng materials and
"~~laser cavlties having a different number or mirrors, such as
four, could be used. Other minor changes from the disclosed
~structure are also considered to be within the scope of the
~,present invention`.
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